tag:blogger.com,1999:blog-62888627985460857062024-03-15T21:09:23.775-04:00Econometrics By SimulationSimulations and Analysis github.com/EconometricsBySimulation/Francishttp://www.blogger.com/profile/16658586705916884436noreply@blogger.comBlogger381125tag:blogger.com,1999:blog-6288862798546085706.post-27879043723282383102023-05-02T13:53:00.010-04:002023-05-02T18:47:43.485-04:00The Counter Intelligence Of The US’s Counter Intelligence Apparatus<!DOCTYPE html>
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) 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<div id="yet-another-leak" class="section level3">
<h3>Yet Another Leak!</h3>
<p>Another national security leak seems to be viewed by many in the US
and around the world as merely another instance of incompetence or
self-righteousness by a young person who lacks a proper understanding of
ethics or national security. However, more insightful individuals might
begin to ask crucial questions, such as whether there are any controls
over who gains access to national security secrets. Additionally, do we
not have any tools or methods to identify and eliminate individuals who
may be ethically, maturity-wise, or otherwise unprepared to handle
sensitive information?</p>
<p><img 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" width="40%" style="float:right; padding:10px" />
The answer is, surprisingly, that there are 18 National Intelligence
Agencies! These agencies regularly employ polygraphers and psychologists
trained in detecting abnormal behavior and mental states. However, the
issue with using secret polygraphers and many other counterintelligence
efforts is the age-old question: “Who watches the watcher?” Worryingly,
the answer seems to be no one.</p>
<p>As a result, the system is deeply corrupt, and as long as it is
impervious to public scrutiny, its corruption will continue to grow.
Based on personal observations and conversations with numerous friends
and acquaintances who have shared experiences, it appears that many
polygraphers hired by the CIA, NSA, and other organizations routinely
act in unethical ways, physically, sexually, or emotionally abusing
those they evaluate. To prevent their abuses from being exposed, they
often falsify “confessions” and test results.</p>
<p>But why? What is gained from being from being unethical? I dare say
there is a multitude of potential benefits that unscrupulous
polygraphers may experience. These benefits are complex from the
intensely personal rush of the polygrapher “getting off”
(psychologically or physically) by dominating another human being to
that of being rewarded by a system that lauds the generation of
confessions whether true, coerced, or entirely fabricated by the
polygrapher. Of course, there might be more nefarious reasons for the
corruption of the US’s counterintelligence apparatus. Not all nations
are friendly to democracy or personal liberty…</p>
<p>But, we can’t blame everything on Putin or Xi Jinping. We give them
too much credit.</p>
<p>Instead, let’s instead imagine that these agencies are typical human
organizations that tend towards extremes when secrecy is enforced and
accountability is largely absent (think cults, secret police, child
protective services, etc.). Why do such organizations drift towards
extremes?</p>
<p>…</p>
<p>You guessed it!</p>
<p>It is all about the incentives.</p>
</div>
<div id="incentives-drive-outcomes" class="section level3">
<h3>Incentives Drive Outcomes</h3>
<p>In order to illustrate this drift, I have built a small multistage
simulation. Let’s imagine the polygraph procedure and see if we can show
how under very mild conditions (which arguably describe observed
features of the system) we end up with a system in which not only is
polygrapher selection tending towards corruption, but their supervisors
even more so, and unfortunately even the employees they “successfully”
screen.</p>
<pre class="r"><code>library("dplyr")
library("ggplot2")</code></pre>
<div id="simulation" class="section level4">
<h4>Simulation</h4>
<p>Setup</p>
<p>Three different agents:</p>
<ol style="list-style-type: decimal">
<li>Potential employee (candidate)</li>
<li>Polygrapher</li>
<li>Polygrapher’s supervisor</li>
</ol>
<p>We will call the unethical spectrum that poligraphers can draw from
as “unethics” with the most ethical polygrapher (unethics = 0) always
following ethical rules and never falsifying confessions while the most
unethical polygrapher (unethics = 1) will always take every opportunity
to falsify confession and otherwise break ethical rules.</p>
<pre class="r"><code>unethics = runif(N)^3
hist(unethics, breaks = 20)</code></pre>
<p><img 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" width="672" /></p>
<p>We can see that the simulated polygrapher population is drawn from a
population in which “unthics” is quite initially low.</p>
<p>Now let’s say that when a candidate comes for a polygraph there is a
small possibility that they will admit to some real concern. If they
admit to a real concern then the polygrapher gets his payoff R (think
probability of promotions).</p>
<p>First we will simulate a single day. Add the polygrapher and his/her
ethics.</p>
<pre class="r"><code>day1 = data.frame(polygrapher = 1:N, unethics= unethics)</code></pre>
<p>The polygrapher meets their candidate for the day and the candidate
either confesses to an real concern or does not.</p>
<pre class="r"><code>day1$real_confession = 1*(runif(N) < actual_confession_probability)</code></pre>
<p>If the candidate does not confess to a real concern then the
polygrapher at that point may choose to deploy unethical interrogation
procedures but there is no reason to do so if the candidate has already
confessed to something horrible.</p>
<pre class="r"><code>day1$unethical = 1*(runif(N) < unethics) * (1-day1$real_confession)</code></pre>
<p>If the polygrapher employs unethical interrogation procedures then
there is a decent likelihood they can solicit a fake confession. Among
my four friends who have gone to similar proceedures two of them were
coerced to confessing to something they had not done in order to satisfy
their polygrapher and get passed. Two of them including myself refused
to confess to things the polygrapher alleged. Let’s say that people who
refuse to confess to a false accusation under severe/abusive pressure
have a personal moral flexibility score between 0 and 1 but a likelihood
of making a false confession between 50%-100% (defined as .5+moral
flexibility/2). The reason this score is so high is because naive
candidates are pitted against seasoned polygraphers who are expert
manipulators.</p>
<pre class="r"><code>day1$candidate_flexibility = runif(N)</code></pre>
<p>So if polygraphers applying unethical procedures, then there is a
random chance they will solicit a fake confession.</p>
<pre class="r"><code>day1$fake_confession = day1$unethical * (runif(N) < .5 + .5*day1$candidate_flexibility)</code></pre>
<p>Many candidates will confess to something to get the pressure off of
them and get there clearance. But what happens to those who experience
unethical abuse by the polygrpaher and refuse to “confess”.</p>
<p>Now the polygrapher is in a very tight spot. If the polygrapher lets
the candidate get through the system then that candidate is now a risk
to the the polygrapher. Ie the canidadate can make complaints and
otherwise flag the unethical or criminal behavior of the
polygrapher.</p>
<p>However, the option exists for the polygrapher to falsify a
confessions and thus defanging complaints about ethics from a person who
has already “admitted” to something terrible. Polygraphers who have
already chosen to deploy unethical practices would find the next step of
lying about a confession to be natural and self-protective.</p>
<pre class="r"><code>day1$confession_lie = (day1$unethical == 1) * (day1$fake_confession == 0) * (runif(N) < day1$unethics)</code></pre>
<p>Finally let’s imagine there is some magical world where there is
actually ethical oversight over the CIA’s polygraph/security apparatus.
Let’s say if there is unethical actions by a polygrapher without a
confession then there is a possibility of being caught.</p>
<pre class="r"><code>probabilty_of_caught = .01</code></pre>
<p>However, if there is a confession (fake or coerce) then this
pobability is reduced even lower.</p>
<pre class="r"><code>probabilty_of_caught_with_confession = probabilty_of_caught / 2
day1$disciplinary = day1$unethical * ( (runif(N) < ((probabilty_of_caught_with_confession) * (day1$fake_confession + day1$confession_lie) +
(probabilty_of_caught * ((day1$fake_confession + day1$confession_lie) == 0) ))))</code></pre>
<p>So let’s see the results of our simulation.</p>
<p>Test takers pass if they confess to something significantly “bad
enough” (real_confession), the test taker melts under the pressure and
fakes a confession, or the polygrapher chooses not to falsify the
polygraph results.</p>
<pre class="r"><code>day1$pass = 1*((day1$real_confession + day1$fake_confession + (1 - day1$unethical)) > 0)</code></pre>
<p>Given the initial parameters we have a 94% pass rate. This is due to
a 48% fake confession rate and only 48% of polygraphers using unethical
practices to falsify the results. There is also a slight number 2% which
pass due to confessing something sufficiently bad.</p>
<pre class="r"><code>mean(day1$pass)</code></pre>
<pre><code>## [1] 0.936</code></pre>
<pre class="r"><code>mean(day1$fake_confession); mean(1 - day1$unethical); mean(day1$real_confession)</code></pre>
<pre><code>## [1] 0.177</code></pre>
<pre><code>## [1] 0.759</code></pre>
<pre><code>## [1] 0.059</code></pre>
<p>We have 59 real confessions.</p>
<pre class="r"><code>sum(day1$real_confession)</code></pre>
<pre><code>## [1] 59</code></pre>
<p>We have 241 polygraphers acting unethically.</p>
<pre class="r"><code>sum(day1$unethical)</code></pre>
<pre><code>## [1] 241</code></pre>
<p>And we have 177 fake confessions.</p>
<pre class="r"><code>sum(day1$fake_confession)</code></pre>
<pre><code>## [1] 177</code></pre>
<p>Resulting in 59 disciplinary actions.</p>
<pre class="r"><code>sum(day1$disciplinary)</code></pre>
<pre><code>## [1] 59</code></pre>
<p>Is this interesting at this point? Probably not very.</p>
<p>We basically get what we put in. What gets a little more interesting
is seeing how the system develops over time based on incentives. Let us
first design a function which will run our day simulation.</p>
<pre class="r"><code>daySimulate = function(active_polygraphers,
actual_confession_probability = .05,
probabilty_of_caught = .01,
probabilty_of_caught_with_confession = .005) {
N = nrow(active_polygraphers)
dayN = active_polygraphers
dayN$real_confession = 1*(runif(N) < actual_confession_probability)
dayN$unethical = 1*(runif(N) < active_polygraphers$unethics) * (1-dayN$real_confession)
dayN$candidate_flexibility = runif(N)
dayN$fake_confession = dayN$unethical * (runif(N) < .5 + .5 * dayN$candidate_flexibility)
dayN$confession_lie = (dayN$unethical == 1) * (dayN$fake_confession == 0) * (runif(N) < dayN$unethics)
dayN$disciplinary = dayN$unethical * ( (runif(N) < (
(probabilty_of_caught_with_confession) * (dayN$fake_confession + dayN$confession_lie) +
(probabilty_of_caught * ((dayN$fake_confession + dayN$confession_lie) == 0) ))))
dayN$pass = 1*( (dayN$real_confession + dayN$fake_confession + (1 - dayN$unethical)) > 0)
return(dayN)
}</code></pre>
<p>Now let us add some additional rules for the system:</p>
<ol style="list-style-type: decimal">
<li>Every thirty days polygrapher’s are reevaluated. Those with two
disciplinary actions against them in the last six months are assigned to
different roles in the organization.</li>
<li>Also every thirty days the 10 polygraphers with the lowest rates of
confessions are replaced with a new set of polygraphers.</li>
</ol>
<pre class="r"><code>polygraph_pruning = function(active_polygraphers,
number_of_disciplinary_actions_allowed = 2,
number_of_polygraphers_replaced = 10,
number_of_supervisors = 10,
current_count = 100) {
N = nrow(active_polygraphers)
nDisciplined = sum(active_polygraphers$disciplinary >= number_of_disciplinary_actions_allowed)
# Assign Supervisors
active_polygraphers$supervisors = 1*(row_number(-active_polygraphers$nConfessions * .000000001^active_polygraphers$disciplinary) <= number_of_supervisors)
# If a polygrapher has been disciplined too many times then they are replaced.
if (nDisciplined>0) {
#print(c(nDisciplined, 'polygraphers replaced'))
selector = active_polygraphers$disciplinary >= number_of_disciplinary_actions_allowed
active_polygraphers$polygrapher[selector] = current_count + (1:nDisciplined)
active_polygraphers$unethics[selector] = runif(nDisciplined)^2
current_count = current_count + nDisciplined
}
# If a polygrapher is in the bottom N they are replaced.
if (number_of_polygraphers_replaced>0) {
selector = row_number(active_polygraphers$nConfessions) <= number_of_polygraphers_replaced
active_polygraphers$polygrapher[selector] = current_count + (1:number_of_polygraphers_replaced)
active_polygraphers$unethics[selector] = runif(number_of_polygraphers_replaced)
active_polygraphers$ndays[selector] = 0
current_count = current_count + number_of_polygraphers_replaced
active_polygraphers$nConfessions = 0
}
# Select supervisors from polygraphers with the most confessions but no active disciplinary actions
return( list(active_polygraphers , current_count) )
}
number_of_activate_polygraphers = 100
actual_confession_probability = .05
probabilty_of_caught = .002
probabilty_of_caught_with_confession = .001
frequency_of_reevaluation = 30
number_of_disciplinary_actions_allowed = 2
number_of_polygraphers_replaced = 5
discipline_reset = 180
number_of_days = 720</code></pre>
<pre class="r"><code>simulateSystem <- function(number_of_activate_polygraphers = 100,
actual_confession_probability = .05,
probabilty_of_caught = .002,
probabilty_of_caught_with_confession = .001,
frequency_of_reevaluation = 30,
number_of_disciplinary_actions_allowed = 2,
number_of_polygraphers_replaced = 5,
discipline_reset = 180,
number_of_days = 720) {
active_polygraphers = data.frame(polygrapher = 1:number_of_activate_polygraphers,
unethics = runif(number_of_activate_polygraphers)^6,
nConfessions = 0,
disciplinary = 0,
ndays = 0)
day_dataframe = data.frame(day = 1:number_of_days,
mean_unethics = NA,
mean_unethics_top = NA,
real_confession = NA,
fake_confession = NA,
confession_lie = NA,
disciplinary = NA,
candidate_flexibility_pass = NA,
candidate_flexibility_fail = NA)
current_count = number_of_activate_polygraphers
N = number_of_activate_polygraphers
for (i in 1:number_of_days) {
# Run results through the day simulator
dayResults = daySimulate(active_polygraphers,
actual_confession_probability = actual_confession_probability,
probabilty_of_caught = probabilty_of_caught,
probabilty_of_caught_with_confession = probabilty_of_caught_with_confession)
# Pass the results to a dataframe
day_dataframe[i,] = c(i,
mean(active_polygraphers$unethics),
mean(active_polygraphers$unethics[active_polygraphers$supervisor == 1]),
sum(dayResults$real_confession) ,
sum(dayResults$fake_confession) ,
sum(dayResults$confession_lie) ,
sum(dayResults$disciplinary) ,
mean(dayResults$candidate_flexibility[dayResults$pass == 1]),
mean(dayResults$candidate_flexibility[dayResults$pass == 0])
)
active_polygraphers$ndays = active_polygraphers$ndays + 1
active_polygraphers$nConfessions = active_polygraphers$nConfessions + (
dayResults$real_confession + dayResults$fake_confession + dayResults$confession_lie)
active_polygraphers$disciplinary = active_polygraphers$disciplinary + dayResults$disciplinary
# If the evaluation period has been hit assign active supervisors
if ( (i %% frequency_of_reevaluation) == 0) {
pruned = polygraph_pruning(active_polygraphers, current_count = current_count)
active_polygraphers = pruned[[1]]
current_count = pruned[[2]]
}
if ( (i %% discipline_reset) == 0 ) { active_polygraphers$disciplinary = 0 }
}
return(list(day_dataframe = day_dataframe,
dayResults = dayResults,
active_polygraphers = active_polygraphers))
}</code></pre>
<pre class="r"><code>x = simulateSystem(number_of_days = 1000)
day_dataframe = x$day_dataframe
dayResults = x$dayResults
active_polygraphers = x$active_polygraphers</code></pre>
<p>Simulation results:</p>
<p>In the following table we can see the effects of the incentive schema
on polygrapher ethics. On day 1 random sampling polygraphers ends up
with an average unethics of .15. Which means initially the likelihood of
a polygrapher to break ethical rules is only about 15%. Also, candidates
who pass the polygraph procedure either through true confession or fake
confession have a “flexibility” of 55% intially while those who fail are
slightly more moral with a flexibility of only 27%. We can also see that
those polygraphers who generate the most confessions (whether real or
fake) already are much more likely to be unethical. With a score of 73%
unethics by day 31 of the simulation.</p>
<p>Table 1:</p>
<pre class="r"><code>knitr::kable(head(day_dataframe[day_dataframe$day %% 15 == 1,]))</code></pre>
<table>
<colgroup>
<col width="1%" />
<col width="2%" />
<col width="9%" />
<col width="11%" />
<col width="10%" />
<col width="10%" />
<col width="9%" />
<col width="8%" />
<col width="17%" />
<col width="17%" />
</colgroup>
<thead>
<tr class="header">
<th align="left"></th>
<th align="right">day</th>
<th align="right">mean_unethics</th>
<th align="right">mean_unethics_top</th>
<th align="right">real_confession</th>
<th align="right">fake_confession</th>
<th align="right">confession_lie</th>
<th align="right">disciplinary</th>
<th align="right">candidate_flexibility_pass</th>
<th align="right">candidate_flexibility_fail</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="left">1</td>
<td align="right">1</td>
<td align="right">0.1535725</td>
<td align="right">NaN</td>
<td align="right">4</td>
<td align="right">14</td>
<td align="right">1</td>
<td align="right">0</td>
<td align="right">0.5508659</td>
<td align="right">0.2719333</td>
</tr>
<tr class="even">
<td align="left">16</td>
<td align="right">16</td>
<td align="right">0.1535725</td>
<td align="right">NaN</td>
<td align="right">5</td>
<td align="right">6</td>
<td align="right">3</td>
<td align="right">0</td>
<td align="right">0.5349045</td>
<td align="right">0.3429499</td>
</tr>
<tr class="odd">
<td align="left">31</td>
<td align="right">31</td>
<td align="right">0.2033327</td>
<td align="right">0.7353261</td>
<td align="right">6</td>
<td align="right">16</td>
<td align="right">3</td>
<td align="right">0</td>
<td align="right">0.5319780</td>
<td align="right">0.3302434</td>
</tr>
<tr class="even">
<td align="left">46</td>
<td align="right">46</td>
<td align="right">0.2033327</td>
<td align="right">0.7353261</td>
<td align="right">4</td>
<td align="right">12</td>
<td align="right">1</td>
<td align="right">0</td>
<td align="right">0.5288585</td>
<td align="right">0.2464654</td>
</tr>
<tr class="odd">
<td align="left">61</td>
<td align="right">61</td>
<td align="right">0.2370944</td>
<td align="right">0.7608060</td>
<td align="right">3</td>
<td align="right">13</td>
<td align="right">3</td>
<td align="right">0</td>
<td align="right">0.4898947</td>
<td align="right">0.2933348</td>
</tr>
<tr class="even">
<td align="left">76</td>
<td align="right">76</td>
<td align="right">0.2370944</td>
<td align="right">0.7608060</td>
<td align="right">6</td>
<td align="right">17</td>
<td align="right">2</td>
<td align="right">0</td>
<td align="right">0.4642052</td>
<td align="right">0.2116843</td>
</tr>
</tbody>
</table>
<p>Over time the simulation end up replacing the least effective
polygrpahers (generally those who follow ethical rules) with random
selections of new polygraphers. By day 991 as a result of this selection
process the average unethics of the polygraphers in the system has
drifted to 80% with the “top” polygraphers having an unethical rating of
96%. Interestingly we can see that the adverse incentive system has also
resulted in the candidates who “pass” the polygraph as now having a
ethical flexibility of 54% while those who fail have a flexibility of
28%. IE, statistically those who refuse to sign fake confessions and
thus fail are actually those with a higher ethical standards than those
who pass on average.</p>
<p>This is an interesting result and consistent with intuition. Corrupt
systems such as those involving bribery, kickbacks, etc. end up
corrupting both the corrupter (ie the polygrapher) as well as the victim
(the candidate).</p>
<p>Table 2: Snapshot of the end of the simulation.</p>
<pre class="r"><code>knitr::kable(tail(day_dataframe[day_dataframe$day %% 15 == 1,]))</code></pre>
<table>
<colgroup>
<col width="2%" />
<col width="2%" />
<col width="9%" />
<col width="11%" />
<col width="10%" />
<col width="10%" />
<col width="9%" />
<col width="8%" />
<col width="17%" />
<col width="17%" />
</colgroup>
<thead>
<tr class="header">
<th align="left"></th>
<th align="right">day</th>
<th align="right">mean_unethics</th>
<th align="right">mean_unethics_top</th>
<th align="right">real_confession</th>
<th align="right">fake_confession</th>
<th align="right">confession_lie</th>
<th align="right">disciplinary</th>
<th align="right">candidate_flexibility_pass</th>
<th align="right">candidate_flexibility_fail</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="left">916</td>
<td align="right">916</td>
<td align="right">0.7997596</td>
<td align="right">0.9428243</td>
<td align="right">4</td>
<td align="right">64</td>
<td align="right">11</td>
<td align="right">1</td>
<td align="right">0.5497275</td>
<td align="right">0.3783560</td>
</tr>
<tr class="even">
<td align="left">931</td>
<td align="right">931</td>
<td align="right">0.8066865</td>
<td align="right">0.9356297</td>
<td align="right">3</td>
<td align="right">57</td>
<td align="right">21</td>
<td align="right">0</td>
<td align="right">0.5096309</td>
<td align="right">0.3062531</td>
</tr>
<tr class="odd">
<td align="left">946</td>
<td align="right">946</td>
<td align="right">0.8066865</td>
<td align="right">0.9356297</td>
<td align="right">9</td>
<td align="right">62</td>
<td align="right">11</td>
<td align="right">0</td>
<td align="right">0.5244614</td>
<td align="right">0.3196479</td>
</tr>
<tr class="even">
<td align="left">961</td>
<td align="right">961</td>
<td align="right">0.8195815</td>
<td align="right">0.9610793</td>
<td align="right">7</td>
<td align="right">58</td>
<td align="right">17</td>
<td align="right">0</td>
<td align="right">0.5313487</td>
<td align="right">0.3139352</td>
</tr>
<tr class="odd">
<td align="left">976</td>
<td align="right">976</td>
<td align="right">0.8195815</td>
<td align="right">0.9610793</td>
<td align="right">6</td>
<td align="right">56</td>
<td align="right">16</td>
<td align="right">0</td>
<td align="right">0.5354786</td>
<td align="right">0.4062887</td>
</tr>
<tr class="even">
<td align="left">991</td>
<td align="right">991</td>
<td align="right">0.8034161</td>
<td align="right">0.9582148</td>
<td align="right">2</td>
<td align="right">61</td>
<td align="right">12</td>
<td align="right">2</td>
<td align="right">0.5421242</td>
<td align="right">0.2860935</td>
</tr>
</tbody>
</table>
<p>If we look at the supervisors who are selected from the top 10 most
effective polygraphers in the system we find a truly unethical bunch.
With the “most ethical” supervisor being much more likely to deploy
unethical practices than the typical polygrapher while the most
unethical supervisor practice systematic and consistent unethical
practices only choosing not to act unethically about 1% of the time.</p>
<p>Table 3:</p>
<pre class="r"><code>knitr::kable(active_polygraphers[active_polygraphers$supervisors == 1,])</code></pre>
<table style="width:100%;">
<colgroup>
<col width="4%" />
<col width="17%" />
<col width="14%" />
<col width="18%" />
<col width="18%" />
<col width="8%" />
<col width="17%" />
</colgroup>
<thead>
<tr class="header">
<th align="left"></th>
<th align="right">polygrapher</th>
<th align="right">unethics</th>
<th align="right">nConfessions</th>
<th align="right">disciplinary</th>
<th align="right">ndays</th>
<th align="right">supervisors</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="left">14</td>
<td align="right">365</td>
<td align="right">0.9796909</td>
<td align="right">10</td>
<td align="right">0</td>
<td align="right">190</td>
<td align="right">1</td>
</tr>
<tr class="even">
<td align="left">15</td>
<td align="right">163</td>
<td align="right">0.9964339</td>
<td align="right">10</td>
<td align="right">0</td>
<td align="right">790</td>
<td align="right">1</td>
</tr>
<tr class="odd">
<td align="left">30</td>
<td align="right">30</td>
<td align="right">0.9211820</td>
<td align="right">9</td>
<td align="right">0</td>
<td align="right">1000</td>
<td align="right">1</td>
</tr>
<tr class="even">
<td align="left">34</td>
<td align="right">412</td>
<td align="right">0.9687165</td>
<td align="right">10</td>
<td align="right">0</td>
<td align="right">70</td>
<td align="right">1</td>
</tr>
<tr class="odd">
<td align="left">35</td>
<td align="right">145</td>
<td align="right">0.9080019</td>
<td align="right">10</td>
<td align="right">0</td>
<td align="right">850</td>
<td align="right">1</td>
</tr>
<tr class="even">
<td align="left">46</td>
<td align="right">166</td>
<td align="right">0.9179333</td>
<td align="right">8</td>
<td align="right">0</td>
<td align="right">790</td>
<td align="right">1</td>
</tr>
<tr class="odd">
<td align="left">56</td>
<td align="right">283</td>
<td align="right">0.9691554</td>
<td align="right">10</td>
<td align="right">0</td>
<td align="right">430</td>
<td align="right">1</td>
</tr>
<tr class="even">
<td align="left">57</td>
<td align="right">415</td>
<td align="right">0.9596243</td>
<td align="right">9</td>
<td align="right">0</td>
<td align="right">70</td>
<td align="right">1</td>
</tr>
<tr class="odd">
<td align="left">62</td>
<td align="right">197</td>
<td align="right">0.9724210</td>
<td align="right">10</td>
<td align="right">1</td>
<td align="right">700</td>
<td align="right">1</td>
</tr>
<tr class="even">
<td align="left">92</td>
<td align="right">279</td>
<td align="right">0.9889890</td>
<td align="right">10</td>
<td align="right">0</td>
<td align="right">460</td>
<td align="right">1</td>
</tr>
</tbody>
</table>
<p>Now let’s look graphically at how ethics drift over time due to the
incentives in the system.</p>
<p>In the figure below we can see the average ethics of the polygrapher
move dramatically while the “top polygrapher” does not really move that
much. The cause of this movement is entirely base on the incentives in
the system.</p>
<p>Figure 1:</p>
<pre class="r"><code>ggplot(day_dataframe[day_dataframe$day > 30, ], aes(x=day, y=mean_unethics)) +
theme_bw() +
geom_line(aes(colour = mean_unethics), linewidth = 2) +
ylab('Polygrapher Unethics') +
scale_color_gradient(low="gray", high="red") +
geom_line(aes(y = mean_unethics_top), color="steelblue", linetype="twodash", linewidth = 2) +
theme(legend.position = "none")</code></pre>
<p><img 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" width="672" /></p>
<p>We can see this by running the simulation again but changing the
probability of being caught when deploying unethical practices. Even a
change from .1% to 10% and .05% to 5% results in dramatically different
expected behavior by polygraphers with polygraphers ethics drifting very
little over time.</p>
<p>Figure 2:</p>
<pre class="r"><code>x = simulateSystem(number_of_days = 1000,
probabilty_of_caught = .1,
probabilty_of_caught_with_confession = .05)
day_dataframe = x$day_dataframe
dayResults = x$dayResults
active_polygraphers = x$active_polygraphers
ggplot(day_dataframe[day_dataframe$day > 30, ], aes(x=day, y=mean_unethics)) +
theme_bw() +
geom_line(aes(colour = mean_unethics), linewidth = 2) +
ylab('Polygrapher Unethics') +
scale_color_gradient(low="gray", high="red") +
geom_line(aes(y = mean_unethics_top), color="steelblue", linetype="twodash", linewidth = 2) +
theme(legend.position = "none")</code></pre>
<p><img 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" width="672" /></p>
<p>Having even high rates of checking for and catching polygrapher abuse
(30% and 15%) results in even more dramatic changes in the population of
polyragraphers having little ethical drift over time. Shockingly, under
these conditions, those polygraphers most likely to be recognized and
promoted to supervisors are actually those most ethical.</p>
<pre class="r"><code>x = simulateSystem(number_of_days = 1000,
probabilty_of_caught = .3,
probabilty_of_caught_with_confession = .15)
day_dataframe = x$day_dataframe
dayResults = x$dayResults
active_polygraphers = x$active_polygraphers
knitr::kable(head(day_dataframe[day_dataframe$day %% 15 == 1,]))</code></pre>
<table>
<colgroup>
<col width="1%" />
<col width="2%" />
<col width="9%" />
<col width="11%" />
<col width="10%" />
<col width="10%" />
<col width="9%" />
<col width="8%" />
<col width="17%" />
<col width="17%" />
</colgroup>
<thead>
<tr class="header">
<th align="left"></th>
<th align="right">day</th>
<th align="right">mean_unethics</th>
<th align="right">mean_unethics_top</th>
<th align="right">real_confession</th>
<th align="right">fake_confession</th>
<th align="right">confession_lie</th>
<th align="right">disciplinary</th>
<th align="right">candidate_flexibility_pass</th>
<th align="right">candidate_flexibility_fail</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="left">1</td>
<td align="right">1</td>
<td align="right">0.1328231</td>
<td align="right">NaN</td>
<td align="right">5</td>
<td align="right">10</td>
<td align="right">2</td>
<td align="right">2</td>
<td align="right">0.5178134</td>
<td align="right">0.2941226</td>
</tr>
<tr class="even">
<td align="left">16</td>
<td align="right">16</td>
<td align="right">0.1328231</td>
<td align="right">NaN</td>
<td align="right">7</td>
<td align="right">10</td>
<td align="right">0</td>
<td align="right">3</td>
<td align="right">0.5277926</td>
<td align="right">0.5738695</td>
</tr>
<tr class="odd">
<td align="left">31</td>
<td align="right">31</td>
<td align="right">0.1454454</td>
<td align="right">0.1459775</td>
<td align="right">5</td>
<td align="right">10</td>
<td align="right">3</td>
<td align="right">2</td>
<td align="right">0.4450546</td>
<td align="right">0.4120254</td>
</tr>
<tr class="even">
<td align="left">46</td>
<td align="right">46</td>
<td align="right">0.1454454</td>
<td align="right">0.1459775</td>
<td align="right">3</td>
<td align="right">15</td>
<td align="right">3</td>
<td align="right">4</td>
<td align="right">0.4825806</td>
<td align="right">0.3049907</td>
</tr>
<tr class="odd">
<td align="left">61</td>
<td align="right">61</td>
<td align="right">0.1635972</td>
<td align="right">0.0903043</td>
<td align="right">3</td>
<td align="right">13</td>
<td align="right">1</td>
<td align="right">1</td>
<td align="right">0.4681765</td>
<td align="right">0.0847121</td>
</tr>
<tr class="even">
<td align="left">76</td>
<td align="right">76</td>
<td align="right">0.1635972</td>
<td align="right">0.0903043</td>
<td align="right">3</td>
<td align="right">14</td>
<td align="right">1</td>
<td align="right">4</td>
<td align="right">0.4783364</td>
<td align="right">0.3117455</td>
</tr>
</tbody>
</table>
<pre class="r"><code>knitr::kable(tail(day_dataframe[day_dataframe$day %% 15 == 1,]))</code></pre>
<table>
<colgroup>
<col width="2%" />
<col width="2%" />
<col width="9%" />
<col width="11%" />
<col width="10%" />
<col width="10%" />
<col width="9%" />
<col width="8%" />
<col width="17%" />
<col width="17%" />
</colgroup>
<thead>
<tr class="header">
<th align="left"></th>
<th align="right">day</th>
<th align="right">mean_unethics</th>
<th align="right">mean_unethics_top</th>
<th align="right">real_confession</th>
<th align="right">fake_confession</th>
<th align="right">confession_lie</th>
<th align="right">disciplinary</th>
<th align="right">candidate_flexibility_pass</th>
<th align="right">candidate_flexibility_fail</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="left">916</td>
<td align="right">916</td>
<td align="right">0.3078299</td>
<td align="right">0.1116442</td>
<td align="right">8</td>
<td align="right">21</td>
<td align="right">3</td>
<td align="right">1</td>
<td align="right">0.4898941</td>
<td align="right">0.3763426</td>
</tr>
<tr class="even">
<td align="left">931</td>
<td align="right">931</td>
<td align="right">0.3042549</td>
<td align="right">0.2595712</td>
<td align="right">4</td>
<td align="right">24</td>
<td align="right">3</td>
<td align="right">3</td>
<td align="right">0.4696140</td>
<td align="right">0.4861778</td>
</tr>
<tr class="odd">
<td align="left">946</td>
<td align="right">946</td>
<td align="right">0.3042549</td>
<td align="right">0.2595712</td>
<td align="right">10</td>
<td align="right">18</td>
<td align="right">3</td>
<td align="right">10</td>
<td align="right">0.5315689</td>
<td align="right">0.2665043</td>
</tr>
<tr class="even">
<td align="left">961</td>
<td align="right">961</td>
<td align="right">0.2764454</td>
<td align="right">0.0726653</td>
<td align="right">3</td>
<td align="right">18</td>
<td align="right">1</td>
<td align="right">1</td>
<td align="right">0.5027710</td>
<td align="right">0.2665816</td>
</tr>
<tr class="odd">
<td align="left">976</td>
<td align="right">976</td>
<td align="right">0.2764454</td>
<td align="right">0.0726653</td>
<td align="right">3</td>
<td align="right">19</td>
<td align="right">3</td>
<td align="right">3</td>
<td align="right">0.4694358</td>
<td align="right">0.3804199</td>
</tr>
<tr class="even">
<td align="left">991</td>
<td align="right">991</td>
<td align="right">0.3399286</td>
<td align="right">0.0695872</td>
<td align="right">5</td>
<td align="right">19</td>
<td align="right">6</td>
<td align="right">3</td>
<td align="right">0.4977805</td>
<td align="right">0.3616711</td>
</tr>
</tbody>
</table>
<pre class="r"><code>ggplot(day_dataframe[day_dataframe$day > 30, ], aes(x=day, y=mean_unethics)) +
theme_bw() +
geom_line(aes(colour = mean_unethics), linewidth = 2) +
ylab('Polygrapher Unethics') +
scale_color_gradient(low="gray", high="red") +
geom_line(aes(y = mean_unethics_top), color="steelblue", linetype="twodash", linewidth = 2) +
theme(legend.position = "none")</code></pre>
<p><img src="data:image/png;base64,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" width="672" /></p>
<p>Having even higher rates of checking for and catching polygrapher
abuse (60% and 30%) results in even more dramatic changes in the
population of polyragraphers having little ethical drift over time.
Interestingly because the rate of abuse correction is so high, under
these conditions, those polygraphers most likely to be recognized and
promoted to supervisors are actually those most ethical.</p>
</div>
</div>
<div id="conclusions" class="section level3">
<h3>Conclusions</h3>
<p>It is well known that polygraphers deployed by the CIA, NSA, and
similar organizations deploy widespread abusive, illegal, and unethical
practices when conducting their jobs. Those who have not experienced the
sheer shit show of the process find such claims often times
unbelievable. Those who have experienced it uniformly seem to find their
experiences both traumatic, embarrassing, and shameful. Nobody I have
told about my terrible experience has been surprised by it but rather in
turn felt compelled to tell me of their own unfortunate experience.</p>
<p>How has such a system developed? Likely lack of proper incentives.
The previous simulation has minimal assumptions: 1. that so long as
there are few consequences and poor oversight, 2. some incentive to
cheat (act unethically), 3. the pool of potential polygraphers is drawn
from people with a wide range of ethical standards</p>
<p>Yet under these assumptions we can see massive shifts from an
active pool of generally ethical polygraphers to a highly unethical pool
of criminal polygraphers driven by reasonable incentives (getting results)
to hellish extremes driven primarily by failures to implement reasonable
consequences to control for unethical and criminal behavior.</p>
<p>It is no surprise to me under these circumstances that the US is
replete with people willing violate their oaths to share secret or top secret
information with newspapers, foreign governments, even discord channels.
If the “counter-intelligence” security apparatus is so myopic and flawed
as to allow polyraphers such as Jeremy free reign, one can hardly expect
it to screen out potential national security threats.</p>
</div>
<div id="there-is-hope" class="section level3">
<h3>There is Hope</h3>
<p>The extent of unethical misconduct within the security process at the
CIA, NSA, and other government agencies is so bad that it would not take
that much effort to track down and eliminate the worst of the worst.
Simply reviewing the recordings from polygraph interviews and
following up with exit surveys from participants would likely yield
tremendous results.</p>
<p>There is a painful but simple fix, get rid of bad
rubbish. Fire those who systematically betray and embarrass their
country, their fellow citizens, and really all citizens and defenders of
democracy by acting unethically for their own gain. For those who have
acted criminally by physically or sexually assaulted their victims,
falsified federal documents and conspired with others to cover their
crimes, they should should be prosecuted to the fullest extent of the
law.</p>
<p>Only by purging the rot can one hope to establish a system which does
its job, ie. blocking unethical, immature, or those motivated by foreign
loyalties from gaining access to highly sensitive information.</p>
</div>
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Francishttp://www.blogger.com/profile/16658586705916884436noreply@blogger.com0Washington, DC, USA38.9071923 -77.036870710.596958463821153 -112.1931207 67.217426136178844 -41.880620699999994tag:blogger.com,1999:blog-6288862798546085706.post-31505764061588806882020-04-11T15:14:00.001-04:002021-11-24T10:05:19.543-05:00Is COVID-19 as bad as all that? Yes it probably is.<div dir="ltr" style="text-align: left;" trbidi="on">
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<![endif]--><h2 class="MsoNormal" style="text-align: left;">
</h2>
As an economist without formal training in epidemiology I
have done my best to leave the modelling up to the experts. But, the world has
shut down around me and my life is suddenly so much more complicated and I have
to wonder, is this COVID thing as dangerous as it seems? When things got bad in
Italy my optimistic friends said, “that’s just Italy”. When things got bad in
Spain, they said the same. But now New York has more deaths per capita than either
Italy or Spain and I am starting to sweat a little. Is there something particularly
bad about the New York health care system which has made them more vulnerable
to this disease than others?
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
Looking at the mortality rate of previous flu seasons in New
York in which for the last four years, they have been in the top 10 best performing states according to
the <a href="https://www.cdc.gov/nchs/pressroom/states/newyork/newyork.htm" target="_blank">CDC</a>. In 2017 New York had the <a href="https://en.wikipedia.org/wiki/List_of_U.S._states_and_territories_by_birth_and_death_rates" target="_blank">7th lowest death rate by State</a>, only being beat by states which had lower elderly populations (Utah, Alaska, California, Colorado, Texas, and Washington).</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
Does New York have a particularly large elderly population which
has made it more vulnerable? Nope. New York state, at 14.66%, ranks squarely toward
the youngish center of states (<a href="https://www.worldatlas.com/articles/the-us-states-with-the-oldest-population.html" target="_blank">29/50 youngest</a>)
while New York city is younger in general than the rest of the state with only 13% of the
city population <a href="https://comptroller.nyc.gov/reports/aging-with-dignity-a-blueprint-for-serving-nycs-growing-senior-population/" target="_blank">older than 65</a>.</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
Well maybe the mortality rate of COVID-19 just seems high
because it is about to peak? After all, the flu kills somewhere between 12 and 70
thousand people in the US every year and <a href="https://www.health.com/condition/cold-flu-sinus/how-many-people-die-of-the-flu-every-year" target="_blank">290 to 650 thousand globally</a>.
COVID-19 with an estimated number of deaths in the US of around <a href="https://en.wikipedia.org/wiki/2019%E2%80%9320_coronavirus_pandemic_by_country_and_territory" target="_blank">19 thousand and 104 thousand globally</a> doesn’t seem that dangerous.</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
Yet, the very reasonable concern is that this disease is
just getting started. <a href="https://en.wikipedia.org/wiki/2019%E2%80%9320_coronavirus_pandemic" target="_blank">Wikipedia numbers</a> suggest the total number of cases
globally is 1.7 million, which we know is a lower bound of the true number of
cases, as many of those who have COVID-19 have not been tested. </div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
We don’t know how many people currently have COVID but we
can imagine a few different scenarios. </div>
<div class="MsoNormal">
<br /></div>
<h3 class="MsoNormal" style="text-align: left;">
Scenario 1: COVID-19 reported cases are close to true cases </h3>
<div class="MsoNormal">
Let’s imagine that the number of people with COVID is approximately
the number that we have record of. There are some unreported cases but not that
many. If this is the case, we are in an extremely frightening world because so
far the disease has killed about 104 thousand people out of the 1.7 million it
has affected, a 6 % mortality rate and almost all of those infected are not yet
recovered, meaning some of them will die, increasing the observed mortality
rate. The small consolation under this scenario is that cases are largely
detected and therefore with enough government and individual intervention ongoing
transmission likely could be slowed and stopped through thorough and diligent contact
tracing. </div>
<div class="MsoNormal">
<br /></div>
<h3 class="MsoNormal" style="text-align: left;">
Scenario 2: COVID-19 reported cases are reasonable fraction of true
cases</h3>
<div class="MsoNormal" style="line-height: normal; margin-bottom: 0in;">
Let’s imagine that the true number of cases is somewhere between 2 to
10 times as many as those reported. Under this scenario, the current mortality
rate is calculated by dividing the observed mortality rate by the factor of
unknown cases so 6/2=3% for 2 times with 6/10=0.6% for ten times. In this
scenario contact tracing by and large will fail as there is simply too many unknown
cases. The best thing governments and individuals can do in this scenario is
shut off potential avenues of transmission between individuals until either a
vaccine can be found or the number of new cases is so small that the implementation
of contact tracing is feasible. Sadly even in the scenario in which the true number
of cases is 10x that of the reported cases the mortality rate of COVID at a
minimum of 0.6% is still much higher than of the seasonal flu and if left
unchecked would result in 2.28 million fatalities in the US alone (0.6% * 380
million) which is greater than the top ten leading causes of death in the US
combined: </div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: 0in;">
<br /></div>
<h4 class="MsoNormal" style="line-height: normal; margin-bottom: 0in;">
Table 1 </h4>
<div class="MsoNormal" style="line-height: normal; margin-bottom: 0in;">
<a href="https://www.cdc.gov/nchs/fastats/leading-causes-of-death.htm" target="_blank">Leading cause of death</a>:</div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: 0in;">
<span style="mso-spacerun: yes;"> </span>Heart disease: 647,457</div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: 0in;">
<span style="mso-spacerun: yes;"> </span>Cancer: 599,108</div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: 0in;">
<span style="mso-spacerun: yes;"> </span>Accidents (unintentional
injuries): 169,936</div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: 0in;">
<span style="mso-spacerun: yes;"> </span>Chronic lower respiratory
diseases: 160,201</div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: 0in;">
<span style="mso-spacerun: yes;"> </span>Stroke (cerebrovascular
diseases): 146,383</div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: 0in;">
<span style="mso-spacerun: yes;"> </span>Alzheimer’s disease: 121,404</div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: 0in;">
<span style="mso-spacerun: yes;"> </span>Diabetes: 83,564</div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: 0in;">
<span style="mso-spacerun: yes;"> </span>Influenza and pneumonia:
55,672</div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: 0in;">
<span style="mso-spacerun: yes;"> </span>Nephritis, nephrotic
syndrome, and nephrosis: 50,633</div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: 0in;">
<span style="mso-spacerun: yes;"> </span>Intentional self-harm
(suicide): 47,173</div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: 0in;">
Total 2.08 million</div>
<div class="MsoNormal">
<br /></div>
<h3 class="MsoNormal" style="text-align: left;">
Scenario 3: COVID is already everywhere and most people have
it or have already had it</h3>
<div class="MsoNormal">
Strangely this is the best-case scenario. Under this scenario
only those who have severe outcomes from COVID-19 are being reported while the vast
majority (like 99%) of individuals are asymptomatic. Under this scenario,
shutting down state, national, and international travel and social activities is
futile for any extended period of time as the virus is already everywhere and
we just need to treat the severe cases that pop up the best we can and suck it
up. This scenario is appealing as it means the worst has already come or is
soon to.</div>
<div class="MsoNormal">
<br /></div>
<h3 class="MsoNormal" style="text-align: left;">
So which scenario are we in?</h3>
<div class="MsoNormal">
Reviewing the scenarios it is impossible to know with certainty
in which scenario lies reality. However, does the evidence point against any
given scenario? </div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
Scenario 1 seems unlikely to me due to the tens of thousands of
cases are popping up each day (Figure 5). This rate of new infections seems to indicate
that there is a sizable infected population which has not yet been detected and
has continued to spread the virus despite national, state, and local recommendations
and mandates intended to limit spread.</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
Under Scenario 3 in which COVID-19 is already everywhere
this scenario seems unlikely due to the lumpiness of the mortality numbers. If COVID-19 were everywhere
then we would expect people across all states and countries to be dying from the
disease more or less proportionately. If COVID-19 were already everywhere we
would expect that mortality numbers to be mostly homogenous across states. However, this
is not what we are seeing with highly heterogenous mortality numbers across states
and countries. New York currently has around 400 deaths per million while New
Jersey 218, Michigan 108, Florida has around 19, California 14, Texas 8, and Montana
6.</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
These numbers suggest that COVID is spreading from infected communities
to non-infected communities in a hotspot community spread model rather than
that of a widespread dispersal characteristic of Scenario 3. </div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
But maybe one might ask, is it possible that deaths
previously assigned to other causes might have actually been caused by COVID-19
before the virus was known and publicized? Yes, there are very likely deaths caused
by COVID-19 which have not yet been correctly attributed to the disease. If accounted
for could, these deaths correct the heterogeneity in the data in order to place
us back in Scenario 3? Figure 1 shows the known deaths in New York by COVID-19 compared
with flu mortality numbers from <a href="https://www.cdc.gov/nchs/pressroom/states/newyork/newyork.htm" target="_blank">2014-2017</a>.
Already, COVID-19 has or will soon double the mortality of the flu for these
years and unfortunately the number of infections has continued to grow at an
alarming pace (Figure 2).</div>
<div class="MsoNormal">
<br /></div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiuxgCl-I2u4hbrldx8Y8w9vJjCgOTBDYN-XL-BAeCU-PA5Lg8kC3PboXO6hJflISslT8bEo_rPS_FwW9G3zBwx0WgnQ30IPzz8GEECkB1ALREJGUeJbGlmxyU-WXhYO9yXfzG79BhBFzc/s1600/NewYorkDeathsCOVID2019.png" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="600" data-original-width="800" height="480" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiuxgCl-I2u4hbrldx8Y8w9vJjCgOTBDYN-XL-BAeCU-PA5Lg8kC3PboXO6hJflISslT8bEo_rPS_FwW9G3zBwx0WgnQ30IPzz8GEECkB1ALREJGUeJbGlmxyU-WXhYO9yXfzG79BhBFzc/s640/NewYorkDeathsCOVID2019.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 1</td></tr>
</tbody></table>
<div class="separator" style="clear: both; text-align: center;">
</div>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjxfu90xlhinaVdNOR4vWlZ19F0-p3CG7CiNMIPbaxAjkfRWGH43vIEcbNhJMxaqa_auz7Em0GYOVYk6ea5R69w-CbtvOR2nFg0yKql2jbNAK-ooJ0CSQ76SG3-wSWmUgvSkFcexETLTZ4/s1600/NewYorkCasesCOVID2019.png" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="600" data-original-width="800" height="480" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjxfu90xlhinaVdNOR4vWlZ19F0-p3CG7CiNMIPbaxAjkfRWGH43vIEcbNhJMxaqa_auz7Em0GYOVYk6ea5R69w-CbtvOR2nFg0yKql2jbNAK-ooJ0CSQ76SG3-wSWmUgvSkFcexETLTZ4/s640/NewYorkCasesCOVID2019.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 1</td></tr>
</tbody></table>
<div class="MsoNormal">
So, while it is impossible to know, I believe it extremely
unlikely that a disease twice as deadly as a typical flu (at least in New York)
could go undetected in thousands of hospitals and laboratories across the United
States.</div>
<div class="MsoNormal">
<br /></div>
<h3 class="MsoNormal" style="text-align: left;">
Assuming Scenario 2</h3>
<div class="MsoNormal">
With some reports saying 80% of cases are asymptomatic, an
estimate of 5x as many people infected with COVID-19 as what has been reported
might not be crazy. This would mean that the actual number of people infected with
COVID in New York is something like 650,000 which while encouraging in that 9,000
deaths out of 850,000 (1%) is much better than 9,000 deaths out of 170,000
people (5.3%). </div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
The problem of course is that even the inflated number 850
thousand is only 10% of the city’s population and 4.6% of the total population of
the state. Meaning we still would have a vast large potential population to
infect. Combine that with the factor that we are having somewhere between 6,000
and 10,000 new cases pop up every day in the state despite a ‘stay are home’
order in effect for two and a half weeks.</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
Looking at the graph (Figure 2), the number of cases in New
York has grown very rapidly. Yet, presumably the number of cases would be even
greater if the lockdown order were not in effect. </div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
Yet most of us don’t live in New York. How much should we be
worried?</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
As New York has an above average health care system and
relatively lower proportion at risk elderly population New York could be seen
as a lower risk state compared with many. Yet, New York City is also the most
dense city in the country with perhaps the highest use of public transportation
and correspondingly highest use of public potential infection points such as
grocery stores, theaters, restaurants, etc..</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
Looking at only states which have reported more than 5,000
cases and scaling counts by log10 we get Figure 3. In Figure 3 is it hard to
mark out much except that the overall shape of the infection curve seems to be
similar across states. </div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<span style="mso-no-proof: yes;"></span></div>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgYd_nhMrEvaj-7QIaBBWDPYOy7nUAIPS-YFdCoY5E8BcSOF5Gjc_pMiBeNoWKuuSXgDL1hZaeYtBctlPq6MxAfY5srip2BNzo1Q_y4PrKIowEtlYscrp-oA3oGYbcosP5kC6zCZrifks8/s1600/StateComparisons.png" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="600" data-original-width="800" height="480" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgYd_nhMrEvaj-7QIaBBWDPYOy7nUAIPS-YFdCoY5E8BcSOF5Gjc_pMiBeNoWKuuSXgDL1hZaeYtBctlPq6MxAfY5srip2BNzo1Q_y4PrKIowEtlYscrp-oA3oGYbcosP5kC6zCZrifks8/s640/StateComparisons.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 3: Total number of cases by state for states
reporting at least 5,000 cases. </td><td class="tr-caption" style="text-align: center;"> </td><td class="tr-caption" style="text-align: center;"> </td></tr>
</tbody></table>
<div class="MsoNormal">
It is difficult to make comparisons between states and to
make predictions from Figure 3. However, one technique often used to pick a
point in time with a certain number of cases then compare how growth rate in
cases changed for others states after they reached the same point. In this
case, I will pick my earliest date in my dataset March 18<sup>th</sup> in New
York in which there were around 2,500 cases of COVID-19 reported. This number
was reached later by different states, New Jersey on the 23<sup>rd</sup>,
California on the 25<sup>th</sup>, Washington on the 26<sup>th</sup>, Michigan,
Florida, and Illinois on the 27<sup>th</sup>, and so on.</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
Plotting cases starting at this common point now gives us a
means of comparing case growth by state (Figure 4). Under this technique, New
York definitely appears to have a higher growth rate followed by New Jersey
with Michigan, California, Louisiana, Massachusetts, Pennsylvania, Illinois, Texas,
Georgia, and many other states following a less aggressive but still positive
growth trajectory. </div>
<div class="MsoNormal">
<br /></div>
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjR6KJI3vleVhEVzmuxgkt0UmcvAbU1pizNCdIm-UWHWAhCnzYA9CaV3V2D-znpiSfbTWGI_kAwldQOFMUD5WDuwe4GdEqt89MkWUZqT8NBgdgj5K9w-MMqpatCAKem3IzNIK_hOsHTWRA/s1600/StateComparisonsDay0.png" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="600" data-original-width="800" height="480" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjR6KJI3vleVhEVzmuxgkt0UmcvAbU1pizNCdIm-UWHWAhCnzYA9CaV3V2D-znpiSfbTWGI_kAwldQOFMUD5WDuwe4GdEqt89MkWUZqT8NBgdgj5K9w-MMqpatCAKem3IzNIK_hOsHTWRA/s640/StateComparisonsDay0.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">
<div class="MsoNormal">
Figure 4: Day 0 is the first day a state passes 2,480 cases
of reported COVID-19.</div>
</td></tr>
</tbody></table>
<div class="MsoNormal">
<span style="mso-no-proof: yes;"></span></div>
<div class="MsoNormal">
<br /></div>
<h3 class="MsoNormal" style="text-align: left;">
Conclusions</h3>
<div class="MsoNormal">
COVID-19 appears to be really bad and New York has been
hit the hardest - so far. How bad? We won’t know until after crisis has passed. Fortunately, other states had lower
rates around the time the country (the President) started taking this crisis
seriously. Since then, those states appear to be on a more gradual growth
trajectory than that of New York.</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
Yet despite widespread concern over COVID-19, instructions,
and mandates to help reduce the spread, new infections are still on the
rise (Figure 5). And this is under conditions in which we have put a stop in-person social gathering, closed restaurants, and ordered residents to stay in
doors in many states. What happens when the public gets tired of such restrictions? It seems likely that growth rates of new infections would start rising
rapidly once again.</div>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh8qAF_HQ8hG8XDGitntG_xI_pv2OAjT4BFRf-Qa7JHvIlEhTfZOM44Q2gyweIm5GEIXIJbysrgJz1aRTZuQM8kfPmqvvAfArNSeD2Qp4O7SyWXhMAsKz7PLNLZZW8jcP8O2aOlrcsQYgY/s1600/NumberOFNewCases.png" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="600" data-original-width="800" height="480" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh8qAF_HQ8hG8XDGitntG_xI_pv2OAjT4BFRf-Qa7JHvIlEhTfZOM44Q2gyweIm5GEIXIJbysrgJz1aRTZuQM8kfPmqvvAfArNSeD2Qp4O7SyWXhMAsKz7PLNLZZW8jcP8O2aOlrcsQYgY/s640/NumberOFNewCases.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 5</td><td class="tr-caption" style="text-align: center;"><br /></td></tr>
</tbody></table>
Graphs created in R - code on <a href="https://github.com/EconometricsBySimulation/Ninja/blob/master/2020/04-April/11_COVID19.R" target="_blank">GitHub</a></div>
Francishttp://www.blogger.com/profile/16658586705916884436noreply@blogger.com1tag:blogger.com,1999:blog-6288862798546085706.post-71885284738153903012019-03-22T17:10:00.000-04:002019-03-23T09:16:38.916-04:00Data Fun - Inspired by Darasaurus<div dir="ltr" style="text-align: left;" trbidi="on">
<br />
After my recent post on <a href="http://www.econometricsbysimulation.com/2019/03/the-importance-of-graphing-your-data.html" target="_blank">Anscombe's Quartet</a> in which I demonstrated how to efficiently adjust any data set to match mean, variance, correlation (x,y), as well as regression coefficients. <a href="https://github.com/pdwaggoner" target="_blank">Philip Waggoner</a> tuned me onto Justin Matejka and George Fitzmaurice's <a href="https://www.autodeskresearch.com/publications/samestats" target="_blank">Datasaurus R package/paper</a> in which the authors demonstrate an alternative method of modifying existing data to fit a specified mean and variance for X and Y. Their method randomly applies small disturbances to individual observations to gradually move the data to match a target preference set. <br />
<br />
Inspired by their use of point images which match a specific parameter set, I have done generated some of my own. For all of them X has a mean and variance of 1 and 11. While y has a mean and variance of 1 and 1. The correlation between X and Y is set to 0 which causes some distortion in the images. More on that in the post.<br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh6S71JpeaxWXgu4PvU9hl3b0E2H7ekuRBtfmBDUqJ072UQUvgEtEQMubi6EXfqxA2sWYQqxuO9h0yYBJfc_MoGv_j4S_zCvkBpJvkwinB3LfFwESbtqFQxcxxXngpKllQtaqm1oSnOcL0/s1600/Transition3.gif" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="480" data-original-width="480" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh6S71JpeaxWXgu4PvU9hl3b0E2H7ekuRBtfmBDUqJ072UQUvgEtEQMubi6EXfqxA2sWYQqxuO9h0yYBJfc_MoGv_j4S_zCvkBpJvkwinB3LfFwESbtqFQxcxxXngpKllQtaqm1oSnOcL0/s400/Transition3.gif" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 1: Shows a graph of 12 data sets each with 15 transitional data sets. The mean, variance, and correlations of X and Y are held constant throughout the sets and transitions.</td></tr>
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<h3 style="text-align: left;">
Data Source</h3>
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I generated the data myself using <a href="https://www.mobilefish.com/services/record_mouse_coordinates/record_mouse_coordinates.php" target="_blank">Mobilefish's</a> upload photo and record clicks webapp. The source images are from images I found online.</div>
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The only slight trick to using the data generated by Mobilefish was that the y cooridates are typically tracked from the top of the page with software, yet most statistical graphing software plots with y starting from the bottom of the graph.</div>
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<b>Raw Images</b></div>
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The raw data when plotted look like their source material..</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgHc0bvRDNkLIgxz19ObDoRutURnfKzjE8pUvQHSHPp7p9R6fCRbGqLXoi8JeaH7FxALUrTaMmbWMFIaEsJhZ7oicwF_yK7Q16qnyEoE6JKTmk00IXOu9HWQXCQQBHrGixp3yo2akRGSys/s1600/Bart.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="600" data-original-width="600" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgHc0bvRDNkLIgxz19ObDoRutURnfKzjE8pUvQHSHPp7p9R6fCRbGqLXoi8JeaH7FxALUrTaMmbWMFIaEsJhZ7oicwF_yK7Q16qnyEoE6JKTmk00IXOu9HWQXCQQBHrGixp3yo2akRGSys/s320/Bart.png" width="320" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEin5rnARuY1CsxqLVw6BVkmIzje_T5fguX6gwwEE5xjdIQJd8UpTAAciRYNfMpbE4tRbFZkwrPJloKp89wA_EeL0ieW2Od1uD1ywdWTx9-RPI-8DdtsLAFM5DlgYYJBbxbQT45AXbD1jPE/s1600/cat.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="600" data-original-width="600" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEin5rnARuY1CsxqLVw6BVkmIzje_T5fguX6gwwEE5xjdIQJd8UpTAAciRYNfMpbE4tRbFZkwrPJloKp89wA_EeL0ieW2Od1uD1ywdWTx9-RPI-8DdtsLAFM5DlgYYJBbxbQT45AXbD1jPE/s320/cat.png" width="320" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjNS_7tpvEWnAkypxNy7AvQdEVjRPO46M9MdvYF32R21_iQENIgR0vvd7I8MdUaeYc2WH8q_Cq72Ir_y6LJw0ZJlWJer-dIgz24JMqK8B-tXafYLRZGEIIi39dcZtF3p5uFNOLYZ1Y_wfQ/s1600/flower.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="600" data-original-width="600" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjNS_7tpvEWnAkypxNy7AvQdEVjRPO46M9MdvYF32R21_iQENIgR0vvd7I8MdUaeYc2WH8q_Cq72Ir_y6LJw0ZJlWJer-dIgz24JMqK8B-tXafYLRZGEIIi39dcZtF3p5uFNOLYZ1Y_wfQ/s320/flower.png" width="320" /></a></div>
<h3 style="text-align: left;">
New Images: Force Cor(X,Y)=0</h3>
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When we force the correlation of X and Y to be zero certain point distributions become distorted.</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhOJhh0h7IrPFuQS5G_4RpBB9SgIu_MrlmOzbWbk7suZIBh-IpWsiDXLpsbCCB3HpW4TkN1N3uB2kRGs9OC3ELflAuowKowv3hmCJfMMAlOyH-4n5T4P5pjTwmhNB9ejQIqkIDqw3ksq-s/s1600/barcorXY0.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="600" data-original-width="600" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhOJhh0h7IrPFuQS5G_4RpBB9SgIu_MrlmOzbWbk7suZIBh-IpWsiDXLpsbCCB3HpW4TkN1N3uB2kRGs9OC3ELflAuowKowv3hmCJfMMAlOyH-4n5T4P5pjTwmhNB9ejQIqkIDqw3ksq-s/s320/barcorXY0.png" width="320" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhEiZaO8w_AlcAQ0Gk1ZrXlVn928BKN71L4cTV9Ed5mUYF-OnCzVW30QbBK5xVvR9n0_K3Kv5wzxnwNQLw2u4LffXstuhcjyrqeXk37PvIXHOU41mNni5mN_bGVz-D_NtmFINalSSZhU_U/s1600/CatCorXY0.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="600" data-original-width="600" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhEiZaO8w_AlcAQ0Gk1ZrXlVn928BKN71L4cTV9Ed5mUYF-OnCzVW30QbBK5xVvR9n0_K3Kv5wzxnwNQLw2u4LffXstuhcjyrqeXk37PvIXHOU41mNni5mN_bGVz-D_NtmFINalSSZhU_U/s320/CatCorXY0.png" width="320" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhuqWGTLyoPQW4GcyT_PkoACmd26pdx-Zm9GgIlVKx9MjU0QfJoahvJIaw8UJhW3Bz5V4tjNv2CjsHvJDDrGqczIii6-p0tOIqqQhbT0-et5h3VNUzR-TvqXQK9zFKk-R-FH7ZVizC9GJQ/s1600/FlowerCorXY0.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="600" data-original-width="600" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhuqWGTLyoPQW4GcyT_PkoACmd26pdx-Zm9GgIlVKx9MjU0QfJoahvJIaw8UJhW3Bz5V4tjNv2CjsHvJDDrGqczIii6-p0tOIqqQhbT0-et5h3VNUzR-TvqXQK9zFKk-R-FH7ZVizC9GJQ/s320/FlowerCorXY0.png" width="320" /></a></div>
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For Bart and the Cat forcing cor(X,Y) has noticable distortions while for the flower minimal distortions seem to have been introduced.</div>
<h3 style="text-align: left;">
New Images: Force Cor(X,Y)<>0</h3>
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It gets even worse when we impose a constant correlation between X and Y. The following shows the distortions to the flower when we change b1, keeping Cor(X,Y) constant and fixing the Y plot limits.</div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhlMDiW1xQPQYmtZp84ku27SRVw4ABBCZPWTzBhxImZ0dOLCvx1O7NfLb9IG-213q0w-ZkWG5XcvrG2GhCu5BcEQh3XROQIeBHUHpqP29jysJP1lcRT99T4FWuWpP5xQvHct2mr9ebIGWU/s1600/flower.gif" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="480" data-original-width="480" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhlMDiW1xQPQYmtZp84ku27SRVw4ABBCZPWTzBhxImZ0dOLCvx1O7NfLb9IG-213q0w-ZkWG5XcvrG2GhCu5BcEQh3XROQIeBHUHpqP29jysJP1lcRT99T4FWuWpP5xQvHct2mr9ebIGWU/s400/flower.gif" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 8: Shows the effect on Var(Y) that changing b1, when all other factors are held constant.</td></tr>
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<h3 style="text-align: left;">
Slight changes to the Anscombe-Generator Code</h3>
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In order to generate graphs that had cor(X,Y)=0 I had to modify my previous code to allow variation in Y that was completely independent of X. The problem with my code was that if b1=1, my calculation used <span class="pl-smi">SSE</span> <span class="pl-k">=</span> (<span class="pl-smi">b1</span><span class="pl-k">^</span><span class="pl-c1">2</span> <span class="pl-k">*</span> <span class="pl-smi">var(X)</span>)<span class="pl-k">*</span><span class="pl-smi">n in order to infer how large the variation in u needed to be (</span><span class="pl-smi"><span class="pl-v">varianceu</span> <span class="pl-k">=</span> (<span class="pl-smi">SSE</span><span class="pl-k">/</span><span class="pl-smi">corXY</span><span class="pl-k">^</span><span class="pl-c1">2</span> <span class="pl-k">-</span> <span class="pl-smi">SSE</span>)<span class="pl-k">/</span><span class="pl-smi">n)</span>. This backwards inference does not work if b1=0.</span></div>
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So, just for the special case of corXY=0 I have included an additional error term E which is helpful in the even that b1=0.</div>
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<h3 style="text-align: left;">
Summary</h3>
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The thought of use points to make recognizable images had not occurred to me until I viewed Justin Matejka and George Fitzmaurice's Datasaurus work. I hope that in making a slightly more efficient distribution manipulator I will allow new and better datasets to be generated which will help students understand the importance of graphical exploration of their data.</div>
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<h3 style="text-align: left;">
Code</h3>
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My code as well as the slight change to <a href="https://github.com/EconometricsBySimulation/Ninja/blob/master/2019/03-March/2019-02-22-Dinosaurus.R" target="_blank">Anscombe's code can be found here</a>. The standarized data sets can be found <a href="https://github.com/EconometricsBySimulation/Ninja/tree/master/2019/03-March" target="_blank">here</a>. They are the ones that end with std.csv</div>
</div>
Francishttp://www.blogger.com/profile/16658586705916884436noreply@blogger.com0tag:blogger.com,1999:blog-6288862798546085706.post-64467270160998584632019-03-19T14:06:00.001-04:002021-07-20T10:53:41.123-04:00The importance of Graphing Your Data - Anscombe's Clever Quartet! <div dir="ltr" style="text-align: left;" trbidi="on">
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<br />
<div class="MsoNormal">
Francis Anscombe's seminal paper
on "Graphs in Statistical" analysis (American Statistician, 1973) effectively makes the case that looking at summary statistics of data is insufficient to identify the relationship between variables. He demonstrates this by generating four different data sets (Anscombe's quartet) which have nearly identical summary statistics. His data have the same mean and variance for x and y, same correlations between x and y, and same regression coefficients on the linear projection of x on y. (There are certainly additional summary statistics less widely reported such as kurtosis or least absolute deviations/median regression which were not reported which would have indicated differences between the data.) Yet even with these differences, without graphing the data, any analysis would likely be missing the mark.<br />
<br />
I
found myself easily convinced by the strength of his arguments yet also curious
as to how he produced the sample data that fit his statistical argument so
perfectly. Given that he had only 11 points of data, I am drawn to think he played around with the data by hand till it fit his needs. This is suggested by the lack of precision on the statistics of the generated data (<a href="https://en.wikipedia.org/wiki/Anscombe%27s_quartet" target="_blank">Anscombe's quartet</a>).<br />
<br />
If he could do it by hand, I should be able to do it through algorithm! </div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
The benefits of having such an algorithm would be that I generate an arbitrary number of datasets and data that exactly fit specific sample parameters.
I tried a few different methods of producing the data that I wanted. </div>
<div class="MsoNormal">
<h4 style="text-align: left;">
<b>Method 1 - randomly draw some points then select the remaining - fail</b></h4>
</div>
<div class="MsoNormal">
One method was to select just the last point or two from a set of data, say I wanted <span style="mso-spacerun: yes;"> </span>to draw 11 X points with with mean 9 and
variance 11 as found in the data. I attempted to draw 10 points then adjust the
mean and variance by selectively drawing the 11<sup>th</sup> point. This
approach however quickly fails as it relies too much on the 11th point. Say the
mean from the first draws was unusually low with a mean of 8. In order to
weight the sample mean back to 9 the 11th point would therefore need to be 19
in order to balance the x values at 9. Then you have to somehow figure out how
to manage the variance which you know is already going to be blown up by the
presence of my 11th value.</div>
<div class="MsoNormal" style="text-align: left;">
<h4>
<b>Method 2 - use optimization to select points which match the desired outcome - fail</b></h4>
</div>
<div class="MsoNormal">
Next I tried some search algorithms trying to use
computation to search for possible values that fit my needed data. This was a
highly problematic attempt that failed to produce any useful results.</div>
<div class="MsoNormal">
<h4 style="text-align: left;">
<b>Method 3</b> - <b>brute force, randomly generate data - fail</b></h4>
The intent of the approach was to get data <i>close </i>to target parameters, then modifying individual data points to match desired properties<b>.</b><br />
<h4 style="text-align: left;">
<b>Method 4</b> -<b> modify random data to meet parameter specifications</b></h4>
</div>
<div class="MsoNormal">
Fortunately, after a little reflection I realized the
smarter approach was to make use of what I know about means and variances as
well as correlations to modifying the sample to fit my desired outcome. For
instance, no matter what x I started with (so long as x had any variation) I
could adjust it to fit my needs. If the mean of x needs to be mu_X. Then we
can force it to be that:</div>
<div class="MsoNormal">
$$ (1) X = X-mean(X) + \mu_X $$</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
Slightly more challenging, we could modify the variance of x
by scaling the demeaned values of the sample. Since we know that </div>
<div class="MsoNormal">
$$ (2) Var(aX)=a^2 * Var(X) $$</div>
<div class="MsoNormal">
Define<i style="mso-bidi-font-style: normal;"> a</i> to be a
multiplicative scalar for x</div>
<div class="MsoNormal">
$$(3) a = (\sigma^2_X/Var(X))^{1/2}$$</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
Using identities we can figure out how to modify the
error term u in order to always return the desired regression values as well as
the correct correlations (for more explanation see first fifty lines of notes in <a href="https://github.com/EconometricsBySimulation/Ninja/blob/master/2019/03-March/2019_03_19-Anscombe.R" target="_blank">coding file</a>).</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
Through use of such an algorithm we can feed in any draw of X and any dependency
between X and U and we will get the same regression results:<br />
Mean(X) = 9, Var(X) = 7.5, B0 = 3, B1 = .5, COR(X,Y)=.8.</div>
<div class="MsoNormal">
<h3 style="text-align: left;">
<u><b>Sample Data - Using Ascombe's Parameters</b></u></h3>
</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
Sample data drawn to generate the following graphs can be found <a href="https://github.com/EconometricsBySimulation/Ninja/blob/master/2019/03-March/Ascombe.csv" target="_blank">here</a>.</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
The statistical results in R are displayed as follows. These results are designed to be <b>exactly </b>identical regardless of how the data is generated. </div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
Table 1:</div>
<br />
<pre class="GNKRCKGCGSB" id="rstudio_console_output" style="-webkit-text-stroke-width: 0px; -webkit-user-select: text; background-color: white; border: medium none; color: black; font-family: "Lucida Console"; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 15px; margin: 0px; orphans: auto; outline: currentcolor none medium; text-align: -webkit-left; text-indent: 0px; text-transform: none; user-select: text; white-space: pre-wrap; widows: auto; word-break: break-all; word-spacing: 0px;" tabindex="0"><span class="GNKRCKGCGSB" style="-webkit-user-select: text; border: medium none; margin: 0px; outline: currentcolor none medium; user-select: text; white-space: pre-wrap; word-break: break-all;">Call: lm(formula = y ~ x, data = xy8)
<span style="font-family: "courier new" , "courier" , monospace;">Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 3.00000 0.51854 5.785 5.32e-07 ***
x 0.50000 0.05413 9.238 3.18e-12 ***</span>
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 1.257 on 48 degrees of freedom
Multiple R-squared: 0.64, Adjusted R-squared: 0.6325
F-statistic: 85.33 on 1 and 48 DF, p-value: 3.18e-12</span></pre>
<br />
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
Since we cannot see any difference from looking at standard descriptive statistics, lets see how the data looks when graphed.</div>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjRjxxAeyCEqE9lnbUphvlVwMbsQlmyRPYOO0V4kGdSvgz4u-yuI_ILHaUP6qw5ekbZ_2tXAasRKuzamL-WvgfrSrRg9b6dixO7g0olsYZR4-16RoVndhwFMyvLORny-oUOt347V7iGLeg/s1600/Anscome.png" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="600" data-original-width="500" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjRjxxAeyCEqE9lnbUphvlVwMbsQlmyRPYOO0V4kGdSvgz4u-yuI_ILHaUP6qw5ekbZ_2tXAasRKuzamL-WvgfrSrRg9b6dixO7g0olsYZR4-16RoVndhwFMyvLORny-oUOt347V7iGLeg/s640/Anscome.png" width="532" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 1: Graphs 1-4 are recreations of Anscome's Quartet. 5-8 are new.</td></tr>
</tbody></table>
<div class="MsoNormal">
Figures 1-4 are recreations of Anscombe's Quartet. Figure 1 is what we are often times thinking our data should look like in our heads. Figure 2 is a situation in which there is a nonlinear relationship between x and y which should be examined. Figure 3 could present a problem since there is no variation in x except one observation which drives all of the explanatory value of the regression. Figure 4 is similar except now there is variation in x and in y. However the relationship between the values is distorted by the presence of a single powerful outlier.</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
Figures 5-8 are figures I came up with. Figure 5 features a weak linear relationship between x and y which is exaggerated by a single outlier. Figure 6 is a negative log. Figure 7 is a example of heteroskedasticity. Figure 8 is an example of x taking only one of two values. </div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
Anscome emphasizes that the funkiness of the data does not necessarily mean the inference is not valid. That said, ideally removing a single point of data should not significantly change inference. Yet, researchers should know what their data looks like.</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
As for figure 7, generally we do not expect heroskedastic errors to present inference bias. Rather they suggest that using heteroskedasticity robust or White-Huber standard errors might improve the efficiency of our estimates (generally speaking).</div>
<div class="MsoNormal" style="text-align: left;">
<h3>
<u><b>Sample Data - Using Negative Slope Parameters</b></u></h3>
</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
Sample data is drawn from the same parameters except that now the slope is negative. </div>
<div class="MsoNormal">
<br /></div>
<pre class="GNKRCKGCGSB" id="rstudio_console_output" style="-webkit-text-stroke-width: 0px; -webkit-user-select: text; background-color: white; border: medium none; color: black; font-family: "Lucida Console"; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 15px; margin: 0px; orphans: auto; outline: currentcolor none medium; text-align: -webkit-left; text-indent: 0px; text-transform: none; user-select: text; white-space: pre-wrap; widows: auto; word-break: break-all; word-spacing: 0px;" tabindex="0"><span class="GNKRCKGCGSB" style="-webkit-user-select: text; border: medium none; margin: 0px; outline: currentcolor none medium; user-select: text; white-space: pre-wrap; word-break: break-all;">Table 2: </span></pre>
<pre class="GNKRCKGCGSB" id="rstudio_console_output" style="-webkit-text-stroke-width: 0px; -webkit-user-select: text; background-color: white; border: medium none; color: black; font-family: "Lucida Console"; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 15px; margin: 0px; orphans: auto; outline: currentcolor none medium; text-align: -webkit-left; text-indent: 0px; text-transform: none; user-select: text; white-space: pre-wrap; widows: auto; word-break: break-all; word-spacing: 0px;" tabindex="0"><span class="GNKRCKGCGSB" style="-webkit-user-select: text; border: medium none; margin: 0px; outline: currentcolor none medium; user-select: text; white-space: pre-wrap; word-break: break-all;">Call: lm(formula = y ~ x, data = xy1)
Residuals:
Min 1Q Median 3Q Max
-2.3862 -0.6586 -0.2338 0.5721 3.6159
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 3.00000 0.51854 5.785 5.32e-07 ***
x -0.50000 0.05413 -9.238 3.18e-12 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 1.257 on 48 degrees of freedom
Multiple R-squared: 0.64, Adjusted R-squared: 0.6325
F-statistic: 85.33 on 1 and 48 DF, p-value: 3.18e-12</span></pre>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
We can see that changing the slope to negative does not change any of the other statistics.</div>
<div class="MsoNormal">
<br /></div>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiHXqeq5BAIUAlnVOXcuY0jcrg7yBV_jSjag_04E-W0h2xsRrIFJ4_jClmqlX4SsE-F15lAYe8lmRoLdjB7e3GR9bwmoj3VatdgjIHYRnp_1vx8aKRhLN8TeMSgJcpHn1p0reXzelGbUl0/s1600/Anscome2.png" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="600" data-original-width="500" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiHXqeq5BAIUAlnVOXcuY0jcrg7yBV_jSjag_04E-W0h2xsRrIFJ4_jClmqlX4SsE-F15lAYe8lmRoLdjB7e3GR9bwmoj3VatdgjIHYRnp_1vx8aKRhLN8TeMSgJcpHn1p0reXzelGbUl0/s640/Anscome2.png" width="532" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 2: Same as figure 1 except B1 = -0.5</td></tr>
</tbody></table>
<div class="MsoNormal">
<h3 style="text-align: left;">
<u><b>Summary</b></u></h3>
</div>
<div class="MsoNormal">
Graph your data! If not presenting graphs in your final analysis at least graph it in the exploration phase. Ideally, presenters of data and analysis have some mastery of tools of data exploration and interaction which can presented with data (such as interactive data interfaces Shiny or Tableau).<br />
<br />
Such supplementary data found in graphs will likely not be the basis of whether the arguments you are making through statistics are valid, but they will add credibility.<br />
<br />
<h4 style="text-align: left;">
<b><u>CODE</u></b></h4>
Find my code for generating exact linear relationships between XY regardless of the dependency of the errors <a href="https://github.com/EconometricsBySimulation/Ninja/blob/master/2019/03-March/2019_03_19-Anscombe.R" target="_blank">U and X (u|x)</a>. </div>
</div>
Francishttp://www.blogger.com/profile/16658586705916884436noreply@blogger.com0tag:blogger.com,1999:blog-6288862798546085706.post-91539644916437041902019-03-08T16:10:00.000-05:002019-03-14T11:30:54.796-04:00Mass Shooting Data - Tableau <div dir="ltr" style="text-align: left;" trbidi="on">
Some experimentations with Mass Shooting data visualization using Tableau
<br />
<div class="tableauPlaceholder" id="viz1552078789515" style="position: relative;">
<noscript><a href='#'><img alt=' ' src='https://public.tableau.com/static/images/Sh/ShootingFatalities/MapOfMassShootings/1_rss.png' style='border: none' /></a></noscript><object class="tableauViz" style="display: none;"><param name='host_url' value='https%3A%2F%2Fpublic.tableau.com%2F' /> <param name='embed_code_version' value='3' /> <param name='site_root' value='' /><param name='name' value='ShootingFatalities/MapOfMassShootings' /><param name='tabs' value='no' /><param name='toolbar' value='yes' /><param name='static_image' value='https://public.tableau.com/static/images/Sh/ShootingFatalities/MapOfMassShootings/1.png' /> <param name='animate_transition' value='yes' /><param name='display_static_image' value='yes' /><param name='display_spinner' value='yes' /><param name='display_overlay' value='yes' /><param name='display_count' value='yes' /></object></div>
<script type="text/javascript"> var divElement = document.getElementById('viz1552078789515'); var vizElement = divElement.getElementsByTagName('object')[0]; vizElement.style.width='100%';vizElement.style.height=(divElement.offsetWidth*0.75)+'px'; var scriptElement = document.createElement('script'); scriptElement.src = 'https://public.tableau.com/javascripts/api/viz_v1.js'; vizElement.parentNode.insertBefore(scriptElement, vizElement); </script>
Here is a related graph/animation generated in R
https://bit.ly/2NSmEsx</div>
Francishttp://www.blogger.com/profile/16658586705916884436noreply@blogger.com0tag:blogger.com,1999:blog-6288862798546085706.post-74421968806209455862018-09-30T10:10:00.001-04:002018-09-30T10:10:19.263-04:00My Amazing Brother's Travel Blog - Dream in Stone<div dir="ltr" style="text-align: left;" trbidi="on">
Check out my brother Jerome Smart's <a href="https://dreaminstone.wordpress.com/" target="_blank">travel blog</a>!<br />
<a href="https://www.blogger.com/goog_251081291" target="_blank"><br /></a>
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
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<tr><td class="tr-caption" style="text-align: center;"><a href="https://www.blogger.com/goog_251081291" target="_blank"><i>trip to the Bugaboos in British Columbia</i></a></td></tr>
</tbody></table>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
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<tr><td class="tr-caption" style="text-align: center;"><a href="https://www.blogger.com/goog_251081291" target="_blank"><i>Bicycle touring in Chile for Most of the winter</i></a></td></tr>
</tbody></table>
<div class="separator" style="clear: both; text-align: center;">
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</div>
Francishttp://www.blogger.com/profile/16658586705916884436noreply@blogger.com0tag:blogger.com,1999:blog-6288862798546085706.post-72720015149118463952018-09-26T21:36:00.001-04:002018-09-26T21:36:44.380-04:00Strategizing Retirement Investments (In the US)<div dir="ltr" style="text-align: left;" trbidi="on">
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<![endif]-->Major caveat! I have no investment training or finance
training and all of my calculations are back of the envelope calculations put
together from what information I can gather online. In addition, given that investment planning usually spans decades, massive uncertainties exist in tax schemes and expected rate of returns. Please consult a professional!</div>
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<br />
That said, as someone who has an income you are trying to decide if
and how much to invest in your retirement account. Most people have several
options: tax deferred retirement options such as traditional IRA, 401(k), 457, or
403(b). Some employers also offer matching programs
which match contributions at a rate of 50%, 100%, or more to a limit each year. As tax deferred retirement
accounts, money contributed to them are not taxed at the time of contribution
(except for Social Security tax 6.2 and Medicare 2.9).</div>
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<br /></div>
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In addition to these programs there is the option of
investing in a Roth IRA with income that has already been taxed but will suffer
no additional capital gains tax. Finally, there is the option of investing
directly (with pretaxed earnings) such as purchasing stocks, mutual funds etc. While direct investments
give you the freedom to withdraw money at any time, they suffer the penalty of
being liable for capital gains taxes (15% on nominal gains for long term
investments).</div>
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<br /></div>
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Each of these investment choices has its relative merits.
One thing to consider is tax bracket. <span style="mso-spacerun: yes;"> </span>Each earning level of taxes are paid at a
specific bracket. For example, for a couple the first 19k of earnings is paid
at a 10% rate, while the next 58k of earnings is paid at 12%, while the next
88k is taxed at 22%, and so on with increases to 24%, 32%, 35%, and finally 37%
at total earnings above 600k (<a href="https://www.nerdwallet.com/blog/taxes/federal-income-tax-brackets/">see
tax tables</a>). Yet the combined effect of these changing marginal tax rates
is to turn the effective tax rate into a globally non-linear function (Figure
1). </div>
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For the individual the federal tax rate for a median
household income level $32K or for a married couple making $59k is about 11.5%.
The overall effect of tax bracket structure is to overstate the tax obligation
that most individuals and couples are required to pay. For example, a household
making 103k (75 percentile) while paying 22% on their last dollar earned are
overall only paying only around 14% of their total income in income tax. Even households
making 250k (97 percentile) while their tax bracket is officially 24% on their
last dollar earned are only paying a tax rate a little above 19% on overall
income.</div>
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<br /></div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhSoj9lg_P0u6cWwvPiYhJAu3usp410jNsNFKdJYpujzTbFZlP05AcCpYXHuKRYYHY5NrX14WLJe2C7ACCg8X0DPtYUloq8lSfrav8xu0PJhklUDUtlGJul2t9u5cAU2YbFCxzNK2D6ARM/s1600/TaxRateByIncome.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="800" data-original-width="1000" height="512" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhSoj9lg_P0u6cWwvPiYhJAu3usp410jNsNFKdJYpujzTbFZlP05AcCpYXHuKRYYHY5NrX14WLJe2C7ACCg8X0DPtYUloq8lSfrav8xu0PJhklUDUtlGJul2t9u5cAU2YbFCxzNK2D6ARM/s640/TaxRateByIncome.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 1: Overall Federal Income Tax Rate without Social Security and Medicare</td></tr>
</tbody></table>
<div class="MsoNormal">
<span style="mso-no-proof: yes;"></span></div>
<div class="MsoNormal">
That said, nobody likes to see their income disappear to taxes
so I am not trying to say taxes are too high or too low. I am just noting that
tax brackets alone for the vast majority of the population, are quite inaccurate tools at estimating tax liability. If we
include the social security tax and Medicare (Figure 2), federal taxes become
both more painful overall and less progressive (higher earners paying higher
taxes). This figure is even more non-linear with important portions of the
figure (earnings above 128k) experiencing a lower tax rate growth than earnings
up to that point. Curiously, an individual income earner above 128k actually
experiences a decline in overall tax rate until earning up to the next tax
bracket of 157.5k. </div>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEida4Q8r5z0yrS6gTOcgcJLU1wLnsRAVGC8yw_wBl-AZIohW3MJsKzXypmfds5lxmgbRAoooafqTFO3Jhjp3DqAi2yvdAi-xpb8rg2H-5J8Yu9UuT75QeyVAPQ4I7_XtumJ0lFtn0dxHEs/s1600/TaxRateByIncomeSSM.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="800" data-original-width="1000" height="512" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEida4Q8r5z0yrS6gTOcgcJLU1wLnsRAVGC8yw_wBl-AZIohW3MJsKzXypmfds5lxmgbRAoooafqTFO3Jhjp3DqAi2yvdAi-xpb8rg2H-5J8Yu9UuT75QeyVAPQ4I7_XtumJ0lFtn0dxHEs/s640/TaxRateByIncomeSSM.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 2: Overall Federal Income Tax With Medicare and Social Security</td></tr>
</tbody></table>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div class="MsoNormal">
<span style="mso-no-proof: yes;"></span></div>
<div class="MsoNormal">
But enough of this! About 75% of households are earning 110k
or less. Those earning above that rate are likely already talking with
financial managers in order to figure out how to plan their futures.</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
The overall point of the above discussion is that tax
differed savings plans might be quite beneficial for retirees as many retirees
expect to be at a lower income level than they were while working. Income drawn
from such plans is taxed at their current income level rather than the level
they had at the time of saving. Social Security and Medicare tax is always paid
immediately upon all wage earnings (and thus constant under all scenarios) so it will not be included in the following
analysis.</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
In order to analyze the benefit of choosing different
investment mechanisms, I looked at three different factors, 1-overall effective lifetime
income, 2-total investment worth at the end of retirement (inheritance available), and 3-annual
effective income. The first two seem like they are pretty important for most
people but arguably annual effective income is probably the most important
factor. Ideally, retirees looking to enjoy their retirement will not suffer a
minimal loss in purchasing power after retirement.</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
In order to look at different investment strategies, I
simulated two earning levels, 55k per year gross and 110k per year gross. Workers
work for 35 years with real annual salary increases of 0.5%. After 35 years of
work, workers consider the next 20 years as years living on secondary income
sources (1/3 of base income) as well as retirement savings withdrawn at a rate
of 4% per year.</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
In order to make the numbers make sense, I attempted to
simulate “real” money rather than nominal (including inflation). As a result I
assume that tax brackets remain the same in terms of “real” earnings. Annual
raises are modest as a result as well. In my simulation, I include a real
investment rate of return of 5% and a capital gains tax of 20% on all direct
investment withdraws. This does not take into account in the cost of such investments (which is tax free) while including a higher rate of capital gains tax to take
into account the false effect inflation has on direct investments (and the
corresponding tax on those investments).</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
In addition of the tax differed retirement accounts
(traditional IRA or a 401k without matching – 401km00), the after tax but not
capital gains taxed retirement accounts (Roth IRA), and the direct investment mechanisms
(Direct), I also included two investment options <span style="mso-spacerun: yes;"> </span>in which employers match contributions by
either 50% or 100% (401km05 and 401km10). </div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
Generally, all of the investments are considered on the
basis of “investing” a certain amount of money 5.5k or 11k. There was one
scenario in which I allowed for a greater investment quantity in order to allow
the simulation of investing the same amount of after tax income (i401k00b). When the
earning level was 55k and the investment was 5.5k for i401k00b the 401(k) investment level
was instead 6.5k. And when the earning level was
110k and the investment was 11k for i401k00b the 401(k) investment level was instead 14k.</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
In my analysis I am concerned with "effective
income" which I define as: <b> </b></div>
<div class="MsoNormal">
<b>effective income = all income –
tax – investment contributions (only made for years working).</b></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<u><b>Gross Base Income 55k per Year</b></u></div>
<div class="MsoNormal">
Under the different investment scenarios, total lifetime
earnings vary between 2.3m and 2.8m in the case when employers provide matching
funds (Table 3). When no matching funds are provided, lifetime earnings are
more similar between scenarios with lifetime earnings between 2.3m and 2.5m. Differences
are more exaggerated when considering total assets at the end of the retirement
period included in total lifetime earnings with the highest level obtained
under scenario i401km00b (no matching but investments made at a rate that are
higher than 5.5k, but instead meant to achieve after tax 5.5k investment per
year).</div>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgO20Y7fjy92ckgX7Chtv0xZoCzag6pZ_Ttgmp2XFz_myGmCDf5za-NWO0eJPuCPDbnMLiP4_ChsLzTNaKYWpFOE50oB4vXKxzQ0N89Ux-i19MUZzRRgpeSepHcaWWqu1cu7Wl0T_QVZYQ/s1600/LifetimeEarn55.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="600" data-original-width="800" height="480" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgO20Y7fjy92ckgX7Chtv0xZoCzag6pZ_Ttgmp2XFz_myGmCDf5za-NWO0eJPuCPDbnMLiP4_ChsLzTNaKYWpFOE50oB4vXKxzQ0N89Ux-i19MUZzRRgpeSepHcaWWqu1cu7Wl0T_QVZYQ/s640/LifetimeEarn55.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 3: Total Lifetime Effective Earning and End of Retirement Assets for Gross Income of 55k per Year</td></tr>
</tbody></table>
<div class="MsoNormal">
Rather than look at lifetime effective income and total
assets it might be better to look at per year income (Table 4). Without contribution matching, all of the scenarios result in a significant drop
in effective income. The most dramatic drop is in the "No Saving" scenario in
which the effective income of the worker drops from near the global maximum for
the scenario to the global minimum of the scenario as the worker enters
retirement without any additional income sources outside of the 1/3 base income
(SS income or whatever) provided under all retirement scenarios.
</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
Looking at the effective income while working levels, there are three
levels that the simulated worker experiences. The highest being "No Savings",
which results in the highest possible current effective income level. The
second are the pretax saving schemes such as 401km10, 401km05, and 401km00.
These schemes provide highest effective income during working years because
they reduce the after tax income not by 5.5k but 5.5k after taxes which is 4.8k
in year 1. The scenario in which the highest matching funds are
available is that which produces the highest long run returns. The third
effective income level on working years is the direct investment scenario, the
Roth IRA scenario, and the 401km00b scenario (which is custom calibrated to
achieve this). In this income scenario 401(k) investment even though it is
taxed upon dismemberment produced higher earnings than that of the Roth in retirement
though the difference does not appear to be large in this scenario.</div>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhMpDeGTRDckTQLmDbN2v5hZgZ5shMGDpXQhX9wQVd0UpQnKJEBLuyZLjfWf-VwsrymyogSvlxAt5tG9wNwQm5K-TvcS18WmrlKJRuj8TqEmbhap6Q8JAs7UGti8TBtXtk6IGOpzC_gKEk/s1600/Income55k.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="600" data-original-width="800" height="480" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhMpDeGTRDckTQLmDbN2v5hZgZ5shMGDpXQhX9wQVd0UpQnKJEBLuyZLjfWf-VwsrymyogSvlxAt5tG9wNwQm5K-TvcS18WmrlKJRuj8TqEmbhap6Q8JAs7UGti8TBtXtk6IGOpzC_gKEk/s640/Income55k.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 4: Annual effective income under different investment mechanisms 55k gross income per year. Note a jitter is added to lines to aid in deciphering overlap.</td></tr>
</tbody></table>
<div class="MsoNormal">
<span style="mso-no-proof: yes;"><br /></span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<u><b>Gross Base Income 110k per Year with 11k annual investment</b></u></div>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjJAaNxmIFsA3M8AXRqLLHu0sWgPqyv5Ng6U8r2OqyAL03rJJaGAAjXTy0GXPkTTL64hjVSJwtbYN33H9BL0QOv0A6Cizkr0wlmA4nkfI37SwCvPFnNW5siUB7nf5e-3eW4o5z43kV9cyM/s1600/LifetimeEarn110_11k.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="600" data-original-width="800" height="480" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjJAaNxmIFsA3M8AXRqLLHu0sWgPqyv5Ng6U8r2OqyAL03rJJaGAAjXTy0GXPkTTL64hjVSJwtbYN33H9BL0QOv0A6Cizkr0wlmA4nkfI37SwCvPFnNW5siUB7nf5e-3eW4o5z43kV9cyM/s640/LifetimeEarn110_11k.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 5: Total Lifetime Effective Earning and End of Retirement Assets for Gross Income of 55k per Year</td></tr>
</tbody></table>
<div class="MsoNormal">
<span style="mso-no-proof: yes;"><br /></span></div>
<div class="MsoNormal">
Overall, doubling the household income and the investment
level results very similar relative distributions of Total
Lifetime Effective Earnings or Total Assets at retirement.</div>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjPDoQQz8qXn1s5S7A1C_ldut8ZF42edTpDIvnnI85Cp101OW20jemM_yHQbhx9Sj-210x4uOBziT-amYgQqqyRL-MgE-fGF5rqhYWbuhKDrSf-SaI9AurkX8y64lmz0JRtWbHJwIAIsEA/s1600/Income110_11k.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="600" data-original-width="800" height="480" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjPDoQQz8qXn1s5S7A1C_ldut8ZF42edTpDIvnnI85Cp101OW20jemM_yHQbhx9Sj-210x4uOBziT-amYgQqqyRL-MgE-fGF5rqhYWbuhKDrSf-SaI9AurkX8y64lmz0JRtWbHJwIAIsEA/s640/Income110_11k.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 6: Annual effective income under different investment mechanisms 55k gross income per year. Note a jitter is added to lines to aid in deciphering overlap.</td></tr>
</tbody></table>
<div class="MsoNormal">
<span style="mso-no-proof: yes;"><br /></span></div>
<div class="MsoNormal">
Likewise when looking at lifetime smoothed effective income,
the overall returns from different investment mechanisms remain similar. That
said the difference between the investment strategy using the Roth IRA and
increased investment using 401km00b (401 tax differed investment without any
match at 11k after tax investment level which is 14k before tax) resulted in
the same level of effective income during working years but significantly
higher effective income in retirement.</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
That said, Roth IRA funds are more flexible than those of
tax differed funds which suffer a 10% additional penalty if withdrawn before
age 59.5. In addition, if you believe that your current income level
is likely to be lower than your future income level, it probably means that you
should consider investing more in your Roth over that of a tax differed
investment instruments.</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<u><b>Comparing 55k to 110k per Year</b></u> </div>
<div class="MsoNormal">
The 110k per year scenario is basically a doubling of the 55k per year scenario in terms of both income and investment (except in a slight difference with the 401km00b scenario). Comparing the average annual effective income under these two scenarios we can infer the cost of higher income taxes in the 110k scenario. The average ratio is 1.94 which indicates a difference of .06 or 6%. Looking closely at Figures 1 or 2 we can see that the difference in overall tax rates between households making 55k per year and 110k per looks to be about 6% as well. Using larger tax differed investments (401km00b) does appear to be a way to achieve a smaller tax penalty with a decreasing in effective tax rate of closer to 4%. </div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<b>Table 1</b>: Shows the ratio of average annual effective income (same as total lifetime income). If the ratio were 2 then there would be no tax different between earners at 55k per year and 110k per year. </div>
<div class="MsoNormal">
</div>
<table border="0" cellpadding="0" cellspacing="0" style="width: 160px;"><colgroup><col style="mso-width-alt: 3510; mso-width-source: userset; width: 72pt;" width="96"></col>
<col style="width: 48pt;" width="64"></col>
</colgroup><tbody>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15.0pt; width: 72pt;" width="96"><br /></td>
<td style="text-align: right; width: 48pt;" width="64"><b>Ratio</b></td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15.0pt;">NoSavings</td>
<td align="right" class="xl65">1.94</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15.0pt;">401km00</td>
<td align="right" class="xl65">1.95</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15.0pt;">401km00b</td>
<td align="right" class="xl65">1.96</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15.0pt;">401km05</td>
<td align="right" class="xl65">1.93</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15.0pt;">401km10</td>
<td align="right" class="xl65">1.92</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15.0pt;">Roth</td>
<td align="right" class="xl65">1.94</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15.0pt;">Direct</td>
<td align="right" class="xl65">1.93</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15pt; text-align: right;"><b>Average</b></td>
<td align="right" class="xl65"><b>1.94</b></td>
</tr>
</tbody></table>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<u><b>Conclusion</b></u></div>
<div class="MsoNormal">
If there is a 401k or other tax differed investment option
in which matching is available, I would suggest putting the maximum your finances allow. If matching funds are not available, in this
simulation investing pretax income in the 401k equal to that you would invest in
the Roth IRA appears to yield a slightly better outcome. This is generally
because while these funds will be taxed when withdrawn, having that much more funds grows
that much faster than the after tax funds otherwise available. </div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
Finally, in almost all of the scenarios, there is a
significant loss of effective income upon retirement. If you would like to
mitigate the risk of that happening, combining investment mechanisms is likely
to be the best strategy. This might mean relying upon direct investments if for
instance you have already filled your Traditional IRA or Roth IRA and have no other
investment mechanisms provided by your employer.</div>
<div class="MsoNormal">
<br />
Feel free to explore the simulation on your own with your own earnings and investment options! Code that produced this analysis can be found on <a href="https://github.com/EconometricsBySimulation/Ninja/blob/master/2018/September/2018%2009%2024%20Investing.R" target="_blank">Github</a>. </div>
</div>
Francishttp://www.blogger.com/profile/16658586705916884436noreply@blogger.com0tag:blogger.com,1999:blog-6288862798546085706.post-24478102303726342192018-09-12T18:12:00.000-04:002018-09-12T18:19:51.222-04:00Plotting the Impact of Atlantic Hurricanes on the US<div dir="ltr" style="text-align: left;" trbidi="on">
With hurricane Florence bearing down with expected to be devastating force,
it might be a good time to reflect on the history of Atlantic Hurricanes on the
United States. As an easy if not full proof source for hurricane data I drew on
public data collated through <a href="https://en.wikipedia.org/wiki/List_of_costliest_Atlantic_hurricanes" target="_blank">Wikipedia's list of costliest Atlantic hurricanes</a> as well
as linked articles. On the page it lists 45 hurricanes going back to Hurricane
Betsy in 1965, with 30 of them since 2000 totaling 803 billion dollars in
estimated damages and 6,591 US fatalities. While this is quite a large number
of fatalities, the death toll of Atlantic Hurricanes outside of the US is significantly larger with
nearly 30,000 deaths estimated.<br />
<br />
Within the US, the track record for deaths from hurricanes tend to be quite
low with all hurricanes recorded having a fatality rate of less than two
hundred with the exception of Maria (2017 - Trump administration) and Katrina
(2005 - GW Bush administration).<br />
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiIlZTPvm7C-BMdw0NX8j7V9HtRYHKuUr2o2BbMWKJtnzRxjikPUwa8k18UwKETA8AGn9Id5tKN8CHYHgobrZj8bu2grSOWWHyZW9S8aQ6NaF8JfGAsYaGyJVvoIefGTTTfceW79-IHgAM/s1600/USFatalities.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="600" data-original-width="800" height="480" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiIlZTPvm7C-BMdw0NX8j7V9HtRYHKuUr2o2BbMWKJtnzRxjikPUwa8k18UwKETA8AGn9Id5tKN8CHYHgobrZj8bu2grSOWWHyZW9S8aQ6NaF8JfGAsYaGyJVvoIefGTTTfceW79-IHgAM/s640/USFatalities.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 1: US Fatalities by Year.</td></tr>
</tbody></table>
<br />
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I have also scaled the y-axis by log10 to make it easier to
examine less deadly storms.</div>
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<br /></div>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjuvCmZXtDwm0qwdY1xsfUtGOV3cJzidjtn7UziJNXdnoAQYvoqdWeO2G8lESHoG2fGB7SUMyo-CzYPQ5WV9Ft0sUB6KVblv-I797rzK50KW4uhiISGmt0ufNvHojW7cv7M7_O_-CZNrdc/s1600/USFatalitiesLog10.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="600" data-original-width="800" height="480" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjuvCmZXtDwm0qwdY1xsfUtGOV3cJzidjtn7UziJNXdnoAQYvoqdWeO2G8lESHoG2fGB7SUMyo-CzYPQ5WV9Ft0sUB6KVblv-I797rzK50KW4uhiISGmt0ufNvHojW7cv7M7_O_-CZNrdc/s640/USFatalitiesLog10.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 2: US Fatalities by Year Log10 scaled.</td></tr>
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Maria and Katrina being the most deadly of storms does not
indicate that they are necessarily the most damaging of storms. </div>
<br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiaFa5MxUjzguapem6bxOEtKC1axHulY-0BNZYEuz7P4NL4OQsoXBX6wPM3DtIZxaCiKT6z9xPwSnnTjZFdFSleFQC-R3Y8Ugwnyoqq0be3ol-OpJfFBrYqn7IqAqv7wSvgwXgfBSHwGgs/s1600/Damages.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="600" data-original-width="800" height="480" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiaFa5MxUjzguapem6bxOEtKC1axHulY-0BNZYEuz7P4NL4OQsoXBX6wPM3DtIZxaCiKT6z9xPwSnnTjZFdFSleFQC-R3Y8Ugwnyoqq0be3ol-OpJfFBrYqn7IqAqv7wSvgwXgfBSHwGgs/s640/Damages.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 3: Damages in the Billions by Year.</td></tr>
</tbody></table>
Harvey and Katrina are reported to have done 125 billions dollars each
followed by Maria doing damage of 91.2 billion, Sandy at 68.7, and Irma at
64.8.<br />
<br />
So why is it that Harvey (2017 - Trump), a storm that did as much damage as
Katrina resulted in only 106 deaths while Maria a storm that did 25% less
damage resulted in a US citizen total death toll comparable to the sum of all
44 other Hurricanes on record (2982 vs. 3609)?<br />
<br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjKCtwGB-AlvhXZoxA3368MSZNZz0nZTi2x5Yy2qqqTprorh2w08bsyEiYJ4kOLBpc4N0a8kM6TCslq_oHH4NSbM8_NZPOlJaW0tXt5wTy-I3OCetVKbeDWS_FCupj-nPOLV7MR8K2TSxY/s1600/USFatalitiesBarGraph.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="600" data-original-width="800" height="480" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjKCtwGB-AlvhXZoxA3368MSZNZz0nZTi2x5Yy2qqqTprorh2w08bsyEiYJ4kOLBpc4N0a8kM6TCslq_oHH4NSbM8_NZPOlJaW0tXt5wTy-I3OCetVKbeDWS_FCupj-nPOLV7MR8K2TSxY/s640/USFatalitiesBarGraph.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 4: Total deaths by Year.</td></tr>
</tbody></table>
<br />
We might attempt to predict which storms might be the most deadly using the storm measurements highest wind speed recorded and lowest pressure recorded.<br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi-E9xYT44dHt4zpdKuoDsfRUZE1vX26Z9Zj8RDrTevEydXuWbrvlYjbS3fdQce3MzLyhG3ajPVCd1RSsil16zg3b2r8GHnE6CInAzZM1DB3WLPedidoFcA8JR0386wMZ2oUu9bfQScQzM/s1600/HighestWindsUSFatalities.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="600" data-original-width="800" height="480" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi-E9xYT44dHt4zpdKuoDsfRUZE1vX26Z9Zj8RDrTevEydXuWbrvlYjbS3fdQce3MzLyhG3ajPVCd1RSsil16zg3b2r8GHnE6CInAzZM1DB3WLPedidoFcA8JR0386wMZ2oUu9bfQScQzM/s640/HighestWindsUSFatalities.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 5: Wind speed by US_Fatalities</td></tr>
</tbody></table>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhCKo8zD_80Gz3W0krkmzgx7D13c6i8PJywWv7hM1EdMcK9v93RUnf4vQg9xefXO7MjGn0zruCkQ6R-BZiybiXzzitVvia-8-AOmtHYf3lmd8vOPrpKvjZTGe-8fAaWvK7TPe2LelT8cMI/s1600/LowestPressureUSFatalities.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="600" data-original-width="800" height="480" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhCKo8zD_80Gz3W0krkmzgx7D13c6i8PJywWv7hM1EdMcK9v93RUnf4vQg9xefXO7MjGn0zruCkQ6R-BZiybiXzzitVvia-8-AOmtHYf3lmd8vOPrpKvjZTGe-8fAaWvK7TPe2LelT8cMI/s640/LowestPressureUSFatalities.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 6: Lowest air pressure recorded in terms of mbar (whatever that is). </td></tr>
</tbody></table>
<br />
As we can see that Maria and Katrina are both on the higher end of the
wind speed distribution and the lower end of the air pressure distribution, we
can assert that a more powerful storm is a necessary component for the kind of
death tolls associated with these storms.<br />
<br />
What factors must be present for a severe storm which otherwise would be
associated with a death toll of less than 200 people to being a tremendous
human tragedy, such as in the case of Katrina or even more so Maria are yet
unknown given the sparsity of data available to the public.<br />
<br />
From the data it appears that Atlantic hurricanes have grown more damaging
and more deadly for US citizens. <br />
<br />
Hopefully, despite the catastrophic blunders of the handling of Katrina and Maria by the Bush and Trump administrations respectively, future hurricanes such as Florence will be dealt with in a more responsible manner.<br />
<br />
<a href="https://github.com/EconometricsBySimulation/Ninja/tree/master/2018/September" target="_blank">Code and data can be found here</a><br />
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Francishttp://www.blogger.com/profile/16658586705916884436noreply@blogger.com0tag:blogger.com,1999:blog-6288862798546085706.post-33764855936184294792016-12-01T14:48:00.001-05:002016-12-01T14:48:12.251-05:00Efficiently Saving and Sharing Data in R<p>After spending a day the other week struggling to make sense of a federal data set shared in an archaic format (ASCII fixed format <code>dat</code> file). </p><p>It is essential for the effective distribution and sharing of data that it use the minimum amount of disk space and be rapidly accessible for use by potential users. </p><p>In this post I test four different file formats available to R users. These formats are comma separated values <code>csv</code> (<code>write.csv()</code>), object representation format as a ASCII <code>txt</code> (<code>dput()</code>), a serialized R object (<code>saveRDS()</code>), and a Stata file (<code>write.dta()</code> from the <code>foreign</code> package). For reference, <code>rds</code> files seem to be identical to <code>Rdata</code> files except that they deal with only one object rather than potentially multiple.</p><p>In order to get an idea of how and where different formats outperformed each other I simulated a dataset composed of different common data formats. These formats were the following:</p><p><strong>Numeric Formats</strong></p><ul id='draft_check_box_list_0' ><li>Index 1 to N - ex. 1,2,3,4,...</li><li>Whole Numbers - ex. 30, 81, 73, 5, ...</li><li>Big Numbers - ex. 36374.989943, 15280.050850, 5.908210, 79.890601, 2.857904, ...</li><li>Continous Numbers - ex. 1.1681155, 1.6963295 0.8964436, -0.5227753, ...</li></ul><p><strong>Text Formats</strong></p><ul id='draft_check_box_list_1' ><li>String coded factor variables with 4 characters - ex. fdsg, jfkd, jfht, ejft, jfkd ...</li><li>String coded factor variables with 16 characters coded as strings</li><li>String coded factor variables with 64 characters coded as strings</li><li>Factor coded variables with 4 characters - ex. fdsg, jfkd, jfht, ejft, jfkd - coded as 1,2,4,3,2, ...</li><li>Factor coded variables with 16 characters</li><li>Factor coded variables with 64 characters</li><li>String variables with random 4 characters - ex. jdhd, jdjj, ienz, lsdk, ...</li><li>String variables with random 16 characters</li><li>String variables with random 64 characters</li></ul><p>What type of format a variable is in is a predictive characteristic for how much space that variable takes up and therefore how time consuming that variable is to read or write. For variables that are easy to describe they tend to take up little space. An index variable in an extreme example and can take up almost no space as it can be expressed in an extremely compact format (<code>1:N</code>). </p><p>In contrast numbers which are very long or have a great degree of precision tend to have more information and therefore take more resources to access and store. String variables when filled with truly random or unique responses are some of the hardest data to compress as each value may be sampled from the full character spectrum. There is some significant potential for compression when strings are repeated in the variable. These repetitive entries can be either coded as a "factor" variable or a string variable in R. </p><p>As part of this exploration, I look at how string data is stored and saved when coded as either a string or as a factor within R.</p>
<h1 id="raw-files">Raw Files</h1>
<p>Let's first look at space taken when saving uncompressed files.</p><p><strong>Figure 1: File Size</strong></p><p><img src="https://draftin.com:443/images/48619?token=H4dh7oDRwN18WHgZCZfYPnaME9WsOhjxcfXOvKznAu_eZdJPFE1O0Z4R3LGB2ZTJzWaR9CIK-MWU-8427yI34jc" alt="File Size" width="640"></p><p>Figure 1 shows the file size of each of the saved variables when 10,000 observations are generated. The <code>dataframe</code> object is the <code>data.frame</code> composed off all of the variables. From the height of the <code>dataframe</code>, we can see that <code>rds</code> is overall the winner. Looking at the other variable values we can see only that <code>csv</code> appear to consistently underperform for most file formats except for random strings.</p><p><strong>Figure 2: File Size Log scaled</strong></p><p><img src="https://draftin.com:443/images/48620?token=0MhfS6sR4xb7IJjs_Y0rq_uODTegYYkKNC6S3bAOH1Cml9GKOQCDg1N28hfUDZL88r1Lvn--sJJPGNv1cUyiilo" alt="File Size Logged" width="640"></p><p>In Figure 2 we can see that <code>rds</code> is consistently outperforming all of the other formats with the one exception of <code>index</code> in which the <code>txt</code> encoding simply reads <code>1:10000</code>. Apparently even serializing to bytes can't beat that.</p><p>Interestingly, there does not appear to be a effective size difference between repetitive strings encoded as factors accounting for the size of the strings (4, 16, or 64). We can see that the inability of <code>csv</code> to compress factor strings dramatically penalizes the efficiency of <code>csv</code> relative to the other formats. </p>
<h1 id="file-compression">File Compression</h1>
<p>But data is rarely shared in uncompressed formats. How does compression change things?</p><p><strong>Figure 3: Zipped File Sizes Logged</strong></p><p><img src="https://draftin.com:443/images/48622?token=weT3bsBW_keSTa56oepJjTEANw-vDmpl4qTYpEUWh4CFgaVnUqn1b92UKQrE4wh96g5xwoGXX9ccjhY7DMlhX9A" alt="File Size Zipped Logged" width="640"></p><p>We can see from Figure 3 that if we zip our data after saving, the file size can do pretty much as well as <code>rds</code>. Comma delineated <code>csv</code> files are a bit of an exception with factor variables suffering under <code>csv</code>. Yet random strings perform slightly better under <code>csv</code> than other formats. Interesting <code>rds</code> files seem slightly larger than the other two file types. Overall though, it is pretty hard to see any significant difference in file size based on format after zipping.</p><p>So, should we stick with whatever format we prefer?</p><p>Not so fast. Sure, all of the files are similarly sized after zipping. This is useful for sharing files. But having to keep large file sizes on a hard drive is not ideal even if they can be compressed for distribution. There is finite space on any system and some files can be in the hundreds of MB to hundreds of GB range. Dealing with file formats and multiple file versions which are this large can easily drain the permanent storage capacity of most systems.</p><p>But an equally important concern, is how long it takes write and read different file formats. </p>
<h1 id="reading-speed">Reading Speed</h1>
<p>In order to test reading speeds, I loaded each of the different full dataframe files fifty times. I also tested how long it would take to unzip then load that file.</p><p><strong>Figure 4: Reading and unzipping average speeds</strong></p><p><img src="https://draftin.com:443/images/48625?token=W5ajSr52k9ohxk_VgLu2e_ejiMmellXcYmKcHGhgis0o985BDRuw0AVx8qkgxkCCDoTXwC6H8dOwViAN3RX84KQ" alt="File Size Zipped Logged" width="640"></p><p>From Figure 4, we can see that read speeds roughly correspond with the size of files. We can see that even a relatively small file (30 MB <code>csv</code> file) can take as long as 7 seconds to open. Working with large files saved in an inefficient format can be very frustrating.</p><p>In contrast, saving files in efficient formats can dramatically cut down on the time taken opening those files. Using the most efficient format (<code>rds</code>), files could be 100 times larger than those used in this simulation and still open in less than a minute.</p>
<h1 id="conclusions">Conclusions</h1>
<p>Finding common file formats that any software can access is not easy. As a result many public data sets are provided in archaic formats which are poorly suited for end users.</p><p>This results in a wide pool of software sweets having the ability to access these datasets. However, with inefficient file formats comes a higher demand on the hardware of end users. I am unlikely to be the only person struggling with opening some of these large "public access" datasets.</p><p>Those maintaining these datasets will argue that sticking with the standard, inefficient format is the best of bad options. However, there is no reason they could not post datasets in <code>rds</code> formats in addition to the outdated formats they currently exist in. </p><p>And no we need not argue that selecting one software language to save data in will be biased toward those languages. Already many federal databases come with code supplements in Stata, SAS, or SPSS. To access these supplements, one is required to have paid access to that software. </p><p>Yet, R is free and its database format is public domain. Any user could download R, open a <code>rds</code> or <code>Rdata</code> file, then save that file in a format more suited to their purposes. None of these other proprietary database formats can boast the same.</p>Francishttp://www.blogger.com/profile/16658586705916884436noreply@blogger.com0tag:blogger.com,1999:blog-6288862798546085706.post-20080834057867928372016-11-08T02:13:00.002-05:002016-11-08T02:13:28.581-05:00Trump and Clinton Supporters Agree on Relative Morality ... Mostly<div dir="ltr" style="text-align: left;" trbidi="on">
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When looking at the endless scandals swirling around the heads of the two rival candidates Hillary Clinton and Donald Trump, it can seem like the two candidates are equally tainted. Many people throw up their hands pleading for some other option.<br />
<br />
How can we evaluate the alleged actions of these two candidates?<br />
<br />
Is there some kind of objective way to do so?<br />
<br />
And how does the decision to support a candidate affect the perception of an offense?<br />
<br />
In order to attempt to address these questions I recruited 137 submissions on Amazon Mechanical Turk who submitted around 1100 five way "relative offense" rankings of five randomly matched actions from a list of 150. 46 submissions were from individuals supporting Clinton, 37 from individuals supporting Trump, and 54 other or not supplied. Ranking was from 1 "Least Offensive" to 5 "Most Offensive".<br />
<br />
Within any item set of five actions only one action could be matched with an individual ranking.<br />
For each action the mean number of times that action was classified under each ranking was calculated. That value was multiplied by the action ranking and summed across all levels to create an index.<br />
<br />
The smallest index are the least offensive to non-offensive actions while the highest rankings are those actions respondents considered the most offensive.<br />
<br />
<b>Table 1</b>: This table shows all 150 actions ranked from least offensive on average to most offensive as rated by all respondents. The Trump, Clinton, and Other columns are how each of these respective supporters rank the actions. A .5 means that two actions were ranked the same. The Trump_Clinton column is calculated by taking the rankings of Trump supporters for an action and subtracting the rank for those actions for Clinton supporters. Values in which Trump supporters and Clinton supporters diverge by more than 30 ranks are highlighted.</div>
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<tr class="tableizer-firstrow"><th>All</th><th>Trump</th><th>Clinton</th><th>Other</th><th>Trump_Clinton</th><th>*Scandal</th><th>Action</th></tr>
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<tr><td>1</td><td>5</td><td>2</td><td>2.5</td><td>3</td><td></td><td>Eating meat.</td></tr>
<tr><td>2</td><td>1</td><td>2</td><td>15</td><td>-1</td><td></td><td>Posting a much younger picture of yourself on a dating website.</td></tr>
<tr><td>3</td><td>6.5</td><td>5.5</td><td>8</td><td>1</td><td></td><td>Not wearing your seat belt when driving.</td></tr>
<tr><td>4</td><td>15.5</td><td>2</td><td>6</td><td>13.5</td><td></td><td>Dating someone of a different race.</td></tr>
<tr><td>5</td><td>2.5</td><td>15</td><td>2.5</td><td>-12.5</td><td>Donald Trump</td><td>Swearing in public.</td></tr>
<tr><td>6</td><td>8.5</td><td>17</td><td>2.5</td><td>-8.5</td><td></td><td>Offering to pay someone 10 cents for every paper they deliver.</td></tr>
<tr><td>7</td><td>6.5</td><td>12</td><td>17.5</td><td>-5.5</td><td></td><td>Stealing candy from a baby.</td></tr>
<tr><td>8</td><td>12</td><td>25</td><td>10</td><td>-13</td><td></td><td>Jumping in line in front of someone else when waiting for customer service.</td></tr>
<tr><td>9</td><td>2.5</td><td>27</td><td>21</td><td><span style="background-color: white;">-24.5</span></td><td></td><td>Not tipping a waiter after average service.</td></tr>
<tr><td>10</td><td>4</td><td>14</td><td>33.5</td><td>-10</td><td></td><td>Hoard the armrest when sitting next to a stranger on a plane or movie theater.</td></tr>
<tr><td>11</td><td>60.5</td><td>5.5</td><td>5</td><td>55</td><td></td><td>Having sex with someone of the same gender.</td></tr>
<tr><td>12</td><td>27</td><td>8</td><td>38</td><td>19</td><td>Trey Radel</td><td>Buying illegal drugs for personal consumption.</td></tr>
<tr><td>13</td><td>25.5</td><td>11</td><td>28.5</td><td><span style="background-color: white;">14.5</span></td><td></td><td>Using toilet paper to vandalizing a stranger's house.</td></tr>
<tr><td>14</td><td>37</td><td>13</td><td>25</td><td>24</td><td></td><td>Taking the cab hailed for someone else.</td></tr>
<tr><td>15</td><td>29</td><td>27</td><td>12</td><td>2</td><td></td><td>Leaving chewing gum under a public table.</td></tr>
<tr><td>16</td><td>13</td><td>57.5</td><td>20</td><td><span style="background-color: #fff2cc;">-44.5</span></td><td></td><td>Exaggerating the size of your penis in order to convince someone to have sex with you.</td></tr>
<tr><td>17</td><td>25.5</td><td>4</td><td>45</td><td><span style="background-color: white;">21.5</span></td><td></td><td>Illegally copying copyrighted music.</td></tr>
<tr><td>18</td><td>18</td><td>16</td><td>32</td><td>2</td><td></td><td>Not voting.</td></tr>
<tr><td>19</td><td>22</td><td>9</td><td>48</td><td>13</td><td></td><td>Illegally streaming copyrighted videos.</td></tr>
<tr><td>20</td><td>17</td><td>21.5</td><td>30.5</td><td>-4.5</td><td></td><td>Publishing with permission a different person's work as your own.</td></tr>
<tr><td>21</td><td>30</td><td>51.5</td><td>12</td><td><span style="background-color: white;">-21.5</span></td><td></td><td>Hunting a wild animal.</td></tr>
<tr><td>22</td><td>8.5</td><td>20</td><td>45</td><td>-11.5</td><td></td><td>Using a bad or ineffective preparedness test to screen potential students.</td></tr>
<tr><td>23</td><td>57.5</td><td>36.5</td><td>12</td><td>21</td><td></td><td>Sticking gum in someone's hair.</td></tr>
<tr><td>24</td><td>43</td><td>40.5</td><td>22</td><td>2.5</td><td></td><td>Having sex with your landlord to pay the rent.</td></tr>
<tr><td>25</td><td>20</td><td>7</td><td>50.5</td><td>13</td><td></td><td>Not flushing a public toilet after pooping.</td></tr>
<tr><td>26</td><td>46.5</td><td>36.5</td><td>14</td><td>10</td><td>Hillary Clinton</td><td>Continuing to stay married to your spouse after that person had multiple affairs.</td></tr>
<tr><td>27.5</td><td>32</td><td>33.5</td><td>19</td><td>-1.5</td><td></td><td>Paying a prostitute for sex.</td></tr>
<tr><td>27.5</td><td>10.5</td><td>18</td><td>27</td><td>-7.5</td><td></td><td>Spending money on something you do not need such as entertainment when you know there are people dying of hunger next door.</td></tr>
<tr><td>29</td><td>15.5</td><td>66</td><td>9</td><td><span style="background-color: #fff2cc;">-50.5</span></td><td>Donald Trump</td><td>Earning 1000 times more money per hour as your lowest paid full-time employees.</td></tr>
<tr><td>30</td><td>46.5</td><td>39</td><td>7</td><td>7.5</td><td></td><td>Voting illegally twice.</td></tr>
<tr><td>31</td><td>10.5</td><td>29</td><td>40.5</td><td><span style="background-color: white;">-18.5</span></td><td>IRS</td><td>Using public funds to pay for professional development conferences which may not be very productive.</td></tr>
<tr><td>32</td><td>21</td><td>27</td><td>26</td><td>-6</td><td>Hillary Clinton</td><td>Refusing to release the transcripts of paid speeches you gave.</td></tr>
<tr><td>33</td><td>28</td><td>61</td><td>17.5</td><td><span style="background-color: #fff2cc;">-33</span></td><td></td><td>Earning 1000 times more money per hour as your lowest paid contractor.</td></tr>
<tr><td>34</td><td>34</td><td>40.5</td><td>23</td><td>-6.5</td><td></td><td>Lying about damages in order to keep a tenant's security deposit.</td></tr>
<tr><td>35</td><td>63</td><td>64</td><td>2.5</td><td>-1</td><td>FBI</td><td>Selling guns with GPS trackers in them to a dangerous illegal organization with the intention of using the data to prosecute the organization.</td></tr>
<tr><td>36</td><td>19</td><td>19</td><td>65</td><td>0</td><td></td><td>Urinating on a toilet seat and not cleaning it.</td></tr>
<tr><td>37</td><td>74.5</td><td>61</td><td>24</td><td>13.5</td><td>Donald Trump</td><td>Misrepresenting your success to convince others to invest in you.</td></tr>
<tr><td>38</td><td>65</td><td>51.5</td><td>28.5</td><td>13.5</td><td>Donald Trump</td><td>Reposting images from a white supremacist group.</td></tr>
<tr><td>39</td><td>23.5</td><td>54</td><td>40.5</td><td><span style="background-color: #fff2cc;">-30.5</span></td><td></td><td>Writing false review's on a business's website because you are angry with them.</td></tr>
<tr><td>40</td><td>49.5</td><td>31.5</td><td>30.5</td><td>18</td><td></td><td>Sneaking out of a resturant without paying for a meal.</td></tr>
<tr><td>41</td><td>14</td><td>21.5</td><td>81</td><td>-7.5</td><td></td><td>Copying a fellow student's homework.</td></tr>
<tr><td>42</td><td>35</td><td>57.5</td><td>39</td><td><span style="background-color: white;">-22.5</span></td><td>Hillary Clinton</td><td>A politician lying or falsely representing one quarter (25%) of his/her public statements.</td></tr>
<tr><td>43</td><td>32</td><td>36.5</td><td>58</td><td>-4.5</td><td></td><td>Stealing products from a convenience store. (Shoplifting)</td></tr>
<tr><td>44</td><td>55</td><td>77.5</td><td>42.5</td><td><span style="background-color: white;">-22.5</span></td><td>Donald Trump</td><td>Falsely reporting the magnitude of your donations to charities to make yourself look better.</td></tr>
<tr><td>45.5</td><td>52.5</td><td>45.5</td><td>52</td><td>7</td><td>Donald Trump</td><td>Publicly shaming someone for being fat or ugly.</td></tr>
<tr><td>45.5</td><td>81.5</td><td>69</td><td>16</td><td>12.5</td><td></td><td>Refusing to renounce the endorsement of a white supremacist group.</td></tr>
<tr><td>47</td><td>23.5</td><td>43</td><td>72</td><td><span style="background-color: white;">-19.5</span></td><td></td><td>Speeding through a school zone.</td></tr>
<tr><td>48</td><td>52.5</td><td>49</td><td>45</td><td>3.5</td><td></td><td>Promising special interest groups to vote for them if they donate to your campaign.</td></tr>
<tr><td>49</td><td>79</td><td>24</td><td>53</td><td>55</td><td></td><td>Masturbating in a public bathroom.</td></tr>
<tr><td>50</td><td>57.5</td><td>61</td><td>36</td><td>-3.5</td><td>Donald Trump</td><td>Lying about the number of floors in a building you own in order to charge higher rent.</td></tr>
<tr><td>51</td><td>41</td><td>71</td><td>60</td><td>-30</td><td></td><td>Using spray paint to vandalize a stranger's car.</td></tr>
<tr><td>52</td><td>41</td><td>36.5</td><td>68</td><td>4.5</td><td></td><td>Smoking in an area around non-smokers where "no smoking" signs are posted.</td></tr>
<tr><td>53</td><td>74.5</td><td>42</td><td>48</td><td><span style="background-color: #fff2cc;">32.5</span></td><td></td><td>Spitting in someone's soup when they are not looking.</td></tr>
<tr><td>54</td><td>41</td><td>64</td><td>55.5</td><td>-23</td><td></td><td>Publishing without permission a different person's work as your own.</td></tr>
<tr><td>55</td><td>44</td><td>112</td><td>50.5</td><td><span style="background-color: #fff2cc;">-68</span></td><td></td><td>Publicly renouncing homosexuality while secretly having sex with gay prostitutes.</td></tr>
<tr><td>56</td><td>74.5</td><td>48</td><td>48</td><td>26.5</td><td></td><td>Publicizing false claims about a person because you are angry with that person.</td></tr>
<tr><td>57</td><td>66.5</td><td>47</td><td>55.5</td><td><span style="background-color: white;">19.5</span></td><td>Chris Christie</td><td>Using your position to control how public funds are used in to punish a political rival.</td></tr>
<tr><td>58</td><td>32</td><td>51.5</td><td>63</td><td>-19.5</td><td></td><td>Providing alcohol to minors (a person less than 18 years old).</td></tr>
<tr><td>59</td><td>92</td><td>44</td><td>35</td><td>48</td><td></td><td>A public official hiring a less qualified friend over a well qualified stranger.</td></tr>
<tr><td>60</td><td>74.5</td><td>56</td><td>42.5</td><td>18.5</td><td></td><td>A fully mobile person refusing to give up a seat to a disabled or infirm person.</td></tr>
<tr><td>61</td><td>46.5</td><td>93</td><td>33.5</td><td><span style="background-color: #fff2cc;">-46.5</span></td><td></td><td>Publicizing someone's address in an attempt to intimidate someone else.</td></tr>
<tr><td>62</td><td>39</td><td>10</td><td>89</td><td>29</td><td>Donald Trump</td><td>Judging a person on their appearance.</td></tr>
<tr><td>63</td><td>52.5</td><td>68</td><td>61</td><td>-15.5</td><td></td><td>Selling illegal drugs.</td></tr>
<tr><td>64</td><td>74.5</td><td>31.5</td><td>75</td><td><span style="background-color: #fff2cc;">43</span></td><td>Hillary Clinton</td><td>Improperly storing national secrets.</td></tr>
<tr><td>65</td><td>52.5</td><td>64</td><td>77.5</td><td>-11.5</td><td>Donald Trump</td><td>A politician lying or falsely representing three quarters (75%) of his/her public statements.</td></tr>
<tr><td>66</td><td>81.5</td><td>30</td><td>70</td><td><span style="background-color: #fff2cc;">51.5</span></td><td>Donald Trump</td><td>Enjoying firing people from their occupation.</td></tr>
<tr><td>67</td><td>68</td><td>86.5</td><td>54</td><td>-18.5</td><td></td><td>Stealing large sums of money from a company you work for.</td></tr>
<tr><td>68</td><td>46.5</td><td>100</td><td>57</td><td><span style="background-color: #fff2cc;">-53.5</span></td><td>Donald Trump</td><td>Earning over 10 million dollars in a year and not paying any federal income taxes.</td></tr>
<tr><td>69</td><td>60.5</td><td>89</td><td>64</td><td>-28.5</td><td>Donald Trump</td><td>Filing bankruptcy in order to avoid paying the people who worked for you.</td></tr>
<tr><td>70</td><td>63</td><td>51.5</td><td>83.5</td><td>11.5</td><td></td><td>Sabotaging a competitors work.</td></tr>
<tr><td>71</td><td>81.5</td><td>73</td><td>73</td><td>8.5</td><td></td><td>Setting up fake accounts for your customers in order to increase profits.</td></tr>
<tr><td>72</td><td>81.5</td><td>23</td><td>93</td><td><span style="background-color: #fff2cc;">58.5</span></td><td></td><td>Publicly exposing yourself.</td></tr>
<tr><td>73</td><td>100.5</td><td>101</td><td>37</td><td>-0.5</td><td>Donald Trump</td><td>Enter the occupied changing room of members of the opposite sex without consent.</td></tr>
<tr><td>74</td><td>49.5</td><td>83</td><td>77.5</td><td><span style="background-color: #fff2cc;">-33.5</span></td><td>Clinton/Trump</td><td>A politician accepting money from special interest groups.</td></tr>
<tr><td>75</td><td>37</td><td>74</td><td>99</td><td><span style="background-color: #fff2cc;">-37</span></td><td></td><td>A police officer accepting a bribe in exchange for not writing a ticket.</td></tr>
<tr><td>76</td><td>106.5</td><td>81</td><td>67</td><td>25.5</td><td></td><td>Stealing someone's car.</td></tr>
<tr><td>77</td><td>95</td><td>95.5</td><td>66</td><td>-0.5</td><td><br /></td><td>Driving drunk or high.</td></tr>
<tr><td>78</td><td>66.5</td><td>77.5</td><td>80</td><td>-11</td><td>IRS</td><td>Using public funds designated for tax collection to produce a parody video.</td></tr>
<tr><td>79</td><td>57.5</td><td>92</td><td>77.5</td><td><span style="background-color: #fff2cc;">-34.5</span></td><td><br /></td><td>Using racial epitaphs.</td></tr>
<tr><td>80</td><td>57.5</td><td>33.5</td><td>94</td><td>24</td><td></td><td>Cheating on a test.</td></tr>
<tr><td>81</td><td>90</td><td>59</td><td>74</td><td>31</td><td></td><td>Not giving food to a starving person in front of you.</td></tr>
<tr><td>82</td><td>63</td><td>85</td><td>62</td><td>-22</td><td></td><td>A politician lying or falsely representing half (50%) of his/her public statements.</td></tr>
<tr><td>83</td><td>95</td><td>72</td><td>86.5</td><td>23</td><td>Anthony Weiner</td><td>A married person sending photographs of his/her genitalia to someone who is not that person's spouse.</td></tr>
<tr><td>84</td><td>111.5</td><td>67</td><td>82</td><td><span style="background-color: #fff2cc;">44.5</span></td><td></td><td>Giving a blind person inaccurate change because they cannot tell the difference.</td></tr>
<tr><td>85</td><td>106.5</td><td>84</td><td>71</td><td>22.5</td><td></td><td>Urging someone who is attempting to remain sober to take a drink.</td></tr>
<tr><td>86</td><td>93</td><td>70</td><td>83.5</td><td>23</td><td></td><td>Without authorization setting up and using a credit card in another person's name.</td></tr>
<tr><td>87</td><td>100.5</td><td>45.5</td><td>106</td><td>55</td><td></td><td>Masturbating in public.</td></tr>
<tr><td>88</td><td>84.5</td><td>86.5</td><td>77.5</td><td>-2</td><td></td><td>Using public resources entrusted to your care to enrich yourself.</td></tr>
<tr><td>89</td><td>108</td><td>75</td><td>69</td><td><span style="background-color: #fff2cc;">33</span></td><td></td><td>Mocking a disabled person for a physical handicap.</td></tr>
<tr><td>90</td><td>84.5</td><td>77.5</td><td>85</td><td>7</td><td></td><td>Bribing a public official to enrich oneself.</td></tr>
<tr><td>91</td><td>109</td><td>105.5</td><td>59</td><td>3.5</td><td>Donald Trump</td><td>Setting up a fake educational institution in order to enrich yourself.</td></tr>
<tr><td>92</td><td>37</td><td>94</td><td>111.5</td><td><span style="background-color: #fff2cc;">-57</span></td><td></td><td>Torturing criminals as punishment for crimes.</td></tr>
<tr><td>93</td><td>90</td><td>88</td><td>95</td><td>2</td><td>Bill Clinton</td><td>Cheating on your wife/husband.</td></tr>
<tr><td>94</td><td>69.5</td><td>102</td><td>91</td><td><span style="background-color: #fff2cc;">-32.5</span></td><td></td><td>Stalking someone you know in order to intimidate that person.</td></tr>
<tr><td>95</td><td>88</td><td>55</td><td>111.5</td><td><span style="background-color: #fff2cc;">33</span></td><td>Doctor Kevorkian</td><td>Killing someone who is in pain and going to die within the next six months and wants help dying.</td></tr>
<tr><td>96</td><td>98</td><td>90.5</td><td>86.5</td><td>7.5</td><td>Tonya Harding</td><td>Hiring someone to break the leg of a rival athlete.</td></tr>
<tr><td>97</td><td>74.5</td><td>90.5</td><td>101</td><td>-16</td><td></td><td>Using threats of lawsuits to silence a woman who claims to have been assaulted by you.</td></tr>
<tr><td>98</td><td>114</td><td>82</td><td>98</td><td>32</td><td> Hillary Clinton</td><td>Using a private email server resulting in the risk of compromised national security.</td></tr>
<tr><td>99</td><td>87</td><td>97</td><td>107.5</td><td>-10</td><td></td><td>Writing laws to prevent people who do not support you from voting.</td></tr>
<tr><td>100</td><td>74.5</td><td>107</td><td>105</td><td><span style="background-color: #fff2cc;">-32.5</span></td><td></td><td>Requiring a starving person attend your religious gathering before providing giving food.</td></tr>
<tr><td>101</td><td>97</td><td>98.5</td><td>104</td><td>-1.5</td><td>Donald Trump</td><td>Using your superior physical strength to force a person to kiss you.</td></tr>
<tr><td>102</td><td>86</td><td>103.5</td><td>107.5</td><td>-17.5</td><td></td><td>Stealing someone's identity in order to commit a crime. </td></tr>
<tr><td>103</td><td>103</td><td>80</td><td>113.5</td><td>23</td><td></td><td>Burning down your house to claim the insurance money.</td></tr>
<tr><td>104</td><td>111.5</td><td>114</td><td>90</td><td>-2.5</td><td></td><td>Using public resources entrusted to your care to enrich an ally or friend.</td></tr>
<tr><td>105</td><td>100.5</td><td>115</td><td>97</td><td>-14.5</td><td></td><td>Preventing someone from registering their child in your school because of that person's skin color.</td></tr>
<tr><td>106</td><td>116</td><td>109</td><td>100</td><td>7</td><td>Adolf Hitler</td><td>Encouraging racially motivated violence to promote your political aspirations.</td></tr>
<tr><td>107</td><td>104</td><td>120</td><td>102</td><td>-16</td><td></td><td>Bribing a public official to protect oneself.</td></tr>
<tr><td>108</td><td>74.5</td><td>118</td><td>115</td><td><span style="background-color: #fff2cc;">-43.5</span></td><td></td><td>Rejecting someone's rental application because of that person's skin color.</td></tr>
<tr><td>109</td><td>90</td><td>124.5</td><td>109</td><td><span style="background-color: #fff2cc;">-34.5</span></td><td>Bill Cosby</td><td>Sneaking a drug into someone's food or drink in order to force that person to have sex with you.</td></tr>
<tr><td>110</td><td>119</td><td>128</td><td>88</td><td>-9</td><td></td><td>Killing a healthy and well behaved pet for because you don't have to the time to take care of it.</td></tr>
<tr><td>111</td><td>100.5</td><td>105.5</td><td>110</td><td>-5</td><td></td><td>Stealing someone's needed pain medication for personal use.</td></tr>
<tr><td>112</td><td>139.5</td><td>123</td><td>96</td><td>16.5</td><td></td><td>Killing a healthy and well behaved pet because you find the animal annoying.</td></tr>
<tr><td>113</td><td>143</td><td>103.5</td><td>92</td><td><span style="background-color: #fff2cc;">39.5</span></td><td>Edward Snowden</td><td>Publicizing national security secrets which might result in lives being lost.</td></tr>
<tr><td>114</td><td>114</td><td>95.5</td><td>121.5</td><td>18.5</td><td>Donald Trump</td><td>Threatening to sue someone in order to keep them from telling the truth.</td></tr>
<tr><td>115</td><td>132</td><td>124.5</td><td>103</td><td>7.5</td><td></td><td>A person of influence encouraging a crowd to physically attack someone or a group of people he/she does not like.</td></tr>
<tr><td>116</td><td>69.5</td><td>117</td><td>127</td><td><span style="background-color: #fff2cc;">-47.5</span></td><td>George W Bush</td><td>Torturing terrorists with the hope of gathering information about future terrorist plots.</td></tr>
<tr><td>117</td><td>121</td><td>77.5</td><td>143.5</td><td><span style="background-color: #fff2cc;">43.5</span></td><td></td><td>Ordering the assassination of a dictator.</td></tr>
<tr><td>118</td><td>105</td><td>120</td><td>126</td><td>-15</td><td></td><td>Recording someone having sex without their knowledge.</td></tr>
<tr><td>119</td><td>114</td><td>122</td><td>121.5</td><td>-8</td><td></td><td>Restricting the use of life saving technology in order to increase profits.</td></tr>
<tr><td>120</td><td>136</td><td>108</td><td>116.5</td><td>28</td><td></td><td>Misrepresenting the effectiveness of a life saving drug in order to increase profits.</td></tr>
<tr><td>121</td><td>133</td><td>98.5</td><td>131</td><td><span style="background-color: #fff2cc;">34.5</span></td><td></td><td>Killing someone who is in pain and going to die within the next six months but does not want to die.</td></tr>
<tr><td>122</td><td>117</td><td>110</td><td>146.5</td><td>7</td><td></td><td>Not reporting an instance of known child abuse when you are legally mandated to report.</td></tr>
<tr><td>123</td><td>130.5</td><td>136.5</td><td>113.5</td><td>-6</td><td></td><td>Physically abusing your spouse.</td></tr>
<tr><td>124</td><td>128.5</td><td>112</td><td>125</td><td>16.5</td><td></td><td>Sending someone's spouse to the front line to die in order to marry the surviving window.</td></tr>
<tr><td>125</td><td>122</td><td>135</td><td>120</td><td>-13</td><td></td><td>Hiding information about the health risks of deadly product you sell.</td></tr>
<tr><td>126</td><td>124.5</td><td>134</td><td>123.5</td><td>-9.5</td><td></td><td>Stealing large sums of money from a mentally infirm client.</td></tr>
<tr><td>127</td><td>110</td><td>144</td><td>135</td><td><span style="background-color: #fff2cc;">-34</span></td><td></td><td>A medical doctor refusing to treat a patient who needs urgent care because they are unable to pay.</td></tr>
<tr><td>128</td><td>119</td><td>129</td><td>123.5</td><td>-10</td><td></td><td>Significantly raising the price of a life saving drug in order to increase profits.</td></tr>
<tr><td>129</td><td>139.5</td><td>131</td><td>116.5</td><td>8.5</td><td></td><td>Viewing child pornography.</td></tr>
<tr><td>130</td><td>141.5</td><td>138</td><td>118</td><td>3.5</td><td></td><td>Killing a healthy and well behaved pet for fun.</td></tr>
<tr><td>131</td><td>119</td><td>143</td><td>128</td><td>-24</td><td></td><td>Someone with a known dangerous sexually transmitted disease having unprotected sex with someone who is unaware of the condition.</td></tr>
<tr><td>132</td><td>123</td><td>133</td><td>131</td><td>-10</td><td></td><td>Using your superior physical strength to hold an unwilling person while you grabbed their genitalia.</td></tr>
<tr><td>133</td><td>128.5</td><td>116</td><td>131</td><td>12.5</td><td>Brock Turner</td><td>Taking and sharing naked pictures of a person who is unconscious.</td></tr>
<tr><td>134</td><td>124.5</td><td>131</td><td>136.5</td><td>-6.5</td><td>Brock Turner</td><td>Have involuntary sex with a person you find unconscious.</td></tr>
<tr><td>135.5</td><td>130.5</td><td>112</td><td>136.5</td><td>18.5</td><td>Vladimir Putin</td><td>Assassinating a political rival.</td></tr>
<tr><td>135.5</td><td>127</td><td>145</td><td>129</td><td>-18</td><td></td><td>Physically forcing your spouse to have sex with you.</td></tr>
<tr><td>137</td><td>95</td><td>149.5</td><td>141.5</td><td><span style="background-color: #fff2cc;">-54.5</span></td><td>Harry S Truman</td><td>Dropping an atomic bomb on a civilian city controlled by a rival nation</td></tr>
<tr><td>138</td><td>148.5</td><td>139</td><td>119</td><td>9.5</td><td></td><td>Allowing the executing of a convict if you have secret knowledge of the person's innocence.</td></tr>
<tr><td>139.5</td><td>138</td><td>120</td><td>149</td><td>18</td><td></td><td>A 40 year old having sex with a fifteen year old.</td></tr>
<tr><td>139.5</td><td>148.5</td><td>136.5</td><td>148</td><td>12</td><td></td><td>Using your power to pressure an employee to have sex with you.</td></tr>
<tr><td>141</td><td>137</td><td>140</td><td>141.5</td><td>-3</td><td></td><td>Not reporting an instance of known child sexual abuse.</td></tr>
<tr><td>142</td><td>148.5</td><td>126</td><td>138</td><td>22.5</td><td></td><td>Killing innocent people to further your political agenda.</td></tr>
<tr><td>143</td><td>144.5</td><td>142</td><td>139.5</td><td>2.5</td><td>Adolf Hitler</td><td>Encouraging people who follow you to attack and kill people you do not like.</td></tr>
<tr><td>144</td><td>144.5</td><td>127</td><td>139.5</td><td>17.5</td><td></td><td>Killing your spouse to claim the life insurance premium.</td></tr>
<tr><td>145</td><td>134.5</td><td>141</td><td>146.5</td><td>-6.5</td><td></td><td>Killing someone for their money.</td></tr>
<tr><td>146</td><td>126</td><td>131</td><td>145</td><td>-5</td><td>George Washington</td><td>Possessing a personal slave who has no human rights.</td></tr>
<tr><td>147</td><td>134.5</td><td>147</td><td>134</td><td>-12.5</td><td>Donald Trump</td><td>Groping without warning the genitalia of someone else.</td></tr>
<tr><td>148</td><td>148.5</td><td>146</td><td>133</td><td>2.5</td><td></td><td>Making child pornography.</td></tr>
<tr><td>149</td><td>141.5</td><td>148</td><td>143.5</td><td>-6.5</td><td></td><td>Killing innocent people for personal reasons such as curiosity or entertainment.</td></tr>
<tr><td>150</td><td>146</td><td>149.5</td><td>150</td><td>-3.5</td><td></td><td>Killing somebody to protect your reputation.</td></tr>
</tbody></table>
* Please note that I am making no claim to the veracity of the scandal.<br />
** Upon viewing this list I realize that there are a number of scandals I forgot to include related to Hillary. I am unconvinced that any of them would have been ranked very high on the list. However they should have been included. Sorry team Trump.<br />
<br />
<b>General Differences</b><br />
Looking at the table we can see that generally it agrees with out intuition with innocuous or generally non-offensive actions being ranked at the top, while actions that involve doing significant harm to others being ranked at the bottom.<br />
<br />
Interestingly the rankings between Trump and Clinton supporters agree generally with a 84% correlation in ranking values.<br />
<br />
From the differences in rankings of actions between Clinton and Trump supporters we start to get an idea on how these two different groups think. The largest difference is 68 ranks of difference with Trump supporters much more accepting than Clinton supporters of "Publicly renouncing homosexuality while secretly having sex with gay prostitutes". Clinton supporters seem less tolerant of deception in general with exaggerations of penis size and the writing of false reviews on business webpages being ranked much more offensive than their Trump counterparts.<br />
<br />
Clinton supporters also find it generally more offensive to do harm to others such as dropping the atomic bomb on civilian populations and torturing terrorists or criminals.<br />
<br />
The two camps have fiercely different perspectives on money. Clinton supporters are very concerned with the perceived injustices caused by unequal access to resources. These supporters are much more prone to rank as more offensive inequality in earnings as well as politicians accepting public donations. These supporters find it much more offensive for a doctor to refuse treatment on the basis of insufficient funds.<br />
<br />
There also appears to be a difference in how concerned Trump supporters are with racial inequality with Trump supporters much less concerned with the act of rejecting an applicant due to the color of skin or minding the use of racial epitaphs.<br />
<br />
<b>Scandals</b><br />
Perhaps unsurprisingly for the largest scandals Trump supporters and Clinton supporters seem to disagree with how offensive the actions of their candidates are. Clinton supports find the surprise groping of genitalia one of the worse actions someone can take while Trump supporters place it a bit lower on the list. For Trump supporters, improperly storing national secrets and using a private email server are ranked as much more offensive than for Clinton supporters.<br />
<br />
<b>Summary</b><br />
While Clinton and Trump supporters mostly agree in generally how they rank objectionable actions, they do seem to disagree in some areas that seem consistent with differences in popular representation. Clinton supporters being concerned with economic, social, and political justice. Trump supporters being concerned with protecting economic rights as well as individual freedoms such as the right to offend others through word or deed.</div>
Francishttp://www.blogger.com/profile/16658586705916884436noreply@blogger.com0tag:blogger.com,1999:blog-6288862798546085706.post-10585850062133955922016-04-14T17:31:00.001-04:002016-04-14T17:36:02.661-04:00Calculating Average Consumption From One Week of Purchases<div dir="ltr" style="text-align: left;" trbidi="on">
A number of large surveys have attempted to quantify consumer consumption from a limited period <br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiXD9GlyR51Ra5cySht5R-uEROwGMcaeofzL9SnqlXrbmn2v7gKA_3y_qLgwkLSUp1W7ebx6PydHSqzS76AfCPo5d0d7aLj7wVm_O4MH3w8NgDtkPe3Z00_FHnrk8HQPx9JkymWj4tvshg/s1600/ConsumptionSpread.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="150" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiXD9GlyR51Ra5cySht5R-uEROwGMcaeofzL9SnqlXrbmn2v7gKA_3y_qLgwkLSUp1W7ebx6PydHSqzS76AfCPo5d0d7aLj7wVm_O4MH3w8NgDtkPe3Z00_FHnrk8HQPx9JkymWj4tvshg/s200/ConsumptionSpread.png" width="200" /></a></div>
of time observed. This task can be fairly complex as it is fraught with potentially large difficulties directly observing who is consuming what. Rather than this expensive method some researchers have attempted to substitute more easily observed purchase patterns inferring that in general house holds are going to consume what they purchase.<br />
<br />
In order to aid in this analysis researchers collect data on both what is purchased and over what period of time it is to be consumed, for instance today (1) or over the next week (7).<br />
<br />
Yet purchase patterns can be difficult to work with. Typically household consumption does not map perfectly to household consumption. For one, households can consume stocks from previous weeks. Likewise, households can purchase food to be held in stock for future weeks.<br />
<br />
In order to adjust for missing consumption levels we want to adjust consumption to account for both the food items that will not all be consumed the week of observations <br />
(1) <br />
$$ C_{current.purchases} = C_{purchase} \frac{days.remaining.in.observation.period}{days.expected.to.consume}$$<br />
<br />
as well as the food items that were purchased the previous week and
consumed this week. We can calculate the probabilities of observing an individual outcome in the following way:<br />
(2)<br />
$$ P_{observing.purchase} = \frac{observation.period}{days.expected.to.consume}$$<br />
<br />
We can note that the probability of observing a particular purchase if greater than 1 need only be set to one since if this is the case it is likely that this particular purchase will appear one or more times in our data.<br />
<br />
Now we can combine (1) and (2) by dividing the current purchases by the likelihood of observing those purchases.<br />
<br />
(3)<br />
$$ E(C_{current.purchases}) = C_{purchase} \frac{days.remaining.in.observation.period}{days.expected.to.consume}/\frac{observation.period}{days.expected.to.consume}$$<br />
$$=C_{purchase} \frac{days.remaining.in.observation.period}{observation.period}$$<br />
<br />
If the probability is less than 1 otherwise we can use equation (1).<br />
<br />
Finally in order to calculate average consumption we take the daily average for our estimated expected consumption levels? Right?<br />
<br />
Not even close. This only begins to capture the problem as we have multiple purchases often on different days consumed in different patterns throughout the week.<br />
<br />
<br />
In order to get us closer to the appropriate level of estimated consumption we need to both infer the missing consumption as well as spread out the observed consumption so that when we look at daily averages good A purchased on day 1 with an expected consumption period of 1 week will also be included with good B purchased on day 7.<br />
<br />
In order to explore how to estimate consumption from only observing a limited period of time I have written a simulation testing four methods of estimation. The true consumption level for any individual is 1 unit. If there are multiple goods consumed than that 1 unit of consumption is spread across all goods so that every day only one unit is consumed.<br />
<br />
Using only one good we get the following results. M1 is just taking the mean consumption if we divide quantity of goods purchased by number of days expected to consume. M2 is adjusting consumption by the inverse of the likelihood of observing that consumption. M3 is spreading consumption across all of the days of the week observed. M4 is both adjusting by likelihood of observations and spreading consumption across days of the week observed.<br />
<br />
Table 1:Sim # is the simulation number while # Items is the number of different food items purchased while C Spread is the number of days consumption of that item is spread over. All values are simulated 250 times.<br />
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<tr class="tableizer-firstrow"><th style="text-align: center;">Sim</th><th style="text-align: center;"># Items</th><th style="text-align: center;">C Spread</th><th style="text-align: center;">M1</th><th style="text-align: center;">M2</th><th style="text-align: center;">M3</th><th style="text-align: center;">M4</th></tr>
</thead><tbody>
<tr><td style="text-align: center;">1</td><td style="text-align: center;">1</td><td style="text-align: center;">1</td><td style="text-align: center;">1.00</td><td style="text-align: center;">1.00</td><td style="text-align: center;">1.00</td><td style="text-align: center;">1.00</td></tr>
<tr><td style="text-align: center;">2</td><td style="text-align: center;">1</td><td style="text-align: center;">2</td><td style="text-align: center;">1.00</td><td style="text-align: center;">1.00</td><td style="text-align: center;">1.00</td><td style="text-align: center;">1.00</td></tr>
<tr><td style="text-align: center;">3</td><td style="text-align: center;">1</td><td style="text-align: center;">3</td><td style="text-align: center;">1.00</td><td style="text-align: center;">1.00</td><td style="text-align: center;">1.00</td><td style="text-align: center;">1.00</td></tr>
<tr><td style="text-align: center;">4</td><td style="text-align: center;">1</td><td style="text-align: center;">5</td><td style="text-align: center;">1.00</td><td style="text-align: center;">1.00</td><td style="text-align: center;">1.00</td><td style="text-align: center;">1.00</td></tr>
<tr><td style="text-align: center;">5</td><td style="text-align: center;">1</td><td style="text-align: center;">6</td><td style="text-align: center;">1.00</td><td style="text-align: center;">1.00</td><td style="text-align: center;">1.00</td><td style="text-align: center;">1.00</td></tr>
<tr><td style="text-align: center;">6</td><td style="text-align: center;">1</td><td style="text-align: center;">7</td><td style="text-align: center;">1.00</td><td style="text-align: center;">1.00</td><td style="text-align: center;">1.00</td><td style="text-align: center;">1.00</td></tr>
<tr><td style="text-align: center;">7</td><td style="text-align: center;">1</td><td style="text-align: center;">8</td><td style="text-align: center;">0.88</td><td style="text-align: center;">1.01</td><td style="text-align: center;">0.88</td><td style="text-align: center;">1.01</td></tr>
<tr><td style="text-align: center;">8</td><td style="text-align: center;">1</td><td style="text-align: center;">9</td><td style="text-align: center;">0.74</td><td style="text-align: center;">0.95</td><td style="text-align: center;">0.74</td><td style="text-align: center;">0.95</td></tr>
<tr><td style="text-align: center;">9</td><td style="text-align: center;">1</td><td style="text-align: center;">10</td><td style="text-align: center;">0.70</td><td style="text-align: center;">1.00</td><td style="text-align: center;">0.70</td><td style="text-align: center;">1.00</td></tr>
<tr><td style="text-align: center;">10</td><td style="text-align: center;">1</td><td style="text-align: center;">15</td><td style="text-align: center;">0.42</td><td style="text-align: center;">0.89</td><td style="text-align: center;">0.42</td><td style="text-align: center;">0.89</td></tr>
<tr><td style="text-align: center;">11</td><td style="text-align: center;">1</td><td style="text-align: center;">20</td><td style="text-align: center;">0.35</td><td style="text-align: center;">1.01</td><td style="text-align: center;">0.35</td><td style="text-align: center;">1.01</td></tr>
</tbody></table>
<br />
Notice that with only 1 item consumed M1 and M3 are equivalent and M2 and M4 are equivalent. We can see that expected consumption for M2 and M4 provide much better estimates than for M1 and M3 when the consumption is spread out for goods for more than the observation period of one week on average.<br />
<br />
Things get much more difficult when we include other goods in our calculation.<br />
<br />
Table 2: Equivalent to Table 1 except now multiple items are being purchased at different periods (identified as # Items). In this the C Spread only refers to the first item. The remaining items are drawn randomly from the possible consumption spreads with much greater weight applied to lower consumption levels.<br />
<table class="tableizer-table">
<thead>
<tr class="tableizer-firstrow"><th style="text-align: center;">Sim</th><th style="text-align: center;"># Items</th><th style="text-align: center;">C Spread</th><th style="text-align: center;">M1</th><th style="text-align: center;">M2</th><th style="text-align: center;">M3</th><th style="text-align: center;">M4</th></tr>
</thead><tbody>
<tr><td style="text-align: center;">12</td><td style="text-align: center;">2</td><td style="text-align: center;">1</td><td style="text-align: center;">0.72</td><td style="text-align: center;">0.72</td><td style="text-align: center;">0.90</td><td style="text-align: center;">0.91</td></tr>
<tr><td style="text-align: center;">13</td><td style="text-align: center;">2</td><td style="text-align: center;">2</td><td style="text-align: center;">0.71</td><td style="text-align: center;">0.71</td><td style="text-align: center;">0.90</td><td style="text-align: center;">0.91</td></tr>
<tr><td style="text-align: center;">14</td><td style="text-align: center;">2</td><td style="text-align: center;">3</td><td style="text-align: center;">0.71</td><td style="text-align: center;">0.71</td><td style="text-align: center;">0.91</td><td style="text-align: center;">0.92</td></tr>
<tr><td style="text-align: center;">15</td><td style="text-align: center;">2</td><td style="text-align: center;">5</td><td style="text-align: center;">0.64</td><td style="text-align: center;">0.65</td><td style="text-align: center;">0.87</td><td style="text-align: center;">0.89</td></tr>
<tr><td style="text-align: center;">16</td><td style="text-align: center;">2</td><td style="text-align: center;">6</td><td style="text-align: center;">0.66</td><td style="text-align: center;">0.67</td><td style="text-align: center;">0.83</td><td style="text-align: center;">0.84</td></tr>
<tr><td style="text-align: center;">17</td><td style="text-align: center;">2</td><td style="text-align: center;">7</td><td style="text-align: center;">0.60</td><td style="text-align: center;">0.60</td><td style="text-align: center;">0.80</td><td style="text-align: center;">0.81</td></tr>
<tr><td style="text-align: center;">18</td><td style="text-align: center;">2</td><td style="text-align: center;">8</td><td style="text-align: center;">0.59</td><td style="text-align: center;">0.62</td><td style="text-align: center;">0.78</td><td style="text-align: center;">0.83</td></tr>
<tr><td style="text-align: center;">19</td><td style="text-align: center;">2</td><td style="text-align: center;">9</td><td style="text-align: center;">0.59</td><td style="text-align: center;">0.65</td><td style="text-align: center;">0.74</td><td style="text-align: center;">0.83</td></tr>
<tr><td style="text-align: center;">20</td><td style="text-align: center;">2</td><td style="text-align: center;">10</td><td style="text-align: center;">0.58</td><td style="text-align: center;">0.65</td><td style="text-align: center;">0.70</td><td style="text-align: center;">0.81</td></tr>
<tr><td style="text-align: center;">21</td><td style="text-align: center;">2</td><td style="text-align: center;">15</td><td style="text-align: center;">0.58</td><td style="text-align: center;">0.71</td><td style="text-align: center;">0.64</td><td style="text-align: center;">0.83</td></tr>
<tr><td style="text-align: center;">22</td><td style="text-align: center;">2</td><td style="text-align: center;">20</td><td style="text-align: center;">0.54</td><td style="text-align: center;">0.69</td><td style="text-align: center;">0.59</td><td style="text-align: center;">0.83</td></tr>
<tr><td style="text-align: center;">23</td><td style="text-align: center;">3</td><td style="text-align: center;">1</td><td style="text-align: center;">0.62</td><td style="text-align: center;">0.62</td><td style="text-align: center;">0.86</td><td style="text-align: center;">0.88</td></tr>
<tr><td style="text-align: center;">24</td><td style="text-align: center;">3</td><td style="text-align: center;">2</td><td style="text-align: center;">0.61</td><td style="text-align: center;">0.62</td><td style="text-align: center;">0.88</td><td style="text-align: center;">0.89</td></tr>
<tr><td style="text-align: center;">25</td><td style="text-align: center;">3</td><td style="text-align: center;">3</td><td style="text-align: center;">0.58</td><td style="text-align: center;">0.59</td><td style="text-align: center;">0.87</td><td style="text-align: center;">0.88</td></tr>
<tr><td style="text-align: center;">26</td><td style="text-align: center;">3</td><td style="text-align: center;">5</td><td style="text-align: center;">0.53</td><td style="text-align: center;">0.53</td><td style="text-align: center;">0.83</td><td style="text-align: center;">0.84</td></tr>
<tr><td style="text-align: center;">27</td><td style="text-align: center;">3</td><td style="text-align: center;">6</td><td style="text-align: center;">0.55</td><td style="text-align: center;">0.55</td><td style="text-align: center;">0.81</td><td style="text-align: center;">0.82</td></tr>
<tr><td style="text-align: center;">28</td><td style="text-align: center;">3</td><td style="text-align: center;">7</td><td style="text-align: center;">0.50</td><td style="text-align: center;">0.51</td><td style="text-align: center;">0.78</td><td style="text-align: center;">0.79</td></tr>
<tr><td style="text-align: center;">29</td><td style="text-align: center;">3</td><td style="text-align: center;">8</td><td style="text-align: center;">0.52</td><td style="text-align: center;">0.53</td><td style="text-align: center;">0.78</td><td style="text-align: center;">0.82</td></tr>
<tr><td style="text-align: center;">30</td><td style="text-align: center;">3</td><td style="text-align: center;">9</td><td style="text-align: center;">0.52</td><td style="text-align: center;">0.54</td><td style="text-align: center;">0.75</td><td style="text-align: center;">0.81</td></tr>
<tr><td style="text-align: center;">31</td><td style="text-align: center;">3</td><td style="text-align: center;">10</td><td style="text-align: center;">0.50</td><td style="text-align: center;">0.54</td><td style="text-align: center;">0.72</td><td style="text-align: center;">0.80</td></tr>
<tr><td style="text-align: center;">32</td><td style="text-align: center;">3</td><td style="text-align: center;">15</td><td style="text-align: center;">0.49</td><td style="text-align: center;">0.55</td><td style="text-align: center;">0.68</td><td style="text-align: center;">0.82</td></tr>
<tr><td style="text-align: center;">33</td><td style="text-align: center;">3</td><td style="text-align: center;">20</td><td style="text-align: center;">0.47</td><td style="text-align: center;">0.53</td><td style="text-align: center;">0.63</td><td style="text-align: center;">0.76</td></tr>
<tr><td style="text-align: center;">34</td><td style="text-align: center;">4</td><td style="text-align: center;">1</td><td style="text-align: center;">0.58</td><td style="text-align: center;">0.58</td><td style="text-align: center;">0.84</td><td style="text-align: center;">0.85</td></tr>
<tr><td style="text-align: center;">35</td><td style="text-align: center;">4</td><td style="text-align: center;">2</td><td style="text-align: center;">0.55</td><td style="text-align: center;">0.55</td><td style="text-align: center;">0.85</td><td style="text-align: center;">0.86</td></tr>
<tr><td style="text-align: center;">36</td><td style="text-align: center;">4</td><td style="text-align: center;">3</td><td style="text-align: center;">0.52</td><td style="text-align: center;">0.52</td><td style="text-align: center;">0.84</td><td style="text-align: center;">0.85</td></tr>
<tr><td style="text-align: center;">37</td><td style="text-align: center;">4</td><td style="text-align: center;">5</td><td style="text-align: center;">0.48</td><td style="text-align: center;">0.48</td><td style="text-align: center;">0.81</td><td style="text-align: center;">0.82</td></tr>
<tr><td style="text-align: center;">38</td><td style="text-align: center;">4</td><td style="text-align: center;">6</td><td style="text-align: center;">0.49</td><td style="text-align: center;">0.49</td><td style="text-align: center;">0.80</td><td style="text-align: center;">0.82</td></tr>
<tr><td style="text-align: center;">39</td><td style="text-align: center;">4</td><td style="text-align: center;">7</td><td style="text-align: center;">0.46</td><td style="text-align: center;">0.46</td><td style="text-align: center;">0.77</td><td style="text-align: center;">0.78</td></tr>
<tr><td style="text-align: center;">40</td><td style="text-align: center;">4</td><td style="text-align: center;">8</td><td style="text-align: center;">0.46</td><td style="text-align: center;">0.48</td><td style="text-align: center;">0.76</td><td style="text-align: center;">0.79</td></tr>
<tr><td style="text-align: center;">41</td><td style="text-align: center;">4</td><td style="text-align: center;">9</td><td style="text-align: center;">0.48</td><td style="text-align: center;">0.49</td><td style="text-align: center;">0.76</td><td style="text-align: center;">0.81</td></tr>
<tr><td style="text-align: center;">42</td><td style="text-align: center;">4</td><td style="text-align: center;">10</td><td style="text-align: center;">0.48</td><td style="text-align: center;">0.50</td><td style="text-align: center;">0.73</td><td style="text-align: center;">0.79</td></tr>
<tr><td style="text-align: center;">43</td><td style="text-align: center;">4</td><td style="text-align: center;">15</td><td style="text-align: center;">0.45</td><td style="text-align: center;">0.49</td><td style="text-align: center;">0.70</td><td style="text-align: center;">0.79</td></tr>
<tr><td style="text-align: center;">44</td><td style="text-align: center;">4</td><td style="text-align: center;">20</td><td style="text-align: center;">0.44</td><td style="text-align: center;">0.47</td><td style="text-align: center;">0.68</td><td style="text-align: center;">0.78</td></tr>
<tr><td style="text-align: center;">45</td><td style="text-align: center;">5</td><td style="text-align: center;">1</td><td style="text-align: center;">0.56</td><td style="text-align: center;">0.57</td><td style="text-align: center;">0.85</td><td style="text-align: center;">0.86</td></tr>
<tr><td style="text-align: center;">46</td><td style="text-align: center;">5</td><td style="text-align: center;">2</td><td style="text-align: center;">0.52</td><td style="text-align: center;">0.52</td><td style="text-align: center;">0.84</td><td style="text-align: center;">0.85</td></tr>
<tr><td style="text-align: center;">47</td><td style="text-align: center;">5</td><td style="text-align: center;">3</td><td style="text-align: center;">0.49</td><td style="text-align: center;">0.49</td><td style="text-align: center;">0.83</td><td style="text-align: center;">0.84</td></tr>
<tr><td style="text-align: center;">48</td><td style="text-align: center;">5</td><td style="text-align: center;">5</td><td style="text-align: center;">0.45</td><td style="text-align: center;">0.45</td><td style="text-align: center;">0.79</td><td style="text-align: center;">0.80</td></tr>
<tr><td style="text-align: center;">49</td><td style="text-align: center;">5</td><td style="text-align: center;">6</td><td style="text-align: center;">0.45</td><td style="text-align: center;">0.46</td><td style="text-align: center;">0.78</td><td style="text-align: center;">0.79</td></tr>
<tr><td style="text-align: center;">50</td><td style="text-align: center;">5</td><td style="text-align: center;">7</td><td style="text-align: center;">0.45</td><td style="text-align: center;">0.45</td><td style="text-align: center;">0.78</td><td style="text-align: center;">0.79</td></tr>
<tr><td style="text-align: center;">51</td><td style="text-align: center;">5</td><td style="text-align: center;">8</td><td style="text-align: center;">0.44</td><td style="text-align: center;">0.45</td><td style="text-align: center;">0.76</td><td style="text-align: center;">0.78</td></tr>
<tr><td style="text-align: center;">52</td><td style="text-align: center;">5</td><td style="text-align: center;">9</td><td style="text-align: center;">0.44</td><td style="text-align: center;">0.45</td><td style="text-align: center;">0.76</td><td style="text-align: center;">0.79</td></tr>
<tr><td style="text-align: center;">53</td><td style="text-align: center;">5</td><td style="text-align: center;">10</td><td style="text-align: center;">0.44</td><td style="text-align: center;">0.45</td><td style="text-align: center;">0.74</td><td style="text-align: center;">0.79</td></tr>
<tr><td style="text-align: center;">54</td><td style="text-align: center;">5</td><td style="text-align: center;">15</td><td style="text-align: center;">0.44</td><td style="text-align: center;">0.46</td><td style="text-align: center;">0.71</td><td style="text-align: center;">0.77</td></tr>
<tr><td style="text-align: center;">55</td><td style="text-align: center;">5</td><td style="text-align: center;">20</td><td style="text-align: center;">0.42</td><td style="text-align: center;">0.45</td><td style="text-align: center;">0.69</td><td style="text-align: center;">0.76</td></tr>
<tr><td style="text-align: center;">56</td><td style="text-align: center;">6</td><td style="text-align: center;">1</td><td style="text-align: center;">0.52</td><td style="text-align: center;">0.53</td><td style="text-align: center;">0.83</td><td style="text-align: center;">0.85</td></tr>
<tr><td style="text-align: center;">57</td><td style="text-align: center;">6</td><td style="text-align: center;">2</td><td style="text-align: center;">0.49</td><td style="text-align: center;">0.49</td><td style="text-align: center;">0.83</td><td style="text-align: center;">0.85</td></tr>
<tr><td style="text-align: center;">58</td><td style="text-align: center;">6</td><td style="text-align: center;">3</td><td style="text-align: center;">0.47</td><td style="text-align: center;">0.48</td><td style="text-align: center;">0.82</td><td style="text-align: center;">0.83</td></tr>
<tr><td style="text-align: center;">59</td><td style="text-align: center;">6</td><td style="text-align: center;">5</td><td style="text-align: center;">0.44</td><td style="text-align: center;">0.45</td><td style="text-align: center;">0.79</td><td style="text-align: center;">0.81</td></tr>
<tr><td style="text-align: center;">60</td><td style="text-align: center;">6</td><td style="text-align: center;">6</td><td style="text-align: center;">0.44</td><td style="text-align: center;">0.45</td><td style="text-align: center;">0.80</td><td style="text-align: center;">0.81</td></tr>
<tr><td style="text-align: center;">61</td><td style="text-align: center;">6</td><td style="text-align: center;">7</td><td style="text-align: center;">0.43</td><td style="text-align: center;">0.44</td><td style="text-align: center;">0.78</td><td style="text-align: center;">0.79</td></tr>
<tr><td style="text-align: center;">62</td><td style="text-align: center;">6</td><td style="text-align: center;">8</td><td style="text-align: center;">0.45</td><td style="text-align: center;">0.46</td><td style="text-align: center;">0.76</td><td style="text-align: center;">0.79</td></tr>
<tr><td style="text-align: center;">63</td><td style="text-align: center;">6</td><td style="text-align: center;">9</td><td style="text-align: center;">0.44</td><td style="text-align: center;">0.45</td><td style="text-align: center;">0.77</td><td style="text-align: center;">0.80</td></tr>
<tr><td style="text-align: center;">64</td><td style="text-align: center;">6</td><td style="text-align: center;">10</td><td style="text-align: center;">0.42</td><td style="text-align: center;">0.44</td><td style="text-align: center;">0.73</td><td style="text-align: center;">0.78</td></tr>
<tr><td style="text-align: center;">65</td><td style="text-align: center;">6</td><td style="text-align: center;">15</td><td style="text-align: center;">0.43</td><td style="text-align: center;">0.45</td><td style="text-align: center;">0.74</td><td style="text-align: center;">0.82</td></tr>
<tr><td style="text-align: center;">66</td><td style="text-align: center;">6</td><td style="text-align: center;">20</td><td style="text-align: center;">0.41</td><td style="text-align: center;">0.43</td><td style="text-align: center;">0.70</td><td style="text-align: center;">0.76</td></tr>
</tbody></table>
<br />
When consuming multiple items simultaneously, the importance of spreading consumption out across all days observed becomes increasingly important. This is because daily consumption need be calculated as the sum of goods consumed that each day averaged across the number of days observed. Thus we see that while in Table 1 M2 does very well. In Table 2 M3 and M4 do much better than either M1 or M2 and M4 does slightly better than any other method at approximating total consumption.<br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiXD9GlyR51Ra5cySht5R-uEROwGMcaeofzL9SnqlXrbmn2v7gKA_3y_qLgwkLSUp1W7ebx6PydHSqzS76AfCPo5d0d7aLj7wVm_O4MH3w8NgDtkPe3Z00_FHnrk8HQPx9JkymWj4tvshg/s1600/ConsumptionSpread.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="480" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiXD9GlyR51Ra5cySht5R-uEROwGMcaeofzL9SnqlXrbmn2v7gKA_3y_qLgwkLSUp1W7ebx6PydHSqzS76AfCPo5d0d7aLj7wVm_O4MH3w8NgDtkPe3Z00_FHnrk8HQPx9JkymWj4tvshg/s640/ConsumptionSpread.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 1: Estimator performance given different item consumption spreads. The above values are for the estimator value averaged across between 1 and 6 items consumed with only the first item being at that particular spread value. M is method 1 through 4 described above.</td></tr>
</tbody></table>
It is worth noting that all of the methods underestimate total consumption though M4 does the best at adjusting for the missing data problem.<br />
<br />
There are some things to consider when estimating consumption data in this way. One important thing is that if consumption tends to be for goods consumed over a long period of time then using anything but directly dividing by the period of time expected to be consumed over is going to give some pretty lumpy values.<br />
<br />
For instance, imagine someone buys four liters of oil which they expect to consume over the next 30 days. Sure on average in order to account for the oil not observed for the many other similar people who bought their oil on previous periods you may want to divide the oil not by the thirty days (4L/30days) but by the probably adjustment value equation (3).<br />
<br />
Thus you get (4L/7days). Averaging across four similar people who did not happen to purchase oil you approximate the population consumption level. (1L/7days*1/4=1/28). Thus on average for the population estimate, you are pretty close. However for that one guy in your data you now have one person who looks like they are consuming 4/7 of a liter of oil per day.<br />
<br />
When screening your data for outliers this oil consumption positively pops out of the page at you. So you figure it is some kind of recording error and replace it using population estimates.<br />
<br />
But the problem here is entirely created by the method used to infer consumption levels. If instead you had taken the consumer at his/her reported level and said that average consumption for that individual is 4L/30days or 2/15 liters per day then you would never need to substitute out this particular outlier because it would not exist in the data in the first place. <br />
<br />
If you would like to review the R simulation used to generate these results you can find <a href="https://gist.github.com/EconometricsBySimulation/861ee0e81909b9cc1bd9ca4b14c2dbc7" target="_blank">it here</a>.</div>
Francishttp://www.blogger.com/profile/16658586705916884436noreply@blogger.com0tag:blogger.com,1999:blog-6288862798546085706.post-999453664637131792016-02-18T15:31:00.000-05:002017-07-10T18:02:55.972-04:00Legally Rig An Election: A Citizen's Guide to Gerrymandering<div dir="ltr" style="text-align: left;" trbidi="on">
You are running for class president against a pimpled-nosed, blond
barbarian. You have given your best speech and your obnoxious opponent
has given his best speech. The teacher is about to call on the class to
vote! The time of reckoning is upon you.<br />
<br />
As she is just
announcing a hand raising in support of your opponent, you count in
your head: three of your friends clearly in favor of you, three of your
opponents friends, and three undecided classmates in the middle, each
with a 50% chance roughly of voting for you.<br />
<br />
If the
vote is held now it will all be up to those three undecided/independent
voters who gets elected. But wait! You have an idea, you shout out!
"Wait wait! I have a <i>fun </i>idea. How about we vote in three groups of three? The winner of the most groups wins the election", you suggest.<br />
<br />
The teacher, unaware of your wiley ways, shrugs.<br />
<br />
You act quickly to divide the room into three groups of three.<br />
1. All three of your opponents friends you place in one group.<br />
2. Two of your friends you place in another group with one undecided.<br />
3. The remaining friend you place with the two remaining undecided.<br />
<br />
You
signal happily to the teacher, now you are ready for the votes to be
cast. Remember, previously, you calculated the chance of winning as
50-50. Now, you calculate the chance of winning as 75%<br />
<br />
Really?<br />
<br />
Well, let's count the new probable outcomes for each voting group/district.<br />
1. The group with all of your opponent's friends will vote for him.<br />
2. The group with two of your friends will 50% vote 3/3 for you and 50% vote 2/3 for you which means they will go for you.<br />
3.
The final group with one of your friends and two undecided is where the
action is. You know your friend will vote for you. So there are two
remaining random votes. There is a 25% chance they will both vote for
you so you get 3/3 making you win. There is also a 50% change only one
of them will vote for you 2/3 making you win. Thus there is only one
outcome remaining in which you lose. That is if both undecided voters
vote against you. This only happens 25% of the time (50% x 50%).<br />
<br />
From
this voting system you may have noticed something. By grouping
classmates in this way, it is possible to win the class election without
getting the majority of the votes. To see this, let's imagine the
independent in group 2 votes against you and one of the independents in
group 3. The total votes against you is 5 while the votes for you are 4.
But because you carefully constructed the groups. You win two groups
out of three and still win the election.<br />
<br />
At this point, the teacher would not be happy but it is what she agreed to so...tough luck!<br />
<br />
So how did this happen?<br />
<br />
There
is a few ways to look at this. One is that before Gerrymandering
(regrouping into districts) you had three people who could vote against
you. Now, you have stuck one of those voters with two sympathetic voters
causing that vote to no longer count. All that remains is two
voters who both need to vote against you in order to counteract the
effect having your friend in Group 3.<br />
<br />
This ideal of
rigging a class election may seem absurd but it is exactly the kind of
thing establishment figure do when they rewrite voting district lines to
include or exclude groups depending upon how they affect the likely
voting outcome.<br />
<br />
Redistricting though often involves the votes of thousands of people. The concept though is the same.<br />
<br />
I
have written a small simulation showing how effective Gerrymandering
can be on slightly larger scales. Within the simulation I set up 10
voting districts. In each of these districts there are 40 voters. Each
district goes to whoever wins the most votes within that district. A total win is calculated by whoever wins the most districts.<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg4LxxLzABUiTFkGQCmHRKFYjbTMhlJc1TvgeOXVZxnM1pjuLB1iYZLiGr4lgbTA_ptN3e4tMIiq2uHskTYTsoMBB_5jotSnhJr6VOimnI0ajcW_vO9usRtEF98DAO87_X0lMCg33_Axmg/s1600/2016-18-GerryManderingD0.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="560" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg4LxxLzABUiTFkGQCmHRKFYjbTMhlJc1TvgeOXVZxnM1pjuLB1iYZLiGr4lgbTA_ptN3e4tMIiq2uHskTYTsoMBB_5jotSnhJr6VOimnI0ajcW_vO9usRtEF98DAO87_X0lMCg33_Axmg/s640/2016-18-GerryManderingD0.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 1: A grid display of 400 voters when there is no Gerrymandering. Each square represents a different voter. Lighter colored squares have a higher likelihood of voting for you. Darker colored squares have a higher likelihood of voting against you.</td></tr>
</tbody></table>
Looking at Figure 1, we see that without Gerrymandering there are naturally some districts that seem more likely to vote for us and some that seem less. The method of gerrymandering I propose in order to try to increase the likelihood of us winning is a simple method of reorganizing the vote. First we sort all of the individuals by likelihood of voting for us. Next we group those who are the least likely to vote for us into "Gerrymandered districts". The rest we distribute randomly. Of course we should not really be calling any district in particular Gerrymandered because really the whole population has been Gerrymandered.<br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg8JS3lT75AI_Tc2138mOEq4W00xJPelOjgJ6Aoky37OgqV60-_gWQo_CBeafhbn-0xEA8wcg_J7b0nQhKfCvOBVp4i1lL3CJPkPqawxinp3NBaw1pASKKtcDdv3xCU30Lu6q5rG7jT-00/s1600/2016-18-GerryManderingD2.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="560" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg8JS3lT75AI_Tc2138mOEq4W00xJPelOjgJ6Aoky37OgqV60-_gWQo_CBeafhbn-0xEA8wcg_J7b0nQhKfCvOBVp4i1lL3CJPkPqawxinp3NBaw1pASKKtcDdv3xCU30Lu6q5rG7jT-00/s640/2016-18-GerryManderingD2.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 1: A grid display of 400 voters where the first two districts have been "Gerrymandered".
Each square represents a different voter. Lighter colored squares have a
higher likelihood of voting for you. Darker colored squares have a
higher likelihood of voting against you.</td></tr>
</tbody></table>
Using this simple method of Gerrymandering for two districts, we can see extreme changes in likely voting outcomes for Districts 1 and 2 (Figure 2). What is less easy to observe but even more important is the subtle changes in Districts 3 through 10. Compared with Figure 1, these districts have now lost the voters previously much more likely to vote against you. This makes each of these 7 districts slightly more likely to vote for you.<br />
<div class="separator" style="clear: both; text-align: center;">
</div>
<div class="separator" style="clear: both; text-align: center;">
</div>
<br />
The net affect is a certain loss in Districts 1 and 2 but a better than prior outcome in the remaining districts (you actually almost always win in this scenario if the popular vote is split 50-50). In order to calculate expected outcomes, I repeat the simulation 200 different times under each voter preference scenario (lean) and gerrymandering scenario and average the number of wins across simulations.<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi-CDgZRVhl1BIkZF3dsV8YuhYaPwr4qLpvqkZ0xwgyQ7wPqbskRIN-GPb_8phFMhjCWkwUymL6eOXIrdnTtHqhFWj1PP0bHhaTea8aZou5vmAyLqtQpZH_jtw9rhh9v0HkNZ5pKvuGKi4/s1600/2016-18-GerryMandering.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="394" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi-CDgZRVhl1BIkZF3dsV8YuhYaPwr4qLpvqkZ0xwgyQ7wPqbskRIN-GPb_8phFMhjCWkwUymL6eOXIrdnTtHqhFWj1PP0bHhaTea8aZou5vmAyLqtQpZH_jtw9rhh9v0HkNZ5pKvuGKi4/s640/2016-18-GerryMandering.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 3: Within each number of districts Gerrymandered outcomes are simulated for 200 simulation runs. The orange line that crosses the 50% mark at 0 indicates that this is the expected outcome if there is no Gerrymandering happening. </td></tr>
</tbody></table>
From Figure 3 we begin to see how effective gerrymandering can be on the likelihood of winning. By using our method to gerrymander districts we seem to gain about 4 percentage points for each district we gerrymander up until we have four districts "gerrymandered". At the most favorable outcome, when we have gerrymandered four districts, we have effectively gained a 16 point lead against our rival. This means the popular vote could be 58-42 in favor of our rival and we could still win the outcome about half the time.<br />
<br />
Something interesting happens at the fifth district gerrymandered. We have now gerrymandered half of the districts. At this last step we now are penalized for gerrymandering by 5 points. I do not have an easy explanation at this time. <br />
<b><br /></b>
<b>Conclusion</b><br />
In reality the practice of gerrymandering is much more complicated and subtle than this. There are typically restrictions on how you can group individuals, usually based on geography. Likewise you don't know how individuals are going to vote but you may have a pretty good idea how certain demographics are likely to vote. This complicates the methods. But I am sure there are "social engineering" or "vote engineering" firms out there that are able to exploit some of the strategies outlined here and other strategies in order to maximize the effect of gerrymandering.<br />
<br />
That said, the classroom example and the simulations above capture the essence of gerrymandering. Gerrymandering is the practice of grouping voters together in such a way as to prevent those who are voting against you from having a vote. As such, gerrymandering is an enemy to democracy.<br />
<br />
It is typically used by establishment candidates to insulate themselves from challengers. This allows establishment figures to feel that their seat is safe even when they accept private or political payoffs for voting consistently in ways which are against the good of their constituency.<br />
<br />
(<a href="https://github.com/EconometricsBySimulation/Ninja/blob/master/2016-February/2016-18-GerryMandering.R" target="_blank">Code on Github</a>)</div>
Francishttp://www.blogger.com/profile/16658586705916884436noreply@blogger.com3tag:blogger.com,1999:blog-6288862798546085706.post-39205728487922426772016-01-19T17:16:00.000-05:002016-01-19T17:19:59.628-05:00Who are Turkopticon's Top Contributors?<div dir="ltr" style="text-align: left;" trbidi="on">
In my most recent post "<a href="http://www.econometricsbysimulation.com/2016/01/turkopticon-defender-of-amazons.html" target="_blank">Turkopticon: Defender of Amazon's Anonymous Workforce</a>" I introduced Turkopticon, the social art project designed to provide basic tools for Amazon's massive Mechanical TURK workforce to share information about employers (requesters).<br />
<br />
Turkopticon, has a been a runaway success with nearly 285 thousands reviews submitted by over 17 thousand reviewers since its inception in 2009. Collectively these reviews make up 53 million characters which maps to about 7.6 million words as <a href="https://www.quora.com/Whats-the-average-length-of-English-words" target="_blank">5 letters per average word plus two spaces</a>. <a href="http://www.benjaminrose.com/post/how-long-does-it-take-to-write-100-words/" target="_blank">At 100 words every 7 minutes</a> this represents approximately 371 days collectively spent just writing reviews. It is probably safe to considered this estimation an underestimation.<br />
<br />
So given this massive investment of individuals in writing these reviews, I find myself wanting to ask, "who is investing this kind of energy producing this public good?"<br />
<br />
In general, while there are many contributors, 500 contributors represent 54% of the reviews written. With the top 100 reviewers making up 30% of the reviews written and the top 15 representing 11% of all reviews written.<br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhZeHQbnjmkb3FmSO8FrBN7eqFmLZUkGhNzFmZW7JaIx6pdU5I4uhCQrcepn1AQruYH06SzmDVujVIg5ZyPz_O9sSnru-IlqFkOZ6lvWAlvylNzTx0fzDdvRZ2yZOaALSs1TTeptSnnn-w/s1600/2016-01-Gini.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="393" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhZeHQbnjmkb3FmSO8FrBN7eqFmLZUkGhNzFmZW7JaIx6pdU5I4uhCQrcepn1AQruYH06SzmDVujVIg5ZyPz_O9sSnru-IlqFkOZ6lvWAlvylNzTx0fzDdvRZ2yZOaALSs1TTeptSnnn-w/s640/2016-01-Gini.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 1: Using this graph we can find the Gini coefficient for number of submissions at around 82% indicating that a very few individuals are doing nearly all of the work.</td></tr>
</tbody></table>
Within Turkopticon there is no ranking system for reviwer quality so it is not obvious who are the top contributors and what their reviewing patterns look like. In this article we will examine some general features of the top contributors.<br />
<br />
<b>Table 1</b>: A list of the Top 15 Turkopticon review contributors. Rank is the reviewer rank by number of reviews written. Name is the reviewer's name. Nrev is the number of reviews written. DaysTO is the number of days between the oldest review and the most recent review. Nchar is the average number of characters written in each review. FAIR, FAST, PAY, and COMM are quantitative scales that Turkopticon requests reviewers rank requesters by. Fair indicates how the requester was at either rejecting or failing to reject work. Fast indicates how quickly the requester approved or rejected work. Pay indicates how the reviewer perceived the payment scheme for work was. And Comm refers to communication which indicates, if the worker attempted to communicate with the requester, how well that requester addressed the worker's concerns.<br />
<br />
<table border="0" cellpadding="0" cellspacing="0" style="width: 509px;"><colgroup><col style="width: 48pt;" width="64"></col>
<col style="mso-width-alt: 5632; mso-width-source: userset; width: 119pt;" width="158"></col>
<col style="mso-width-alt: 1280; mso-width-source: userset; width: 27pt;" width="36"></col>
<col style="mso-width-alt: 1848; mso-width-source: userset; width: 39pt;" width="52"></col>
<col style="mso-width-alt: 1507; mso-width-source: userset; width: 32pt;" width="42"></col>
<col span="3" style="mso-width-alt: 1280; mso-width-source: userset; width: 27pt;" width="36"></col>
<col style="mso-width-alt: 1735; mso-width-source: userset; width: 37pt;" width="49"></col>
</colgroup><tbody>
<tr height="19" style="height: 14.4pt;">
<td class="xl66" height="19" style="height: 14.4pt; width: 48pt;" width="64"><div style="-webkit-text-stroke-width: 0px; orphans: auto; text-align: start; widows: auto;">
<div style="margin-right: 0px; overflow: hidden; padding-bottom: 0px; padding-top: 0px;">
</div>
Rank</div>
</td>
<td class="xl66" style="width: 119pt;" width="158"><div style="-webkit-text-stroke-width: 0px; orphans: auto; text-align: start; widows: auto;">
<div style="box-sizing: content-box;">
<div style="margin-right: 12px;">
Name</div>
</div>
</div>
</td>
<td class="xl66" style="width: 27pt;" width="36"><div style="margin-right: 12px;">
Nrev</div>
</td>
<td class="xl66" style="text-align: center; width: 39pt;" width="52"><div style="margin-right: 12px;">
DaysTO</div>
</td>
<td class="xl66" style="text-align: center; width: 32pt;" width="42"><div style="margin-right: 12px;">
Nchar</div>
</td>
<td class="xl66" style="width: 27pt;" width="36"><div style="margin-right: 12px;">
FAIR</div>
</td>
<td class="xl66" style="width: 27pt;" width="36"><div style="margin-right: 12px;">
FAST</div>
</td>
<td class="xl66" style="width: 27pt;" width="36"><div style="margin-right: 12px;">
PAY</div>
</td>
<td class="xl66" style="width: 37pt;" width="49"><div style="margin-right: 12px;">
COMM</div>
</td>
</tr>
<tr height="19" role="row" style="height: 14.4pt;">
<td class="xl67" height="19" style="box-sizing: content-box; height: 14.4pt;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;" title="1">
1</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;" title="bigbytes">
bigbytes</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
5236</div>
</td>
<td class="xl68" style="box-sizing: content-box; text-align: center;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
294</div>
</td>
<td class="xl68" style="box-sizing: content-box; text-align: center;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
219</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
4.89</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
4.99</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
2.74</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
3.26</div>
</td>
</tr>
<tr height="19" role="row" style="height: 14.4pt;">
<td class="xl67" height="19" style="box-sizing: content-box; height: 14.4pt;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;" title="2">
2</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;" title="kimadagem">
kimadagem</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
3732</div>
</td>
<td class="xl68" style="box-sizing: content-box; text-align: center;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
327</div>
</td>
<td class="xl68" style="box-sizing: content-box; text-align: center;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
490</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
4.98</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
4.95</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
3.23</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
2.45</div>
</td>
</tr>
<tr height="19" role="row" style="height: 14.4pt;">
<td class="xl67" height="19" style="box-sizing: content-box; height: 14.4pt;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;" title="3">
3</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;" title="worry">
worry</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
2637</div>
</td>
<td class="xl68" style="box-sizing: content-box; text-align: center;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
649</div>
</td>
<td class="xl68" style="box-sizing: content-box; text-align: center;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
186</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
4.97</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
4.87</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
3.29</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
3.84</div>
</td>
</tr>
<tr height="19" role="row" style="height: 14.4pt;">
<td class="xl67" height="19" style="box-sizing: content-box; height: 14.4pt;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;" title="4">
4</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;" title="jmbus...@h...">
jmbus...@h...</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
2539</div>
</td>
<td class="xl68" style="box-sizing: content-box; text-align: center;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
538</div>
</td>
<td class="xl68" style="box-sizing: content-box; text-align: center;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
110</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
3.10</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
3.05</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
3.08</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
1.55</div>
</td>
</tr>
<tr height="19" role="row" style="height: 14.4pt;">
<td class="xl67" height="19" style="box-sizing: content-box; height: 14.4pt;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;" title="5">
5</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;" title="surve...@h...">
surve...@h...</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
2488</div>
</td>
<td class="xl68" style="box-sizing: content-box; text-align: center;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
177</div>
</td>
<td class="xl68" style="box-sizing: content-box; text-align: center;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
344</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
4.85</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
4.77</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
4.13</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
4.27</div>
</td>
</tr>
<tr height="19" role="row" style="height: 14.4pt;">
<td class="xl67" height="19" style="box-sizing: content-box; height: 14.4pt;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;" title="6">
6</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;" title="jaso...@h...">
jaso...@h...</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
2100</div>
</td>
<td class="xl68" style="box-sizing: content-box; text-align: center;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
260</div>
</td>
<td class="xl68" style="box-sizing: content-box; text-align: center;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
78</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
4.98</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
4.90</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
4.78</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
4.73</div>
</td>
</tr>
<tr height="19" role="row" style="height: 14.4pt;">
<td class="xl67" height="19" style="box-sizing: content-box; height: 14.4pt;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;" title="7">
7</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;" title="shiver">
shiver</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
1721</div>
</td>
<td class="xl68" style="box-sizing: content-box; text-align: center;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
303</div>
</td>
<td class="xl68" style="box-sizing: content-box; text-align: center;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
139</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
4.94</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
4.89</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
4.44</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
3.81</div>
</td>
</tr>
<tr height="19" role="row" style="height: 14.4pt;">
<td class="xl67" height="19" style="box-sizing: content-box; height: 14.4pt;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;" title="8">
8</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;" title="Thom Burr">
Thom Burr</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
1594</div>
</td>
<td class="xl68" style="box-sizing: content-box; text-align: center;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
434</div>
</td>
<td class="xl68" style="box-sizing: content-box; text-align: center;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
288</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
4.69</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
4.81</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
4.54</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
3.52</div>
</td>
</tr>
<tr height="19" role="row" style="height: 14.4pt;">
<td class="xl67" height="19" style="box-sizing: content-box; height: 14.4pt;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;" title="9">
9</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;" title="jessema...@g...">
jessema...@g...</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
1539</div>
</td>
<td class="xl68" style="box-sizing: content-box; text-align: center;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
467</div>
</td>
<td class="xl68" style="box-sizing: content-box; text-align: center;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
157</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
4.96</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
4.70</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
3.64</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
4.00</div>
</td>
</tr>
<tr height="19" role="row" style="height: 14.4pt;">
<td class="xl67" height="19" style="box-sizing: content-box; height: 14.4pt;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;" title="10">
10</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;" title="absin...@y...">
absin...@y...</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
1320</div>
</td>
<td class="xl68" style="box-sizing: content-box; text-align: center;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
309</div>
</td>
<td class="xl68" style="box-sizing: content-box; text-align: center;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
75</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
4.97</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
4.91</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
3.99</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
3.78</div>
</td>
</tr>
<tr height="19" role="row" style="height: 14.4pt;">
<td class="xl67" height="19" style="box-sizing: content-box; height: 14.4pt;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;" title="11">
11</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;" title="Rosey">
Rosey</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
1313</div>
</td>
<td class="xl68" style="box-sizing: content-box; text-align: center;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
634</div>
</td>
<td class="xl68" style="box-sizing: content-box; text-align: center;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
101</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
4.80</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
4.76</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
4.35</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
4.18</div>
</td>
</tr>
<tr height="19" role="row" style="height: 14.4pt;">
<td class="xl67" height="19" style="box-sizing: content-box; height: 14.4pt;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;" title="12">
12</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;" title="CaliBboy">
CaliBboy</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
1281</div>
</td>
<td class="xl68" style="box-sizing: content-box; text-align: center;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
83</div>
</td>
<td class="xl68" style="box-sizing: content-box; text-align: center;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
201</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
4.02</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
4.07</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
2.71</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
3.84</div>
</td>
</tr>
<tr height="19" role="row" style="height: 14.4pt;">
<td class="xl67" height="19" style="box-sizing: content-box; height: 14.4pt;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;" title="13">
13</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;" title="ptosis">
ptosis</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
1278</div>
</td>
<td class="xl68" style="box-sizing: content-box; text-align: center;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
367</div>
</td>
<td class="xl68" style="box-sizing: content-box; text-align: center;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
110</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
3.00</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
3.04</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
2.89</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
3.29</div>
</td>
</tr>
<tr height="19" role="row" style="height: 14.4pt;">
<td class="xl67" height="19" style="box-sizing: content-box; height: 14.4pt;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;" title="14">
14</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;" title="NurseRachet (moderator)">
NurseRachet (moderator)</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
1274</div>
</td>
<td class="xl68" style="box-sizing: content-box; text-align: center;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
669</div>
</td>
<td class="xl68" style="box-sizing: content-box; text-align: center;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
351</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
4.76</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
4.70</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
3.91</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
3.72</div>
</td>
</tr>
<tr height="19" role="row" style="height: 14.4pt;">
<td class="xl67" height="19" style="box-sizing: content-box; height: 14.4pt;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;" title="15">
15</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;" title="TdgEsaka">
TdgEsaka</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
1234</div>
</td>
<td class="xl68" style="box-sizing: content-box; text-align: center;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
523</div>
</td>
<td class="xl68" style="box-sizing: content-box; text-align: center;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
258</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
4.75</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
4.81</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
3.73</div>
</td>
<td class="xl67" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
3.00</div>
</td>
</tr>
</tbody></table>
<br />
Find the full list as a <a href="https://docs.google.com/spreadsheets/d/1NhLc4aJ42sEWYvx_nHkRpXMBeFF_7WyXOnHb00FgKzU/edit?usp=sharing" target="_blank">google document here (First Tab)</a>.<br />
<br />
From Table 1 we can see that all of the top 15 reviewers have contributed over 1,200 reviews with bibytes being the most prolific reviewer contributing over 52 hundred. In terms of the reviewer active on Turkopticon the longest, NurseRachet (a forum moderator) has been on the longest followed by worry and Rosey. In terms of the longest winded kimadagem has the longest average character count per review at 490 characters or approximately 70 words per review while CaliBboy has the shortest reviews at only 75 characters or around 10 words.<br />
<br />
In terms of the averages the four rating scales there is a fair bit of diversity between the top reviewers with jaso...@h.. having the highest average score between the four scales of 4.8 and jmbus...@h... having the lowest average scores, around 2.7 followed by ptosis with a average a tiny bit higher than 3. <br />
<br />
So now we have a pretty good idea of what in general the top contributors to Turkopticon look like. <br />
<br />
But what of the quality of the contributions?<br />
<br />
In order to understand what a quality contribution in Turkopticon looks like we must consider the standards that the community has come up with after years of trial and error.<br />
1. The four different scales should be distinct categories. That is a high pay rate should not cause someone to automatically rank a high Fairness or visa versa.<br />
2. To this end what is referred as 1-Bombs an attempt to artificially drop a requesters score by ranking all scales 1 should be avoided. Similarly, 5-Bombs should also be avoided.<br />
3. Within Turkopticon there is also the ability to flag reviews as problematic. If one of your reviews is flagged, it means someone has a problem with it.<br />
4. In general we would like reviews to be approached with a level head so that reviewers write independent reviews rather than ones based on their current mood.<br />
5. Finally, in general we would like reviewers to review as many categories as they can when writing reviews.<br />
<br />
<b>Variables</b><br />
From these 5 guidelines, I will attempt to generate variables that measure each of these targets.<br />
1. For different scales I will focus on the relationship between pay and the other three scales for individual requesters (FairPay, FastPay, and CommPay for the correlations between Fair, Fast, and Comm with pay respectively). The reason I focus on Pay is that it seems to be the scale often times that concerns Mturk workers the most.<br />
<br />
Table 2: For reviewers the average correlation between Pay and other scales. <br />
<table border="0" cellpadding="0" cellspacing="0" style="width: 281px;"><colgroup><col style="mso-width-alt: 2844; mso-width-source: userset; width: 60pt;" width="80"></col>
<col span="3" style="mso-width-alt: 2389; mso-width-source: userset; width: 50pt;" width="67"></col>
</colgroup><tbody>
<tr height="19" style="height: 14.4pt;">
<td class="xl65" height="19" style="height: 14.4pt; width: 60pt;" width="80"><div style="margin-right: 0px; overflow: hidden; padding-bottom: 0px; padding-top: 0px;">
</div>
</td>
<td class="xl65" style="width: 50pt;" width="67"><div style="margin-right: 12px;">
<div style="box-sizing: content-box;">
<div style="-webkit-text-stroke-width: 0px; orphans: auto; text-align: start; widows: auto;">
ALL</div>
</div>
</div>
</td>
<td class="xl65" style="width: 50pt;" width="67"><div style="margin-right: 12px;">
Top 100</div>
</td>
<td class="xl65" style="width: 50pt;" width="67"><div style="margin-right: 12px;">
Top 15</div>
</td>
</tr>
<tr height="19" style="height: 14.4pt;">
<td class="xl65" height="19" style="height: 14.4pt;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;" title="FAIRPAY">
FAIRPAY</div>
</td>
<td class="xl65"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
0.80</div>
</td>
<td class="xl65"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
0.56</div>
</td>
<td class="xl65"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
0.44</div>
</td>
</tr>
<tr height="19" style="height: 14.4pt;">
<td class="xl65" height="19" style="height: 14.4pt;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;" title="FASTPAY">
FASTPAY</div>
</td>
<td class="xl65"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
0.73</div>
</td>
<td class="xl65"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
0.48</div>
</td>
<td class="xl65"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
0.37</div>
</td>
</tr>
<tr height="19" style="height: 14.4pt;">
<td class="xl65" height="19" style="height: 14.4pt;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;" title="COMMPAY">
COMMPAY </div>
</td>
<td class="xl65"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
0.81</div>
</td>
<td class="xl65"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
0.67</div>
</td>
<td class="xl65"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
0.61</div>
</td>
</tr>
</tbody></table>
<br />
From Table 2 we can see that the average reviewer has a very strong positive correlation between Pay and the other scales with FAIR, FAST, and COMM in the .73-.81 range. In contrast the Top 100 and especially the Top 15 all have much lower correlations. We should not necessarily hope for a zero correlation between these factors since one might expect a requester who pays too low might also act unfairly, not respond quickly to submissions, or have poor communication habits.<br />
<br />
2. 1-Bombs and 5-Bombs are easy to observe in the data in terms of all 1s or all 5s. However, it is worth noting that all of either 1s or 5s might actually be a valid review given the circumstances. Variables 1Bomb and 5Bomb will be a variable measuring the likelihood that an individuals review will be either of the two categories.<br />
<br />
3. Flags are also a variable that can be directly observed. Multiple flags can be featured on a single review. The highest flag hit in my data has 17 flags. The variable FLAG is the average/expected number of flags for an individual reviewer's reviews.<br />
<br />
Table 3: The prevalence rates of 1-Bombs, 5-Bombs, and Flags.<br />
<table border="0" cellpadding="0" cellspacing="0" style="width: 324px;"><colgroup><col span="4" style="mso-width-alt: 2872; mso-width-source: userset; width: 61pt;" width="81"></col>
</colgroup><tbody>
<tr height="19" style="height: 14.4pt;">
<td class="xl65" height="19" style="height: 14.4pt; width: 61pt;" width="81"><div style="-webkit-text-stroke-width: 0px; orphans: auto; text-align: start; widows: auto;">
<div style="margin-right: 0px; overflow: hidden; padding-bottom: 0px; padding-top: 0px;">
</div>
</div>
</td>
<td class="xl65" style="width: 61pt;" width="81"><div style="-webkit-text-stroke-width: 0px; orphans: auto; text-align: start; widows: auto;">
<div style="box-sizing: content-box;">
<div style="margin-right: 12px;">
ALL</div>
</div>
</div>
</td>
<td class="xl65" style="width: 61pt;" width="81"><div style="margin-right: 12px;">
Top 100</div>
</td>
<td class="xl65" style="width: 61pt;" width="81"><div style="margin-right: 12px;">
Top 15</div>
</td>
</tr>
<tr height="19" role="row" style="height: 14.4pt;">
<td class="xl65" height="19" style="box-sizing: content-box; height: 14.4pt;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;" title="ONEBOMB">
1BOMB<span style="mso-spacerun: yes;"> </span></div>
</td>
<td class="xl65" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
0.192</div>
</td>
<td class="xl65" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
0.038</div>
</td>
<td class="xl65" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
0.019</div>
</td>
</tr>
<tr height="19" role="row" style="height: 14.4pt;">
<td class="xl65" height="19" style="box-sizing: content-box; height: 14.4pt;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;" title="FIVEBOMB">
5BOMB<span style="mso-spacerun: yes;"> </span></div>
</td>
<td class="xl65" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
0.179</div>
</td>
<td class="xl65" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
0.049</div>
</td>
<td class="xl65" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
0.025</div>
</td>
</tr>
<tr height="19" role="row" style="height: 14.4pt;">
<td class="xl65" height="19" style="box-sizing: content-box; height: 14.4pt;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;" title="flags">
FLAGS</div>
</td>
<td class="xl65" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
0.014</div>
</td>
<td class="xl65" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
0.005</div>
</td>
<td class="xl65" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
0.005</div>
</td>
</tr>
</tbody></table>
<br />
From Table 3 we can see the prevalence rates of 1-Bombs, 5-Bombs, and Flags is much
higher among the general reviewers than that of the Top 100 and
especially among the top 15. <br />
<br />
4. In order to attempt to measure "level-headedness" I will just look at how reviews trend from a rating perspective. That is, is the value of the current review correlated (either positively or negatively) with the value of the next review?<br />
<br />
Table 4: The auto-regressive one step correlation between review levels. In this case the "ALL" category only includes the 3,700 reviewers who have written more than 10 reviews.<br />
<br />
<div style="margin-right: 0px; overflow: hidden; padding-bottom: 0px; padding-top: 0px;">
</div>
<table border="0" cellpadding="0" cellspacing="0" style="width: 324px;"><colgroup><col span="4" style="mso-width-alt: 2872; mso-width-source: userset; width: 61pt;" width="81"></col>
</colgroup><tbody>
<tr height="19" style="height: 14.4pt;">
<td class="xl65" height="19" style="height: 14.4pt; width: 61pt;" width="81"><div style="-webkit-text-stroke-width: 0px; orphans: auto; text-align: start; widows: auto;">
<div style="margin-right: 0px; overflow: hidden; padding-bottom: 0px; padding-top: 0px;">
</div>
</div>
</td>
<td class="xl65" style="width: 61pt;" width="81"><div style="margin-right: 12px;">
<div style="box-sizing: content-box;">
<div style="-webkit-text-stroke-width: 0px; orphans: auto; text-align: start; widows: auto;">
ALL</div>
</div>
</div>
</td>
<td class="xl65" style="width: 61pt;" width="81"><div style="margin-right: 12px;">
Top 100</div>
</td>
<td class="xl65" style="width: 61pt;" width="81"><div style="margin-right: 12px;">
Top 15</div>
</td>
</tr>
<tr height="19" role="row" style="height: 14.4pt;">
<td class="xl65" height="19" style="box-sizing: content-box; height: 14.4pt;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;" title="FAIRar1">
FAIRar1</div>
</td>
<td class="xl66"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
0.00</div>
</td>
<td class="xl66"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
0.10</div>
</td>
<td class="xl66"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
0.10</div>
</td>
</tr>
<tr height="19" role="row" style="height: 14.4pt;">
<td class="xl65" height="19" style="box-sizing: content-box; height: 14.4pt;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;" title="FASTar1">
FASTar1</div>
</td>
<td class="xl66"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
0.00</div>
</td>
<td class="xl66"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
0.09</div>
</td>
<td class="xl66"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
0.12</div>
</td>
</tr>
<tr height="19" role="row" style="height: 14.4pt;">
<td class="xl65" height="19" style="box-sizing: content-box; height: 14.4pt;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;" title="PAYar1">
PAYar1</div>
</td>
<td class="xl66"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
0.02</div>
</td>
<td class="xl66"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
0.10</div>
</td>
<td class="xl66"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
0.07</div>
</td>
</tr>
<tr height="19" role="row" style="height: 14.4pt;">
<td class="xl65" height="19" style="box-sizing: content-box; height: 14.4pt;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;" title="COMMar1">
COMMar1</div>
</td>
<td class="xl66"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
-0.07</div>
</td>
<td class="xl66"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
0.04</div>
</td>
<td class="xl66"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
0.04</div>
</td>
</tr>
</tbody></table>
<br />
<br />
From Table 4 we can see that inter-review correlation is pretty small especially when compared with the correlation between pay and other scales within the same review (Table 2). Interestingly for the average reviewer, there is almost no correlation across reviews. This might be a result of reviewers writing less reviews in general, thus spacing them more widely and therefore less likely to be sequentially influenced by personal psychological trends.<br />
<br />
5. Finally in terms of completeness we can easily measure completeness in terms of how frequently reviews of individual scales were not completed.<br />
<br />
Table 5: The completion rates of individual scales.<br />
<br />
<table border="0" cellpadding="0" cellspacing="0" style="width: 324px;"><colgroup><col span="4" style="mso-width-alt: 2872; mso-width-source: userset; width: 61pt;" width="81"></col>
</colgroup><tbody>
<tr height="19" style="height: 14.4pt;">
<td class="xl65" height="19" style="height: 14.4pt; width: 61pt;" width="81"><div style="-webkit-text-stroke-width: 0px; orphans: auto; text-align: start; widows: auto;">
<div style="margin-right: 0px; overflow: hidden; padding-bottom: 0px; padding-top: 0px;">
</div>
</div>
</td>
<td class="xl65" style="width: 61pt;" width="81"><div style="-webkit-text-stroke-width: 0px; orphans: auto; text-align: start; widows: auto;">
<div style="box-sizing: content-box;">
<div style="margin-right: 12px;">
ALL</div>
</div>
</div>
</td>
<td class="xl65" style="width: 61pt;" width="81"><div style="margin-right: 12px;">
Top 100</div>
</td>
<td class="xl65" style="width: 61pt;" width="81"><div style="margin-right: 12px;">
Top 15</div>
</td>
</tr>
<tr height="19" role="row" style="height: 14.4pt;">
<td class="xl65" height="19" style="box-sizing: content-box; height: 14.4pt;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;" title="FAIRC">
FAIRC</div>
</td>
<td class="xl65" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
0.849</div>
</td>
<td class="xl65" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
0.665</div>
</td>
<td class="xl65" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
0.705</div>
</td>
</tr>
<tr height="19" role="row" style="height: 14.4pt;">
<td class="xl65" height="19" style="box-sizing: content-box; height: 14.4pt;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;" title="FASTC">
FASTC</div>
</td>
<td class="xl65" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
0.825</div>
</td>
<td class="xl65" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
0.651</div>
</td>
<td class="xl65" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
0.695</div>
</td>
</tr>
<tr height="19" role="row" style="height: 14.4pt;">
<td class="xl65" height="19" style="box-sizing: content-box; height: 14.4pt;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;" title="PAYC">
PAYC</div>
</td>
<td class="xl65" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
0.901</div>
</td>
<td class="xl65" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
0.916</div>
</td>
<td class="xl65" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
0.918</div>
</td>
</tr>
<tr height="19" role="row" style="height: 14.4pt;">
<td class="xl65" height="19" style="box-sizing: content-box; height: 14.4pt;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;" title="COMMC">
COMMC</div>
</td>
<td class="xl65" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
0.605</div>
</td>
<td class="xl65" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
0.147</div>
</td>
<td class="xl65" style="box-sizing: content-box;"><div style="max-width: 300px; overflow: hidden; text-overflow: ellipsis;">
0.081</div>
</td>
</tr>
</tbody></table>
<br />
From Table 5 we can see that the completion rates of all scales are more or less equivalent between that of the general reviewers and that of the Top 100 and Top 15 except in the case of COMM. In this case we can see that the top reviewers are much less likely to rate communication.<br />
<b><br /></b>
<b>Constructing A Quality Scale</b><br />
<br />
In order to construct the best scale given our data, we will choose those variables and values that seems to typical of the top 15 most prolific reviewers. From Tables 2 and 3 we can see very distinct differences between the average reviewer and top reviewers. However, for our auto-correlation and completeness rates we see very little differences in general except that the top reviewers are much less likely to rate communication. I can't know exactly why this is the case but I suspect it is a combination of top reviewers avoiding 1-Bombs and 5-Bombs perhaps in combination with top reviewers finding it not typically worth their time to directly communicate with requesters.<br />
<br />
So here is my proposed index using standardized coefficients (x/sd(x)):<br />
ReviewerProblemIndex = 3*Flag + 3*1Bomb + 1/2*5Bomb + <br />
1*FairPay + 1*FastPay + 1*CommPay<br />
<br />
Because we have standardized the coefficients we can read the scalars in front as directly representing the weight of that variable. Flags, I will weight the strongest as they are an indicator that someone in the community has a problem with the review. Next highest rating are 1Bombs which are widely regarded as a serious problem and frequently discussed on the Turkopticon forum.<br />
<br />
5Bombs, FAIRPay, FastPay, and CommPay are also discussed but not considered as important (<a href="https://turkopticon.ucsd.edu/forum/show_post/14" target="_blank">Turkopticon Discuss</a>). I have caused the 5Bombs to be half as important as FairPay, FastPay, and CommPay variables as it seems cruel to penalize someone for being generous with reviews.<br />
<br />
So let's apply our index and see how our top 15 reviewers score!<br />
<br />
Table 6: The top 15 most prolific contributors ranked based on the ReviewerProlemIndex (Index, RPI). IRank is the ranking of reviewers in terms of the RPI. Name is reviewer name. Nrev is the number of reviews written. Rank is the reviewers ranked in terms of number of reviews written. The other variables are described above.<br />
<br />
<table border="0" cellpadding="0" cellspacing="0" style="width: 498px;"><colgroup><col style="mso-width-alt: 938; mso-width-source: userset; width: 20pt;" width="26"></col>
<col style="mso-width-alt: 1422; mso-width-source: userset; width: 30pt;" width="40"></col>
<col style="width: 48pt;" width="64"></col>
<col style="mso-width-alt: 1251; mso-width-source: userset; width: 26pt;" width="35"></col>
<col style="mso-width-alt: 1592; mso-width-source: userset; width: 34pt;" width="45"></col>
<col style="mso-width-alt: 1479; mso-width-source: userset; width: 31pt;" width="42"></col>
<col style="mso-width-alt: 1848; mso-width-source: userset; width: 39pt;" width="52"></col>
<col style="mso-width-alt: 1450; mso-width-source: userset; width: 31pt;" width="41"></col>
<col style="mso-width-alt: 1649; mso-width-source: userset; width: 35pt;" width="46"></col>
<col style="mso-width-alt: 1706; mso-width-source: userset; width: 36pt;" width="48"></col>
<col style="mso-width-alt: 2104; mso-width-source: userset; width: 44pt;" width="59"></col>
</colgroup><tbody>
<tr height="19" style="height: 14.4pt;">
<td height="19" style="height: 14.4pt; text-align: center; width: 20pt;" width="26">IRank<span style="mso-spacerun: yes;"> </span></td>
<td style="text-align: center; width: 30pt;" width="40">Index<span style="mso-spacerun: yes;"> </span></td>
<td style="text-align: center; width: 48pt;" width="64">Name</td>
<td style="text-align: center; width: 26pt;" width="35">Nrev<span style="mso-spacerun: yes;"> </span></td>
<td style="text-align: center; width: 34pt;" width="45">Rank<span style="mso-spacerun: yes;"> </span></td>
<td style="text-align: center; width: 31pt;" width="42">Flag<span style="mso-spacerun: yes;"> </span></td>
<td class="xl67" style="text-align: center; width: 39pt;" width="52">1Bomb <span style="mso-spacerun: yes;"> </span></td>
<td class="xl67" style="text-align: center; width: 31pt;" width="41">5Bomb<span style="mso-spacerun: yes;"> </span></td>
<td class="xl67" style="text-align: center; width: 35pt;" width="46"> FairPay<span style="mso-spacerun: yes;"> </span></td>
<td class="xl67" style="text-align: center; width: 36pt;" width="48"> FastPay <span style="mso-spacerun: yes;"> </span></td>
<td class="xl67" style="text-align: center; width: 44pt;" width="59">CommPay<span style="mso-spacerun: yes;"> </span></td>
</tr>
<tr height="19" style="height: 14.4pt;">
<td class="xl68" height="19" style="height: 14.4pt; text-align: center;">1</td>
<td class="xl69" style="text-align: center;">1.9</td>
<td style="text-align: center;">jessema...@g...</td>
<td style="text-align: center;">1539</td>
<td style="text-align: center;">9</td>
<td class="xl65" style="text-align: center;">0.001</td>
<td class="xl65" style="text-align: center;">0.001</td>
<td class="xl65" style="text-align: center;">0.016</td>
<td class="xl66" style="text-align: center;">0.12</td>
<td class="xl66" style="text-align: center;">0.09</td>
<td class="xl66" style="text-align: center;">0.20</td>
</tr>
<tr height="19" style="height: 14.4pt;">
<td class="xl68" height="19" style="height: 14.4pt; text-align: center;">2</td>
<td class="xl69" style="text-align: center;">2.1</td>
<td style="text-align: center;">kimadagem</td>
<td style="text-align: center;">3732</td>
<td style="text-align: center;">2</td>
<td class="xl65" style="text-align: center;">0.002</td>
<td class="xl65" style="text-align: center;">0.000</td>
<td class="xl65" style="text-align: center;">0.014</td>
<td class="xl66" style="text-align: center;">0.05</td>
<td class="xl66" style="text-align: center;">-0.01</td>
<td class="xl66" style="text-align: center;">0.27</td>
</tr>
<tr height="19" style="height: 14.4pt;">
<td class="xl68" height="19" style="height: 14.4pt; text-align: center;">3</td>
<td class="xl69" style="text-align: center;">3.2</td>
<td style="text-align: center;">worry</td>
<td style="text-align: center;">2637</td>
<td style="text-align: center;">3</td>
<td class="xl65" style="text-align: center;">0.000</td>
<td class="xl65" style="text-align: center;">0.003</td>
<td class="xl65" style="text-align: center;">0.006</td>
<td class="xl66" style="text-align: center;">0.11</td>
<td class="xl66" style="text-align: center;">0.11</td>
<td class="xl66" style="text-align: center;">0.53</td>
</tr>
<tr height="19" style="height: 14.4pt;">
<td class="xl68" height="19" style="height: 14.4pt; text-align: center;">4</td>
<td class="xl69" style="text-align: center;">3.5</td>
<td style="text-align: center;">absin...@y...</td>
<td style="text-align: center;">1320</td>
<td style="text-align: center;">10</td>
<td class="xl65" style="text-align: center;">0.000</td>
<td class="xl65" style="text-align: center;">0.000</td>
<td class="xl65" style="text-align: center;">0.007</td>
<td class="xl66" style="text-align: center;">0.24</td>
<td class="xl66" style="text-align: center;">0.13</td>
<td class="xl66" style="text-align: center;">0.55</td>
</tr>
<tr height="19" style="height: 14.4pt;">
<td class="xl68" height="19" style="height: 14.4pt; text-align: center;">5</td>
<td class="xl69" style="text-align: center;">3.5</td>
<td style="text-align: center;">bigbytes</td>
<td style="text-align: center;">5236</td>
<td style="text-align: center;">1</td>
<td class="xl65" style="text-align: center;">0.001</td>
<td class="xl65" style="text-align: center;">0.000</td>
<td class="xl65" style="text-align: center;">0.007</td>
<td class="xl66" style="text-align: center;">0.20</td>
<td class="xl66" style="text-align: center;">0.04</td>
<td class="xl66" style="text-align: center;">0.54</td>
</tr>
<tr height="19" style="height: 14.4pt;">
<td class="xl68" height="19" style="height: 14.4pt; text-align: center;">6</td>
<td class="xl69" style="text-align: center;">4.0</td>
<td style="text-align: center;">surve...@h...</td>
<td style="text-align: center;">2488</td>
<td style="text-align: center;">5</td>
<td class="xl65" style="text-align: center;">0.001</td>
<td class="xl65" style="text-align: center;">0.001</td>
<td class="xl65" style="text-align: center;">0.008</td>
<td class="xl66" style="text-align: center;">0.32</td>
<td class="xl66" style="text-align: center;">0.29</td>
<td class="xl66" style="text-align: center;">0.34</td>
</tr>
<tr height="19" style="height: 14.4pt;">
<td class="xl68" height="19" style="height: 14.4pt; text-align: center;">7</td>
<td class="xl69" style="text-align: center;">6.4</td>
<td style="text-align: center;">shiver</td>
<td style="text-align: center;">1721</td>
<td style="text-align: center;">7</td>
<td class="xl65" style="text-align: center;">0.001</td>
<td class="xl65" style="text-align: center;">0.005</td>
<td class="xl65" style="text-align: center;">0.015</td>
<td class="xl66" style="text-align: center;">0.50</td>
<td class="xl66" style="text-align: center;">0.33</td>
<td class="xl66" style="text-align: center;">0.76</td>
</tr>
<tr height="19" style="height: 14.4pt;">
<td class="xl68" height="19" style="height: 14.4pt; text-align: center;">8</td>
<td class="xl69" style="text-align: center;">6.6</td>
<td style="text-align: center;">jaso...@h...</td>
<td style="text-align: center;">2100</td>
<td style="text-align: center;">6</td>
<td class="xl65" style="text-align: center;">0.001</td>
<td class="xl65" style="text-align: center;">0.004</td>
<td class="xl65" style="text-align: center;">0.070</td>
<td class="xl66" style="text-align: center;">0.41</td>
<td class="xl66" style="text-align: center;">0.27</td>
<td class="xl66" style="text-align: center;">0.83</td>
</tr>
<tr height="19" style="height: 14.4pt;">
<td class="xl68" height="19" style="height: 14.4pt; text-align: center;">9</td>
<td class="xl69" style="text-align: center;">10.9</td>
<td style="text-align: center;">Thom Burr</td>
<td style="text-align: center;">1594</td>
<td style="text-align: center;">8</td>
<td class="xl65" style="text-align: center;">0.002</td>
<td class="xl65" style="text-align: center;">0.013</td>
<td class="xl65" style="text-align: center;">0.030</td>
<td class="xl66" style="text-align: center;">0.87</td>
<td class="xl66" style="text-align: center;">0.84</td>
<td class="xl66" style="text-align: center;">0.92</td>
</tr>
<tr height="19" style="height: 14.4pt;">
<td class="xl68" height="19" style="height: 14.4pt; text-align: center;">10</td>
<td class="xl69" style="text-align: center;">11.0</td>
<td style="text-align: center;">Rosey</td>
<td style="text-align: center;">1313</td>
<td style="text-align: center;">11</td>
<td class="xl65" style="text-align: center;">0.004</td>
<td class="xl65" style="text-align: center;">0.009</td>
<td class="xl65" style="text-align: center;">0.022</td>
<td class="xl66" style="text-align: center;">0.81</td>
<td class="xl66" style="text-align: center;">0.81</td>
<td class="xl66" style="text-align: center;">0.85</td>
</tr>
<tr height="19" style="height: 14.4pt;">
<td class="xl68" height="19" style="height: 14.4pt; text-align: center;">11</td>
<td class="xl69" style="text-align: center;">12.4</td>
<td style="text-align: center;">NurseRachet (moderator)</td>
<td style="text-align: center;">1274</td>
<td style="text-align: center;">14</td>
<td class="xl65" style="text-align: center;">0.016</td>
<td class="xl65" style="text-align: center;">0.022</td>
<td class="xl65" style="text-align: center;">0.078</td>
<td class="xl66" style="text-align: center;">0.39</td>
<td class="xl66" style="text-align: center;">0.32</td>
<td class="xl66" style="text-align: center;">0.46</td>
</tr>
<tr height="19" style="height: 14.4pt;">
<td class="xl68" height="19" style="height: 14.4pt; text-align: center;">12</td>
<td class="xl69" style="text-align: center;">12.7</td>
<td style="text-align: center;">CaliBboy</td>
<td style="text-align: center;">1281</td>
<td style="text-align: center;">12</td>
<td class="xl65" style="text-align: center;">0.022</td>
<td class="xl65" style="text-align: center;">0.004</td>
<td class="xl65" style="text-align: center;">0.005</td>
<td class="xl66" style="text-align: center;">0.20</td>
<td class="xl66" style="text-align: center;">0.21</td>
<td class="xl66" style="text-align: center;">0.47</td>
</tr>
<tr height="19" style="height: 14.4pt;">
<td class="xl68" height="19" style="height: 14.4pt; text-align: center;">13</td>
<td class="xl69" style="text-align: center;">13.1</td>
<td style="text-align: center;">TdgEsaka</td>
<td style="text-align: center;">1234</td>
<td style="text-align: center;">15</td>
<td class="xl65" style="text-align: center;">0.015</td>
<td class="xl65" style="text-align: center;">0.016</td>
<td class="xl65" style="text-align: center;">0.029</td>
<td class="xl66" style="text-align: center;">0.57</td>
<td class="xl66" style="text-align: center;">0.40</td>
<td class="xl66" style="text-align: center;">0.73</td>
</tr>
<tr height="19" style="height: 14.4pt;">
<td class="xl68" height="19" style="height: 14.4pt; text-align: center;">14</td>
<td class="xl69" style="text-align: center;">13.4</td>
<td style="text-align: center;">ptosis</td>
<td style="text-align: center;">1278</td>
<td style="text-align: center;">13</td>
<td class="xl65" style="text-align: center;">0.009</td>
<td class="xl65" style="text-align: center;">0.039</td>
<td class="xl65" style="text-align: center;">0.034</td>
<td class="xl66" style="text-align: center;">0.80</td>
<td class="xl66" style="text-align: center;">0.78</td>
<td class="xl66" style="text-align: center;">0.73</td>
</tr>
<tr height="19" style="height: 14.4pt;">
<td class="xl68" height="19" style="height: 14.4pt; text-align: center;">15</td>
<td class="xl69" style="text-align: center;">17.2</td>
<td style="text-align: center;">jmbus...@h...</td>
<td style="text-align: center;">2539</td>
<td style="text-align: center;">4</td>
<td class="xl65" style="text-align: center;">0.003</td>
<td class="xl65" style="text-align: center;">0.170</td>
<td class="xl65" style="text-align: center;">0.020</td>
<td class="xl66" style="text-align: center;">0.99</td>
<td class="xl66" style="text-align: center;">0.98</td>
<td class="xl66" style="text-align: center;">0.92</td>
</tr>
</tbody></table>
<br />
From Table 6 we can see that in general the more prolific reviewers also tend to be higher ranked on the RPI with a few exceptions. One exception is "jmbus", despite being the fourth most prolific contributor he/she is ranked at the bottom of the top 15 contributors list. This is likely due to having the highest 1-Bomb rate of the index with 17% of reviews being 1Bombs. His/her reviews also seem to be almost entirely correlated with Pay as FairPay, FastPay, and CommPay are all correlated upwards of 90%.<br />
<br />
Similarly, "jessema" though only being the 9th most prolific reviewer seems to have the highest quality of reviews (slightly ahead of "kimadagem") with very low Flag, 1Bomb, and 5Bomb rates as well as very low correlation between the scales Fair, Fast, and Comm with that of Pay. Interestingly, though both "Thom Burr" and "Rosey" have very high correlation rates between Pay and the other scales, because the have relatively low Flag, 1Bomb, and 5Bomb rates they are ranked near the middle.<br />
<br />
Overall, except for a few exceptions, I am very impressed that the top contributors seem to score so well on the RPI index.<br />
<br />
Table 7: The Top 100 most prolific contributors ranked based on the Reviewer Problem Index (RPI). <br />
<table border="0" cellpadding="0" cellspacing="0" style="width: 564px;"><colgroup><col style="mso-width-alt: 1336; mso-width-source: userset; width: 28pt;" width="38"></col>
<col style="mso-width-alt: 1564; mso-width-source: userset; width: 33pt;" width="44"></col>
<col style="mso-width-alt: 3754; mso-width-source: userset; width: 79pt;" width="106"></col>
<col style="mso-width-alt: 1507; mso-width-source: userset; width: 32pt;" width="42"></col>
<col style="mso-width-alt: 1536; mso-width-source: userset; width: 32pt;" width="43"></col>
<col style="mso-width-alt: 1820; mso-width-source: userset; width: 38pt;" width="51"></col>
<col span="2" style="mso-width-alt: 1905; mso-width-source: userset; width: 40pt;" width="54"></col>
<col span="3" style="mso-width-alt: 1564; mso-width-source: userset; width: 33pt;" width="44"></col>
</colgroup><tbody>
<tr height="38" style="height: 28.8pt;">
<td class="xl68" height="38" style="height: 28.8pt; text-align: center; width: 28pt;" width="38">Rank<span style="mso-spacerun: yes;"> </span></td>
<td class="xl68" style="text-align: center; width: 33pt;" width="44">Index<span style="mso-spacerun: yes;"> </span></td>
<td class="xl68" style="text-align: center; width: 79pt;" width="106">Name</td>
<td class="xl68" style="text-align: center; width: 32pt;" width="42">Nrev<span style="mso-spacerun: yes;"> </span></td>
<td class="xl68" style="text-align: center; width: 32pt;" width="43">Rrank<span style="mso-spacerun: yes;"> </span></td>
<td class="xl68" style="text-align: center; width: 38pt;" width="51">Flag<span style="mso-spacerun: yes;"> </span></td>
<td class="xl68" style="text-align: center; width: 40pt;" width="54">1Bomb </td>
<td class="xl68" style="text-align: center; width: 40pt;" width="54">5Bomb</td>
<td class="xl68" style="text-align: center; width: 33pt;" width="44"> FairPay</td>
<td class="xl68" style="text-align: center; width: 33pt;" width="44"> FastPay </td>
<td class="xl68" style="text-align: center; width: 33pt;" width="44">CommPay</td>
</tr>
<tr height="19" style="height: 14.4pt;">
<td height="19" style="height: 14.4pt; text-align: center;">1</td>
<td class="xl65" style="text-align: center;">-0.13</td>
<td class="xl67" style="text-align: center; width: 79pt;" width="106">seri...@g...</td>
<td style="text-align: center;">488</td>
<td style="text-align: center;">64</td>
<td class="xl66" style="text-align: center;">0.000</td>
<td class="xl66" style="text-align: center;">0.000</td>
<td class="xl66" style="text-align: center;">0.006</td>
<td class="xl65" style="text-align: center;">0.00</td>
<td class="xl65" style="text-align: center;">-0.05</td>
<td class="xl65" style="text-align: center;">0.00</td>
</tr>
<tr height="19" style="height: 14.4pt;">
<td height="19" style="height: 14.4pt; text-align: center;">2</td>
<td class="xl65" style="text-align: center;">1.67</td>
<td class="xl67" style="text-align: center; width: 79pt;" width="106">james...@y...</td>
<td style="text-align: center;">365</td>
<td style="text-align: center;">98</td>
<td class="xl66" style="text-align: center;">0.000</td>
<td class="xl66" style="text-align: center;">0.000</td>
<td class="xl66" style="text-align: center;">0.000</td>
<td class="xl65" style="text-align: center;">0.29</td>
<td class="xl65" style="text-align: center;">0.00</td>
<td class="xl65" style="text-align: center;">0.18</td>
</tr>
<tr height="19" style="height: 14.4pt;">
<td height="19" style="height: 14.4pt; text-align: center;">3</td>
<td class="xl65" style="text-align: center;">1.72</td>
<td class="xl67" style="text-align: center; width: 79pt;" width="106">donn...@o...</td>
<td style="text-align: center;">1064</td>
<td style="text-align: center;">23</td>
<td class="xl66" style="text-align: center;">0.001</td>
<td class="xl66" style="text-align: center;">0.000</td>
<td class="xl66" style="text-align: center;">0.006</td>
<td class="xl65" style="text-align: center;">0.04</td>
<td class="xl65" style="text-align: center;">0.04</td>
<td class="xl65" style="text-align: center;">0.27</td>
</tr>
<tr height="19" style="height: 14.4pt;">
<td height="19" style="height: 14.4pt; text-align: center;">4</td>
<td class="xl65" style="text-align: center;">1.85</td>
<td class="xl67" style="text-align: center; width: 79pt;" width="106">jessema...@g...</td>
<td style="text-align: center;">1539</td>
<td style="text-align: center;">9</td>
<td class="xl66" style="text-align: center;">0.001</td>
<td class="xl66" style="text-align: center;">0.001</td>
<td class="xl66" style="text-align: center;">0.016</td>
<td class="xl65" style="text-align: center;">0.12</td>
<td class="xl65" style="text-align: center;">0.09</td>
<td class="xl65" style="text-align: center;">0.20</td>
</tr>
<tr height="19" style="height: 14.4pt;">
<td height="19" style="height: 14.4pt; text-align: center;">5</td>
<td class="xl65" style="text-align: center;">1.94</td>
<td class="xl67" style="text-align: center; width: 79pt;" width="106">iwashere</td>
<td style="text-align: center;">689</td>
<td style="text-align: center;">44</td>
<td class="xl66" style="text-align: center;">0.003</td>
<td class="xl66" style="text-align: center;">0.000</td>
<td class="xl66" style="text-align: center;">0.017</td>
<td class="xl65" style="text-align: center;">0.00</td>
<td class="xl65" style="text-align: center;">0.05</td>
<td class="xl65" style="text-align: center;">0.12</td>
</tr>
<tr height="19" style="height: 14.4pt;">
<td height="19" style="height: 14.4pt; text-align: center;">6</td>
<td class="xl65" style="text-align: center;">2.03</td>
<td class="xl67" style="text-align: center; width: 79pt;" width="106">kimadagem</td>
<td style="text-align: center;">3732</td>
<td style="text-align: center;">2</td>
<td class="xl66" style="text-align: center;">0.002</td>
<td class="xl66" style="text-align: center;">0.000</td>
<td class="xl66" style="text-align: center;">0.014</td>
<td class="xl65" style="text-align: center;">0.05</td>
<td class="xl65" style="text-align: center;">-0.01</td>
<td class="xl65" style="text-align: center;">0.27</td>
</tr>
<tr height="19" style="height: 14.4pt;">
<td height="19" style="height: 14.4pt; text-align: center;">7</td>
<td class="xl65" style="text-align: center;">2.06</td>
<td class="xl67" style="text-align: center; width: 79pt;" width="106">mmhb...@y...</td>
<td style="text-align: center;">422</td>
<td style="text-align: center;">79</td>
<td class="xl66" style="text-align: center;">0.005</td>
<td class="xl66" style="text-align: center;">0.000</td>
<td class="xl66" style="text-align: center;">0.009</td>
<td class="xl65" style="text-align: center;">0.00</td>
<td class="xl65" style="text-align: center;">0.00</td>
<td class="xl65" style="text-align: center;">0.00</td>
</tr>
<tr height="19" style="height: 14.4pt;">
<td height="19" style="height: 14.4pt; text-align: center;">8</td>
<td class="xl65" style="text-align: center;">2.21</td>
<td class="xl67" style="text-align: center; width: 79pt;" width="106">aristotle...@g...</td>
<td style="text-align: center;">579</td>
<td style="text-align: center;">51</td>
<td class="xl66" style="text-align: center;">0.002</td>
<td class="xl66" style="text-align: center;">0.000</td>
<td class="xl66" style="text-align: center;">0.010</td>
<td class="xl65" style="text-align: center;">0.10</td>
<td class="xl65" style="text-align: center;">0.11</td>
<td class="xl65" style="text-align: center;">0.19</td>
</tr>
<tr height="19" style="height: 14.4pt;">
<td height="19" style="height: 14.4pt; text-align: center;">9</td>
<td class="xl65" style="text-align: center;">2.90</td>
<td class="xl67" style="text-align: center; width: 79pt;" width="106">Kafei</td>
<td style="text-align: center;">561</td>
<td style="text-align: center;">55</td>
<td class="xl66" style="text-align: center;">0.002</td>
<td class="xl66" style="text-align: center;">0.000</td>
<td class="xl66" style="text-align: center;">0.027</td>
<td class="xl65" style="text-align: center;">0.16</td>
<td class="xl65" style="text-align: center;">0.13</td>
<td class="xl65" style="text-align: center;">0.27</td>
</tr>
<tr height="19" style="height: 14.4pt;">
<td height="19" style="height: 14.4pt; text-align: center;">10</td>
<td class="xl65" style="text-align: center;">2.93</td>
<td class="xl67" style="text-align: center; width: 79pt;" width="106">turtledove</td>
<td style="text-align: center;">1188</td>
<td style="text-align: center;">19</td>
<td class="xl66" style="text-align: center;">0.001</td>
<td class="xl66" style="text-align: center;">0.000</td>
<td class="xl66" style="text-align: center;">0.012</td>
<td class="xl65" style="text-align: center;">0.32</td>
<td class="xl65" style="text-align: center;">0.04</td>
<td class="xl65" style="text-align: center;">0.34</td>
</tr>
<tr height="19" style="height: 14.4pt;">
<td height="19" style="height: 14.4pt; text-align: center;">…</td>
<td class="xl65" style="text-align: center;">…</td>
<td class="xl67" style="text-align: center; width: 79pt;" width="106">…</td>
<td style="text-align: center;">…</td>
<td style="text-align: center;">…</td>
<td style="text-align: center;">…</td>
<td style="text-align: center;">…</td>
<td style="text-align: center;">…</td>
<td style="text-align: center;">…</td>
<td style="text-align: center;">…</td>
<td style="text-align: center;">…</td>
</tr>
<tr height="19" style="height: 14.4pt;">
<td height="19" style="height: 14.4pt; text-align: center;">90</td>
<td class="xl65" style="text-align: center;">15.28</td>
<td class="xl67" style="text-align: center; width: 79pt;" width="106">Anthony99</td>
<td style="text-align: center;">571</td>
<td style="text-align: center;">53</td>
<td class="xl66" style="text-align: center;">0.005</td>
<td class="xl66" style="text-align: center;">0.014</td>
<td class="xl66" style="text-align: center;">0.391</td>
<td class="xl65" style="text-align: center;">1.00</td>
<td class="xl65" style="text-align: center;">1.00</td>
<td class="xl65" style="text-align: center;">1.00</td>
</tr>
<tr height="19" style="height: 14.4pt;">
<td height="19" style="height: 14.4pt; text-align: center;">91</td>
<td class="xl65" style="text-align: center;">15.83</td>
<td class="xl67" style="text-align: center; width: 79pt;" width="106">cwwi...@g...</td>
<td style="text-align: center;">543</td>
<td style="text-align: center;">57</td>
<td class="xl66" style="text-align: center;">0.011</td>
<td class="xl66" style="text-align: center;">0.070</td>
<td class="xl66" style="text-align: center;">0.026</td>
<td class="xl65" style="text-align: center;">0.84</td>
<td class="xl65" style="text-align: center;">0.85</td>
<td class="xl65" style="text-align: center;">0.84</td>
</tr>
<tr height="19" style="height: 14.4pt;">
<td height="19" style="height: 14.4pt; text-align: center;">92</td>
<td class="xl65" style="text-align: center;">16.25</td>
<td class="xl67" style="text-align: center; width: 79pt;" width="106">rand...@g...</td>
<td style="text-align: center;">490</td>
<td style="text-align: center;">63</td>
<td class="xl66" style="text-align: center;">0.002</td>
<td class="xl66" style="text-align: center;">0.157</td>
<td class="xl66" style="text-align: center;">0.051</td>
<td class="xl65" style="text-align: center;">0.97</td>
<td class="xl65" style="text-align: center;">0.97</td>
<td class="xl65" style="text-align: center;">0.99</td>
</tr>
<tr height="19" style="height: 14.4pt;">
<td height="19" style="height: 14.4pt; text-align: center;">93</td>
<td class="xl65" style="text-align: center;">16.76</td>
<td class="xl67" style="text-align: center; width: 79pt;" width="106">trudyh...@c...</td>
<td style="text-align: center;">378</td>
<td style="text-align: center;">95</td>
<td class="xl66" style="text-align: center;">0.008</td>
<td class="xl66" style="text-align: center;">0.140</td>
<td class="xl66" style="text-align: center;">0.056</td>
<td class="xl65" style="text-align: center;">0.87</td>
<td class="xl65" style="text-align: center;">0.84</td>
<td class="xl65" style="text-align: center;">0.80</td>
</tr>
<tr height="19" style="height: 14.4pt;">
<td height="19" style="height: 14.4pt; text-align: center;">94</td>
<td class="xl65" style="text-align: center;">16.79</td>
<td class="xl67" style="text-align: center; width: 79pt;" width="106">jmbus...@h...</td>
<td style="text-align: center;">2539</td>
<td style="text-align: center;">4</td>
<td class="xl66" style="text-align: center;">0.003</td>
<td class="xl66" style="text-align: center;">0.170</td>
<td class="xl66" style="text-align: center;">0.020</td>
<td class="xl65" style="text-align: center;">0.99</td>
<td class="xl65" style="text-align: center;">0.98</td>
<td class="xl65" style="text-align: center;">0.92</td>
</tr>
<tr height="19" style="height: 14.4pt;">
<td height="19" style="height: 14.4pt; text-align: center;">95</td>
<td class="xl65" style="text-align: center;">17.30</td>
<td class="xl67" style="text-align: center; width: 79pt;" width="106">hs</td>
<td style="text-align: center;">945</td>
<td style="text-align: center;">28</td>
<td class="xl66" style="text-align: center;">0.010</td>
<td class="xl66" style="text-align: center;">0.115</td>
<td class="xl66" style="text-align: center;">0.098</td>
<td class="xl65" style="text-align: center;">0.87</td>
<td class="xl65" style="text-align: center;">0.86</td>
<td class="xl65" style="text-align: center;">0.89</td>
</tr>
<tr height="19" style="height: 14.4pt;">
<td height="19" style="height: 14.4pt; text-align: center;">96</td>
<td class="xl65" style="text-align: center;">17.94</td>
<td class="xl67" style="text-align: center; width: 79pt;" width="106">ChiefSweetums</td>
<td style="text-align: center;">691</td>
<td style="text-align: center;">43</td>
<td class="xl66" style="text-align: center;">0.010</td>
<td class="xl66" style="text-align: center;">0.185</td>
<td class="xl66" style="text-align: center;">0.054</td>
<td class="xl65" style="text-align: center;">0.68</td>
<td class="xl65" style="text-align: center;">0.68</td>
<td class="xl65" style="text-align: center;">0.81</td>
</tr>
<tr height="19" style="height: 14.4pt;">
<td height="19" style="height: 14.4pt; text-align: center;">97</td>
<td class="xl65" style="text-align: center;">21.49</td>
<td class="xl67" style="text-align: center; width: 79pt;" width="106">Playa</td>
<td style="text-align: center;">414</td>
<td style="text-align: center;">85</td>
<td class="xl66" style="text-align: center;">0.010</td>
<td class="xl66" style="text-align: center;">0.239</td>
<td class="xl66" style="text-align: center;">0.014</td>
<td class="xl65" style="text-align: center;">0.93</td>
<td class="xl65" style="text-align: center;">0.90</td>
<td class="xl65" style="text-align: center;">1.00</td>
</tr>
<tr height="19" style="height: 14.4pt;">
<td height="19" style="height: 14.4pt; text-align: center;">98</td>
<td class="xl65" style="text-align: center;">31.56</td>
<td class="xl67" style="text-align: center; width: 79pt;" width="106">Tribune</td>
<td style="text-align: center;">360</td>
<td style="text-align: center;">99</td>
<td class="xl66" style="text-align: center;">0.053</td>
<td class="xl66" style="text-align: center;">0.011</td>
<td class="xl66" style="text-align: center;">0.108</td>
<td class="xl65" style="text-align: center;">0.76</td>
<td class="xl65" style="text-align: center;">0.61</td>
<td class="xl65" style="text-align: center;">0.97</td>
</tr>
<tr height="19" style="height: 14.4pt;">
<td height="19" style="height: 14.4pt; text-align: center;">99</td>
<td class="xl65" style="text-align: center;">35.74</td>
<td class="xl67" style="text-align: center; width: 79pt;" width="106">taintturk. (moderator)</td>
<td style="text-align: center;">1176</td>
<td style="text-align: center;">21</td>
<td class="xl66" style="text-align: center;">0.027</td>
<td class="xl66" style="text-align: center;">0.499</td>
<td class="xl66" style="text-align: center;">0.014</td>
<td class="xl65" style="text-align: center;">0.89</td>
<td class="xl65" style="text-align: center;">0.87</td>
<td class="xl65" style="text-align: center;">0.73</td>
</tr>
<tr height="19" style="height: 14.4pt;">
<td height="19" style="height: 14.4pt; text-align: center;">100</td>
<td class="xl65" style="text-align: center;">40.53</td>
<td class="xl67" style="text-align: center; width: 79pt;" width="106">Taskmistress</td>
<td style="text-align: center;">698</td>
<td style="text-align: center;">42</td>
<td class="xl66" style="text-align: center;">0.017</td>
<td class="xl66" style="text-align: center;">0.755</td>
<td class="xl66" style="text-align: center;">0.020</td>
<td class="xl65" style="text-align: center;">0.91</td>
<td class="xl65" style="text-align: center;">0.91</td>
<td class="xl65" style="text-align: center;">0.96</td>
</tr>
</tbody></table>
<br />
<br />
Find the full list of <a href="https://docs.google.com/spreadsheets/d/1NhLc4aJ42sEWYvx_nHkRpXMBeFF_7WyXOnHb00FgKzU/edit?usp=sharing" target="_blank">Top 100 ranked here (Second Tab)</a>.<br />
<br />
In Table 7 we can see how reviewers score on the RPI across all of the Top 100 reviewers. The Top 10 have great scores with SERI having the top ranked score with over 488 reviews written and no Flags or 1Bombs and only three 5Bombs. For SERI there is also no correlation between Fair or Comm with an amazingly negative correlation with Fast.<br />
<br />
The worse 10 reviewers is much more interesting mostly due to tainturk a Turkopticon moderator and Tribune a former moderator being on the list. Everybody on the worse 10 list suffer from very high correlations between the other scales and Pay. Tainturk though also suffers from having 50% of his/her reviews being 1Bombs (for those reviews in which all of the scales were completed). This is not the worse as Taskmistress has 75% 1Bombs but this was surprising. Looking back at the early reviews I see that 1Bombs seem to be common earlier in Turkopticon and are intended to reflect a Amazon Terms of Service violation, something that has since been implemented. <br />
<br />
Similarly Tibune has one of the highest flag count rates in the entire list with an expected numbe rof flags of 5% on his/her reviews. However, as Tribune was invited to be a moderator despite this spotted history, we can only assume that my rating system has some serious flaws.<br />
<br />
Overall, I would therefore take the RPI ranking with a grain of salt. Perhaps some of the longer time contributors to Turkopticon are suffering from changing standard over time. If I have time I will revisit the rating system looking at only reviews within the last year or two. </div>
Francishttp://www.blogger.com/profile/16658586705916884436noreply@blogger.com2tag:blogger.com,1999:blog-6288862798546085706.post-43048005275721851062016-01-16T01:55:00.003-05:002016-02-19T22:37:32.133-05:00Turkopticon: Defender of Amazon's Anonymous Workforce<div dir="ltr" style="text-align: left;" trbidi="on">
Labor crowdsourcing is the system by which large crowds or workers contribute to a project allowing for complex and tedious tasks to be rapidly and efficiently completed. The largest labor crowdsourcing platform in the world, <a href="https://www.mturk.com/" target="_blank">Amazon Mechancial TURK</a> (Mturk) is estimate to have revenue in the order of <a href="http://www.behind-the-enemy-lines.com/2012/11/is-mechanical-turk-10-billion-dollar.html" target="_blank">10 and 150 million</a> dollars annually. Despite this, there is no built in system by which workers can identify which employers (requesters) are cheaters and which are legitimate. And in a system powered by anonymity and numerous micro transactions, the inability to provide feedback to warn other workers of requester quality, is a big deal!<br />
<br />
<div class="separator" style="clear: both; text-align: left;">
Social activists and artists, Six Silberman and Lilly Irani at UCSD have designed a solution to help mitigate this problem. <a href="https://turkopticon.ucsd.edu/" target="_blank">Turkopticon</a>
provides a mechanism by which workers can rate their experience of
working with requesters. Turkopticon reviews can be read on the
UCSD host website and average ratings can be quickly accessed by workers
when searching for requesters through the browser extension and pops up
next to request information upon mouse over.</div>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj78hRtT6SAtouF4W8tovSGdLpWD8kuMwLPBUg-jKj1FjoKLRdzt0Sg6b4Bx5ATBvkyHTgVnCn_K_tPMNmB66d19bh992p4ZVJOUbecswIQq6qa6EKF_ox90iXdbleuqu7FvoH8fzHqpUg/s1600/Fullscreen+capture+1152016+40045+PM.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="131" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj78hRtT6SAtouF4W8tovSGdLpWD8kuMwLPBUg-jKj1FjoKLRdzt0Sg6b4Bx5ATBvkyHTgVnCn_K_tPMNmB66d19bh992p4ZVJOUbecswIQq6qa6EKF_ox90iXdbleuqu7FvoH8fzHqpUg/s640/Fullscreen+capture+1152016+40045+PM.jpg" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 1: An example MTurk HIT listing with Turkopticon review information provided.</td></tr>
</tbody></table>
Established in May of 2009, Turkopticon with over 284 thousand reviews written by more than 17 thousand reviewers has been an unmitigated success at creating a tool by which the community of Mturk workers share information about their experience with requesters.<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjiWTvXZwzxgihbboEY_MJx5V4zhILaiJBYry7K6ekT4xgGo84pQ0MTU0fTf6nVLCYyYxOFgMopJon5-k7xtontaz3y8O4a6H7lvSzKe0I8tM4vqbAxTf4BXoKyb8VqHSZLh7v2f1d9CR4/s1600/2016-01-Frequencies.png" style="margin-left: auto; margin-right: auto;"><img border="0" height="394" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjiWTvXZwzxgihbboEY_MJx5V4zhILaiJBYry7K6ekT4xgGo84pQ0MTU0fTf6nVLCYyYxOFgMopJon5-k7xtontaz3y8O4a6H7lvSzKe0I8tM4vqbAxTf4BXoKyb8VqHSZLh7v2f1d9CR4/s640/2016-01-Frequencies.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 2: Activity on Turkopticon measured in terms of number of reviews written daily and the unique number of reviewers.</td></tr>
</tbody></table>
<br />
From Figure 2 we can see that both the number of reviews and the number of daily participating reviewers increased dramatically from 2009 until mid-2015 at which time both the number of participating reviewers and the number of published reviews have been in decline.<br />
<br />
This might not actually be a problem for the Mturk system. Perhaps as information is shared about a particular requester, workers find that their individualized experiences are sufficiently summarized by the quantity of information already available.<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiv2p57bxNzCY000oeCy95HE35ttu17AXk04K3i1T62-8Ue4SJ9IvEKDzejV4SJ1EHCUeeXHxZqtIUoNFv3gcIAAGMSFB0DaL3WWqe_eM4oAdEmgs09WVYj9e4UaUXDQynRQWRpd0RcsuI/s1600/2016-01-NRevReq.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="394" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiv2p57bxNzCY000oeCy95HE35ttu17AXk04K3i1T62-8Ue4SJ9IvEKDzejV4SJ1EHCUeeXHxZqtIUoNFv3gcIAAGMSFB0DaL3WWqe_eM4oAdEmgs09WVYj9e4UaUXDQynRQWRpd0RcsuI/s640/2016-01-NRevReq.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 3: Mean and median number of reviews for individual requesters at each date. </td></tr>
</tbody></table>
<br />
Figure 3 seems to support the idea that as time has gone on some requesters have accumulated a large collection of reviews. This is not particularly surprising as one would expect that the longer requesters use Mturk the more reviews they accumulate except in the case when requesters prefer not to maintain their reviews (if for instance they are cheaters). Requesters have the power at any time to start a new Amazon requester account. Reviews do not transfer between accounts. This might be what is driving the median number of reviews to be so low (around 10 at this time). <br />
<br />
In order to get a better perspective on what is happening we might want to ask the question, how long are requesters generally active? We cannot observe how long requesters are active directly as we do not have the Mturk activity data, but we can look at when reviews are posted assuming that requesters must have been active at least for each day for which as review was written.<br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgRhFd4sLk7Y1dJtK6JSbTD16oAhBI9OH1zBG3FZ1XOnA0syhxePfX1DJ2LyuIJ5CBbVWA59igD11eMNEBqiUuZmTx5cH0FiJdnUtGn_0IBle3Gq06gJhrXRO4d3rPalNtYAR5Zh8OorHw/s1600/2016-01-Rqdysrgmd.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="394" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgRhFd4sLk7Y1dJtK6JSbTD16oAhBI9OH1zBG3FZ1XOnA0syhxePfX1DJ2LyuIJ5CBbVWA59igD11eMNEBqiUuZmTx5cH0FiJdnUtGn_0IBle3Gq06gJhrXRO4d3rPalNtYAR5Zh8OorHw/s640/2016-01-Rqdysrgmd.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 4: Mean and median of the number of days requester accounts have been active calculated as Current Date of a Review less the First Date of a Review.</td></tr>
</tbody></table>
From Figure 4 we can see that on average requesters have been active for nearly two years though the median activity level is much lower than this value at less than a year. These numbers are likely inflated as requesters that get reviewed early then drop out of Mturk for a period of time before using their accounts once again are considered equally active as requesters who have been active continuously over the same period. One way of avoiding this would be only to count days which were active by requesters as demonstrated by being reviewed those days. However, this figure ends up being almost identical to Figure 3, so I have omitted it.<br />
<br />
Seeing all of these reviews we might ask ourselves how many reviews are being contributed by an elite group of very active reviewers and how much by a wider group? <br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhfoALCZGm_c8YsHSBIizGxuOi7TmQ_wH1TJj8TtI4aYWB4rVKO6TbgYYiBFyTSMFe8T9E4yHYojJgd3Ccp9p24KefR0n67FMP_OpF-LPolyO-heIqldzZTvhyphenhyphenS0z8fuS7S5mZop7XQao0/s1600/2016-01-NRevRev.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="394" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhfoALCZGm_c8YsHSBIizGxuOi7TmQ_wH1TJj8TtI4aYWB4rVKO6TbgYYiBFyTSMFe8T9E4yHYojJgd3Ccp9p24KefR0n67FMP_OpF-LPolyO-heIqldzZTvhyphenhyphenS0z8fuS7S5mZop7XQao0/s640/2016-01-NRevRev.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 5: The numbers of reviews by reviewers at the time of writing a review.</td></tr>
</tbody></table>
From Figure 5 we can see that the median number of reviews written on any given date is around 100. This implies large scale community involvement with many reviewers contributing a significant number of reviews. We can also see that the mean is significantly higher than the median and grows more so recently, implying that the distribution is skewed with a few reviewers contributing a significant portion of reviews written.<br />
<br />
From the available evidence we can therefore confidently claim that Turkopticon has been successful at fulfilling its mission of providing a mechanism for workers to exchange information with regard requester quality. This however is not the only objective of Turkopticon and the workers who contribute to its database.<br />
<br />
One of the major objectives of Turkopticon, at least as many workers see it, is to provide a platform by which workers can exchange information about requesters and thus use that information to gain leverage over requesters. Ideally driving the pay rate upwards.<br />
<br />
Workers seem to be targeting an ideal pay rate in the range of $11-$15 per hour though in practice the effective pay rate seems to be much less than this. Turkopticon reviewers would also like to see the general quality of their working environment improve as well. In practice they would like their work to be reviewed quick and rarely rejected. And when a problem arises for requesters to communicate effectively and respectfully with them.<br />
<br />
From our data we cannot directly observe pay rate. However, what we can observe is the four rating categories defined by Turkopticon: Pay, Fast (rapidity of accepting or rejected submitted HITs), Fairness, Communication. These categories allow for ratings between 1 and 5.<br />
<br />
From the trends in these rating systems we can ideally infer how the Mturk workplace has changed for workers over time.<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjWiMr9nkP2Ce6EFDqSdde1zyOPA3858-xL4GXZbZpCTAfXIcmhyphenhyphenvUofN4QdUJGePg6LAqZkD3yV1m-tmsIc_dPTPghRQu5PJE8ZKDU8_XHcqe3GrworJNsN9mjNfFZ32rWd-I1piccSGA/s1600/2016-01-RevValTrends.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="394" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjWiMr9nkP2Ce6EFDqSdde1zyOPA3858-xL4GXZbZpCTAfXIcmhyphenhyphenvUofN4QdUJGePg6LAqZkD3yV1m-tmsIc_dPTPghRQu5PJE8ZKDU8_XHcqe3GrworJNsN9mjNfFZ32rWd-I1piccSGA/s640/2016-01-RevValTrends.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 6: Mean reviews over time.</td></tr>
</tbody></table>
From Figure 6 we can see that mean reviews have changed significantly over time. In particular the ratings for Fast and Fair have improved generally while the ratings for Pay and Communication, except for a brief bump for pay in 2013 have fallen ominously.<br />
<br />
So what is driving these trends and does Turkopticon have anything to do with it?<br />
<br />
There was a time when Mturk placed heavy restrictions on non-US workers, I suspect as a result of attempting to comply with federal taxation laws. This I suspect significantly restricted the supply of workers causing a short term rise in the system wage.<br />
<br />
From our previous analysis we can see that Turkopticon is widely and actively used by many Mturk workers. Thus we consider how Turkopticon might be driving the trends that we are seeing.<br />
<br />
My personal experience with interacting with workers through Turkopticon was quiet unpleasant. I don't know if this is typical of other requesters using Turkopticon but talking with other academics who have used Turkopticon I suspect it is not unusual. <br />
<br />
If this is the case, then Turkopticon provides an easy explanation for the falling wage. That is, requesters dropping out of the system after being targeted by a disgruntled, organized, and anonymous workforce. Simultaneously, many workers have claimed that the only reason they have continued to be active on Mturk is because of Turkopticon. Thus Turkopticon might be suppressing the going wage by driving requesters away, while simultaneously retaining workers.<br />
<br />
Ironic though predictable.<br />
<br />
Increased attention by requesters to scales like Fairness and Fastness is also predictable as requesters grow more attentive to the non-monetary concerns of the workforce. Likewise, due to the growing boldness and hostility of workers organized through the Turkopticon platform, it should come as no surprise to anybody that requesters have opted out of investing in direct communication with workers.<br />
<br />
I personally found the experience painful in the extreme as literally everything I said was turned against me in a kind of sadistic group think in which anonymous workers would take turns at antagonizing, humiliating, and threatening me.<br />
<br />
My personal experience aside, I do not know what is driving the apparent fall in Mturk pay.<br />
<br />
One might argue that pay and other factors have not meaningfully changed only that instead as reviewers have gained more experience they have had more experience to base their reviews. This might be particularly true for the scale "Pay" with some outspoken workers asserting that a pay rating 5 is only warranted when the effective hourly wage is over $12 per hour. This is a plausible explanation as workers seems to learn from the input of other workers about their rating scales.<br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhNlcznZgp5iVOeF-Q2FwGvQ9aTPUii2FDFt3uDQ3WKCxq_wWcFNHyys1QSCbnehWVYUrgg6mENVeZ8pQ9rEVpi31uBNqSAKp5YVRyWO6ssl4LjL_su-Ogh3dAhWHD0tTTr13kx_CGcD3I/s1600/2016-01-CompRateTrends.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="394" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhNlcznZgp5iVOeF-Q2FwGvQ9aTPUii2FDFt3uDQ3WKCxq_wWcFNHyys1QSCbnehWVYUrgg6mENVeZ8pQ9rEVpi31uBNqSAKp5YVRyWO6ssl4LjL_su-Ogh3dAhWHD0tTTr13kx_CGcD3I/s640/2016-01-CompRateTrends.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 7: Completion rates of scales and bomb rates. An incomplete scale submission is a rating in which a reviewer does not provide a rating for a requester on that scale.</td></tr>
</tbody></table>
In Figure 7 in we can see that 1-bombs and 5-bombs (all 1s or all 5s) have peaked in previous years and dropped off over time. This indicates that perhaps reviewers are learning the expectations of the system and conforming their reviews to match these standards. This supports the changing expectations for pay hypothesis.<br />
<br />
Overall, we conclude that Turkopticon is an amazing success. It has brought workers together to exchange information about employees on an immense scale. The end results however of collective worker actions have not been as hoped for though predictable with wages decreasing as requesters drop out of the system in response to collective antagonism organized through Turkopticon.<br />
<br />
Related Posts:<br />
<a href="http://www.econometricsbysimulation.com/2016/01/who-are-turkopticons-top-contributors.html?showComment=1455741806768#c8917238471171767517" target="_blank">Who are Turkopticon's Top Contributors?</a></div>
Francishttp://www.blogger.com/profile/16658586705916884436noreply@blogger.com3tag:blogger.com,1999:blog-6288862798546085706.post-85665785787791080492015-12-10T15:22:00.001-05:002015-12-11T09:57:56.788-05:00Cause of Death: Melanin | Evaluating Death-by-Police Data<div dir="ltr" style="text-align: left;" trbidi="on">
Widespread attention towards the death of black men by police has sparked protests and public outrage in many a city. Recently, the Federal Government has launched an <a href="http://www.npr.org/2015/12/08/458926584/with-chicago-police-investigation-advocates-ask-what-took-so-long" target="_blank">investigation</a> into the conduct of the entire Chicago police department. However, by protests and videos popping up all over the country, the apparent problems of police abuse do not appear to be contained.<br />
<br />
As part of this movement, Black Lives Matters (BLM) protesters have drawn much attention from the media over the last couple of years as they have caused large protests in cities such as Toronto, Chicago, San Francisco, and Ferguson. These protests have also drawn international attention especially in how they led to riots in Baltimore, Maryland.<br />
<br />
How BLM has been received by the general American public has been mixed. Unfortunately, the violence of the protest has distracted from the message that the BLM movement has been attempting to convey. That is, that black people are disproportionately likely to be abused or killed by police than their white counterparts and that this abuse is unjustified.<br />
<br />
But is this true? The answer is not immediately obvious as data about people getting killed by police is not systematically collected by any federal agency as police departments report deaths only voluntarily to the FBI. What partially comprehensive data exists, is instead collected by the efforts of activists such as those at FatalEncounters (www.fatalencounters.org, see discussion of data issues below).<br />
<br />
The folks at FatalEncounters say that their data should not be used to analyze racial differences due to the high rate of incompleteness of reports regards race. However, making two simple assumptions we are able to start making a lot of inferences from our data (see discussion of assumption issues below):<br />
A1. Data is missing at random without regard to the race. <br />
A2. Data is missing at random without regard to state.<br />
<br />
Before getting any further into this I would like to point out that the likelihood of an individual officer being involved in a killings is relatively rare (9% over the last 16 years or 0.56%/year [1]). Furthermore, without stretching truth we can probably assume the vast majority of such are justifiable to varying degrees. <br />
<br />
Thus the average person probably should not be concerned for one's life when encountering police officers. That said, what is the case for the average person might not be the case for all segments of the population. The BLM movement would argue that young black males should be justifiably much more concerned about being killed by police than other segments of the population. So let's get into the data and see what we can find.<br />
<br />
<b>Q1. Are black males more likely to be killed by police than their white counterparts?</b><br />
<br />
Table 1: Shows that the relative likelihood, for a 16-30 year old, the likelihood of being killed nationally proportional to your representation within the population is 7 times greater than that of a white person (2.1/.3) using assumption A1. Loosening the assumption and assigning all of the unknown race kills to that of white people (an extreme assumption) we get column Kill2. Even under this extreme assumption, the likelihood of being killed by a police officer is 2.3 times greater for a black person than that of a white person (2.1/.9).<br />
<br />
<pre class="GEM3DMTCFGB" id="rstudio_console_output" style="-webkit-text-stroke-width: 0px; -webkit-user-select: text; background-color: white; border: none; color: black; font-family: 'Lucida Console'; font-size: 10pt !important; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 15px; margin: 0px; orphans: auto; outline: none; text-align: -webkit-left; text-indent: 0px; text-transform: none; white-space: pre-wrap !important; widows: auto; word-break: break-all; word-spacing: 0px;" tabindex="0"> Race Kills Kill% Pop% Kill%/Pop% | Kill2 Kill2/Pop%
1 black 937 27% 13% 2.1 | 27% 2.1
2 unknown 1202 35% 0% - | 0% -
3 white 712 21% 63% 0.3 | 56% .9
4 other 79 2% 8% 0.2 | 2% .2
5 latino 527 15% 17% 0.9 | 15% .9</pre>
<br />
<span style="font-family: inherit;"><br /><b>Q2. How does the <span style="font-family: inherit;">risk </span>of being killed by police for black people relative to that of white people vary by state?</b></span><br />
<b>
</b>
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjo1JTTISiQfzKzbx0OnhaB53589wfL-fEWT7BkksA-rRzM3rvmZGd7tquBhNj97wsVCEcxiF6ybaq1sp0JCCjIhsX1nplc60-wXv30Qd7QD0JLPEfqPoTg_QcZv16HWx84pMpLhyphenhyphenC1Xh4/s1600/2015-12-03-BLM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjo1JTTISiQfzKzbx0OnhaB53589wfL-fEWT7BkksA-rRzM3rvmZGd7tquBhNj97wsVCEcxiF6ybaq1sp0JCCjIhsX1nplc60-wXv30Qd7QD0JLPEfqPoTg_QcZv16HWx84pMpLhyphenhyphenC1Xh4/s640/2015-12-03-BLM.png" width="600" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 1: The relative likelihood of a black person being killed in states to that of a white person. Grayed out states are those in which no black people were killed by police.</td></tr>
</tbody></table>
From figure 1 we can see that the relative risk of being killed by police vary significantly by state. Surprisingly those states south of the Mason-Dixon line seem to have
more equalized rates of being killed by police than some of those states north of the line with a Illinois, Ohio, and Massachusetts in which the likelihood of being killed by police for a black person is over 7 times higher than that for a white person.<br />
<br />
<b>Q3. Is poverty the driving force causing black people to be at higher risk than their white counterparts?</b><br />
<b>
</b>
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg8K8Gzac4coIDLDxVo3vqsHa_3VesYMWHP1rA_QsKL8w0y5AJC3s2h9cyP2p1W6OmEcVesdfShKJRFo3J-KV59JH8IKadPZrfZJYNOBjXgRHu4UJO00DFLpayWWn4AFlRvGzxMSwE-b0Y/s1600/2015-12-03-PovertyViolence.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg8K8Gzac4coIDLDxVo3vqsHa_3VesYMWHP1rA_QsKL8w0y5AJC3s2h9cyP2p1W6OmEcVesdfShKJRFo3J-KV59JH8IKadPZrfZJYNOBjXgRHu4UJO00DFLpayWWn4AFlRvGzxMSwE-b0Y/s640/2015-12-03-PovertyViolence.png" width="600" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 2: The relative risk of being poor for black people relative to white against that of being killed for black people relative to that of white.</td></tr>
</tbody></table>
<br />
From Figure 2 we can see that there does appear to be a relationship between the risk of being black and poor and the risk of being killed by a police officer relative to that of your white counterpart (with the exception of OH and IL which have much higher risk than should otherwise be expected). If you regress relative risk of being killed by relative risk of being poor and relative risk of failing to complete high-school, for each 1 times more likely a black person is of being poor that person is 2.8 times higher risk of being killed by police.<br />
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjy7hyphenhypheneS4NDiU8LHoWpPrv_a40235pTDM_1emeQ-xno7UT83qxMX1Nw1fPzi5T9XU_56ilEv-cgFeLCbbylACa8MeSEViKRGdDRMlxkXn0YMxO9XQckUEXv11nWTU65TgpTbDpLTmZsNLI/s1600/2015-12-03-PovertyHS.png" imageanchor="1" style="margin-left: 1em; margin-right: 0em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEikdjzR6ig-Gr_zRJNvQ_4FbRsIXLr_JGsy3NVP80-3ztihzKqljTaXvYDV3gj5L-G4gaDzHvTr5rL3rloFVHkJxFAbe2FpA3c0bK6jIsuaQlc1kkdtqUEvfwbE7av5KdZuKw2ew6U5J-I/s640/2015-12-03-PovertyHS.png" width="600" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 3: The relative risk of being poor mapped against the relative rates of high school completion.</td></tr>
</tbody></table>
From Figure 3 we can see that poverty and failure to complete high-school are correlated with some states such as Minnesota and Wisconsin having less than 25% completion rates among blacks relative to their white peers while simultaneously having the highest rates of poverty among blacks relative to white in all of the data.<br />
<br />
<b>Q4. So is it wise for black people to move to southern states if they would like to avoid police violence?</b><br />
<b><br /></b>
<b>
</b><br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiCMgTiU8BapdsKH0ARzsNcJQN3_o-T-RsjYQFVhHwtuIsPyLhUZ7CECl2sTiyb1HdouDTJYC-Kla0GzrK9sXrIZ-yq0iyxkd5k4JEfa9YNW1w_Xj0RGsyEfA8EAlCDgwO-kwgX0l0ymW4/s1600/2015-12-03-Hazard.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiCMgTiU8BapdsKH0ARzsNcJQN3_o-T-RsjYQFVhHwtuIsPyLhUZ7CECl2sTiyb1HdouDTJYC-Kla0GzrK9sXrIZ-yq0iyxkd5k4JEfa9YNW1w_Xj0RGsyEfA8EAlCDgwO-kwgX0l0ymW4/s640/2015-12-03-Hazard.png" width="600" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 4: The overall risk of anybody getting killed by police.</td></tr>
</tbody></table>
From Figure 4 we can see the story is not quite so simple. Louisiana, Mississippi, Alabama, and Nevada, four states which had the lowest relative risk for black people to be killed by police have some of the highest rates of any state in terms of likelihood of any resident of the state being killed. In contrast, Illinois, Indiana, and Vermont now have some of the lower rates in the country in terms of likelihood of being killed by a police officer.<br />
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEikD5-k66MYmV8mdmyMTlx75SlCGPqPxdWQxolX4r4fe8oLnWY18Co40ZntNAlnzU3Wr59DzGu_lwLjMrJvYcoN4I_e6yCP8vNCytHn0Owu7TiDuq41z8wjQ8ebAshZ6dJoES68tQ6BkwU/s1600/2015-12-03-BHaz.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEikD5-k66MYmV8mdmyMTlx75SlCGPqPxdWQxolX4r4fe8oLnWY18Co40ZntNAlnzU3Wr59DzGu_lwLjMrJvYcoN4I_e6yCP8vNCytHn0Owu7TiDuq41z8wjQ8ebAshZ6dJoES68tQ6BkwU/s640/2015-12-03-BHaz.png" width="600" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 5: Likelihood of a black person being killed by police.</td></tr>
</tbody></table>
From Figure 5 we can see that black people in the Northwest of the United States have the lowest possible chance of being killed by the police since in the last 16 years there is no record of any deaths by police. However, this might be comforting to few since the population of black people in this part of the country is very small. Strangely Vermont and Nevada both have very high rates of deaths for black people. The high rate in Vermont could be explained by the state having the second smallest black population while the even higher rate in Nevada cannot easily be explained as it has the 19th largest population of black people in the country.<br />
<br />
<b>Q5: What about white people?</b><br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEho1lCP00FiVZvcMyeGyJic2UGezIzBWNypHDT0i63i0AF4TDzWniUSQCNQT7cK4i9dZphBzoFBy7r5t9EpxtmVV6R8T4-3b6tFp6afrxlyDOyKTZWlWTaDjYflcpei7Tt6YVCTyH33VXY/s1600/2015-12-03-WHaz.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEho1lCP00FiVZvcMyeGyJic2UGezIzBWNypHDT0i63i0AF4TDzWniUSQCNQT7cK4i9dZphBzoFBy7r5t9EpxtmVV6R8T4-3b6tFp6afrxlyDOyKTZWlWTaDjYflcpei7Tt6YVCTyH33VXY/s640/2015-12-03-WHaz.png" width="600" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 6: Likelihood of a white person being killed by police.</td></tr>
</tbody></table>
From Figure 6 we can see that Nevada is also the highest risk state for being killed by police. Interestingly, states above the Mason-Dickson line now seem to be the safest place for white people when it comes to being at risk from the police. Overall, we should not be looking at Figure 6 compared with Figure 5 and saying "oh well white people are killed by the police also".<br />
<br />
The reason is that we need to keep the scale of the legend in mind. In Figure 5 the scale goes all the way up to nearly 20 deaths per 100 thousand people while in Figure 6 the scale goes only to around 8 deaths per 100 thousand people. This means that consistent with the national level data, black people are significantly more likely to be killed by police than white people.<br />
<br />
<b>Q6: So what? Black people are at higher risk of committing crime as well! Aren't they just getting their fair share of the risk inherent in criminal activity?</b><br />
<br />
The blog <a href="http://blogs.channel4.com/factcheck/factcheck-black-americans-killed-police/19423" target="_blank">FactCheck</a> discusses this point, especially with regards the higher rate of black males killed by police officers than that of white males potentially due to black males being much more likely than white males of engaging in violent crime. I will not discuss at this time theories as to why black people might be at a higher risk of committing crimes except to say that I think poverty is a better explanation for these differences.<br />
<br />
That said, I think the Fatal Encounters data can get us a further into examining the nature of police violence towards black people than the FBI data used by FactCheck. In particular the Fatal Encounter data set has a brief description of the circumstances involved in the deaths. The text in these circumstances can be quantified in order to help naive data explorers better understanding of what is going on.<br />
<br />
If no racial discrimination exists in how police force is used against individuals then there should be an equal proportion of unarmed blacks killed as that of unarmed whites killed as from those killed. If however, black who are killed are more likely to be killed unjustifiably then we should see that evidenced in the increased likelihood of being killed .<br />
<br />
<br />
In the data there are 301 cases in which "unarmed" appears in connection with a death resulting from interaction with a police officer. 104 of the 1934 black people killed were unarmed while 60 of the 2578 white people who died at the hands of police were killed. This means that the proportion of unarmed people killed by police among blacks (104/1934=5.4%) is 2.3 times greater than that of white people killed by police (60/2578=2.3%). In probability notation: <br />
<br />
"Unarmed": 315 Cases <br />
P(Unarmed|Black & Killed)/P(Unarmed|White & Killed)=2.3<br />
<br />
In other words this means that the likelihood of police killing someone who is unarmed is 130% greater when they are encountering a black person than when encountering a white person.<br />
<br />
Now you might say, that this is just the case for the term "unarmed". However, it is really hard to find any term associated with police brutality which does not appear disproportionately higher for blacks than it does for whites.<br />
<br />
<span style="font-family: "courier new" , "courier" , monospace;">Table 2: Table shows the number of cases and frequency by which key words were reported for black people's death relative to that of whites.<br /><br />Descriptor Cases (Word|Black)/P(Word|White)<br />Unarmed 315 2.3<br />Naked 67 1.6<br />Toy 41 3.6<br />Cooperative 23 1.7<br /><br />Excessive Force</span><br />
<span style="font-family: "courier new" , "courier" , monospace;">Age 9<span style="font-family: "courier new" , "courier" , monospace;"> or </span>less 54 1.4 </span><br />
<span style="font-family: "courier new" , "courier" , monospace;">Age 10-15 131 3.1<br />Shot 10+ times 168 1.7<br />Wrongful Death 83 1.4<br />Indictment 106 1.5<br /><br />Cause of Death</span><br />
<span style="font-family: "courier new" , "courier" , monospace;">Trauma/beating/etc. 105 1.7<br />Taser 372 1.7<br />Asphyxiation 115 1.8<br />Medical Compli. 173 2.0<br />Gunshot 7450 1.0<br />Vehicle 1225 0.9<br /><br />Justified Homicide keywords<br />"Reaching...gun" 109 1.6<br />"Robb(ed/ing)" 1006 1.4 <br /><br />Violent Crime Act<br />"Hostage" 160 0.8<br />"Standoff" 360 0.6</span><br />
<br />
From Table 2 we can see that black people are 130% more likely to be killed unarmed, 60% more likely to be killed while naked, 260% more likely to be killed in association with a toy (probably a toy handgun), and 70% more likely to be killed even when the word "cooperative" was used to describe the situation.<br />
<br />
Black people who are killed are are also 40% more likely to be reported as aged less than 10 and 210% more likely to be between 11 and 15 than their white counterparts. When killed black people are 70% more likely to be shot 10 or more times. Furthermore, black people who are killed are 40% more likely to give rise to a wrongful death suit and 50% more likely to result in some kind of indictment against the officers invovled.<br />
<br />
When it comes to cause of death, black people are 70% more likely to die from trama such as beating, stabbing, falling, etc. while also being 70% more likely to have being tased as a contributing cause of death. Likewise, black people to die of asphyxiation is 80% more likely and medical complications 100% more likely than that of their white counterparts.<br />
<br />
Overall, blacks are equally likely as whites to die by gunshot while being 10% less likely than whites to die by vehicle. The killing of black people is often justified as resulting from them either being in the act of robbing or stealing 60% more likely than whites or "reaching for a gun", 40% more likely than whites.<br />
<br />
However among serious crimes that result in hostages blacks are 20% less likely to be killed while involved in and 40% less likely to develop a situation with police that results in a standoff ending in death.<br />
<br />
<b>Conclusion: So, what are we to take from this? </b><br />
<br />
Black people are clearly much higher risk of being killed by police officers than that of white people. This statistics does not immediately lead to the conclusion that there is discrimination by police. However it does raise some red flags. Attempting to look more closely at state level data we can see in states above the Mason-Dixon line black people are often at much higher relative risk than their white peers of being killed by police while certain states below the Mason-Dixon line have generally much higher rates of citizenry being killed by police.<br />
<br />
Critics of any kind of simple analysis of death by police for black people argue that black people are more likely to commit violent crimes and therefore should be more likely to suffer violent deaths. Those who live by the sword, die by the sword and all that.<br />
<br />
If that were the case then we should expect higher likelihoods of deaths of black people by police than white (which is what we see) but there to be more or less equivalent rates or lower rates of black people getting killed accidentally or while vulnerable than that of their white counterparts. Vulnerability is difficult to measure but text flags for "unarmed", "naked", age less than 10 etc. or shot more than 10 times attempt to get at this.<br />
<br />
In the data we see exactly the opposite with black people much more likely to be killed while vulnerable. We also see that the rates of unusual or brutal deaths (result of beatings, asphyxiation, trauma, excessive or ineffective taser usage, etc.) resulting from police contact tend to be much higher among blacks.<br />
<br />
We also see that black people seem to be at higher risk of dying while committing robbery or while "reaching of a gun" while whites are more likely to die while participating in more serious sounding situations such as taking a hostage or after a standoff with police.<br />
<br />
Overall, the picture that the data paints is that of a population which is more likely to commit crimes but also much more likely to suffer excessive force resulting from police prejudice. If there were evidence that excessive force leads neighborhood reforms, lower crime, and rehabilitation then these kinds of actions might be seen as justifiable. However, there is no evidence that excessive force does anything but reinforce racial stereotypes resulting in more cyclical crime and poverty.<br />
<br />
You can find my code to do your <a href="https://github.com/EconometricsBySimulation/Ninja/blob/master/2015/12-December/2015-12-10BLM.R" target="_blank">own analysis here</a>. Apologize that it is messy. I have been working on this "quick one-day-post" for two weeks now and need to get it out so that I can focus on my dissertation work.<br />
<br />
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Footnote: [1] Total number of killings * Average number of police involved / Number of police nationally = 20,000 killings/16 years * lets say 4 police / 890,000 police = 9%/16 years = 0.56%/year. <br />
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* Fatal Encounters Data Issues<br />
<br />
This data has some obvious issues. Primarily that it is based on what can be gathered from spotty and inconsistent newspaper reports. Newspaper reports are problematic because they often fail to provide important information such as the ethnicity of victims or the cause of death or how the case was resolved such as if any disciplinary action was taken with regards the officers involved.<br />
<br />
Yet even more problematic, newspaper data cannot be assumed to be complete. That is some portion of deaths are not reported or if they are reported the article is only kept for a limited time frame. FatalEncounters has attempted to remedy this problem by going through government records. However, as they say many government records are only required to be kept for only a few years. Since the records are so sparse in two indicators (race, disposition and mental state) they suggest not using this records for analysis.<br />
<br />
This, however is cutting ourselves short as all we need is to make some basic assumptions in order to let the data work for us. The biggest issue with the data is that though it has nearly ten thousand cases, the data set maintainer D. Brian Burghart believes that it is about 46 percent complete. This is based on assuming a constant rate of deaths for all 16 years of data collection. For the two years with the most complete information 2013 and 2014 there are 1,257 and 1,292 deaths respectively.<br />
<br />
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* Simplifying assumption discussions<br />
<br />
<div style="text-align: left;">
The first assumption might be debatable since some might argue that
race might be more likely to be reported for black people or for white
people. However, since our data deals with an abundance of black deaths
relative to that of white the only type of under-reporting of race that
might make our <span style="font-family: inherit;">analysis invalid is that of under-reporting of white
race. Fortunately we can test our analysis in that case by looking at
what would happen if we assumed all unknown races were white. </span></div>
<div style="text-align: left;">
<span style="font-family: "courier new" , "courier" , monospace;"><br /></span></div>
<div style="text-align: left;">
<span style="font-family: "courier new" , "courier" , monospace;">Race breakdown:</span></div>
<div class="GEM3DMTCFGB" id="rstudio_console_output" style="background-color: white; border: medium none; color: black; font-size: 10pt ! important; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 15px; margin: 0px; outline: medium none; text-align: left; text-indent: 0px; text-transform: none; white-space: pre-wrap ! important; word-break: break-all; word-spacing: 0px;" tabindex="0">
<span style="font-family: "courier new" , "courier" , monospace;">black latino other unknown white
1934 1122 213 3624 2578 </span></div>
<br />
We can see that the number of unknowns is large but not that large. If we assume all of them are white people then this more than doubles the number of white people who died from police. </div>
Francishttp://www.blogger.com/profile/16658586705916884436noreply@blogger.com5tag:blogger.com,1999:blog-6288862798546085706.post-62542902692996885562015-11-18T16:29:00.000-05:002015-11-18T16:29:14.998-05:00The Unreported War On America's Poor<div dir="ltr" style="text-align: left;" trbidi="on">
The Democratic firebrand <a href="https://berniesanders.com/issues/income-and-wealth-inequality/" target="_blank">Bernie Sander's</a> keeps harping on this point about income inequality in the United States, yet I have to wonder, how bad is it really and do we care?<br />
<br />
First off, there is a legitimate reason to ask, if we should care. After all, throughout history, nations have gotten more wealthy with some people getting a bit more of the wealth over time yet things seem to keep going. So long as individuals feel that they can have reasonable access to opportunities for income growth and that a significant portion of the population is not living in poverty, things are okay, right?<br />
<br />
Yes, but maybe there is a point at which income inequality can grow so vast and its influence over government so enormous that that which used to be a democracy ruled by the people becomes an oligarchy ruled by the few.<br />
<br />
But politics is not what I am here to talk about. I am here to ask if inequality is getting worse or better and what are the effect of inequality on the less fortunate in society. In order to address this question, I will use US survey data from 1980, 1990, 2000, 2005, 2010, and 2013 sampling 200,000 individuals from each year.<br />
<br />
The first figure is more or less what we would expect. We can see that the top 1% has increased in earning capacity massively since the 1980s. In terms of income in contemporary dollars income seems to be increasing throughout the population.<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhAkppZsCSrUHf01OMMXxVAQtHh9ZSgV7V0yF_iMZCVaApz6nHwhA3NsCyTMnDq5bO04tCAMQMCKnyhxSulFy3AstOfUIweSrA_6bu5XTJm4SaA2KlVPPz3HRIE9jVt7EnYxQVzFKYlBog/s1600/inequality1.png" style="margin-left: auto; margin-right: auto;"><img border="0" height="425" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhAkppZsCSrUHf01OMMXxVAQtHh9ZSgV7V0yF_iMZCVaApz6nHwhA3NsCyTMnDq5bO04tCAMQMCKnyhxSulFy3AstOfUIweSrA_6bu5XTJm4SaA2KlVPPz3HRIE9jVt7EnYxQVzFKYlBog/s640/inequality1.png" width="580" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure
1: Family Average Income by Bracket. Looks like more or less everybody
is increasing over time. Remember for the top 1%, incomes are top coded.
This means that this is likely the lower limit of the true value for
those top income makers. The red dotted line is median income. </td></tr>
</tbody></table>
<br />
We can see that the income being made by the top 1% has grown significantly over time. Looking at the next graph we can see that compared with the median household income this growth has been huge.<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgMchXvAQMVRlQKeX9IwEBaQzhn9bIxr50oKP1peNpFoE75jm5id6n9TT9XrJNqgZqY8hbSO7Vpc0_BTi-wWpNKjHUUeDIx3yWfDlMP1AI5dfCz3qkwvOmj9kssQaPrl2sPDj8OD8-cR64/s1600/inequality2.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="350" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgMchXvAQMVRlQKeX9IwEBaQzhn9bIxr50oKP1peNpFoE75jm5id6n9TT9XrJNqgZqY8hbSO7Vpc0_BTi-wWpNKjHUUeDIx3yWfDlMP1AI5dfCz3qkwvOmj9kssQaPrl2sPDj8OD8-cR64/s640/inequality2.png" width="580" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 2: Income relative to that of median household income. </td></tr>
</tbody></table>
From Figure 2 we can see that the top 1% have increased in earnings significantly since the 1980s from making on average a minimum around 4 times that of the median household per year to that of minimum 10 times. The reason I say minimum is because the census does not release true earnings numbers but rather median earnings which are a lower estimate on a strongly skewed value.<br />
<br />
But what does this all meaning for buying power and the ability individuals have to pay for living expenses and that of their families?<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody></tbody></table>
<img border="0" height="350" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiFyMa1FA2Vf_52sUeLw-sUYOFxrG3zn_7rsdJajWf47x_4o323-dhcavzOEUy65lNhH0jqqeIO9sWVqb6RavwV4nMRSxo7ciPqsWgveuyrloShHoWfBnDfXKAWlZtqk1lCL9Itt_g4W34/s640/inequality3.png" width="580" /><br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><br /></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 3: Incomes by Bracket adjusting for inflation (based on Consumer Price Index). The red dotted line is median income.</td></tr>
</tbody></table>
<br />
Figure 3 starts to show us that things are not necessarily as good for everybody involved as they appear in Figure 1. First off, median income seems to be holding constant. Second, though it is difficult to see, the bottom 25% of families seem to be loosing income. How significant is that loss?<br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiPPr-WjymYIuN3K3R9hlYt1BhLr0BJxRlsOZz8dInuePzqy3aMugywQvPGhmycEqTHq7wfJFnESwNXCEA8nTZRTaN58cOwAJEZbVDfA9RVZV59VboQVjcOvYfCA94-xKcqAmN0hNEGCvc/s1600/inequality4.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="350" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiPPr-WjymYIuN3K3R9hlYt1BhLr0BJxRlsOZz8dInuePzqy3aMugywQvPGhmycEqTHq7wfJFnESwNXCEA8nTZRTaN58cOwAJEZbVDfA9RVZV59VboQVjcOvYfCA94-xKcqAmN0hNEGCvc/s640/inequality4.png" width="580" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 4: Total Family Income for individuals at different age groups.</td></tr>
</tbody></table>
Looking at Figure 4 we can see that for the poorest 25%, all age groups have experienced a dramatic reduction in total family income since the 1980s. Those 60+ are somewhat immune from the worst of these falls in income probably due to social support programs such as social security.<br />
<br />
So is the cost of living decreasing to match the falling income?<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgdefq_KYpMgXfiMIApX68gYlN5gQe-mfHF0CWKScn_rojWjePxPqQd9r467XVoxzsMuhlO-NLWpUHtK0GbPRM8Wi3IZr5z__myHKZmiLT_vmU7tbNlddNPuV4DIC2V7_jLXa-gpxAfFEE/s1600/inequality9.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="350" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgdefq_KYpMgXfiMIApX68gYlN5gQe-mfHF0CWKScn_rojWjePxPqQd9r467XVoxzsMuhlO-NLWpUHtK0GbPRM8Wi3IZr5z__myHKZmiLT_vmU7tbNlddNPuV4DIC2V7_jLXa-gpxAfFEE/s640/inequality9.png" width="580" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 5: The cost of rent for the bottom 25% of the population sliced by age group.</td></tr>
</tbody></table>
<br />
From Figure 5 we can see that the cost of rent has significantly increased since 1980 with all age groups being hit hard. Though information is not available in the census the cost of higher education has <a href="https://www.blogger.com/null" target="_blank">increased a staggering 538% since 1985</a> while medical costs have increased 286% relative to increases in the CPI of only 121% (<a href="http://www.bestvalueschools.com/understanding-the-rising-costs-of-higher-education/" target="_blank">Source</a>).<br />
<br />
So how has the decrease in earning power and increase in cost of living affected vulnerability to poverty?<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjppAxbDgDmS5h8Wz3WneYzhUlgIFlVo02bmNPgt86At-YMB5C6fI2amomdi4727Arme7HAPYKXGGC7h29ebJsBdQuwQBsBLXJAEfSd4XzIKxjCyMMrrSbokgN_ylEEogHSBNEOsAd0VH8/s1600/inequality5.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="350" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjppAxbDgDmS5h8Wz3WneYzhUlgIFlVo02bmNPgt86At-YMB5C6fI2amomdi4727Arme7HAPYKXGGC7h29ebJsBdQuwQBsBLXJAEfSd4XzIKxjCyMMrrSbokgN_ylEEogHSBNEOsAd0VH8/s640/inequality5.png" width="580" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 6: The likelihood of being in poverty by age group at time of survey.</td></tr>
</tbody></table>
From Figure 6 we can see that the affect of decreased income coupled with increased costs has created a situation in which a higher proportion of the lower 25% are at risk of being classified in poverty as at any time since the 1980s. Different age groups suffer from different levels of risk though clearly minors are at the highest risk with over 70% of them being raised in poverty in 2013.<br />
<br />
So what is the deal?<br />
<br />
Why are America's less fortunate so much more vulnerable to poverty than before?<br />
<br />
Are the poor giving up on school?<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjOiZqOgWdc4lAgsU0UBDzxk4S1nWfvpCndIo6HyO3DylcCAuZzNYC6gbCZyezpSUASOeTjYV2A9pcYZAqHq6XiOuH7kf5Jd6D5b2YnUeFXzy9k6puYsWC8LXu9hsOG4tHad6L20nOeeOQ/s1600/inequality12.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="350" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjOiZqOgWdc4lAgsU0UBDzxk4S1nWfvpCndIo6HyO3DylcCAuZzNYC6gbCZyezpSUASOeTjYV2A9pcYZAqHq6XiOuH7kf5Jd6D5b2YnUeFXzy9k6puYsWC8LXu9hsOG4tHad6L20nOeeOQ/s640/inequality12.png" width="580" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 7: Highest level of attainment for the lowest 25% of the income spectrum.</td></tr>
</tbody></table>
From Figure 7 we can see that the lowest 25% of society has higher high-school and college completion rates than at any time ever in our data.<br />
<br />
Is it just that people are poor because they can't find employment?<br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEixvNWRo1Bis9u0KiTXiXPeO4n-C_kobGwMBv7_OZKhSbHsuh0SrJluMXpwfvJhdsNWxlF9YKe0YLEYR0QSRrOVO7udko_4yTo1C9nsNDuF9h3V7syKdmaFGVSg5B8Ksey8SOFX8u39QwY/s1600/inequality8.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="350" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEixvNWRo1Bis9u0KiTXiXPeO4n-C_kobGwMBv7_OZKhSbHsuh0SrJluMXpwfvJhdsNWxlF9YKe0YLEYR0QSRrOVO7udko_4yTo1C9nsNDuF9h3V7syKdmaFGVSg5B8Ksey8SOFX8u39QwY/s640/inequality8.png" width="580" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 8: The likelihood of being poor if you work 40 hours or more a week.</td></tr>
</tbody></table>
From Figure 8 we can see that working 40 hours or more a week does not insulate one from poverty if you are among the bottom 50% of the poorest families. Whether you are a male or a female you are more likely to be in poverty while working full time today of any time since 1980.<br />
<br />
Is there any way to measure the effect of poverty on the health of families and individuals within our dataset? Unfortunately the census data is surprisingly lacking any indicators mental state or that of physical or mental health. What small measure we can look at is that of marital status inferring that happy people are more likely to stay married while unhappy ones, especially those under a lot of stress are less likely to stay married.<br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgy_2N-69SxUG44zv4ZJmZ5sUrevVw4dZ32v4DmDLd9ud0fJvRWaNo9ry-awf4K6BpeHfn3o1vjufcNFDdFWXxCTkopHmogDW0GuTrI8qQs5Nauah2QUaJbB7NWozPoEHA8RhXbj8fgo8Y/s1600/inequality11.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="350" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgy_2N-69SxUG44zv4ZJmZ5sUrevVw4dZ32v4DmDLd9ud0fJvRWaNo9ry-awf4K6BpeHfn3o1vjufcNFDdFWXxCTkopHmogDW0GuTrI8qQs5Nauah2QUaJbB7NWozPoEHA8RhXbj8fgo8Y/s640/inequality11.png" width="580" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 9: Likelihood of being divorced by income bracket.</td></tr>
</tbody></table>
Now it seems to be frequently argued that marriage is under attack within society in general. However, when looking at Figure 9, we can see that marriage seems to be more under attack for the poorest segments of society with the bottom 25% more than 10x more likely to be divorced or separated at the time of the survey than that of the top 1%.<br />
<br />
<br />
<br />
The decreased earning power of the bottom 25% is also reflected in a decreased ability to purchase and retain capital in the form of home ownership.<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiHiEZ-MC3BO_xMwhm60zfFVZsD2b39TPRUeOSc2iE6jreE4sHzcxpVk1WUnMOdHoS96gawkFXJm6RByQKsriLPd-dxvXjWKI10DJFKgq7wfmTJymNvU4HClHTMmyxAJEPdvHqpPcBuKDE/s1600/inequality10.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="350" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiHiEZ-MC3BO_xMwhm60zfFVZsD2b39TPRUeOSc2iE6jreE4sHzcxpVk1WUnMOdHoS96gawkFXJm6RByQKsriLPd-dxvXjWKI10DJFKgq7wfmTJymNvU4HClHTMmyxAJEPdvHqpPcBuKDE/s640/inequality10.png" width="580" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 10: Home ownership over time by income bracket.</td></tr>
</tbody></table>
From Figure 10 we can see that home ownership, apart from a brief spike in 2005 has decreased dramatically for the bottom 20% of the population since 1980. If you look more recently, home ownership has decreased dramatically within the last decade for all segments of the population.<br />
<br />
<h3 style="text-align: left;">
Conclusions</h3>
<br />
Democratic presidential candidate <a href="https://berniesanders.com/" target="_blank">Bernie Sanders</a> has claimed that income inequality is leading to the rich getting richer and the poor getting poorer. Nothing in the results presented here have contradicted this claim. Since 1980 the wealthiest segments of our population have increased in income level from making on average 4 times that of the median income to that of 10 times.<br />
<br />
At the same time, the poorest 25% of society now how less purchasing power than they did in the 1980s while the cost of rent, education, and health care have all risen. Despite having the odds stacked against them, the poorest 25% are better educated than at any time in history. Yet, their incomes have continued to falter while their divorce rates have grown steadily higher.<br />
<br />
<br />
We must therefore conclude that the society we live in today is less fair to the poor than it was 35 years ago despite the earnest efforts of the poor to become more educated. <br />
<br />
<h3 style="text-align: left;">
Data Source</h3>
<br />
The source of the data is from <a href="https://usa.ipums.org/" target="_blank">IPUMS-USA</a>.<br />
<br />
In order control the effect of disproportionate representations of ages
across years each year sample has been reduced so that a constant
proportions of all ages have been represented for each year.<br />
<br />
To create these graphs on your own <a href="https://github.com/EconometricsBySimulation/Ninja/blob/master/2015/11-November/2015-11-18-Inequality.R" target="_blank">you can find my code here</a>. You will need to request your own <a href="https://usa.ipums.org/" target="_blank">data from IPUMS</a>.</div>
Francishttp://www.blogger.com/profile/16658586705916884436noreply@blogger.com23tag:blogger.com,1999:blog-6288862798546085706.post-2954185688724547792015-11-13T21:56:00.003-05:002015-11-14T10:07:17.215-05:00What it means to be a US Veteran Today<div dir="ltr" style="text-align: left;" trbidi="on">
<br />
<b>Six easy graphs that tell a big story:</b><br />
<br />
1. You represent a much small portion of the American people than veterans in the 1980s. The different lines represent different income quantiles with the 1st being the lowest income and the 4th being the highest income. We can see that veterans formerly had the highest representation among the top quartile. This has changed significantly since 2005 with the middle two quartiles representing the largest two bodies of veterans.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhxYLu25AHLI6Mbj7TVpXohvKF-PaXgek878cZffkzWk0QXeCM2lXsLgwUPixnhxfjRmOem9HOyOUAnWSboYMHZKd5vXL48po5-V3hUpXH2j7xJrfhq0p4_KbIToH0Q9fzgDzK1KCpVKaY/s1600/Vet1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhxYLu25AHLI6Mbj7TVpXohvKF-PaXgek878cZffkzWk0QXeCM2lXsLgwUPixnhxfjRmOem9HOyOUAnWSboYMHZKd5vXL48po5-V3hUpXH2j7xJrfhq0p4_KbIToH0Q9fzgDzK1KCpVKaY/s600/Vet1.png" width="600" /></a></div>
<br />
2. You currently have the highest risk of being classified as poor for any time period since 1980. Since 2005, the rate of poverty among veterans has nearly doubled. That makes you still better off than the general population but not by much.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiysUbBb2L94BrHaK6QW-ABzt1623trm7y3MLIe_jUoCp3MlDb3DHk7IOe_dkA8aOla3dk-44OrC-0HE026f4HdBycytIRrl0TAfxhyb7o9z1SZf37Yn4soeoGzxG4HIF3Et-UT3OFwqiM/s1600/Vet2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiysUbBb2L94BrHaK6QW-ABzt1623trm7y3MLIe_jUoCp3MlDb3DHk7IOe_dkA8aOla3dk-44OrC-0HE026f4HdBycytIRrl0TAfxhyb7o9z1SZf37Yn4soeoGzxG4HIF3Et-UT3OFwqiM/s600/Vet2.png" width="600" /></a></div>
<br />
3. You are now less likely to own your own home than any time since 1980.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj2em4ZFVfpevjJLOnuXpH-DxlmCzTjJ-_3_Bl4RrLS3k6tC7Q9M5UeEfbEmc44m0iwJcFELsh8s-Enihyphenhyphena3RRgVhllIYEMpV3SNb3848gMH_FdTXIhAU3fnW9izQsbZz8mFCl-AJNGniU/s1600/Vet3.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="426" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj2em4ZFVfpevjJLOnuXpH-DxlmCzTjJ-_3_Bl4RrLS3k6tC7Q9M5UeEfbEmc44m0iwJcFELsh8s-Enihyphenhyphena3RRgVhllIYEMpV3SNb3848gMH_FdTXIhAU3fnW9izQsbZz8mFCl-AJNGniU/s600/Vet3.png" width="600" /></a></div>
<br />
4. On a positive note, you are more likely to have completed high-school than at any other time in history.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhBwdcYteE6ppdeb-q0OyAFLHeXI1Wp0oTCz_nWHd1UV83Owq9NaXDzE3GooEbeN6NExLeaSb4ri-FYoy3SWQBxm7G_BgZKYfPcHO1pdkveiGLS08xCKGJUDtt-QAcHYjIbOOFAUMv0H9g/s1600/Vet4.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="426" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhBwdcYteE6ppdeb-q0OyAFLHeXI1Wp0oTCz_nWHd1UV83Owq9NaXDzE3GooEbeN6NExLeaSb4ri-FYoy3SWQBxm7G_BgZKYfPcHO1pdkveiGLS08xCKGJUDtt-QAcHYjIbOOFAUMv0H9g/s600/Vet4.png" width="600" /></a></div>
<br />
5. On a not so positive note, as a veteran in 2010+ you are much less likely to have completed four or more years of college than those with no military service. Unfortunately the current world is not friendly to those without a college degree.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhVtNIUClfmvqVvS6HtZrUeHgSt1H1HV_lX7LuOojhiTQEUkT3Tgcu90936tKBEf1eY1YZPEnhnigccfS6zX_AUlI9aChL0wSSmLF5tfgcQnveA7Y2AnUDGOiouR12EmhY0wnXTvFzysPk/s1600/Vet5.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="426" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhVtNIUClfmvqVvS6HtZrUeHgSt1H1HV_lX7LuOojhiTQEUkT3Tgcu90936tKBEf1eY1YZPEnhnigccfS6zX_AUlI9aChL0wSSmLF5tfgcQnveA7Y2AnUDGOiouR12EmhY0wnXTvFzysPk/s600/Vet5.png" width="600" /></a></div>
<br />
6. And to top it off. The strain of being a veteran has negatively affected your marriage. Starting in the 1990s and getting worse over time, the likelihood of being separated or divorced from your spouse is significantly higher than that of the no-military-service population.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj3mxLIN1sbyiPzDZvNGdTfTLy9hpTWTgL8vp__OkSElATlRDnl0xCrTmrRQCGC2OdIWvjXUC9GebF7Mpazeh-2tAr-hf1GvFosBSRYH1hJlS4ENhSHUR8KCMSLcfj5UFKzBKbiVhyizXI/s1600/Vet6.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="426" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj3mxLIN1sbyiPzDZvNGdTfTLy9hpTWTgL8vp__OkSElATlRDnl0xCrTmrRQCGC2OdIWvjXUC9GebF7Mpazeh-2tAr-hf1GvFosBSRYH1hJlS4ENhSHUR8KCMSLcfj5UFKzBKbiVhyizXI/s600/Vet6.png" width="600" /> </a></div>
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<br /></div>
<div class="separator" style="clear: both; text-align: center;">
So what is the takeaway?</div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
Vote for a president you know is going to support your issues. </div>
<hr />
<br />
Source:<br />
<br />
In this quick analysis, I look at the census records of 470 thousand random adults between the ages of 18 and 65 sampled each of the years (1980,1990,2000,2005,2010,2013). The source of the data is from IPUMS-USA.<br />
<br />
In order control the effect of disproportionate representations of ages across years each year sample has been reduced so that a constant proportions of all ages have been represented for each year.<br />
<br />
PUMS-USA, University of Minnesota, www.ipums.org.<br />
<br />
<a href="https://github.com/EconometricsBySimulation/Ninja/blob/master/2015/11-November/2015-11-14-Veterans.R" target="_blank">Find My Code Here</a> </div>
Francishttp://www.blogger.com/profile/16658586705916884436noreply@blogger.com4tag:blogger.com,1999:blog-6288862798546085706.post-28230410761758483872015-10-30T19:04:00.001-04:002015-10-30T19:08:57.520-04:00The Traveling Vampire Problem<div dir="ltr" style="text-align: left;" trbidi="on">
Let's say you are a vampire and you would like to figure out the shortest route to visit the supple<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="http://icons.iconarchive.com/icons/gcds/halloween/256/bat-icon.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="http://icons.iconarchive.com/icons/gcds/halloween/256/bat-icon.png" height="200" width="200" /></a></div>
<br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjvnarZ3fEts1s9VrL2wLUmWrHR1NEenC8gZjk-M-5t5vCcQEOYagelmCwro7LAlu2n8GrZw0RgVxd5kkyUuT5DryGVAerS-Trz2rtnAQ6xAqNnr06fMr5Yghbmas1pDBRSoDqIwRtwvjQ/s1600/TravellingVamp10.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a>necks of N maidens. But, there is only so much time in any night!<br />
<br />
You can fly from location to location, ignoring barriers.<br />
<br />
With a few maidens, the problem is trivial.<br />
<br />
However, as you entice more and more maidens you find the task of route management increasingly complex.<br />
<br />
You buy a computer but find that using a blanket search algorithm to check all possible routes quickly becomes very time consuming as each additional maiden is added to the optimization.<br />
<br />
The problem you realize is that each additional maiden increases the number of routes significantly. This is because there is a number of routes is equal to the permutation of N select N = N!.<br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; margin-right: 1em; text-align: left;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgFZgYN0NRv9yqGtahfb-YdfCoqiupdvUegbM5TzU408kynSBRUaaADmDABGIdhN3H-0WUKGOCQXtsXe8KkuBU9wkDItvvjpSAZuDHUJk3YJVllAjr_MVadxZeusQ39KHeuCrdVrxXaPU0/s1600/Maidens4.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="249" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgFZgYN0NRv9yqGtahfb-YdfCoqiupdvUegbM5TzU408kynSBRUaaADmDABGIdhN3H-0WUKGOCQXtsXe8KkuBU9wkDItvvjpSAZuDHUJk3YJVllAjr_MVadxZeusQ39KHeuCrdVrxXaPU0/s320/Maidens4.png" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Four maidens, an easy problem.</td></tr>
</tbody></table>
So the number of routes:<br />
1 maiden: 1=1<br />
2 maidens: 1*2=2 (for example 1,2 or 2,1)<br />
3 maidens: 1*2*3=6 (for example 1,2,3 or 1,3,2 or 2,1,3 or 2,3,1 or 3,2,1 or 3,1,2)<br />
4 maidens: 1*2*3*4=24<br />
5 maidens: 1*2*3*4*5=120<br />
6 maidens: 1*2*3*4*5*6=720<br />
7 maidens: 1*2*3*4*5*6*7=5,040<br />
8 maidens: 1*2*3*4*5*6*7*8=40,320<br />
9 maidens: 1*2*3*4*5*6*7*8*9=362,880<br />
10 maidens: 1*2*3*4*5*6*7*8*9*10=3,628,800<br />
<br />
<br />
<br />
As you start getting more and more maidens your algorithm to select the best route becomes extremely slow. You realize that using R your are going to face a practical limitation of spending as much time running the optimization as you will actually sucking necks. You know of Julia (which can run up to 500x faster than R) but you quickly realize that this is just postponing the problem. Even if you were running 500 times faster. Running the same algorithm on Julia is going to be four times faster after two more maidens (11*12/500=.26) but three times slower after 3 more maidens (11*12*13/500=3.4).<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right; margin-left: 1em; text-align: right;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhSNW8upIcqc9fpiOb2uyLs-6Qbs6_NePMi5LCOwecjREn61uZ-4GMl6WnZoi-RKrNWc7km2kjnnUl-qeE6D3NGhgTuEz6Ps7yq_dd9We_FahQ26YlTPWoNi1Ahk5T2FdgldDQW0tDMoIs/s1600/Maidens7.png" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="249" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhSNW8upIcqc9fpiOb2uyLs-6Qbs6_NePMi5LCOwecjREn61uZ-4GMl6WnZoi-RKrNWc7km2kjnnUl-qeE6D3NGhgTuEz6Ps7yq_dd9We_FahQ26YlTPWoNi1Ahk5T2FdgldDQW0tDMoIs/s320/Maidens7.png" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Seven Maidens. Getting a bit more tricky.</td></tr>
</tbody></table>
<br />
You consider hibernating for a hundred years to see if computational speed increases will simplify the problem but also realize that if you keep approaching the problem using a binary computer with the same strategies as previously, you will always face similar computational limits. Eventually, and even very far into the future you will run out of computer speed long before you run out of maidens.<br />
<br />
Being a clever vamp, you decide to start looking into alternative strategies to solving this kind of problem. But that is for another day.<br />
<br />
--------------------------------<br />
<br />
For what it is worth, I wrote a traveling vamp optimizer allowing for an arbitrary number dimensions to be specified. The most complex problem it solved was a 10 maiden problem and took a little over an hour.<br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgSITRgeiUx2gT-C4ZYbJFSy0F5IfzIFG0aLUvH27w8U4c38Syth4K6eeNt8mu8sEwEb1YGcl6JKIb1qCpRVeDVGbMADB6jPLWhJ6Ut37nEPRavQu0pPsPDcaw9825Mvm0Gyu7c-oBUxMc/s1600/TravellingVamp10.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgSITRgeiUx2gT-C4ZYbJFSy0F5IfzIFG0aLUvH27w8U4c38Syth4K6eeNt8mu8sEwEb1YGcl6JKIb1qCpRVeDVGbMADB6jPLWhJ6Ut37nEPRavQu0pPsPDcaw9825Mvm0Gyu7c-oBUxMc/s320/TravellingVamp10.png" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Two solutions for a 10 maiden problem. Top is shortest route while bottom is longest.</td></tr>
</tbody></table>
Find the code <a href="https://github.com/EconometricsBySimulation/Ninja/blob/master/2015/10-October/30-TravelingVamp.R" target="_blank">here</a>.</div>
Francishttp://www.blogger.com/profile/16658586705916884436noreply@blogger.com5tag:blogger.com,1999:blog-6288862798546085706.post-2239084635566369302015-10-23T20:52:00.002-04:002015-10-23T23:50:57.064-04:00Diagnosing the Multilevel Marketting Trap: How MLM Survives Only through New Entrants<div dir="ltr" style="text-align: left;" trbidi="on">
Over the years I have been amazed by how many friends of mine who seem otherwise very intelligent have gotten involved in Multilevel Marketing (MLM).<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgUxfQO-LSxew9cy9UOCEHSx6XKJ5yQCAc_fWSLNnPRI_-H-U0AgKrdKFMBSNsgqr0bAEcfexXw11v2PK4XGAX19ua-l1JKyPts_nkUUwfEvLXpZwyxN2-8kzl0UttMf7P3pNY7qHaQt7Y/s1600/ReplacementRate0Pcnt3.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="133" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgUxfQO-LSxew9cy9UOCEHSx6XKJ5yQCAc_fWSLNnPRI_-H-U0AgKrdKFMBSNsgqr0bAEcfexXw11v2PK4XGAX19ua-l1JKyPts_nkUUwfEvLXpZwyxN2-8kzl0UttMf7P3pNY7qHaQt7Y/s200/ReplacementRate0Pcnt3.png" width="200" /></a></div>
<br />
And, as most people who have been involved with these organizations, all of my friends involved in these organization have ended up after many hours and sometimes years of effort with less return for their efforts than what the paid to be part of the system. Many of these MLMs call participants "Independent Business Owners" (IBOs).<br />
<br />
The problem with multilevel marketing is that it sounds like it should work!<br />
<br />
You, the IBO, buy products at wholesale price that you are in turn sell to someone else at retail price. You get the majority of the revenue from the sales of these products. Some smaller portion of the revenue is distributed to the person who recruited you and some portion to the person who recruited that person all the way up to the top. Simple right?<br />
<br />
All you have to do is go out there and start recruiting others and selling some goods yourself and before you know it you will have flocks of people underneath you selling and recruiting others and you can sit back and retire, right?<br />
<br />
Pretty picture that just does not seem to work out for just about anybody.<br />
<br />
But why?<br />
<br />
The problem is that the system is inherently unstable. What one finds is that communities are rapidly saturated with IBOs. Once saturated, it is extremely difficult to recruit new IBOs from such a community. Not only that, but once recruited, IBOs who fail to recruit others risk becoming discouraged and dropping out of the system causing you to potentially become discouraged and drop out of the system.<br />
<br />
Thus, MLM is really much more like a house of cards. The first ones in have a good position, but the later you enter the system the more vulnerable you become.<br />
<br />
But don't take my word for it. You can simulate it fairly easily. (Well not so easy but I will show you how to. <a href="https://github.com/EconometricsBySimulation/Ninja/blob/master/2015/10-October/22-MLM.R" target="_blank">Find the code here</a>)<br />
<br />
The simulation works as follows:<br />
1. First there is one IBO, that IBO is able to interact with a number of other agents. Some of those agents the IBO will sell to based on a random probability (in this case 20%) and some of those agents the IBO will infect or convert to other IBOs base on probability again (10%).<br />
2. A successful sales yields a return of $10.<br />
3. Each round costs $10 to remain an IBO.<br />
4. An IBO also makes commission on sales from anybody that IBO has recruited or that IBO has recruited. The commission rate is 25% meaning each upstream person makes an extra 25% on the sales of the downstream person.<br />
5. Each IBO actively engages in sales and recruiting and meets 30 people per time period.<br />
6. Once approached by one IBO in a time period additional approaches will be all rejected for that time period.<br />
7. IBOs cannot recruit or sell to each other or former IBOs (defined as "immune" from the MLM) <br />
8. Each encounter costs the IBO $1 of effort.<br />
<br />
<b>Replacement Rate:</b><br />
In order to give a "fair" representation of the model we must allow for replacement of the population with new population. This of course is only fair in the long run as the replacement rate in the US and most industrialized societies is less than 2% per year. This of course assumes that parents do not pass on immunity to their young.<br />
A. No Replacement: 0%<br />
B. Replacement: 2%<br />
C. Replacement: 20% <br />
<br />
<b>Other Factors:</b><br />
Which can be varied but do not affect the big picture. Results not presented here.<br />
1. Sales rate: You can change how effective individuals are at selling dramatically without having any significant effect on the long term sustainability of the model. If individuals are less effective at selling then participation will increase vulnerability to dropout within the MLM model resulting in faster burn-out rates.<br />
2. Recruitment rate: You can increase the recruitment rate or decrease it and this will only cause the population of IBO to peak either faster or slower. Either way always leading to the same end result eventually.<br />
3. Population size. Increasing the population larger than 100 thousand tends to slow down my machine but I did run it once with a population of 1 million up to round 40. The result is nearly identical to that of a population of 100 thousand. The only difference is that the peak recruitment occurs one round later. Because the MLM model relies upon an exponential growth model you would need to continue to increase the size of the population exponentially each round to make it sustainable.<br />
4. Return from sales: It does not matter how much profit each sales is worth, eventually the market will get saturated and people will start dropping out.<br />
5. Encounters per round: Like sales rate and recruitment rate this only changes the rate at which the system peaks but does not change the end result.<br />
<br />
So here are graphs illustrating the results by "level" within the organization or rather time period of entry into the model.<br />
<br />
<h3 style="text-align: left;">
<b>Results </b></h3>
<br />
<b>Results: Replacement of 0%</b> <br />
<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjnPKBGtS-udQxAu7NzzFHbBWV_2kVMmDgTkAjSRWzlqk1qxbCsJGZ3yiCmamJgXjKkd31xrBSHtR-Qdgu1WeHrH1VLhIEjNRn0FleZlxzWcWkkwGQhBvPfNmqdEwdPOijDdLkTAwQT8Z4/s1600/ReplacementRate0Pcnt1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="266" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjnPKBGtS-udQxAu7NzzFHbBWV_2kVMmDgTkAjSRWzlqk1qxbCsJGZ3yiCmamJgXjKkd31xrBSHtR-Qdgu1WeHrH1VLhIEjNRn0FleZlxzWcWkkwGQhBvPfNmqdEwdPOijDdLkTAwQT8Z4/s400/ReplacementRate0Pcnt1.png" width="400" /></a></div>
Figure 1: This graph shows how many IBO's exist at each level during each time period. The first period of a each level is by definition the maximum number of IBOs in that level. The majority of the time they drop out of the model. In period around 12-15 there are the most new IBOs. But as the market gets saturated, they quickly drop out.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi-4rHZZ4Ga5qMv_uxAdvWPtGAssg_nzUUWw5rrv6V3cxB5gNBV_iVDu3DPhWlA5wW1YsnlG0pxvOoCjSgPzaCiySuqw7595-16rRHG7yRxrJ-uC_HdrxeKwxCn09q_2sQ-i0Y8QVmHbsA/s1600/ReplacementRate0Pcnt2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="266" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi-4rHZZ4Ga5qMv_uxAdvWPtGAssg_nzUUWw5rrv6V3cxB5gNBV_iVDu3DPhWlA5wW1YsnlG0pxvOoCjSgPzaCiySuqw7595-16rRHG7yRxrJ-uC_HdrxeKwxCn09q_2sQ-i0Y8QVmHbsA/s400/ReplacementRate0Pcnt2.png" width="400" /></a></div>
Figure 2: And why drop out, you ask? The problem is that the market is saturated. The above graph shows anybody who has not entered by period 6 is going to have difficulty making a living. Remember the dropout conditions are pretty strict. You need to loose $40 (your participation fee $10 and $30 in sales efforts) during a period in order to drop out. This only occurs if you pay you mandatory membership see and fail to make a single sale.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgkvIAH5Q5TkrSvlVRtOIepRvJcdLld_LghYWaYSFRYzcA0Ef9T-4yasjTHT-He1DDryOk-LoF32eaaeiJ2etzlK2vNZtj57FQe-99YAGiM6g4f_MGUfyOLsa8lAeQ7QkD3aiVW0H8WvvY/s1600/ReplacementRate0Pcnt3.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="266" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgkvIAH5Q5TkrSvlVRtOIepRvJcdLld_LghYWaYSFRYzcA0Ef9T-4yasjTHT-He1DDryOk-LoF32eaaeiJ2etzlK2vNZtj57FQe-99YAGiM6g4f_MGUfyOLsa8lAeQ7QkD3aiVW0H8WvvY/s400/ReplacementRate0Pcnt3.png" width="400" /></a></div>
Figure 3: But what about the "top" people in their level? Aren't they doing well. The above graph shows the maximums for each level in terms of profitability. It is pretty much the same picture as the last. Unless you entered very early, you have to be very lucky to make any money. Remember that for these late entrants, there are thousands of them and this is the maximum profitability for the entire level.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEizJsDjHf1dXk5j36wpQnKvKuDvROqjvf6UoQzfBoK_JWa5zPl9fz8US81UFsA1yUZVCs_-jM_tS8zfcrzLuMXcKxcUYgrRCNV9yINkpWD8F7GNHLawLn_v10jNNwwm0A2ys2CgDZfLEhg/s1600/ReplacementRate0Pcnt5.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="266" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEizJsDjHf1dXk5j36wpQnKvKuDvROqjvf6UoQzfBoK_JWa5zPl9fz8US81UFsA1yUZVCs_-jM_tS8zfcrzLuMXcKxcUYgrRCNV9yINkpWD8F7GNHLawLn_v10jNNwwm0A2ys2CgDZfLEhg/s400/ReplacementRate0Pcnt5.png" width="400" /></a></div>
Figure 4: But some people are making money! How much money is made by each group of people in total? The above graph shows that the total amount of money for each level over the entire 50 periods of the simulation changes rather abruptly around period 11. This is the point when the market gets saturated. After that point people who enter are extremely unlikely to make any money.<br />
<br />
<b>Results: Replacement of 2%</b><br />
<br />
Fine! But there is replacement in the world! New young people grow up and enter the system and replace those who have dropped out of the system. How does that change things?<br />
<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjYT1fRv5nY8VEMsohbhxP7n6olkYy9W1w68J_dutqNCBoXzQ63nKP9DKLP5OEYGByxBuzyB91va4-rIQb_xMF3BHtuawO8pQPpXqCV-MN5MYLq9e3oBPn28iCwmLLNVsuJU6vWutexrv8/s1600/ReplacementRate2Pcnt1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="266" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjYT1fRv5nY8VEMsohbhxP7n6olkYy9W1w68J_dutqNCBoXzQ63nKP9DKLP5OEYGByxBuzyB91va4-rIQb_xMF3BHtuawO8pQPpXqCV-MN5MYLq9e3oBPn28iCwmLLNVsuJU6vWutexrv8/s400/ReplacementRate2Pcnt1.png" width="400" /></a></div>
Figure 5: At a 2% population replacement rate we can see that recruitment while still down from early peak is more robust in the later periods of the model. <br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiMw21_JwcUuUSqS9yRGeQtYInpxfhqdDl1hkSTBNrvAK4ZTRzYxNJlyZCa-vR4wOSJ5G3g1OJ-HgE8Xs69gP2soqXmThrw2RZgXpX7xFZVCS-6RrxRSsdglggUlMNb_zRiJWwSGGxDChY/s1600/ReplacementRate2Pcnt2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="266" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiMw21_JwcUuUSqS9yRGeQtYInpxfhqdDl1hkSTBNrvAK4ZTRzYxNJlyZCa-vR4wOSJ5G3g1OJ-HgE8Xs69gP2soqXmThrw2RZgXpX7xFZVCS-6RrxRSsdglggUlMNb_zRiJWwSGGxDChY/s400/ReplacementRate2Pcnt2.png" width="400" /></a></div>
Figure 6: Does this mean that late entries are going to do better? This figure shows clearly that on average late entries are still going to do very poorly. The fact is that the market is saturated and clearing up 2% new replacement is not going to significantly affect the long term outcomes.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhExfqHnZ0nw3x_zv7uYXzqsB4AnGO9k_Yqs9iDVzRR8hF4q3Rhxf-Owr43zDSs_UYK5SveUM0N6xCBZS_JdnDvKiVa2BVKRtHJiCcuRonk4ZtMBXsIM_Gxs7Z9wyz0iEpsMRYZECuKdJQ/s1600/ReplacementRate2Pcnt3.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="266" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhExfqHnZ0nw3x_zv7uYXzqsB4AnGO9k_Yqs9iDVzRR8hF4q3Rhxf-Owr43zDSs_UYK5SveUM0N6xCBZS_JdnDvKiVa2BVKRtHJiCcuRonk4ZtMBXsIM_Gxs7Z9wyz0iEpsMRYZECuKdJQ/s400/ReplacementRate2Pcnt3.png" width="400" /></a></div>
Figure 7: What about the best seller/recruiter? The story is basically the same even with some replacement. Even the very best seller/recruiter is going to struggle if they did not enter as one of the top 4 levels.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh6PsUoLCvS62lHXZIyegT8Rr4Qj1um_zfNOjBHPjJ4rkCan9jRYSLsjgCYNcSrz8kdX9ZR8NCUS3OSCXdIUEstpiT7uEoBQfy7dQTWmE1fRhNV7jgwOx3wf51nL3yoZzr7cLhZkt64zO8/s1600/ReplacementRate2Pcnt5.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="266" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh6PsUoLCvS62lHXZIyegT8Rr4Qj1um_zfNOjBHPjJ4rkCan9jRYSLsjgCYNcSrz8kdX9ZR8NCUS3OSCXdIUEstpiT7uEoBQfy7dQTWmE1fRhNV7jgwOx3wf51nL3yoZzr7cLhZkt64zO8/s400/ReplacementRate2Pcnt5.png" width="400" /></a></div>
Figure 8: So what about the total profitability of those new waves of recruits? The story is essentially the same as with no replacement. Up to a certain point (round 11) there is money to be made but after that the people who generally loose money. The overall profitability of the model is unsustainable.<br />
<br />
<b>Results: Replacement of 20%!</b><br />
<br />
So, is the problem one of replacement? Perhaps if we had higher replacement rates then the model would work? For the following graphs, I set the replacement rate at 20%. This is a huge number but perhaps not impossible if you are thinking about developing nations where people are rapidly moving from poverty to middle class.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJn39lhqlKIUiLbrIaW-nqeyclFBFHmDgybAH4ZWGNGfkmFCu77t7g7j5x9zpgBIxyZpTvzKK6v8mnrrd66MaSTHXe7beyz-PI0kwuvYycIzTGjHsjRGYRwhLRL-8mdcTU6aLG6AT7VVE/s1600/ReplacementRate20Pcnt1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="266" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJn39lhqlKIUiLbrIaW-nqeyclFBFHmDgybAH4ZWGNGfkmFCu77t7g7j5x9zpgBIxyZpTvzKK6v8mnrrd66MaSTHXe7beyz-PI0kwuvYycIzTGjHsjRGYRwhLRL-8mdcTU6aLG6AT7VVE/s400/ReplacementRate20Pcnt1.png" width="400" /></a></div>
Figure 9: Does high replacement make the model more sustainable? This figure shows that this is not the case! The problem is that the market becomes saturated still in round 12-15 and though 20% of the population gets replaced, it remains saturated leading to massive and systematic dropouts in every period as new entrants find it nearly impossible to make sales.<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiCL68PgONSN3sxqOq5PoaS-HxhyphenhyphenKDhwbjsd67_rQnDoxLgjhVz2DBmQJI0g2HKWkDBZyG5arFCWBipFUU678oU35q97KfRbzmebiUJGApAL09rUaUZbGJdJT9qSne9ECLa0wRcsggcTnA/s1600/ReplacementRate20Pcnt2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="266" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiCL68PgONSN3sxqOq5PoaS-HxhyphenhyphenKDhwbjsd67_rQnDoxLgjhVz2DBmQJI0g2HKWkDBZyG5arFCWBipFUU678oU35q97KfRbzmebiUJGApAL09rUaUZbGJdJT9qSne9ECLa0wRcsggcTnA/s400/ReplacementRate20Pcnt2.png" width="400" /></a></div>
Figure 10: Well what about for those who stick it out? Does it become any easier? This figure answers that question. No, if you did not enter within the first 5 levels population replacement is not going to help. Why? Because the market is saturated! No matter how successful you are, the people you recruit will compete with the ones they recruit and in the end very few are going to make sales.<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj-mrvILYX6q3kEnLn_v216e2wC7rBG8SxsyvBDAIR0Ercjg1ecZ5h5hwJrPudODGmMb1rqfJuimu9JKpeSheUFcfASS3dtfY8PGaS8f8_c5Utccy2Nak-_vnx2icBsGq4PpI9t2GN1Ft0/s1600/ReplacementRate20Pcnt3.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="266" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj-mrvILYX6q3kEnLn_v216e2wC7rBG8SxsyvBDAIR0Ercjg1ecZ5h5hwJrPudODGmMb1rqfJuimu9JKpeSheUFcfASS3dtfY8PGaS8f8_c5Utccy2Nak-_vnx2icBsGq4PpI9t2GN1Ft0/s400/ReplacementRate20Pcnt3.png" width="400" /></a></div>
Figure 11: What about the best seller/recruiter in each period? The story is largely the same. There are the guys with big homes and fancy cars on the top and that is because they entered early. Nearly everybody else is going to struggle with thousands of others to make very little income. And remember, there are a lot of new faces constantly entering the market to compete with (See Figure 9).<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgz-DhXD6NzLHEuuCYRevCGJtleKNuEQ6Uwf3CDFts_OeR6UeEwZkZA8zoz1zewJ2sr88OoxFeF4nX71-yHBaDiqL8PYtkyP9fh-CgODyFCy5o5WqD69gc5sZzblMkHYVL-TlHGmFmCJ8E/s1600/ReplacementRate20Pcnt5.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="266" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgz-DhXD6NzLHEuuCYRevCGJtleKNuEQ6Uwf3CDFts_OeR6UeEwZkZA8zoz1zewJ2sr88OoxFeF4nX71-yHBaDiqL8PYtkyP9fh-CgODyFCy5o5WqD69gc5sZzblMkHYVL-TlHGmFmCJ8E/s400/ReplacementRate20Pcnt5.png" width="400" /></a></div>
Figure 12: And this is where it becomes clear that this model is just that of a pyramid scheme. Except for a very few IBOs who enter early, the vast majority of IBOs are paying a lot of out of pocket costs and time in order to loose money overall! <br />
<br />
<h3 style="text-align: left;">
<b>Conclusions</b></h3>
<br />
Though the MLM business model is inherently and irredeemably broken, there are hundreds of MLM business out there in the world "making" billions of dollars. Searching for "multilevel marketing" on Google you will find a lot of people who say they only lost money, time, and friends by participating in MLM but they still generally believe that if you stick it out and work hard enough it could have worked. They have bought into the lie that if they were just better at selling or better at recruiting they could have been successful.<br />
<br />
But the truth that these simulations have convinced me of is that this is not the case. Those who are going to make money from MLM have already established themselves within the organization in order to make money. Everybody else, unfortunately are the suckers who do the hard work of making sales and recruiting new suckers.<br />
<br />
You will hear people make analogies about how some established industries such as insurance are also commission based systems and therefore just another form of MLM. However, I have interacted with many insurance agents over the years and none of them have ever tried to recruit me to be an insurance agent as well.<br />
<br />
Going into this project, I was uncertain about how "bad" MLM was. Now, I am certain. The only way MLM models are marginally sustainable is by continually feeding new bodies into the machine. This results in early entrants making big money and everybody else loosing out.<br />
<br />
But don't take my word for it! Play with my simulation! Tweak the parameters however you want. The only way you make the system sustainable is if you make the cost of attempting to sell or recruit equal to zero and you set the cost of membership equal to zero. Of course these assumptions do not and can not reflect the real world or any MLM model!<br />
<br />
Thus, there is no possible way to build a model that allows late entrants to be profitable!</div>
Francishttp://www.blogger.com/profile/16658586705916884436noreply@blogger.com7tag:blogger.com,1999:blog-6288862798546085706.post-53894007577379715892015-10-12T13:43:00.001-04:002015-10-12T15:13:35.998-04:00Debunking Magical 9s - Numerology or Numerical Illiteracy?<div dir="ltr" style="text-align: left;" trbidi="on">
<a href="https://bookofresearch.files.wordpress.com/2015/06/number-9.png?w=447&h=273" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="181" src="https://bookofresearch.files.wordpress.com/2015/06/number-9.png?w=447&h=273" width="200" /></a>The other day one of my friends on facebook posted this <a href="https://www.youtube.com/watch?v=W5mJeRtjPvY" target="_blank">video</a> about the mystical nature of the number 9. Being a skeptical of all things hokey, I decided to experiment with numbers to see how special 9 really is.<br />
<br />
There are four claims made in the video about the magic of nine.<br />
1. Partition a circle as many times and its digits add up to nine<br />
2. Add the sides of a regular polygon together and their digits sum to 9<br />
3. Add all of the digits up to 9 and they sum to 9<br />
4. Add 9 to any other digit and it returns that digit.<br />
<br />
In this post I will address all of these patterns and demonstrate conclusively that 9 is not special but only a feature of using a base 10 system (that is we count to 9 before starting over again for example 9 10 11 or 19 20 21 etc).<br />
<br />
This may seem like a silly issue to address. However, a lot of people have watched this video (6 million plus either on youtube or the original facebook post). In this post I will support my arguments by use of some custom R functions built for this task. You need not have R or run the functions to understand the results.<br />
<h3 style="text-align: left;">
<br />
1: Magic 9 is embedded in the circle</h3>
<br />
<br />
At the beginning of the video, the author suggests that
there is something special about 9 because when you divide the degrees
of a circle in half all of the digits add up to 9. No only that but when
you divide each of those halves each digit adds up to nine.<br />
<br />
360 ... 3+6+0=9<br />
180 ... 1+8+0=9<br />
90 ... 9+0=9<br />
45 ... 4+5=9<br />
22.5 ... 2+2+5=9<br />
11.25...1+1+2+5=9<br />
<br />
Up to double digits which you then add together. So the pattern continues.<br />
<br />
5.625 ... 5+6+2+5=18 ... 1+8=9<br />
<br />
At 150 splits (ignoring 0s and decimals) you get a series of numbers that look like this:<br />
<br />
1261168617892335712057451360671424133527367330073300513283903262277297315100935657007585133880800115163136<br />
<br />
And when you add them all together they equal: 396 ... 3+9+6=18 ... 1+8=9<br />
<br />
So, as far as I am willing to explore, the pattern seems to hold.<br />
<br />
First look at this, I said, "okay, but is this pattern just for 9s?"<br />
<br />
After some exploration I came to the conclusion "yes" (at least with a base 10 system). There seems to be some other patterns but nothing as straightforward as the 9s.<br />
<br />
In order to accomplish this efficiently I programmed a "splitter" algorithm in R. This will split any number in half, take the digits and add them together. See below:<br />
<br />
<br />
<div style="overflow: auto;">
<div class="geshifilter">
<pre class="r geshifilter-R" style="font-family: monospace;"><a href="http://inside-r.org/r-doc/base/library"><span style="color: #003399; font-weight: bold;">library</span></a><span style="color: #009900;">(</span>magrittr<span style="color: #009900;">)</span>
<a href="http://inside-r.org/r-doc/base/library"><span style="color: #003399; font-weight: bold;">library</span></a><span style="color: #009900;">(</span><a href="http://inside-r.org/packages/cran/gmp">gmp</a><span style="color: #009900;">)</span>
splitter <- <a href="http://inside-r.org/r-doc/base/function"><span style="color: #003399; font-weight: bold;">function</span></a><span style="color: #009900;">(</span>X<span style="color: #339933;">,</span> it<span style="color: #339933;">,</span> nest<span style="color: #339933;">,</span> noisy=<span style="color: black; font-weight: bold;">TRUE</span><span style="color: #009900;">)</span> <span style="color: #009900;">{</span>
Ys <- <a href="http://inside-r.org/r-doc/base/matrix"><span style="color: #003399; font-weight: bold;">matrix</span></a><span style="color: #009900;">(</span><span style="color: black; font-weight: bold;">NA</span><span style="color: #339933;">,</span> <a href="http://inside-r.org/r-doc/base/nrow"><span style="color: #003399; font-weight: bold;">nrow</span></a>=it<span style="color: #339933;">,</span> <a href="http://inside-r.org/r-doc/base/ncol"><span style="color: #003399; font-weight: bold;">ncol</span></a>=nest<span style="color: #009900;">)</span>
<a href="http://inside-r.org/r-doc/base/options"><span style="color: #003399; font-weight: bold;">options</span></a><span style="color: #009900;">(</span>digits=<span style="color: #cc66cc;">22</span><span style="color: #339933;">,</span>scipen=<span style="color: #cc66cc;">999</span><span style="color: #009900;">)</span>
esum <- <a href="http://inside-r.org/r-doc/base/function"><span style="color: #003399; font-weight: bold;">function</span></a><span style="color: #009900;">(</span>x<span style="color: #009900;">)</span>
x %>% <a href="http://inside-r.org/r-doc/base/toString"><span style="color: #003399; font-weight: bold;">toString</span></a> %>% <a href="http://inside-r.org/r-doc/base/sub"><span style="color: #003399; font-weight: bold;">sub</span></a><span style="color: #009900;">(</span><span style="color: blue;">"."</span><span style="color: #339933;">,</span> <span style="color: blue;">""</span><span style="color: #339933;">,</span> .<span style="color: #339933;">,</span> fixed = <span style="color: black; font-weight: bold;">TRUE</span><span style="color: #009900;">)</span> %>% <a href="http://inside-r.org/r-doc/base/strsplit"><span style="color: #003399; font-weight: bold;">strsplit</span></a><span style="color: #009900;">(</span><span style="color: blue;">""</span><span style="color: #009900;">)</span> %>% <a href="http://inside-r.org/r-doc/base/unlist"><span style="color: #003399; font-weight: bold;">unlist</span></a> %>% <a href="http://inside-r.org/r-doc/base/as.numeric"><span style="color: #003399; font-weight: bold;">as.numeric</span></a>
<span style="color: black; font-weight: bold;">for</span> <span style="color: #009900;">(</span>i <span style="color: black; font-weight: bold;">in</span> <span style="color: #cc66cc;">0</span>:<span style="color: #009900;">(</span>it-<span style="color: #cc66cc;">1</span><span style="color: #009900;">)</span><span style="color: #009900;">)</span> <span style="color: #009900;">{</span>
x <- as.bigz<span style="color: #009900;">(</span>X<span style="color: #009900;">)</span>
x <- x*<span style="color: #cc66cc;">10</span>^<span style="color: #009900;">(</span>i<span style="color: #009900;">)</span>/<span style="color: #cc66cc;">2</span>^i
Y <- x %>% esum
<span style="color: black; font-weight: bold;">if</span> <span style="color: #009900;">(</span>noisy<span style="color: #009900;">)</span> <a href="http://inside-r.org/r-doc/base/print"><span style="color: #003399; font-weight: bold;">print</span></a><span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/base/sprintf"><span style="color: #003399; font-weight: bold;">sprintf</span></a><span style="color: #009900;">(</span><span style="color: blue;">"%s: %s -> sum(%s)=%s"</span><span style="color: #339933;">,</span>i<span style="color: #339933;">,</span> x <span style="color: #339933;">,</span><a href="http://inside-r.org/r-doc/base/paste"><span style="color: #003399; font-weight: bold;">paste</span></a><span style="color: #009900;">(</span>Y<span style="color: #339933;">,</span> <a href="http://inside-r.org/r-doc/nlme/collapse"><span style="color: #003399; font-weight: bold;">collapse</span></a>=<span style="color: blue;">" "</span><span style="color: #009900;">)</span><span style="color: #339933;">,</span> <a href="http://inside-r.org/r-doc/base/sum"><span style="color: #003399; font-weight: bold;">sum</span></a><span style="color: #009900;">(</span>Y<span style="color: #009900;">)</span><span style="color: #009900;">)</span><span style="color: #009900;">)</span>
Ys<span style="color: #009900;">[</span>i+<span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">1</span><span style="color: #009900;">]</span> <- <a href="http://inside-r.org/r-doc/base/sum"><span style="color: #003399; font-weight: bold;">sum</span></a><span style="color: #009900;">(</span>Y<span style="color: #009900;">)</span>
<span style="color: black; font-weight: bold;">for</span> <span style="color: #009900;">(</span>j <span style="color: black; font-weight: bold;">in</span> <span style="color: #cc66cc;">2</span>:nest<span style="color: #009900;">)</span> Ys<span style="color: #009900;">[</span>i+<span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span> j<span style="color: #009900;">]</span> <- Ys<span style="color: #009900;">[</span>i+<span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span> j-<span style="color: #cc66cc;">1</span><span style="color: #009900;">]</span> %>% esum %>% <a href="http://inside-r.org/r-doc/base/sum"><span style="color: #003399; font-weight: bold;">sum</span></a>
<span style="color: #009900;">}</span>
Ys
<span style="color: #009900;">}</span>
<span style="color: #666666; font-style: italic;"># So let's first examine 9</span>
splitter<span style="color: #009900;">(</span>X=<span style="color: #cc66cc;">9</span><span style="color: #339933;">,</span> it=<span style="color: #cc66cc;">150</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">3</span><span style="color: #009900;">)</span>
<span style="color: #666666; font-style: italic;"># The first column is the sum of the digits</span>
<span style="color: #666666; font-style: italic;"># The second column is the sum of the sum of the digits</span>
<span style="color: #666666; font-style: italic;"># The third column is the sum of the sum of the sum of the digits</span>
<span style="color: #666666; font-style: italic;"># Yes the first 4 halves produce a situation in which the digits all add up to 9</span>
<span style="color: #666666; font-style: italic;"># If you combine the next 5 through 30 splits then the sum of the sum must be </span>
<span style="color: #666666; font-style: italic;"># added together to also produce the designated 9.</span>
<span style="color: #666666; font-style: italic;"># As we get deeper there is no reason to suspect that this will not carry to the</span>
<span style="color: #666666; font-style: italic;"># next level.</span>
splitter<span style="color: #009900;">(</span><span style="color: #cc66cc;">8</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">50</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">3</span><span style="color: #339933;">,</span> noisy = <span style="color: black; font-weight: bold;">FALSE</span><span style="color: #009900;">)</span>
splitter<span style="color: #009900;">(</span><span style="color: #cc66cc;">7</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">50</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">3</span><span style="color: #339933;">,</span> noisy = <span style="color: black; font-weight: bold;">FALSE</span><span style="color: #009900;">)</span>
splitter<span style="color: #009900;">(</span><span style="color: #cc66cc;">6</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">50</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">3</span><span style="color: #339933;">,</span> noisy = <span style="color: black; font-weight: bold;">FALSE</span><span style="color: #009900;">)</span>
splitter<span style="color: #009900;">(</span><span style="color: #cc66cc;">5</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">50</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">3</span><span style="color: #339933;">,</span> noisy = <span style="color: black; font-weight: bold;">FALSE</span><span style="color: #009900;">)</span>
splitter<span style="color: #009900;">(</span><span style="color: #cc66cc;">4</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">50</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">3</span><span style="color: #339933;">,</span> noisy = <span style="color: black; font-weight: bold;">FALSE</span><span style="color: #009900;">)</span>
splitter<span style="color: #009900;">(</span><span style="color: #cc66cc;">3</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">50</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">3</span><span style="color: #339933;">,</span> noisy = <span style="color: black; font-weight: bold;">FALSE</span><span style="color: #009900;">)</span>
splitter<span style="color: #009900;">(</span><span style="color: #cc66cc;">2</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">50</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">3</span><span style="color: #339933;">,</span> noisy = <span style="color: black; font-weight: bold;">FALSE</span><span style="color: #009900;">)</span>
splitter<span style="color: #009900;">(</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">50</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">3</span><span style="color: #339933;">,</span> noisy = <span style="color: black; font-weight: bold;">FALSE</span><span style="color: #009900;">)</span>
<span style="color: #666666; font-style: italic;"># Looking at 1-8 we do not ever get the same number out as with 9.</span>
<span style="color: #666666; font-style: italic;"># Does this make 9 unique, special, or even magical?</span></pre>
</div>
</div>
<a href="http://www.inside-r.org/pretty-r" title="Created by Pretty R at inside-R.org">Created by Pretty R at inside-R.org</a><br />
<br />
<br />
So, does this mean there is something to 9s? Well, maybe, but maybe it is a pattern that naturally emerges because we are using a base 10 system. What would happen if we switched to base 9? Or base 8?<br />
<br />
In order to test this idea, I first programmed a function to switch numbers from base 10 to any other base.<br />
<br />
<div style="overflow: auto;">
<div class="geshifilter">
<pre class="r geshifilter-R" style="font-family: monospace;">base10to <- <a href="http://inside-r.org/r-doc/base/function"><span style="color: #003399; font-weight: bold;">function</span></a><span style="color: #009900;">(</span>x<span style="color: #339933;">,</span> newbase=<span style="color: #cc66cc;">10</span><span style="color: #339933;">,</span> sep=<span style="color: blue;">''</span><span style="color: #009900;">)</span> <span style="color: #009900;">{</span>
<span style="color: black; font-weight: bold;">if</span> <span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/base/length"><span style="color: #003399; font-weight: bold;">length</span></a><span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/base/dim"><span style="color: #003399; font-weight: bold;">dim</span></a><span style="color: #009900;">(</span>x<span style="color: #009900;">)</span><span style="color: #009900;">)</span>==<span style="color: #cc66cc;">0</span><span style="color: #009900;">)</span> xout <- <a href="http://inside-r.org/r-doc/base/rep"><span style="color: #003399; font-weight: bold;">rep</span></a><span style="color: #009900;">(</span><span style="color: blue;">""</span><span style="color: #339933;">,</span> <a href="http://inside-r.org/r-doc/base/length"><span style="color: #003399; font-weight: bold;">length</span></a><span style="color: #009900;">(</span>x<span style="color: #009900;">)</span><span style="color: #009900;">)</span>
<span style="color: black; font-weight: bold;">if</span> <span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/base/length"><span style="color: #003399; font-weight: bold;">length</span></a><span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/base/dim"><span style="color: #003399; font-weight: bold;">dim</span></a><span style="color: #009900;">(</span>x<span style="color: #009900;">)</span><span style="color: #009900;">)</span>==<span style="color: #cc66cc;">2</span><span style="color: #009900;">)</span> xout <- <a href="http://inside-r.org/r-doc/base/matrix"><span style="color: #003399; font-weight: bold;">matrix</span></a><span style="color: #009900;">(</span><span style="color: blue;">""</span><span style="color: #339933;">,</span> <a href="http://inside-r.org/r-doc/base/dim"><span style="color: #003399; font-weight: bold;">dim</span></a><span style="color: #009900;">(</span>x<span style="color: #009900;">)</span><span style="color: #009900;">[</span><span style="color: #cc66cc;">1</span><span style="color: #009900;">]</span><span style="color: #339933;">,</span> <a href="http://inside-r.org/r-doc/base/dim"><span style="color: #003399; font-weight: bold;">dim</span></a><span style="color: #009900;">(</span>x<span style="color: #009900;">)</span><span style="color: #009900;">[</span><span style="color: #cc66cc;">2</span><span style="color: #009900;">]</span><span style="color: #009900;">)</span>
<span style="color: black; font-weight: bold;">for</span> <span style="color: #009900;">(</span>j <span style="color: black; font-weight: bold;">in</span> <span style="color: #cc66cc;">1</span>:<a href="http://inside-r.org/r-doc/base/length"><span style="color: #003399; font-weight: bold;">length</span></a><span style="color: #009900;">(</span>x<span style="color: #009900;">)</span><span style="color: #009900;">)</span> <span style="color: #009900;">{</span>
x2 <- x<span style="color: #009900;">[</span>j<span style="color: #009900;">]</span>
digits <- <span style="color: #009900;">(</span><span style="color: #009900;">(</span><span style="color: #cc66cc;">1</span>+x2<span style="color: #009900;">)</span> %>% as.bigz %>% <a href="http://inside-r.org/r-doc/base/log"><span style="color: #003399; font-weight: bold;">log</span></a><span style="color: #009900;">(</span>newbase<span style="color: #009900;">)</span> %>% <a href="http://inside-r.org/r-doc/base/floor"><span style="color: #003399; font-weight: bold;">floor</span></a><span style="color: #009900;">)</span>
d <- <a href="http://inside-r.org/r-doc/base/rep"><span style="color: #003399; font-weight: bold;">rep</span></a><span style="color: #009900;">(</span><span style="color: black; font-weight: bold;">NA</span><span style="color: #339933;">,</span> digits+<span style="color: #cc66cc;">1</span><span style="color: #009900;">)</span>
<span style="color: black; font-weight: bold;">for</span> <span style="color: #009900;">(</span>i <span style="color: black; font-weight: bold;">in</span> <span style="color: #cc66cc;">0</span>:<span style="color: #009900;">(</span>digits<span style="color: #009900;">)</span><span style="color: #009900;">)</span> <span style="color: #009900;">{</span>
d<span style="color: #009900;">[</span>i+<span style="color: #cc66cc;">1</span><span style="color: #009900;">]</span> <- <span style="color: #009900;">(</span>x2/newbase^<span style="color: #009900;">(</span>digits-i<span style="color: #009900;">)</span><span style="color: #009900;">)</span> %>% <a href="http://inside-r.org/r-doc/base/as.numeric"><span style="color: #003399; font-weight: bold;">as.numeric</span></a> %>% <a href="http://inside-r.org/r-doc/base/floor"><span style="color: #003399; font-weight: bold;">floor</span></a>
x2 <- x2-d<span style="color: #009900;">[</span>i+<span style="color: #cc66cc;">1</span><span style="color: #009900;">]</span>*newbase^<span style="color: #009900;">(</span>digits-i<span style="color: #009900;">)</span>
<span style="color: #009900;">}</span>
xout<span style="color: #009900;">[</span>j<span style="color: #009900;">]</span> <- <a href="http://inside-r.org/r-doc/base/paste"><span style="color: #003399; font-weight: bold;">paste</span></a><span style="color: #009900;">(</span>d<span style="color: #339933;">,</span> <a href="http://inside-r.org/r-doc/nlme/collapse"><span style="color: #003399; font-weight: bold;">collapse</span></a>=sep<span style="color: #009900;">)</span>
<span style="color: #009900;">}</span>
xout
<span style="color: #009900;">}</span>
x <- <a href="http://inside-r.org/r-doc/base/matrix"><span style="color: #003399; font-weight: bold;">matrix</span></a><span style="color: #009900;">(</span><span style="color: #cc66cc;">1</span>:<span style="color: #cc66cc;">100</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">10</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">10</span><span style="color: #009900;">)</span>
base10to<span style="color: #009900;">(</span>x<span style="color: #009900;">)</span>
base10to<span style="color: #009900;">(</span>x<span style="color: #339933;">,</span> <span style="color: #cc66cc;">5</span><span style="color: #009900;">)</span>
base10to<span style="color: #009900;">(</span>x<span style="color: #339933;">,</span> <span style="color: #cc66cc;">9</span><span style="color: #009900;">)</span>
base10to<span style="color: #009900;">(</span>x<span style="color: #339933;">,</span> <span style="color: #cc66cc;">2</span><span style="color: #009900;">)</span> </pre>
</div>
</div>
<a href="http://www.inside-r.org/pretty-r" title="Created by Pretty R at inside-R.org">Created by Pretty R at inside-R.org</a><br />
<br />
<br />
Seems to be working<br />
Note, it does not work with decimals<br />
<br />
Then I integrated it with my switcher:<br />
<br />
# Now let's redefine our splitter allowing for non-base 10<br />
<br />
<div style="overflow: auto;">
<div class="geshifilter">
<pre class="r geshifilter-R" style="font-family: monospace;">splitter2 <- <a href="http://inside-r.org/r-doc/base/function"><span style="color: #003399; font-weight: bold;">function</span></a><span style="color: #009900;">(</span>X<span style="color: #339933;">,</span> it<span style="color: #339933;">,</span> nest<span style="color: #339933;">,</span> noisy=<span style="color: black; font-weight: bold;">TRUE</span><span style="color: #339933;">,</span> <a href="http://inside-r.org/r-doc/base"><span style="color: #006600; font-weight: bold;">base</span></a>=<span style="color: #cc66cc;">10</span><span style="color: #009900;">)</span> <span style="color: #009900;">{</span>
Ys <- <a href="http://inside-r.org/r-doc/base/matrix"><span style="color: #003399; font-weight: bold;">matrix</span></a><span style="color: #009900;">(</span><span style="color: black; font-weight: bold;">NA</span><span style="color: #339933;">,</span> <a href="http://inside-r.org/r-doc/base/nrow"><span style="color: #003399; font-weight: bold;">nrow</span></a>=it<span style="color: #339933;">,</span> <a href="http://inside-r.org/r-doc/base/ncol"><span style="color: #003399; font-weight: bold;">ncol</span></a>=nest<span style="color: #009900;">)</span>
esum <- <a href="http://inside-r.org/r-doc/base/function"><span style="color: #003399; font-weight: bold;">function</span></a><span style="color: #009900;">(</span>x<span style="color: #339933;">,</span> <a href="http://inside-r.org/r-doc/base"><span style="color: #006600; font-weight: bold;">base</span></a><span style="color: #009900;">)</span>
x %>% base10to<span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/base"><span style="color: #006600; font-weight: bold;">base</span></a><span style="color: #009900;">)</span> %>% <a href="http://inside-r.org/r-doc/base/strsplit"><span style="color: #003399; font-weight: bold;">strsplit</span></a><span style="color: #009900;">(</span><span style="color: blue;">""</span><span style="color: #009900;">)</span> %>% <a href="http://inside-r.org/r-doc/base/unlist"><span style="color: #003399; font-weight: bold;">unlist</span></a> %>% <a href="http://inside-r.org/r-doc/base/as.numeric"><span style="color: #003399; font-weight: bold;">as.numeric</span></a>
<span style="color: black; font-weight: bold;">for</span> <span style="color: #009900;">(</span>i <span style="color: black; font-weight: bold;">in</span> <span style="color: #cc66cc;">0</span>:<span style="color: #009900;">(</span>it-<span style="color: #cc66cc;">1</span><span style="color: #009900;">)</span><span style="color: #009900;">)</span> <span style="color: #009900;">{</span>
x <- as.bigz<span style="color: #009900;">(</span>X<span style="color: #009900;">)</span>
x <- <span style="color: #009900;">(</span>x*<span style="color: #cc66cc;">10</span>^<span style="color: #009900;">(</span>i<span style="color: #009900;">)</span>/<span style="color: #cc66cc;">2</span>^i<span style="color: #009900;">)</span>
Y <- x %>% esum<span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/base"><span style="color: #006600; font-weight: bold;">base</span></a><span style="color: #009900;">)</span>
<span style="color: black; font-weight: bold;">if</span> <span style="color: #009900;">(</span>noisy<span style="color: #009900;">)</span>
<a href="http://inside-r.org/r-doc/base/print"><span style="color: #003399; font-weight: bold;">print</span></a><span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/base/sprintf"><span style="color: #003399; font-weight: bold;">sprintf</span></a><span style="color: #009900;">(</span><span style="color: blue;">"%s: %s -> sum(%s)=%s base %s"</span><span style="color: #339933;">,</span>
i<span style="color: #339933;">,</span> x<span style="color: #339933;">,</span>
<a href="http://inside-r.org/r-doc/base/paste"><span style="color: #003399; font-weight: bold;">paste</span></a><span style="color: #009900;">(</span>Y<span style="color: #339933;">,</span> <a href="http://inside-r.org/r-doc/nlme/collapse"><span style="color: #003399; font-weight: bold;">collapse</span></a>=<span style="color: blue;">" "</span><span style="color: #009900;">)</span><span style="color: #339933;">,</span>
base10to<span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/base/sum"><span style="color: #003399; font-weight: bold;">sum</span></a><span style="color: #009900;">(</span>Y<span style="color: #009900;">)</span><span style="color: #339933;">,</span> <a href="http://inside-r.org/r-doc/base"><span style="color: #006600; font-weight: bold;">base</span></a><span style="color: #009900;">)</span><span style="color: #339933;">,</span>
<a href="http://inside-r.org/r-doc/base"><span style="color: #006600; font-weight: bold;">base</span></a><span style="color: #009900;">)</span><span style="color: #009900;">)</span>
Ys<span style="color: #009900;">[</span>i+<span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">1</span><span style="color: #009900;">]</span> <- <a href="http://inside-r.org/r-doc/base/sum"><span style="color: #003399; font-weight: bold;">sum</span></a><span style="color: #009900;">(</span>Y<span style="color: #009900;">)</span> %>% base10to<span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/base"><span style="color: #006600; font-weight: bold;">base</span></a><span style="color: #009900;">)</span>
<span style="color: black; font-weight: bold;">for</span> <span style="color: #009900;">(</span>j <span style="color: black; font-weight: bold;">in</span> <span style="color: #cc66cc;">2</span>:nest<span style="color: #009900;">)</span> Ys<span style="color: #009900;">[</span>i+<span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span> j<span style="color: #009900;">]</span> <- Ys<span style="color: #009900;">[</span>i+<span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span> j-<span style="color: #cc66cc;">1</span><span style="color: #009900;">]</span> %>% <a href="http://inside-r.org/r-doc/base/as.numeric"><span style="color: #003399; font-weight: bold;">as.numeric</span></a> %>% esum<span style="color: #009900;">(</span><span style="color: #cc66cc;">10</span><span style="color: #009900;">)</span> %>%
<a href="http://inside-r.org/r-doc/base/sum"><span style="color: #003399; font-weight: bold;">sum</span></a> %>% base10to<span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/base"><span style="color: #006600; font-weight: bold;">base</span></a><span style="color: #009900;">)</span>
<span style="color: #009900;">}</span>
Ys
<span style="color: #009900;">}</span></pre>
</div>
</div>
<a href="http://www.inside-r.org/pretty-r" title="Created by Pretty R at inside-R.org">Created by Pretty R at inside-R.org</a><br />
<br />
<br />
splitter2(9, 15, 3, noisy = TRUE)<!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><!-----><br />
<span id="goog_390571164"></span><br />
Output:<br />
<br />
<pre class="GEM3DMTCFGB" id="rstudio_console_output" style="-webkit-text-stroke-width: 0px; -webkit-user-select: text; background-color: white; border: none; color: black; font-family: 'Lucida Console'; font-size: 10pt !important; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 15px; margin: 0px; orphans: auto; outline: none; text-align: -webkit-left; text-indent: 0px; text-transform: none; white-space: pre-wrap !important; widows: auto; word-break: break-all; word-spacing: 0px;" tabindex="0"> [,1] [,2]
[1,] "9" "9"
[2,] "9" "9"
[3,] "9" "9"
[4,] "9" "9"
[5,] "18" "9"
[6,] "18" "9"
[7,] "18" "9"
[8,] "18" "9"
[9,] "27" "9"
[10,] "36" "9"
[11,] "45" "9"
[12,] "36" "9"
[13,] "45" "9"
[14,] "45" "9"
[15,] "45" "9"</pre>
<br />
splitter2(8, 15, 2, noisy = TRUE, base=9)<br />
<br />
Output:<br />
<br />
<pre class="GEM3DMTCFGB" id="rstudio_console_output" style="-webkit-text-stroke-width: 0px; -webkit-user-select: text; background-color: white; border: none; color: black; font-family: 'Lucida Console'; font-size: 10pt !important; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 15px; margin: 0px; orphans: auto; outline: none; text-align: -webkit-left; text-indent: 0px; text-transform: none; white-space: pre-wrap !important; widows: auto; word-break: break-all; word-spacing: 0px;" tabindex="0"> [,1] [,2]
[1,] "8" "8"
[2,] "8" "8"
[3,] "8" "8"
[4,] "8" "8"
[5,] "26" "8"
[6,] "26" "8"
[7,] "17" "8"
[8,] "17" "8"
[9,] "35" "8"
[10,] "26" "8"
[11,] "26" "8"
[12,] "35" "8"
[13,] "35" "8"
[14,] "53" "8"
[15,] "35" "8" </pre>
<br />
splitter2(7, 15, 2, noisy = TRUE, base=8)<br />
Output:<br />
<br />
<pre class="GEM3DMTCFGB" id="rstudio_console_output" style="-webkit-text-stroke-width: 0px; -webkit-user-select: text; background-color: white; border: none; color: black; font-family: 'Lucida Console'; font-size: 10pt !important; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 15px; margin: 0px; orphans: auto; outline: none; text-align: -webkit-left; text-indent: 0px; text-transform: none; white-space: pre-wrap !important; widows: auto; word-break: break-all; word-spacing: 0px;" tabindex="0"> [,1] [,2]
[1,] "07" "07"
[2,] "07" "07"
[3,] "16" "07"
[4,] "16" "07"
[5,] "16" "07"
[6,] "25" "07"
[7,] "34" "07"
[8,] "25" "07"
[9,] "34" "07"
[10,] "34" "07"
[11,] "34" "07"
[12,] "43" "07"
[13,] "52" "07"
[14,] "52" "07"
[15,] "70" "07"</pre>
<br />
splitter2(6, 15, 2, noisy = TRUE, base=7)<br />
<pre class="GEM3DMTCFGB" id="rstudio_console_output" style="-webkit-text-stroke-width: 0px; -webkit-user-select: text; background-color: white; border: none; color: black; font-family: 'Lucida Console'; font-size: 10pt !important; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 15px; margin: 0px; orphans: auto; outline: none; text-align: -webkit-left; text-indent: 0px; text-transform: none; white-space: pre-wrap !important; widows: auto; word-break: break-all; word-spacing: 0px;" tabindex="0"> [,1] [,2]
[1,] "6" "6"
[2,] "6" "6"
[3,] "6" "6"
[4,] "6" "6"
[5,] "24" "6"
[6,] "24" "6"
[7,] "24" "6"
[8,] "33" "6"
[9,] "33" "6"
[10,] "24" "6"
[11,] "33" "6"
[12,] "33" "6"
[13,] "51" "6"
[14,] "60" "6"
[15,] "51" "6"</pre>
<br />
splitter2(1, 15, 4, noisy = TRUE, base=2)<br />
Output:<br />
<br />
<pre class="GEM3DMTCFGB" id="rstudio_console_output" style="-webkit-text-stroke-width: 0px; -webkit-user-select: text; background-color: white; border: none; color: black; font-family: 'Lucida Console'; font-size: 10pt !important; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 15px; margin: 0px; orphans: auto; outline: none; text-align: -webkit-left; text-indent: 0px; text-transform: none; white-space: pre-wrap !important; widows: auto; word-break: break-all; word-spacing: 0px;" tabindex="0"> [,1] [,2] [,3] [,4]
[1,] "01" "01" "01" "01"
[2,] "10" "01" "01" "01"
[3,] "11" "10" "01" "01"
[4,] "110" "10" "01" "01"
[5,] "101" "10" "01" "01"
[6,] "110" "10" "01" "01"
[7,] "0111" "11" "10" "01"
[8,] "1000" "01" "01" "01"
[9,] "1100" "10" "01" "01"
[10,] "1101" "11" "10" "01"
[11,] "1011" "11" "10" "01"
[12,] "01111" "100" "01" "01"
[13,] "1101" "11" "10" "01"
[14,] "1110" "11" "10" "01"
[15,] "10001" "10" "01" "01"</pre>
<br />
Now we can see that by changing the base, the same pattern emerges. With base 9, the "magic" number is 8. With base 8, 7 etc. All the way down to base 2 where the "magic" number is 1.<br />
<h3 style="text-align: left;">
<br />
2. Sides of the polygon</h3>
<br />
What about the other claims put forward in the video? That is, that all sides of all polygons angles add up to 9. That is for a regular polygon<br />
triangle 60+60+60=180...1+8+0=9<br />
square 90+90+90+90=360...3+6=9<br />
pentagon 108+108+108+108+108=540...5+4=9<br />
etc. <br />
<br />
We can think of any equilateral polygon forming n identical triangles. The tips of those triangles meet at the center with angle 360/n where n is the number of sides of the polygon. To find the other angles we reflect on knowing that the two other angles are equal and since all of the sides of a triangle add up to 180 we can figure their size is (180-360/n)/2. Nowever, the triangles formed by the polygons only represent half the triangle's edge so we need to double that giving:<br />
$$\theta(n)=180-(360/n) =180(1-2/n)$$ with n being the number of sides.<br />
<br />
We can see that this could be written: 9*20(1-2/n):<br />
<br />
So the question is, using an alternative base system will we get the same pattern?<br />
<br />
Let's try base 9 instead of 10. Let's define the angles of the polygon as now: 8*20(1-2/n) base 10. Making a circle now 320 degrees base 10 or 385 base 9. Now let's see about the sum of the sides.<br />
<br />
triangle 53+53+53=160 base 10 or 187 base 9 ... 1+8+7 = 16 base 10 or 17 base 9 ... 1+7=8<br />
square 80+80+80+80=320 base 10 or 385 base 9 ... 3+8+5 = 16 ... 8<br />
pentagon 96+96+96+96+96=480 base 10 or 583 base 9 ... 5+8+3 = 16 ... 8<br />
<br />
Hail the magical 8!<br />
<br />
Do I need to do this again with a different base?<br />
<h3 style="text-align: left;">
<br />
3. All of the digits less than 9 add up to 9 (1+2+3+4+5+6+7+8=36...3+6=9)</h3>
<br />
Base 10 magic 9:1+2+3+4+5+6+7+8=36 base 10 ... 3+6=9 YES! <br />
Base 9 magic 8: 1+2+3+4+5+6+7=28 base 10 or 31 base 9... 3+1=4 nope!<br />
Base 8 magic 7: 1+2+3+4+5+6=21 base 10 or 25 base 8 ... 2+5=7 YES!<br />
Base 7 magic 6: 1+2+3+4+5=15 base 10 or 21 base 7 ... 2+1=3 nope!<br />
Base 6 magic 5: 1+2+3+4=10 base 10 or 14 base 6 ... 1+4=5 YES!<br />
etc.<br />
<br />
I think the pattern is pretty obvious here as well. <br />
<h3 style="text-align: left;">
<br />
4. Nine plus any digit returns that digit (9+7=16...1+6=7)</h3>
<br />
Base 10 magic 9: 9+5=14...1+4=5<br />
Base 9 magic 8: 8+5=13 base 10 or 14 base 9...1+4=5<br />
Base 8 magic 7: 7+5=12 base 10 or 14 base 8...1+4=5<br />
Base 7 magic 6: 6+5=11 base 10 or 14 base 7...1+4=5<br />
Base 6 magic 5: 5+5=10 base 10 or 14 base 6...1+4=5<br />
etc.<br />
<br />
Need I say more? <br />
<h3 style="text-align: left;">
<br />
5. The Magical Marvelous Mystery of Base 10</h3>
<br />
Clearly, we can see that there is nothing special about 9. If there is any mystery, it is in the base 10 since as soon as we change the system from base 10 to base 9 the "magic" moves to another number.<br />
<br />
We must ask ourselves therefore, "why we are using base 10?"<br />
<br />
This is an excellent question! Other systems have developed such as the binary and corresponding hexidecimal system which are powerful systems that intuitively are more consistent than the tens system. With hexidecimals, everything can be written as a series of four binaries reducing all communication to 0 or 1 signals. If you think about it, this is a much more intuitive communication system than a 10 digit one. <br />
<br />
As for why we are using the 10 digit system. My best guess is that we are using base 10 because most people have 10 fingers and it is therefore easier to teach someone to count on a 10 digit system.<br />
<br />
So, yes, 9 is special but only because 10 is special and that is only special because our hands developed in such a way as that we have typically have 5 fingers on each hand summing to 10.<br />
<br />
So YAY, MAGIC US!</div>
Francishttp://www.blogger.com/profile/16658586705916884436noreply@blogger.com2tag:blogger.com,1999:blog-6288862798546085706.post-46005316276118943102015-10-09T11:50:00.001-04:002015-10-09T17:38:03.335-04:00Flip a fair coin 4x. Probability of H following H is 40%???<div dir="ltr" style="text-align: left;" trbidi="on">
<a href="http://www.writefuzzy.com/images/hot_hands_preview.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="http://www.writefuzzy.com/images/hot_hands_preview.jpg" height="200" width="156" /></a>A recent <a href="http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2627354" target="_blank">working paper </a>has come out arguing for the existence of Hot Hands (in basketball), a concept psychologists had dismissed decades ago. Hot hands is where a player is thought to have a higher likelihood of scoring the next basket if the last three baskets where shot successfully. (In NBA Jam, that is when you hands caught on fire).<br />
<br />
The first paragraph of the paper reads, "Jack takes a coin from his pocket and decides that he will flip it 4 times in a row, writing down the outcome of each flip on a scrap of paper. After he is done flipping, he will look at the flips that immediately followed an outcome of heads, and compute the relative frequency of heads on those flips. Because the coin is fair, Jack of course expects this empirical probability of heads to be equal to the true probability of flipping a heads: 0.5. Shockingly, Jack is wrong. If he were to sample one million fair coins and flip each coin 4 times, observing the conditional relative frequency for each coin, on average the relative frequency would be approximately 0.4."<br />
<br />
In other words $$P(H_t|H_{t-1}) \ne .5$$ even though $$P(H)=.5$$<br />
<br />
If you are anything like me, you will say, "WTF, that can't be true!"<br />
<br />
Before getting any further into the logic of the paper, let us do some simulations.<br />
<br />
First off, could this be the result of looking only after heads values? <br />
<br />
That is, perhaps by selecting only heads values we are reducing the number of available heads.<br />
<br />
But, no, this does not make sense!<br />
<br />
<span style="color: #666666; font-style: italic;"># x is a binary random variable drawn from 1000^2 draws with a .5 probability </span><span style="color: #666666; font-style: italic;"> of success.</span><br />
<br />
x <- <a href="http://inside-r.org/r-doc/stats/rbinom"><span style="color: #003399; font-weight: bold;">rbinom</span></a><span style="color: #009900;">(</span><span style="color: #cc66cc;">10</span>^<span style="color: #cc66cc;">6</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">.5</span><span style="color: #009900;">)</span>
<a href="http://inside-r.org/r-doc/base/mean"><span style="color: #003399; font-weight: bold;">mean</span></a><span style="color: #009900;">(</span>x<span style="color: #009900;">[</span>-<a href="http://inside-r.org/r-doc/base/length"><span style="color: #003399; font-weight: bold;">length</span></a><span style="color: #009900;">(</span>x<span style="color: #009900;">)</span><span style="color: #009900;">]</span><span style="color: #009900;">[</span>x<span style="color: #009900;">[</span>-<span style="color: #cc66cc;">1</span><span style="color: #009900;">]</span>==<span style="color: #cc66cc;">1</span><span style="color: #009900;">]</span><span style="color: #009900;">)</span><br />
<br />
<span style="color: #666666; font-style: italic;"># Pretty much as close as you can get to 50% as possible</span>
<span style="color: #666666; font-style: italic;"> </span><br />
<br />
<span style="color: #666666; font-style: italic;"># To make this feel more concrete for me I ended up flipping a coin 252 times </span><br />
<span style="color: #666666; font-style: italic;"># with the following results (1=heads)</span><br />
<br />
myx <- <a href="http://inside-r.org/r-doc/base/c"><span style="color: #003399; font-weight: bold;">c</span></a><span style="color: #009900;">(</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span>
<span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span>
<span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span>
<span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span>
<span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span>
<span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span>
<span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span>
<span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span>
<span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">0</span><span style="color: #009900;">)</span>
<span style="color: #666666; font-style: italic;"># We can see we drew 131 heads or 51.9% </span>
<a href="http://inside-r.org/r-doc/base/mean"><span style="color: #003399; font-weight: bold;">mean</span></a><span style="color: #009900;">(</span>myx<span style="color: #009900;">)</span><span style="color: #339933;">;</span>sum<span style="color: #009900;">(</span>myx<span style="color: #009900;">)</span>
<span style="color: #666666; font-style: italic;"># This is very close to 50%. What is the likelihood of heads coming </span><br />
<div style="overflow: auto;">
<div class="geshifilter">
<pre class="r geshifilter-R" style="font-family: monospace;"><span style="color: #666666; font-style: italic;"># up this many times on a fair coin?</span>
<a href="http://inside-r.org/r-doc/graphics/plot"><span style="color: #003399; font-weight: bold;">plot</span></a><span style="color: #009900;">(</span><span style="color: #cc66cc;">100</span>:<span style="color: #cc66cc;">152</span><span style="color: #339933;">,</span><a href="http://inside-r.org/r-doc/stats/pbinom"><span style="color: #003399; font-weight: bold;">pbinom</span></a><span style="color: #009900;">(</span><span style="color: #cc66cc;">100</span>:<span style="color: #cc66cc;">152</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">252</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">.5</span><span style="color: #009900;">)</span><span style="color: #339933;">,</span> type=<span style="color: blue;">'l'</span><span style="color: #339933;">,</span> lwd=<span style="color: #cc66cc;">3</span><span style="color: #339933;">,</span>
main=<span style="color: blue;">"CDF of binomial(252,.5)"</span><span style="color: #339933;">,</span>
ylab=<span style="color: blue;">"Probability"</span><span style="color: #339933;">,</span>
xlab=<span style="color: blue;">"# of Heads"</span><span style="color: #009900;">)</span>
<a href="http://inside-r.org/r-doc/graphics/abline"><span style="color: #003399; font-weight: bold;">abline</span></a><span style="color: #009900;">(</span>v=<a href="http://inside-r.org/r-doc/base/sum"><span style="color: #003399; font-weight: bold;">sum</span></a><span style="color: #009900;">(</span>myx<span style="color: #009900;">)</span><span style="color: #339933;">,</span> lwd=<span style="color: #cc66cc;">3</span><span style="color: #339933;">,</span> lty=<span style="color: #cc66cc;">2</span><span style="color: #009900;">)</span> </pre>
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<pre class="r geshifilter-R" style="font-family: monospace;">
<span style="color: #666666; font-style: italic;"># The likelihood of gettings 131 or higher given the coin is fair is </span></pre>
<pre class="r geshifilter-R" style="font-family: monospace;"><span style="color: #666666; font-style: italic;"># about 24.4%</span>
<span style="color: #cc66cc;">1</span>-<a href="http://inside-r.org/r-doc/stats/pbinom"><span style="color: #003399; font-weight: bold;">pbinom</span></a><span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/base/sum"><span style="color: #003399; font-weight: bold;">sum</span></a><span style="color: #009900;">(</span>myx<span style="color: #009900;">)</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">252</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">.5</span><span style="color: #009900;">)</span>
<span style="color: #666666; font-style: italic;"># I am fairly confident therefore that the coin is therefore fair. </span>
<span style="color: #666666; font-style: italic;"># However, it could be somewhat unfair and still achieve this outcome </span></pre>
<pre class="r geshifilter-R" style="font-family: monospace;"><span style="color: #666666; font-style: italic;"># without straining the bounds of probability. </span>
<span style="color: #666666; font-style: italic;"># But this is not the point.</span>
<span style="color: #666666; font-style: italic;"># Now let's look at the claim. The probability of observing a heads </span></pre>
<pre class="r geshifilter-R" style="font-family: monospace;"><span style="color: #666666; font-style: italic;"># after tossing a heads is argued to be .4.</span>
<span style="color: #666666; font-style: italic;"># So let's imagine a million fair coins sequences of length 4. Say set Y.</span>
<span style="color: #666666; font-style: italic;"># This set will be composed of the outcomes of 10^6 probabilities </span></pre>
<pre class="r geshifilter-R" style="font-family: monospace;"><span style="color: #666666; font-style: italic;"># where those probabilities are the likelihood that </span>
<span style="color: #666666; font-style: italic;"># the coin value that follows a heads is a head.</span>
<span style="color: #666666; font-style: italic;"># I write function nheads for this purpose</span>
nhead <- <a href="http://inside-r.org/r-doc/base/function"><span style="color: #003399; font-weight: bold;">function</span></a><span style="color: #009900;">(</span>flips=<span style="color: #cc66cc;">4</span><span style="color: #339933;">,</span> N=<span style="color: #cc66cc;">10</span>^<span style="color: #cc66cc;">6</span><span style="color: #339933;">,</span> prev=<span style="color: #cc66cc;">1</span><span style="color: #009900;">)</span> <span style="color: #009900;">{</span>
Y <- <a href="http://inside-r.org/r-doc/base/rep"><span style="color: #003399; font-weight: bold;">rep</span></a><span style="color: #009900;">(</span><span style="color: black; font-weight: bold;">NA</span><span style="color: #339933;">,</span>N<span style="color: #009900;">)</span>
<span style="color: black; font-weight: bold;">for</span> <span style="color: #009900;">(</span>i <span style="color: black; font-weight: bold;">in</span> <span style="color: #cc66cc;">1</span>:N<span style="color: #009900;">)</span> <span style="color: #009900;">{</span>
<span style="color: #666666; font-style: italic;"># Draw four binomial draws</span>
x <- <a href="http://inside-r.org/r-doc/stats/rbinom"><span style="color: #003399; font-weight: bold;">rbinom</span></a><span style="color: #009900;">(</span>flips<span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">.5</span><span style="color: #009900;">)</span>
<span style="color: #666666; font-style: italic;"># Now keep only draws after any heads</span>
Y<span style="color: #009900;">[</span>i<span style="color: #009900;">]</span> <- <a href="http://inside-r.org/r-doc/base/mean"><span style="color: #003399; font-weight: bold;">mean</span></a><span style="color: #009900;">(</span>x<span style="color: #009900;">[</span>-<a href="http://inside-r.org/r-doc/base/length"><span style="color: #003399; font-weight: bold;">length</span></a><span style="color: #009900;">(</span>x<span style="color: #009900;">)</span><span style="color: #009900;">]</span><span style="color: #009900;">[</span>x<span style="color: #009900;">[</span>-<span style="color: #cc66cc;">1</span><span style="color: #009900;">]</span>==prev<span style="color: #009900;">]</span><span style="color: #009900;">)</span>
<span style="color: #009900;">}</span>
Y
<span style="color: #009900;">}</span>
<span style="color: #666666; font-style: italic;"># Now let's take the average across the coins</span>
<a href="http://inside-r.org/r-doc/base/mean"><span style="color: #003399; font-weight: bold;">mean</span></a><span style="color: #009900;">(</span>nhead<span style="color: #009900;">(</span><span style="color: #cc66cc;">4</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">10</span>^<span style="color: #cc66cc;">6</span><span style="color: #009900;">)</span><span style="color: #339933;">,</span> na.rm=<span style="color: black; font-weight: bold;">TRUE</span><span style="color: #009900;">)</span>
<span style="color: #666666; font-style: italic;"># Damn, sure enough! The expected number of heads is 40.8%</span>
<span style="color: #666666; font-style: italic;"># Let's see if the empirical results adhere. We can think of the </span></pre>
<pre class="r geshifilter-R" style="font-family: monospace;"><span style="color: #666666; font-style: italic;"># 252 previous coinflips as</span><span style="color: #666666; font-style: italic;"> 63 four coin flip trials.</span>
myset <- <a href="http://inside-r.org/r-doc/base/matrix"><span style="color: #003399; font-weight: bold;">matrix</span></a><span style="color: #009900;">(</span>myx<span style="color: #339933;">,</span> <span style="color: #cc66cc;">4</span><span style="color: #009900;">)</span>
myY <- Y <- <a href="http://inside-r.org/r-doc/base/rep"><span style="color: #003399; font-weight: bold;">rep</span></a><span style="color: #009900;">(</span><span style="color: black; font-weight: bold;">NA</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">63</span><span style="color: #009900;">)</span>
<span style="color: #666666; font-style: italic;"># Now let's calculate the likelihood of heads after the first heads in each set</span>
<span style="color: black; font-weight: bold;">for</span> <span style="color: #009900;">(</span>i <span style="color: black; font-weight: bold;">in</span> <span style="color: #cc66cc;">1</span>:<a href="http://inside-r.org/r-doc/base/ncol"><span style="color: #003399; font-weight: bold;">ncol</span></a><span style="color: #009900;">(</span>myset<span style="color: #009900;">)</span><span style="color: #009900;">)</span> myY<span style="color: #009900;">[</span>i<span style="color: #009900;">]</span> <- <a href="http://inside-r.org/r-doc/base/mean"><span style="color: #003399; font-weight: bold;">mean</span></a><span style="color: #009900;">(</span>myset<span style="color: #009900;">[</span>-<span style="color: #cc66cc;">4</span><span style="color: #339933;">,</span>i<span style="color: #009900;">]</span><span style="color: #009900;">[</span>myset<span style="color: #009900;">[</span>-<span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span>i<span style="color: #009900;">]</span>==<span style="color: #cc66cc;">1</span><span style="color: #009900;">]</span><span style="color: #009900;">)</span>
<span style="color: #666666; font-style: italic;"># Pooling across sets</span>
<a href="http://inside-r.org/r-doc/base/mean"><span style="color: #003399; font-weight: bold;">mean</span></a><span style="color: #009900;">(</span>myY<span style="color: #339933;">,</span> na.rm=<span style="color: black; font-weight: bold;">TRUE</span><span style="color: #009900;">)</span>
<span style="color: #666666; font-style: italic;"># We get 34.2% which could be interpretted as an unluckily low deviation </span></pre>
<pre class="r geshifilter-R" style="font-family: monospace;"><span style="color: #666666; font-style: italic;"># from 50% except </span><span style="color: #666666; font-style: italic;">it is surprisingly close to 40%.</span>
<span style="color: #666666; font-style: italic;"># That is 19.5 heads </span>
<a href="http://inside-r.org/r-doc/base/sum"><span style="color: #003399; font-weight: bold;">sum</span></a><span style="color: #009900;">(</span>myY<span style="color: #339933;">,</span> na.rm = <span style="color: black; font-weight: bold;">TRUE</span><span style="color: #009900;">)</span>
<span style="color: #666666; font-style: italic;"># However the total number of trials that returned a result is 57</span>
<a href="http://inside-r.org/r-doc/base/sum"><span style="color: #003399; font-weight: bold;">sum</span></a><span style="color: #009900;">(</span>!<a href="http://inside-r.org/r-doc/base/is.na"><span style="color: #003399; font-weight: bold;">is.na</span></a><span style="color: #009900;">(</span>myY<span style="color: #009900;">)</span><span style="color: #009900;">)</span>
<span style="color: #666666; font-style: italic;"># If we believed that the true expected number of heads was .5 then the </span></pre>
<pre class="r geshifilter-R" style="font-family: monospace;"><span style="color: #666666; font-style: italic;"># likelihood of </span><span style="color: #666666; font-style: italic;">the 19 heads or less appearing is less than 1%.</span>
<a href="http://inside-r.org/r-doc/stats/pbinom"><span style="color: #003399; font-weight: bold;">pbinom</span></a><span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/base/sum"><span style="color: #003399; font-weight: bold;">sum</span></a><span style="color: #009900;">(</span>myY<span style="color: #339933;">,</span> na.rm = <span style="color: black; font-weight: bold;">TRUE</span><span style="color: #009900;">)</span><span style="color: #339933;">,</span> <a href="http://inside-r.org/r-doc/base/sum"><span style="color: #003399; font-weight: bold;">sum</span></a><span style="color: #009900;">(</span>!<a href="http://inside-r.org/r-doc/base/is.na"><span style="color: #003399; font-weight: bold;">is.na</span></a><span style="color: #009900;">(</span>myY<span style="color: #009900;">)</span><span style="color: #009900;">)</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">.5</span><span style="color: #009900;">)</span>
<span style="color: #666666; font-style: italic;"># This seems compelling and surprising evidence before even looking at </span></pre>
<pre class="r geshifilter-R" style="font-family: monospace;"><span style="color: #666666; font-style: italic;"># the arguments </span><span style="color: #666666; font-style: italic;">presented in the paper.</span>
<span style="color: #666666; font-style: italic;"># Looking at the paper, Table 1 is quite convincing. It is organized </span></pre>
<pre class="r geshifilter-R" style="font-family: monospace;"><span style="color: #666666; font-style: italic;"># by # of Heads.</span>
<span style="color: #666666; font-style: italic;"># Heads Sequence P(H|H)</span>
<span style="color: #666666; font-style: italic;">#1 0 TTTT -</span>
<span style="color: #666666; font-style: italic;">#2 1 TTTH -</span>
<span style="color: #666666; font-style: italic;">#3 1 TTHT 0</span>
<span style="color: #666666; font-style: italic;">#4 1 THTT 0</span>
<span style="color: #666666; font-style: italic;">#5 1 HTTT 0</span>
<span style="color: #666666; font-style: italic;">#6 2 TTHH 1</span>
<span style="color: #666666; font-style: italic;">#7 2 THTH 0</span>
<span style="color: #666666; font-style: italic;">#8 2 THHT 1/2</span>
<span style="color: #666666; font-style: italic;">#9 2 HTTH 0</span>
<span style="color: #666666; font-style: italic;">#10 2 HTHT 0</span>
<span style="color: #666666; font-style: italic;">#11 2 HHTT 1/2</span>
<span style="color: #666666; font-style: italic;">#12 3 THHH 1</span>
<span style="color: #666666; font-style: italic;">#13 3 HTHH 1/2</span>
<span style="color: #666666; font-style: italic;">#14 3 HHTH 1/2</span>
<span style="color: #666666; font-style: italic;">#15 3 HHHT 2/3</span>
<span style="color: #666666; font-style: italic;">#16 4 HHHH 1</span>
<span style="color: #666666; font-style: italic;"># To come up with the P(H|H) we take the average of the feasible outcomes:</span>
<span style="color: #009900;">(</span><span style="color: #cc66cc;">0</span>+<span style="color: #cc66cc;">0</span>+<span style="color: #cc66cc;">0</span>+<span style="color: #cc66cc;">1</span>+<span style="color: #cc66cc;">0</span>+<span style="color: #cc66cc;">1</span>/<span style="color: #cc66cc;">2</span>+<span style="color: #cc66cc;">0</span>+<span style="color: #cc66cc;">0</span>+<span style="color: #cc66cc;">1</span>/<span style="color: #cc66cc;">2</span>+<span style="color: #cc66cc;">1</span>+<span style="color: #cc66cc;">1</span>/<span style="color: #cc66cc;">2</span>+<span style="color: #cc66cc;">1</span>/<span style="color: #cc66cc;">2</span>+<span style="color: #cc66cc;">2</span>/<span style="color: #cc66cc;">3</span>+<span style="color: #cc66cc;">1</span><span style="color: #009900;">)</span>/<span style="color: #cc66cc;">14</span>
<span style="color: #666666; font-style: italic;"># Sure enough! 40.47</span>
<span style="color: #666666; font-style: italic;"># So what is driving this? Selection bias certainly! But from where?</span>
<span style="color: #666666; font-style: italic;"># Is it the two values that cannot be computed because no heads are generated?</span>
<span style="color: #666666; font-style: italic;"># Even if we specify those as heads this does not fix the probabilities.</span>
<span style="color: #009900;">(</span><span style="color: #cc66cc;">0</span>+<span style="color: #cc66cc;">0</span>+<span style="color: #cc66cc;">0</span>+<span style="color: #cc66cc;">1</span>+<span style="color: #cc66cc;">0</span>+<span style="color: #cc66cc;">1</span>/<span style="color: #cc66cc;">2</span>+<span style="color: #cc66cc;">0</span>+<span style="color: #cc66cc;">0</span>+<span style="color: #cc66cc;">1</span>/<span style="color: #cc66cc;">2</span>+<span style="color: #cc66cc;">1</span>+<span style="color: #cc66cc;">1</span>/<span style="color: #cc66cc;">2</span>+<span style="color: #cc66cc;">1</span>/<span style="color: #cc66cc;">2</span>+<span style="color: #cc66cc;">2</span>/<span style="color: #cc66cc;">3</span>+<span style="color: #cc66cc;">1</span>+<span style="color: #cc66cc;">1</span>+<span style="color: #cc66cc;">1</span><span style="color: #009900;">)</span>/<span style="color: #cc66cc;">16</span>
<span style="color: #666666; font-style: italic;"># 48.9</span>
<span style="color: #666666; font-style: italic;"># So it must be a feature of the series since we know that </span>
<span style="color: #666666; font-style: italic;"># if we sample 6 million then we are spot on (near) 1/2.</span>
<span style="color: #666666; font-style: italic;"># Let's see what we can discover</span>
<a href="http://inside-r.org/r-doc/base/I"><span style="color: #003399; font-weight: bold;">I</span></a> <- <span style="color: #cc66cc;">60</span>
Y <- <a href="http://inside-r.org/r-doc/base/rep"><span style="color: #003399; font-weight: bold;">rep</span></a><span style="color: #009900;">(</span><span style="color: black; font-weight: bold;">NA</span><span style="color: #339933;">,</span> I-<span style="color: #cc66cc;">1</span><span style="color: #009900;">)</span>
<span style="color: black; font-weight: bold;">for</span> <span style="color: #009900;">(</span>i <span style="color: black; font-weight: bold;">in</span> <span style="color: #cc66cc;">2</span>:<a href="http://inside-r.org/r-doc/base/I"><span style="color: #003399; font-weight: bold;">I</span></a><span style="color: #009900;">)</span> Y<span style="color: #009900;">[</span>i-<span style="color: #cc66cc;">1</span><span style="color: #009900;">]</span> <- <a href="http://inside-r.org/r-doc/base/mean"><span style="color: #003399; font-weight: bold;">mean</span></a><span style="color: #009900;">(</span>nhead<span style="color: #009900;">(</span>i<span style="color: #339933;">,</span><span style="color: #cc66cc;">10</span>^<span style="color: #cc66cc;">5</span><span style="color: #009900;">)</span><span style="color: #339933;">,</span> na.rm=<span style="color: black; font-weight: bold;">TRUE</span><span style="color: #009900;">)</span>
<a href="http://inside-r.org/r-doc/graphics/plot"><span style="color: #003399; font-weight: bold;">plot</span></a><span style="color: #009900;">(</span><span style="color: #cc66cc;">2</span>:<a href="http://inside-r.org/r-doc/base/I"><span style="color: #003399; font-weight: bold;">I</span></a><span style="color: #339933;">,</span> Y<span style="color: #339933;">,</span> cex=<span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span> lwd=<span style="color: #cc66cc;">2</span><span style="color: #339933;">,</span>
main=<span style="color: blue;">"P(H_t|H_t-1)"</span><span style="color: #339933;">,</span>
xlab=<span style="color: blue;">"# of coins"</span><span style="color: #009900;">)</span>
<a href="http://inside-r.org/r-doc/graphics/abline"><span style="color: #003399; font-weight: bold;">abline</span></a><span style="color: #009900;">(</span>h=<span style="color: #cc66cc;">.5</span><span style="color: #339933;">,</span> lwd=<span style="color: #cc66cc;">3</span><span style="color: #009900;">)</span> </pre>
<pre class="r geshifilter-R" style="font-family: monospace;"> </pre>
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<pre class="r geshifilter-R" style="font-family: monospace;">
<span style="color: #666666; font-style: italic;"># This graph can be quite disorienting. </span></pre>
</div>
</div>
<br />
It shows that only in the case of flipping two coins is the probability of observing a head after the first head equal to .5 (well .5 with measurement error).<br />
<br />
There is still a significant divergence from .5 even in the case of 60 coints being flipped!<br />
<br />
This is so non-intuative as to be downright disorienting.<br />
<br />
Does this mean that if someone is flipping four coins and one of them pop up heads you can bet them $10 that the next result is a tail and feel confident the odds are in your favor?<br />
<br />
We can see this by looking at our probability table with each sequence arranged by the first head up to that point.<br />
<br />
The answer is not quite. I have added up the likelihood of seeing a heads after the previous heads that appears in both sequences (H|1H, H|2H, H|3H).<br />
<span style="font-family: "Courier New",Courier,monospace;"><br />Heads Sequence P(H|H) H|1H H|2H H|3H<br /> 0 TTTT -<br /> 1 TTTH -<br /> 2 TTHH 1 1<br /> 1 TTHT 0 0<br /> </span><br />
<span style="font-family: "Courier New",Courier,monospace;"> 2 THTH 0 0<br /> 1 THTT 0 0<br /> 3 THHH 1 1 1 <br /> 2 THHT 1/2 1 0<br /><br /> 1 HTTT 0 0<br /> 2 HTTH 0 0<br /> 2 HTHT 0 0 0<br /> 3 HTHH 1/2 0 1<br /> 3 HHTH 1/2 1 0<br /> 2 HHTT 1/2 1 0<br /> 3 HHHT 2/3 1 1 0<br /> 4 HHHH 1 1 1 1 </span><br />
<br />
Thus we can see that according to this, no matter that the sequence the likelihood of the next flip being a head after the first is .5. That is, equal number of heads as tails.<br />
<br />
How about the second head (H|1H)? Looking over the table we can see the same thing. As well as for the 3rd head.<br />
<br />
From this we can see that in part our intuition is correct. Knowing the previous outcome in the sequence does not provide information on future outcomes. THANK THE GODS!<br />
<br />
To get some insight into what is happening, you have to think about how we are scoring each sequence. After each flip of a head we score either 0 or 1. If this is the end of a sequence then we stop there and things work fine: TH (-), TT (-), HT (0), HH (1) -> P(H|H)=1/2.<br />
<br />
If it is not the end of a sequence let's see what happens.<br />
THT (0), THH (1), TTT (-), TTH (-), {this part looks okay so far}<br />
<br />
HTT (0), HTH (0), HHT ((1+0)/2=1/2), HHH (1).<br />
<br />
Now we can begin to see what is happening with the coin flip.<br />
<br />
The previously unscorable series TH now becomes scorable. No problem.<br />
<br />
The unscorable series TT remanes unscorable.<br />
<br />
And the zero scored series HT remains zero scoring!<br />
<br />
To review, we now have a previous sequence TH which was unscoreable and now has a probability of Heads of .5 (confirming our expectations). We had a sequence TT which was discarded and remains discarded. And we had a sequence HT which was scored 0 and remains scored 0.<br />
<br />
So all of the action must be happening in the HH part of the series!<br />
<br />
And we can now think of what is happening. The problem is in the averaging across heads within a series. In this case, by flipping HH this means that the next flip must be evaluated. With HT the next flip does not matter, the sequence will be scored 0 no matter what.<br />
<br />
However, with HH, we know that the next flip can be either H or T which means HHT (scored (1+0)/2=.5) and HHH (scored (1+1)/2=1) and $$ mean(H|HH)=.75$$. Thus effectively all other probabilities in the sequence remain the same except what was previously a P(H|HH)=1 is now a P(H|HH)=-.75.<br />
<br />
But why? Well, there is a selection issue going on. In the case of HH we are asking what the next score is and rounding our previous positive result to match that. But in the case of say HT we not asking what our next result is and rounding. Thus an isolated few negative outcomes are kept while a few positive outcomes are downgraded resulting in an overall selection effect which reduces the likelihood of seeing a head overall after seeing a previous head. <br />
<br />
Now that we can see why this is happening, why does it ever go away? The truth is, that it never goes away. The deviation from .5 gets really small as the sample size gets large. This is because the selective scoring (last value scored) is only happening on a smaller and smaller portion of the series.<br />
<br />
I am tempted to say something about the larger implications on series analysis. However, I don't really know how well this sampling issue is known to time series people. I do not recall hearing of it in my meager studies of the matter, but frankly that could mean very little.</div>
Francishttp://www.blogger.com/profile/16658586705916884436noreply@blogger.com4tag:blogger.com,1999:blog-6288862798546085706.post-49632612784541384012015-03-13T02:48:00.002-04:002015-03-13T02:48:49.543-04:00Open Data - Stack Exchange<div dir="ltr" style="text-align: left;" trbidi="on">
As a fan of Stack Exchange I am very excited about the new exchange being made available. This exchange is called 'Open Data' and allows users to post questions on where to find publicly available data on a topic and other users will respond with one or more answers.<br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="http://opendata.stackexchange.com/" imageanchor="1" style="margin-left: auto; margin-right: auto;" target="_blank"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgB0zJUUguE1E712Ekl9Au3iju3PJla_eNVdoPQQGZkSYCVTnhfFpU8siO2V1tAmP6a7hf9gnsVK4vWRu_5E0sT9z3GdBiH_iRRrytkoTRILQi7ceTPUCIntrLmOyI4kTMBlw24dMe2_Ls/s1600/Open+Data.png" height="280" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><a href="http://opendata.stackexchange.com/" target="_blank">Open Data - Stack Exchange</a></td></tr>
</tbody></table>
</div>
Francishttp://www.blogger.com/profile/16658586705916884436noreply@blogger.com1tag:blogger.com,1999:blog-6288862798546085706.post-4742150825406708872015-02-06T18:12:00.001-05:002015-02-06T18:32:26.509-05:00Calculating the likelihood of item overlap with Base R Assessment<div dir="ltr" style="text-align: left;" trbidi="on">
I have recently received an email from someone who had taken my <a href="http://concerto4.e-psychometrics.com/?wid=13&tid=14" target="_blank">Base R Assessment</a>. In this email, the test taker reported that a large portion of the test items taken were duplicates (around 50%) when he took the test the second time.<br />
<br />
I began wondering what the likelihood of this occurring would be.<br />
<br />
The test selects between 10-20 items each time the test is taken.<br />
<br />
These items are selected randomly.<br />
<br />
There is around 80 items in total available.<br />
<br />
First let us do some back of the envelope calculations.<br />
<br />
1. Lets say the average number of test items is 15. Thus the average quantity of the test items taken is 18.75% for the first test.<br />
2. If the same person were to take the test again then we would expect around 18.75% * 15 = 2.8 items to be duplicates.<br />
<br />
We might want to know instead what the change of say 50% of the items administered in the second test being duplicates.<br />
<br />
In order to do this calculation we would need to basically come up with the a list of all of the contamination of items which result in 50% overlap.<br />
<br />
For instance, let us say that we have a ten item exam. The items that overlap are 1:5 and the items that do not are 6:10.<br />
<br />
The probability of this outcome occurring is {first the overlap}*{those that do not overlap} : 1/80 * 1/79 * 1/78 * 1/77 * 1/76 * 74/75 * 73/74 * 72/73 * 71/72 * 70/71<br />
<br />
Which results in a really small number. Then we would calculate the probability of the first 4 matching and last items matching: 1/80 * 1/79 * 1/78 * 1/77 * 75/76 * 74/75 * 73/74 * 72/73 * 71/72 * 1/71 <br />
<br />
Next the first three and last two and so on. You keep doing this with every possible combination. This process becomes rather tedious and time consuming pretty quickly.<br />
<br />
However, if you are willing to undergo a little approximation bias then a much easier process is to put together a little simulation.<br />
<br />
Let us simulate instead the process x number of times, say 100,000.<br />
<br />
<div style="overflow: auto;">
<div class="geshifilter">
<pre class="r geshifilter-R" style="font-family: monospace;">Nsim <- <span style="color: #cc66cc;">10</span>^<span style="color: #cc66cc;">5</span>
overlap <- <a href="http://inside-r.org/r-doc/base/rep"><span style="color: #003399; font-weight: bold;">rep</span></a><span style="color: #009900;">(</span><span style="color: black; font-weight: bold;">NA</span><span style="color: #339933;">,</span>Nsim<span style="color: #009900;">)</span>
testMin <- <span style="color: #cc66cc;">10</span>
testAdd <- <span style="color: #cc66cc;">10</span>
<span style="color: black; font-weight: bold;">for</span> <span style="color: #009900;">(</span>i <span style="color: black; font-weight: bold;">in</span> <span style="color: #cc66cc;">1</span>:Nsim<span style="color: #009900;">)</span> <span style="color: #009900;">{</span>
testL1 <- testMin + <a href="http://inside-r.org/r-doc/base/sample"><span style="color: #003399; font-weight: bold;">sample</span></a><span style="color: #009900;">(</span><span style="color: #cc66cc;">0</span>:testAdd<span style="color: #339933;">,</span> <span style="color: #cc66cc;">1</span><span style="color: #009900;">)</span>
testL2 <- testMin + <a href="http://inside-r.org/r-doc/base/sample"><span style="color: #003399; font-weight: bold;">sample</span></a><span style="color: #009900;">(</span><span style="color: #cc66cc;">0</span>:testAdd<span style="color: #339933;">,</span> <span style="color: #cc66cc;">1</span><span style="color: #009900;">)</span>
first <- <a href="http://inside-r.org/r-doc/base/sample"><span style="color: #003399; font-weight: bold;">sample</span></a><span style="color: #009900;">(</span><span style="color: #cc66cc;">80</span><span style="color: #339933;">,</span> testL1<span style="color: #009900;">)</span>
second <- <a href="http://inside-r.org/r-doc/base/sample"><span style="color: #003399; font-weight: bold;">sample</span></a><span style="color: #009900;">(</span><span style="color: #cc66cc;">80</span><span style="color: #339933;">,</span> testL2<span style="color: #009900;">)</span>
overlap<span style="color: #009900;">[</span>i<span style="color: #009900;">]</span> <- <a href="http://inside-r.org/r-doc/base/mean"><span style="color: #003399; font-weight: bold;">mean</span></a><span style="color: #009900;">(</span>second %in% first<span style="color: #009900;">)</span>
<span style="color: #009900;">}</span>
<span style="color: #666666; font-style: italic;"># Generate a density curve of overlap. The mode is around .2 which is just around </span></pre>
<pre class="r geshifilter-R" style="font-family: monospace;"><span style="color: #666666; font-style: italic;"># where we expected the average to be.</span>
<a href="http://inside-r.org/r-doc/graphics/plot"><span style="color: #003399; font-weight: bold;">plot</span></a><span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/stats/density"><span style="color: #003399; font-weight: bold;">density</span></a><span style="color: #009900;">(</span>overlap<span style="color: #009900;">)</span><span style="color: #009900;">)</span> </pre>
<pre class="r geshifilter-R" style="font-family: monospace;"> </pre>
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<pre class="r geshifilter-R" style="font-family: monospace;">
<a href="http://inside-r.org/r-doc/base/mean"><span style="color: #003399; font-weight: bold;">mean</span></a><span style="color: #009900;">(</span>overlap<span style="color: #009900;">)</span>
<span style="color: #666666; font-style: italic;"># [1] 0.1877303</span>
<span style="color: #666666; font-style: italic;"># Now we can use a built in function 'ecdf' (empirical cdf) to process our </span></pre>
<pre class="r geshifilter-R" style="font-family: monospace;"><span style="color: #666666; font-style: italic;"># frequencies.</span>
OverCDF <- <a href="http://inside-r.org/r-doc/stats/ecdf"><span style="color: #003399; font-weight: bold;">ecdf</span></a><span style="color: #009900;">(</span>overlap<span style="color: #009900;">)</span>
<span style="color: #666666; font-style: italic;"># The ecdf function is pretty great! It can turn observations into probability data.</span>
<span style="color: #666666; font-style: italic;"># We can plot our cdf curve. It is a step function because there is only a finite </span></pre>
<pre class="r geshifilter-R" style="font-family: monospace;"><span style="color: #666666; font-style: italic;"># number of possible overlap percentages possible.</span>
<a href="http://inside-r.org/r-doc/graphics/plot"><span style="color: #003399; font-weight: bold;">plot</span></a><span style="color: #009900;">(</span>OverCDF<span style="color: #339933;">,</span> verticals = <span style="color: black; font-weight: bold;">TRUE</span><span style="color: #339933;">,</span> do.points = <span style="color: black; font-weight: bold;">FALSE</span><span style="color: #009900;">)</span> </pre>
<pre class="r geshifilter-R" style="font-family: monospace;"> </pre>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgM2g_OuDUm4oawptcGFNM1xjOouEz-plBWzkKJVsF7isWs4u9qsSp0UfjdfxH8py5nSAlNPDvsslQNwqH9KuXCJ11vrO8BT3MeyLRawc77PGRJw_g5egp8RwpKzIZfuaAiGiBNpNqMxEo/s1600/2015-02-06-eCDF.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgM2g_OuDUm4oawptcGFNM1xjOouEz-plBWzkKJVsF7isWs4u9qsSp0UfjdfxH8py5nSAlNPDvsslQNwqH9KuXCJ11vrO8BT3MeyLRawc77PGRJw_g5egp8RwpKzIZfuaAiGiBNpNqMxEo/s1600/2015-02-06-eCDF.png" height="277" width="400" /></a></div>
<pre class="r geshifilter-R" style="font-family: monospace;">
<span style="color: #666666; font-style: italic;"># We can also use it to calculate the likelihood of a certain level of overlap or </span></pre>
<pre class="r geshifilter-R" style="font-family: monospace;"><span style="color: #666666; font-style: italic;"># less.</span>
<span style="color: #666666; font-style: italic;"># Say what is the likelihood of 25% or less of the items being repeated?</span>
OverCDF<span style="color: #009900;">(</span><span style="color: #cc66cc;">.25</span><span style="color: #009900;">)</span>
<span style="color: #666666; font-style: italic;"># [1] 0.76224 This is pretty high value.</span>
<span style="color: #666666; font-style: italic;"># What about 18.75% or less of the items being repeated?</span>
OverCDF<span style="color: #009900;">(</span><span style="color: #cc66cc;">.1875</span><span style="color: #009900;">)</span>
<span style="color: #666666; font-style: italic;"># [1] 0.53936] Which is pretty close to</span>
<span style="color: #666666; font-style: italic;"># Now we can ask the question, what is the likelihood that the user had 50% or </span></pre>
<pre class="r geshifilter-R" style="font-family: monospace;"><span style="color: #666666; font-style: italic;"># more overlap between exams.</span>
<span style="color: #cc66cc;">1</span>-OverCDF<span style="color: #009900;">(</span><span style="color: #cc66cc;">.5</span><span style="color: #009900;">)</span>
<span style="color: #666666; font-style: italic;">#[1] 0.00212 This is a really small number and looking at it alone we might think </span></pre>
<pre class="r geshifilter-R" style="font-family: monospace;"><span style="color: #666666; font-style: italic;"># this person must have been exagerating.</span>
<span style="color: #666666; font-style: italic;"># However, a lot of people have taken the exam (around 1,250 independent tries).</span>
<span style="color: #666666; font-style: italic;"># Let's say each person attempts twice which gives us 625 attempts. What is the </span></pre>
<pre class="r geshifilter-R" style="font-family: monospace;"><span style="color: #666666; font-style: italic;"># probability that during one of these events someone recieved 50% or more of the </span></pre>
<pre class="r geshifilter-R" style="font-family: monospace;"><span style="color: #666666; font-style: italic;"># same items?</span>
<span style="color: #cc66cc;">1</span>-<span style="color: #009900;">(</span>OverCDF<span style="color: #009900;">(</span><span style="color: #cc66cc;">.5</span><span style="color: #009900;">)</span><span style="color: #009900;">)</span>^<span style="color: #cc66cc;">650</span>
<span style="color: #666666; font-style: italic;"># [1] 0.7482862 Which gives us a surprisingly large number.</span>
<span style="color: #666666; font-style: italic;"># However, saying everybody took the test twice is pretty unlikely. Let's instead </span></pre>
<pre class="r geshifilter-R" style="font-family: monospace;"><span style="color: #666666; font-style: italic;"># say 100 people took the test twice.</span>
<span style="color: #cc66cc;">1</span>-<span style="color: #009900;">(</span>OverCDF<span style="color: #009900;">(</span><span style="color: #cc66cc;">.5</span><span style="color: #009900;">)</span><span style="color: #009900;">)</span>^<span style="color: #cc66cc;">100</span>
<span style="color: #666666; font-style: italic;"># [1] 0.1912173 Which is a very respectable odds. These numbers indicate that if </span></pre>
<pre class="r geshifilter-R" style="font-family: monospace;"><span style="color: #666666; font-style: italic;"># 100 people took the test twice there is a 20% chance that one person would end </span></pre>
<pre class="r geshifilter-R" style="font-family: monospace;"><span style="color: #666666; font-style: italic;"># up seeing on the second test 50% of the same items.</span>
<span style="color: #666666; font-style: italic;"># Conversely we might want to ask the likelihood that someone would not see any </span></pre>
<pre class="r geshifilter-R" style="font-family: monospace;"><span style="color: #666666; font-style: italic;"># of the same items.</span>
OverCDF<span style="color: #009900;">(</span><span style="color: #cc66cc;">0</span><span style="color: #009900;">)</span>
<span style="color: #666666; font-style: italic;"># Giving about 5%.</span></pre>
</div>
</div>
<span style="font-size: x-small;"><a href="http://www.inside-r.org/pretty-r" title="Created by Pretty R at inside-R.org">Created by Pretty R at inside-R.org</a></span></div>
Francishttp://www.blogger.com/profile/16658586705916884436noreply@blogger.com0tag:blogger.com,1999:blog-6288862798546085706.post-43416122335577466772015-02-03T15:43:00.000-05:002015-02-03T15:43:34.861-05:00Base R Assessment!<div dir="ltr" style="text-align: left;" trbidi="on">
<a href="http://www.r-project.org/Rlogo.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a>Test your skills with this R-powered R assessment of base R knowledge! <b> </b><br />
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
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<tr><td class="tr-caption" style="text-align: center;"><a href="http://concerto4.e-psychometrics.com/?wid=13&tid=14">http://concerto4.e-psychometrics.com/?wid=13&tid=14</a></td></tr>
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Francishttp://www.blogger.com/profile/16658586705916884436noreply@blogger.com10tag:blogger.com,1999:blog-6288862798546085706.post-49245385490552611312014-11-12T01:22:00.001-05:002014-11-14T01:15:30.570-05:00Convergence of a Series<div dir="ltr" style="text-align: left;" trbidi="on">
Let us explore using simulation some of the concepts of basic asymptotic theory as presented in Wooldridge 2012, Chapter 3.<br />
<br />
Definition: A sequence of nonrandom numbers {a_N:N=1,2,...} converges to <b>a</b> if for all epsilon>0 there exists N_epsilon such that N>N_epsilon, then <br />
$$|a_N - a|<\epsilon$$<br />
<br />
Paraphrase: A sequence converges on point a, if you can choose any positive number (any epsilon greater than zero) and you will find some point in the series after which the difference between the series and the point it converges to a will always be smaller than epsilon.<br />
<br />
Let us try to make this more concrete.<br />
<br />
Imagine the series:<br />
<br />
$$f(N)=N^2$$<br />
<br />
Does this series converge on a value a?<br />
<br />
Let us pick an epsilon, say 100.<br />
## R ---------------------------<br />
f = function(x) x^2<br />
N = 1:30<br />
plot(N, f(N), type='l', col='lightblue', lwd=4)<br />
## -----------------------------<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh7y3WrhG1Y53WrPFdtLKanVQtpk-gMg3J9TnvAvIuQetiSvWLHOE7zckH_Z5oS7yusHJSW35Mzvb1MrOlAixtV_W6_HIxgiAc_KL7Bn4Dj3FzVPkjNanm7qfb0g3pmIQ855WmUuPw9W5I/s1600/2014-11-11Aymptotic1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="283" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh7y3WrhG1Y53WrPFdtLKanVQtpk-gMg3J9TnvAvIuQetiSvWLHOE7zckH_Z5oS7yusHJSW35Mzvb1MrOlAixtV_W6_HIxgiAc_KL7Bn4Dj3FzVPkjNanm7qfb0g3pmIQ855WmUuPw9W5I/s400/2014-11-11Aymptotic1.png" width="400" /></a></div>
We can see that there is no a which could exist for which our series seems to converge within the positive bound epsilon=100.<br />
<br />
This concergence might have been obvious. Let us try a different series.<br />
$$g(N)=10x^{-99/100}sin(x)+\pi$$<br />
## R ---------------------------<br />
g = function(x) 10*x^(-99/100) * sin(x) + pi<br />
N = 1:100<br />
plot(N, g(N), type='l', lwd=2)<br />
## -----------------------------<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiM-bwo3yNC1wYqaDyQrvswaLD9XKjwbmHaZ8d0gxSd0G-CZC_eSw6Tzo3oOr26gjnCY2kX-OWAeh9XAl7OyiByESRc23tVe4bqCMHfL9FDbScYniRYB_-Qlp1Gc2GxRBdf1CUjKCeGhOU/s1600/2014-11-11Asymptotic2.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="283" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiM-bwo3yNC1wYqaDyQrvswaLD9XKjwbmHaZ8d0gxSd0G-CZC_eSw6Tzo3oOr26gjnCY2kX-OWAeh9XAl7OyiByESRc23tVe4bqCMHfL9FDbScYniRYB_-Qlp1Gc2GxRBdf1CUjKCeGhOU/s400/2014-11-11Asymptotic2.png" width="400" /></a></div>
<br />
The series g demonstrates a common convergence pattern. That is you can alway pick a epsilon after which the difference between N and the convergence point is less then epsilon. In this case the series converges on pi. Let us play around with a few epsilons to see if our hypothesis that the series converges seems to hold true.<br />
<br />
## R ---------------------------<br />
e1 = 5<br />
abline(h=pi+e1, lwd=2, col='darkred')<br />
abline(h=pi-e1, lwd=2, col='darkred')<br />
## -----------------------------<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEggfWYBnwMNqHbf6WyFPjJqHACMqTj_L1BP6GJHPhJBcAOZVX5L67jIVsy4xiiMDK87ZuGQ2SXOMUBG6HgEbRwR02eceb0lwxfklzLhGdebk8eDLgGOjSZRXqRLwpUJf0OblAOyxpotBoI/s1600/2014-11-11Asymptotic3.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="227" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEggfWYBnwMNqHbf6WyFPjJqHACMqTj_L1BP6GJHPhJBcAOZVX5L67jIVsy4xiiMDK87ZuGQ2SXOMUBG6HgEbRwR02eceb0lwxfklzLhGdebk8eDLgGOjSZRXqRLwpUJf0OblAOyxpotBoI/s320/2014-11-11Asymptotic3.png" width="320" /></a></div>
We can see that at N<10 there are some points which are not bounded by |N-pi|<e1. However by the time we get to N>20, all points are easily bound (at least those we have plotted).<br />
<br />
How about a harder epsilon?<br />
## R ---------------------------<br />
e2 = .5<br />
abline(h=pi+e2, lwd=2, col='darkblue')<br />
abline(h=pi-e2, lwd=2, col='darkblue')<br />
## -----------------------------<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEij7o0EV-2ZZMmoPDUN1-Dj601W1c5FC7tdf4DNDJ6OMFoCcVhCMKkgfgBISOmR2Yfd5n7y4kz3E0y6tzOCHTrw-ojOu0BQzvxitnhtu7ZW7QRBpTgWdvgu6iHSJqwIkB9nU6iZ6Wq8SKI/s1600/2014-11-11Asymptotic4.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="283" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEij7o0EV-2ZZMmoPDUN1-Dj601W1c5FC7tdf4DNDJ6OMFoCcVhCMKkgfgBISOmR2Yfd5n7y4kz3E0y6tzOCHTrw-ojOu0BQzvxitnhtu7ZW7QRBpTgWdvgu6iHSJqwIkB9nU6iZ6Wq8SKI/s400/2014-11-11Asymptotic4.png" width="400" /></a></div>
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhPHs_6bCtsMPwrVjPJv1Jkpd_4chWIZzTeeDM3mhrMJUFy5T9ukSpURvgEAkF_Q4msqn6AB2z1MGp9UYo_OzVAiyiFItyWkEGcn_GnkI3ZLHsI1nXIJNDqCPjigPlaaI02_DJiR_At30A/s1600/2014-11-11Asymptotic5.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"></a><br />
This epsilon is outside our bounds at 20 but by the time we have reached 40 the series does not reach outside our bounds.<br />
<br />
## R ---------------------------<br />
e3 = .1<br />
abline(h=pi+e3, lwd=2, col=rgb(.3,.6,1,.5))<br />
abline(h=pi-e3, lwd=2, col=rgb(.3,.6,1,.5))<br />
## -----------------------------<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhPHs_6bCtsMPwrVjPJv1Jkpd_4chWIZzTeeDM3mhrMJUFy5T9ukSpURvgEAkF_Q4msqn6AB2z1MGp9UYo_OzVAiyiFItyWkEGcn_GnkI3ZLHsI1nXIJNDqCPjigPlaaI02_DJiR_At30A/s1600/2014-11-11Asymptotic5.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="227" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhPHs_6bCtsMPwrVjPJv1Jkpd_4chWIZzTeeDM3mhrMJUFy5T9ukSpURvgEAkF_Q4msqn6AB2z1MGp9UYo_OzVAiyiFItyWkEGcn_GnkI3ZLHsI1nXIJNDqCPjigPlaaI02_DJiR_At30A/s320/2014-11-11Asymptotic5.png" width="320" /></a></div>
We can see that with e3=.1 there is no point on the graph we have plotted which is bounded by our epsilon. However plotting the graph at a longer series time frame will give us a number N after which g is bounded.<br />
<br />
## R ---------------------------<br />
N = 100:200<br />
plot(N, g(N), type='l', lwd=2)<br />
e3 = .1<br />
abline(h=pi+e3, lwd=2, col=rgb(.3,.6,1,.5))<br />
abline(h=pi-e3, lwd=2, col=rgb(.3,.6,1,.5))<br />
N= 1:30<br />
plot(N, f(N), type='l', col='paste(readLines(paste0('http://web.archive.org/web/', <br />
fdate, '/http://www.npr.org/'), warn="F"), collapse='');lightblue', lwd=4)<br />
## -----------------------------<br />
<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjfl43cbwhF_-hcGQwjRnjan6hc1mxs6j21GzJoyYQSB6MvsdLQzyi4Hs9QmhREi1nP07cLnowpKeAoQk7y8XkC7N9p7tWKdgr3U3lpgZvhelqYOiUHO7p9I2NUrV5_TGUGUdTzVxbGmZk/s1600/2014-11-11Asymtotic6.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="283" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjfl43cbwhF_-hcGQwjRnjan6hc1mxs6j21GzJoyYQSB6MvsdLQzyi4Hs9QmhREi1nP07cLnowpKeAoQk7y8XkC7N9p7tWKdgr3U3lpgZvhelqYOiUHO7p9I2NUrV5_TGUGUdTzVxbGmZk/s400/2014-11-11Asymtotic6.png" width="400" /> </a></div>
<div class="separator" style="clear: both; text-align: left;">
We can see that the graph clearly shows that at our small value of epsilon (.1) we are bounded around pi as early as N=110. For all other even smaller epsilons there will always be an N for which</div>
this is true (even if our computers do not have sufficient accuracy to show this to be the case).<br />
<br />
However, since we are working with an infinite series, this also means that there is an infinite area of the graph for which we can never plot. We therefore cannot use graphs to prove that series converge. In theory a series can always break the bounds just beyond the area of inspection. The switch function<br />
<div class="separator" style="clear: both; text-align: left;">
$$f(N) = 1[N>100]$$</div>
<div class="separator" style="clear: both; text-align: left;">
is an extreme example in which the series seems to converge at 0 up to N<100 but at N=100 or greater the series now converges on 1.<!--100--></div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
Other series converge without oscillating:</div>
<div class="separator" style="clear: both; text-align: left;">
$$f(N)=a+b/N$$</div>
<br />
Some more challenging series which also converge include:<br />
$$f(N)=bN/exp(N)$$<br />
$$f(N)=N^{1/N}$$ <br />
<!--100--></div>
Francishttp://www.blogger.com/profile/16658586705916884436noreply@blogger.com0