Month: December 2016

How can you be sure that the voting machines in southeast Kansas were rigged?

How can I be so sure? Couldn’t there be some other cause of the bias?  That was the most common inquiry at my presentation Saturday, when I explained my exit poll results to the people who helped collect the data and had a vested interest in understanding the results.  I may have come across as a bit defensive in regard to this question.  I’m sorry if I did.  It’s hard to articulate the depth of my certainty, but I’ll try.

I carefully set up these exit polls to compare the official vote count by machine type.  The only legitimate concern regarding the meaning of these results is a biased sample. Not everybody tells the truth.  Some people delight in giving false answers to surveys.  How are you going to account for that? It’s a fair concern.

While I cannot prove that didn’t happen (at least, not without access to the ballots, which isn’t permitted), this is part of the normal error I expect.  It always helps to state assumptions explicitly.

INTROVERTS, LIARS, AND IDIOTS ASSUMPTION : THESE TRAITS ARE RANDOMLY DISTRIBUTED AMONG ALL CANDIDATES AND POLITICAL PARTIES.  I am assuming that that people who were less likely to participate (introverts) or more likely to fudge their answer (liars) or make mistakes (idiots) in filling out the survey did not differ in their response to our exit poll.

I received the following email that sums up this concern nicely and also suggests a couple of ways to check that hypothesis.

Hi Beth,

The observed discrepancies between official results and your poll results very clearly show that Clinton (D) voters were more strongly represented in those polled than in the official vote count; Trump (R) voters were less well represented.  There are  many possible explanations for this discrepancy.  One hypothesis is that a certain percentage of voters “held their nose and voted for X”  and would never have participated in the poll.  If these voters tended to be more of one party than the other, than that party would be less represented in the polls.   

Fortunately, your data provide a means to test this hypothesis about the “missing minority”, for it leads to this prediction:  
If a “missing minority” was biased towards X, then sites at which X had a greater percentage of the votes would be least affected by vote disparities.

A corollary prediction:  sites having the highest response rate would be least affected by vote disparities.

Have at it!
Annie

The main reason I find this hypothesis implausible is that the discrepancies for the Supreme Court judges were twice as large and followed the same pattern as the Pres. race discrepancies. There’s no reason to think more people ‘held their nose’ for judges than president!

Regarding those two predictions:

  1.  The sites with the greatest discrepancies were machine counts for SE Wichita, Urban  Wichita and Cowley.  The sites with the highest %Trump voters were Cowley, SW Wichita and Sumner.  No correlation there.
  2. The site with the lowest response rate, Sumner with 25%, also had the lowest discrepancies between the exit poll and the official results for the Pres. race.

In short, we do not see the other data relationships we would expect if the introverts liars and idiots assumption were false.  There is no reason to assume these individuals were more likely to vote for one candidate than another resulting in the bias in our data.

Summary of the 2016 Citizens Exit Polls in Kansas

 

The exit poll results from  all five polling locations in Southeast Kansas show strong evidence of election fraud in both the patterns and size of the errors.

I had major concerns with the accuracy of our voting machines based on my previous analyses, which is why these exit polls were run. The results confirm those suspicions.

Exit Poll Errors for Kansas Supreme Court Judges with Pres. Race Errors
Exit Poll Errors for Kansas Supreme Court Judges and Pres. Race

I designed this exit poll to check whether or not our voting machines are giving us accurate counts.  I looked into our local election statistics in the past and found concerning indications of fraud in the data.   There is no public official reconciliation of the paper records with the official vote counts provided by machine nor are citizens allowed access to do it.  I have the credentials to do this; I have a Ph.D. in statistics and have been certified by the ASQ as a quality engineer since 1987. I was able to recruit enough concerned voters to man the exit polls from open to close on election day.

Voters were asked how they voted – by machine, a scanned paper ballot, or an uncounted provisional ballot.   Results from the polling location give us the breakdown by machine votes and scanned ballots, which can be directly compared. The electronic voting machines used in all three Kansas counties were ES&S Ivotronic.  The paper ballot scanning equipment varied, but was all from the same manufacturer: ES&S.

The results from these exit polls tell a consistent, albeit unpleasant, story:  Our electronic voting machines should not be trusted.  Scanned paper ballots have been impacted as well, but due to some technical issues regarding the data, results on that type of counting machinery are less compelling.  Scanned paper ballot results often continued the pattern of the voting machine results, which does add to the weight of evidence against the accuracy of the official results.

I have posted the data from our exit poll and the corresponding official vote counts at Exit Poll Data

These exit poll results clearly point to manipulation of the machine counts of our votes. These are not random errors. There is no other reasonable explanation for large and consistent errors in favor (or against) particular candidates in this situation.

  • pres-results-chart-1
    Exit Poll Errors for Presidential Race
    Exit Poll Errors for Senate Race
    Exit Poll Errors for Senate Race
    Exit Poll Errors for 4th Congressional Race
    Exit Poll Errors for 4th Congressional Race
    Exit Poll Errors for Kansas Supreme Court Judges by Judge
    Exit Poll Errors for Kansas Supreme Court Judges by Judge

    Presidential race results show votes shifted from Clinton to Trump in four of the five locations – all except Sumner County. 

  • Votes in the Senate and 4th district Rep races were skewed toward the Libertarians at all five exit poll locations.  
  • The data from the Supreme Court Judges show Yes votes stolen in four of the five locations – all except Sumner County, where they received extra Yes votes.    

The analysis details are posted at Analysis of 2016 Citizens Exit Poll in Southeast Kansas

There is one ray of sunshine in these results – while the size of the shifts are cause for grave concern about the accuracy of the vote count, they are not sufficient to have altered the outcome in any of the races mentioned above.  Kansas was Trump territory.  The Judges all retained their positions.  No Libertarians won.

This ‘ray of sunshine’ is limited to these results.  Races polled at only one or two polling locations look even worse. There was a more than 10% shift in votes from Norton to O’Donnell in the Sedgwick County Commissioner third district race, easily sufficient to alter the winner*.  The data from these local races may only affect a portion of the voters at the polling site. For that reason, the data from those races is not as solid.  The lower quantity and quality of data in those races reduces  confidence in any conclusions regarding the results.

Who’s doing this and How?  I don’t know. My analyses shows which candidates lost votes or benefited, but that’s not justification for assuming they are knowledgeable regarding the vote theft.  There’s only one conclusion about the perpetrators I can come to.

Multiple Agents – The profile of errors from Sumner County is so different from the other sites, I can conclude that more than one agent successfully altered voting machine counts in S.E. Kansas polling stations.

 

Analysis of 2016 Citizens Exit Poll in Southeast Kansas

The post is a detailed analysis of races that were common to all five exit polls   linked here:   exit poll data

In the absence of election fraud, the difference in vote share between the official count and an exit poll (called the error) will be randomly distributed (both positive and negative) and relatively small.  If voting machine counts have been altered, we will see telltale patterns in these error measurements. We can determine if our machine votes are being counted honestly or if some candidates benefit and others are victimized by election fraud.  The exit poll results from  all five polling locations show strong evidence of election fraud in both the patterns and size of the errors.

 

SE Wichita President Race % Vote Share for Official Count and Exit Poll
SE Wichita President Race % Vote Share for Official Count and Exit Poll

EXAMPLE: The graph above shows the results for the presidential race from SE Wichita. According to the machine totals, Hillary Clinton received 435 votes out of 983 cast on the voting machines there.  That’s a 44.25% vote share.  Our exit poll data showed Hillary Clinton received 306 votes out of 645 survey responses to this question from voters who cast their votes on those same machines at that polling location.  That’s a 47.44% vote share.  The difference between those two values, -3.19%, is the error, illustrated in the graph below. This error measurement is computed for each candidate, race, type of voting equipment and polling location.

There were some  problems with some of the data. I have included data from all five sites for their electronic voting machine counts.  The link above gives the raw data for both voting machines and scanned paper ballots for all five sites, but only three of the five sites had sufficiently high quality data to be included in this analysis. This post discusses what data was left out and why.

Presidential race results show votes shifted from Clinton to Trump in four of the five locations.  The errors for the presidential candidates by site and voting equipment are shown in the table below.

Exit Poll Errors for Presidential Race
Exit Poll Errors for Presidential Race

These values are also shown in the chart below.  Johnson and Stein errors look random and reasonable.  Clinton and Trump errors are much larger and roughly match on the DRE machines with votes shifting from Clinton to Trump in four of the five polling locations.

pres-results-chart-1
Exit Poll Errors for Presidential Race

To statistically analyze the size of errors, use the hypergeometric distribution.  This computation is available in EXCEL as HYPGEOM.DIST.  It takes into account both the size of the population (total voters in the official count) and the sample size (total exit poll responses) in computing the probability of getting an error as large or larger than our exit poll had. See this post for the technical details about how this computation is done.

The p-values for two-sided tests are given in tables below.  Yellow indicates a statistical flag, a probability of less than 5% occurring if there was no election fraud.  Bold red numbers indicate probabilities of less than 1 in 1,000.

pres-results-table-2
Probabilities for the Exit Poll Results of the Presidential Race

The p-values clearly confirm the initial impression generated by the graph above: voting machine election fraud occurred in four of the five polling locations shifting votes from Clinton to Trump.

One interesting detail – Jill Stein actually received more scanned paper ballot votes in our exit poll in SW Wichita that they recorded at that site.   Since that can’t actually happen without errors or dishonesty, that probability is an absolute zero.  I wrote out ‘Zero’ to distinguish this situation from 0.0000 which indicates a probability that is below 0.00005 but still above zero.

The Senate and 4th district Rep races were skewed toward the Libertarians.   

The only pattern in these two races was that the Libertarians ALWAYS benefitted from the errors, with higher machine counts than exit poll percentages.  Both Democrat and Republican candidates lost votes, in some cases by suspiciously large amounts approximating the size of the error of another candidate.

Polling locations differed considerably.  Sumner county looks as if votes were taken from Moran (R ) in the Senate, but even more from Giroux (D) in the 4th Cong. Dist and undervotes for both races were increased.  Independent candidate Miranda Allen for the 4th district benefited by an unusual amount in the machine vote counts in all three Sedgwick County polling locations.  These errors look like fraud.

Below are tables and graphs of the errors between the official results and the exit poll results  for the Kansas Senate and 4th Congressional Districts and tables of the p-values for those errors.

Exit Poll Errors for Senate Race
Exit Poll Errors for Senate Race
Probabilities for the Exit Poll Results of the Senate Race
Probabilities for the Exit Poll Results of the Senate Race
Exit Poll Errors for Senate Race
Exit Poll Errors for Senate Race
Exit Poll Errors for 4th Congressional Race
Exit Poll Errors for 4th Congressional Race
Probabilities for the Exit Poll Results of the 4th Cong. Race
Probabilities for the Exit Poll Results of the 4th Cong. Race
Exit Poll Errors for 4th Congressional Race
Exit Poll Errors for 4th Congressional Race

The data from the Supreme Court Judges show the most clarity.  The pattern that fits across all five judges cannot be denied. In addition, the magnitude of the errors also exceeds that found in the other three races.

The four Supreme Court judges actively opposed by Gov. Brownback had Yes votes stolen in same four locations that favored Trump.  The only positive error is a tiny one for Nuss in the SE Wichita location, with the remaining errors for those four sites all showing negative for all five judges.  Sumner, different once again, showed only positive errors (More Yes votes) for all five judges

Stegall, Brownback’s only appointee up for retention, has results identical in direction to the other four, but smaller in magnitude.  He has only one slightly improbable dearth of yes votes in the scanned paper ballots in the SW Wichita location.  For Stegall, only the fact that his pattern matches the others is a sign of fraud against him. For the other judges, both the size and pattern of the errors testify to the rigging of the official counts by the machines.

Below are tables and graphs of the errors between the official results and the exit poll results  for the Kansas Supreme Court Judges Retention Votes  and tables of the p-values for those errors.   Multiple graphs of the judges are shown, grouping by judge (as previous graphs) and grouping by location.  That latter makes it undeniable that all sites show signs of corruption, although not in agreement  on the preferred direction.  Finally, a graph showing the judges next to a graph of the presidential candidates on the same scale.

Exit Poll Errors for Kansas Supreme Court Judges
Exit Poll Errors for Kansas Supreme Court Judges
Probabilities for the Exit Poll Results of the Kansas Supreme Court Judges
Probabilities for the Exit Poll Results of the Kansas Supreme Court Judges
Exit Poll Errors for Kansas Supreme Court Judges by Location
Exit Poll Errors for Kansas Supreme Court Judges by Location
Exit Poll Errors for Kansas Supreme Court Judges by Judge
Exit Poll Errors for Kansas Supreme Court Judges by Judge
Exit Poll Errors for Kansas Supreme Court Judges with Pres. Race Errors
Exit Poll Errors for Kansas Supreme Court Judges with Pres. Race Errors

This last comparison, putting the errors for the presidential race on the same scale as the judges, actually startled me when I first graphed it and I was expecting it.  The average size of the errors should be approximately the same for all the races since they are all drawing from a near identical sample of voters.  To a statistician, this increase in the magnitude of the error for the judges is another flashing red light saying that these machine results have been rigged. Rigged in different ways in different places, but all of the sites with exit polls show the telltale signs of the corruption.

 

 

What data was excluded from my analysis and why:

ALL of the raw data from all five exit polling locations has been posted. However, I had concerns about some of the data collected and that I will not be including it in my analysis at all.  This is not unusual in any research endeavor.  Prior to analysis the data must be vetted for accuracy and validity.  I exclude data from my analysis when I feel including the data could lead to erroneous conclusions regarding election fraud occurring.

I am not including the scanned paper ballot survey data from the Urban Wichita and Sumner County sites.  eta: The Cowley County Paper Ballot data is also being excluded.  See update at end of post.  The reason is that when I look at the response rate for the different methods of voting, I see signs of potential problems at those two locations.

I am concerned with the relatively low response rate for provisional ballots and relatively high rate for the scanned paper ballots.  I suspect that in those two sites, some provisional voters mistakenly indicated the scanned paper ballot.  This was a relatively easy mistake for voters to make; they might not be tuned into the difference between them.

Since one hypothesis I’ll be testing later is whether or not the provisional voters’ choices were different from the counted ballots, this concern renders the data from those sites as inconclusive. Under this circumstance, voter error is a reasonable alternative explanation to election fraud for any statistically significant differences.  Because my main concern is with the voting machine results, I decided not to include the results for the scanned paper ballots from those two sites in my analysis.  I may revisit this assumption later if the provisional votes are not found to be significantly different from the votes that were counted.

On the other hand, since the leakage appears to shift voters from provisional to scanned paper ballots, the data from provisional voters can be considered representative.  However, only the Urban Wichita provisional data will be analyzed because the Sumner County provisional sample had only 13 surveys; not large enough to draw any conclusions from.

I am keeping the provisional surveys from the SW and SE locations even though had much higher rates of provisional voters, with the SW location claiming 101% response rate, with one more provisional survey than the official count.  Clearly we had at least one confused survey taker.  But since the response rates for the machine and scanned paper ballots are similar in those cases, my assessment is that people who voted provisionally were simply more likely to complete one of surveys.  They were worried their official vote wouldn’t be counted.  One such voters complained bitterly to us about it while filling out our survey. Suddenly, their name had simply vanished from the registration books despite having voted there regularly in the past!  One of our volunteers had the same experience.  This excess of provisional voters does not seem likely due to contamination from the scanned paper ballot  voters, so the data from provisional voters  can be considered representative.

Blanks – They’re a technical issue for surveys.  There are two sorts of blanks with respect to survey responses.  A survey taker might not indicate an answer on one or more questions.  These were coded NR (No response) and were not included in any further analysis.  Valid responses to other questions were retained.  Overvotes on any question were treated the same.

We included ‘Write in or left blank’ as an option to the candidates as much as possible. Space on the survey form was at a premium, and some site managers deciding against including it on all questions.  I insisted on it for the questions asked on all surveys.  I felt it of particular importance for the presidential election given the candidate selection.  For those three questions, people who didn’t answer that question are removed from the sample, but we can compare the rates for write-in or left blank with the number of write-ins and undervotes on the official results.  For other questions, including the judges, undervotes and ‘write-in or left blank’ are taken out of the sample and all subsequent computations unless specifically stated otherwise.

These choices do affect the p-value computations of the hypergeometric distribution given in my tables.

ETA: Cowley County Paper Ballot Data removed from original analysis

On Feb 11th, I spoke with the Women for Kansas Cowley County (W4K-CC) Meeting.  We discussed the results of the exit poll they had run on Nov. 8th.  The Karen Madison, the Cowley County  county clerk/election officer was there and made some details about their data aggregation method I was previously unaware of.  The totals for the Cowley County Mail In Ballots are included with totals for the Paper Ballots cast on election data at the polling location.  I does NOT include provisional ballots, but the inclusion of the mail-in ballots in those totals makes it no longer an apples-to-apples comparison as at the remaining two Wichita sties.

As a  result, I have removed that dataset from my upcoming peer-reviewed publication.   I have decided to leave my original blog post unchanged while updating this post and discussing the implications of removing the data in a future post.  I will post details regarding publication of my paper once they are finalized.  It will be available on-line on an open access journal site prior to publication on paper this summer.

Hypergeometric p-value computation for Exit Poll Results using Excel

This post is a primer on how to test exit poll results with official results using the Hypergeometric distribution function in EXCEL.  You can check my computed p-values for the exit poll results using this formula.

The Hypergeometric distribution is used to determine the probability (p-value) of getting a random sample, drawn without replacement, as extreme or more so given the population that the sample is drawn from.  If that wording sounds unnecessarily complex, I sympathize. Unfortunately, precision is often complicated to articulate.  This definition is hard to parse and you need a working knowledge of what the statistical terms and phrases mean.

“With” versus “without” replacement is an important descriptor of a random sample.  A situation with replacement is akin to selecting a card from a deck, then returning it back to the deck before drawing another card. Without replacement is selecting a second card from the 51 remaining in the deck.

This nuance in the drawing of the sample affects the basic assumptions statisticians build equations from. Different statistical distributions have been developed to handle the two situations.  Because voters were only asked once to fill out our survey, the exit poll sample is ‘without replacement’ and the Hypergeometric distribution is the most appropriate choice for testing the size of the errors.

Another important and relevant statistical concept:  One-sided and Two-sided tests.

Most distributions, including the Hypergeometric distribution, have the majority of data crowded around the average and the data gets sparser the farther away from the average. This type of distribution has ‘tails’.  There are the two directions of tails relative to the average value: upper and lower.

Tails of a distribution
Tails of a distribution

When we perform a statistical test, we are looking at the deviations from what is expected given the underlying distribution of the data.  In some cases, we may only be interested in deviations in a particular direction – high or low.  In those cases, we can increase the precision of our test by only looking at one end of the distribution. This is called a one-tailed test.

In other situations, we are interested in differences in either direction, so we are examining both the upper and lower tails of the distribution.  In our exit polling data, we are looking at the deviations both positive and negative, to determine if either are unusually large.  Therefore, it is a two-sided test.

The EXCEL HYPERGEOM.DIST function computes only the lower tail p-value.  This result can be manipulated to find the upper tail probability. Both need to be computed. This EXCEL function requires five inputs:

  1. Sample Success – This is the total number of exit poll surveys for the candidate in that race at that polling place using that voting mechanism.
  2. Sample size – This is the total number of usable exit poll surveys from voters for that race at that polling place using that voting mechanism.
  3. Population success – This is the total number of voters for the candidate in that race at that polling place using that voting mechanism.
  4. Population size – This is the total number of voters for that race at that polling place using that voting mechanism.
  5. Cumulative – Input 1. This is a technical detail of the statistical test.  A zero will result in the probability of getting exactly the results we input, no more and no less.  Putting a one here gives the lower tail probability, which is what we want.

EXAMPLE:  Hillary Clinton received 435 votes out of 983 cast on the voting machines at the SE site.  That’s a 44.25% vote share.  Our exit poll data showed Hillary Clinton received 306 votes out of 645 survey responses to this question from voters who cast their votes on those same machines at that polling location.  That’s a 47.44% vote share.  The difference between those two values, -3.19%, is the error. This error measurement is computed for each candidate, race, type of voting equipment and polling location.

Use EXCEL function HYPERGEOM.DIST with the following inputs:

  • Sample_s = 306
  • Number_Sample = 645
  • Population_s = 435
  • Number_pop = 983
  • Cumulative = 1

Lower Tail P-value for Clinton, Machine Votes, SE Wichita

= HYPERGEOM.DIST(306,645,435,983,1) = 0.9979

Whoa!!  I thought you said Hillary got cheated?  This result is a near certainty.

That’s because our exit poll sample had a larger percentage of Hillary voters than the official results did.  Her exit poll results lie in the upper tail of the distribution, well above the official average.  We just computed the p-value for the lower tail i.e. the probability of randomly getting as many Hillary votes as we did (306) or LESS.

Next we need to compute the probability of randomly getting as many exit poll votes as she did or MORE.  The upper tail of the distribution.  Through the magic of math, we can find the upper tail probability with a modification to this function.

Subtract 1 from our sample size and compute the lower tail probability for that sample size.  Then subtract that lower tail probability from 1 to get the correct upper tail p-value.

Upper Tail p-value for Clinton, Machine Votes, SE Wichita

= 1.0 – HYPERGEOM.DIST(305,645,435,983,1) = .00325

Finally, because we did not specify in advance what direction we expected to see, this is a two-tailed test.  For two-tailed tests of this nature, the p-value is computed as double the minimum one-tailed p-value, capped at 1.0.

Two-tailed p-value for Clinton, Machine Votes, SE Wichita = 2*0.00325 = 0.0065.

Finally, putting it all together in one cell, nesting the needed functions:

Two-tailed p-value for Clinton, Machine Votes, SE Wichita

   =2*MIN(+HYPGEOM.DIST(306,645,435,983,1), 1-HYPGEOM.DIST(305,645,435,983,1), 0.5)

 

 

Picture from http://www.ats.ucla.edu/stat/mult_pkg/faq/pvalue1.gif