Sunday, October 23, 2016

A Response to Election Fraud Claims and "Electoral Systems in Crisis"

The world is complex.  As statisticians and data scientists, our job is to create models that describe that complexity, and reduce it to simplified equations from which we can understand and predict how the world acts and reacts.  This is a story of what occurs when we use models that oversimplify the world, and fail to adequately describe its complexity.  It is also a response to a paper (found here) that mentioned my prior work on election fraud.  In the paper there was an attempted, but non-substantial critique of my work, which I will address later in this post.     

Early this summer I was approached online by a journalist claiming ABC News credentials and stating that she was doing a story on "Election Fraud" and asking for my involvement in the project.  It was quite a busy summer for me, but I said I might be interested in participating.  That interest quickly waned as I learned three things:
  • The Press Credentials Were Not Relevant.  While the journalist used her ABC affiliation to get me on board, after further questioning on the details of the project, I learned it had nothing to do with ABC.
  • The Talent For the Problem Seemed Incorrect.  Early conversations with the journalist demonstrated a poor understanding of highly dimensional statistical problems, both by herself and the other team members.  There was also no demographer on the team, though what we were dealing with certainly has demographic elements.
  • The Authors Weren't Interested in Legitimate Falsification.  After interacting with the lead author, journalist lulu Fries’dat and observing the nature of the work, I found the authors were not interested in actual scientific falsification of theory.  They were already convinced by the evidence, and real steps at falsification were futile.
As a result, I opted out of the project.  Then, in late July, the resulting paper started to be circulated with a half-attempted critique of my work.  I read the paper, reacted, sent it to a few friends with the general question: should I respond?  

The consensus from friends was that I should not respond, for a few reasons including the poor quality of the science, the fact that the statistical work was far too shoddy to be published in any serious academic journal, and the general belief that I shouldn't waste my time.

I let the paper go for a few months, but it kept bothering me.  And, with context in the run-up to the US presidential election, I felt I needed to respond, for two reasons:
  • Rhetoric of Systemic Rigging.  Throughout this election cycle, especially from the Bernie Sanders campaign, but also from the Donald Trump campaign, there has been a substantial dialogue on the idea that the "system is rigged."  This has ranged from the economic system, but also the electoral system.  My worst nightmare here is that we wake up November 9th, Trump has lost the election, but massive social unrest occurs due to his followers believing he was robbed.  This paper (Fries’dat,  and Sampietro)  would certainly feed that sentiment, such that this response is necessary.
  • Involvement of Fritz Scheuren: Fritz is a former President of the American Statistical Association, and is at least being name dropped in this paper.  The list of authors has him as "with" so not a primary author on the piece but at least we should view him as a contributor to the general concepts in the paper.  Though it's disappointing that Scheuren would sign on to poor research, he's certainly free to do so.  My concern here is that his name will lend credibility to otherwise implausible analytical techniques.


In April 2015 I became aware of a Kansas statistician named Beth Clarkson who was making some fairly astounding claims.  She essentially claimed that she had found evidence of massive fraud during a statistical analysis of voting records.  I was at first intrigued and dug deep into the data, and posted in a series of three posts in April 2015.  For this background section, I have pulled out and edited those three posts, though the original posts are still available on this blog.  


A Wichita State University statistician filed a lawsuit in Sedgwick County Court regarding the Kansas 2014 election.  She is trying to gain access to voting machine tallies to rule out the potential of voter fraud. 

Clarkson, a statistician, who works as a QA engineer, has found some "voting anomalies"... essentially that Republicans receive larger than expected vote shares in larger precincts.  Keep in mind that QA (Quality Assurance) engineers are trained to look for anomalies, things you wouldn't expect in data, and focus on them so that systems don't fail. 

Of note from her original article:
“This is not just an anomaly that occurred in one place,” Clarkson said. “It is a pattern that has occurred repeatedly in elections across the United States.”

"The pattern could be voter fraud or a demographic trend that has not been picked up by extensive polling, she said."

When we consider these comments on their face, considering they come from a research statistician, they don't seem to be out of the ordinary.  Just a researcher looking into anomalies, searching for potential causes.  I did think that putting "voter fraud" out there as a possibility seemed a little aggressive at this point, but didn't see this as an issue that would get a lot of attention.  But consider the political climate of Kansas in early 2015:

  1. The political climate in Kansas right now is tense, largely due to a highly contested gubernatorial election in 2014.  In that election, many polls and sources projected Democratic challenger Paul Davis to win, by a narrow margin, however unpopular Republican incumbent Sam Brownback won by three points. 
  2. Progressives are especially upset because they just lost an election, which their leaders told them would be a fairly easy win.
  3. I've seen the Clarkson article above posted by many progressive friends as fodder, evidence, and proof that, statistically speaking, Brownback was probably re-elected due to election fraud.
This seems to be a heating-up massive conspiracy theory.  But let's be calm and analyze:

What we know

From Clarkson's comments, she has no evidence of voter fraud.  She has found a small statistical anomaly that exists nationwide and wants to use Kansas to verify that it isn't due to fraud or voting machine issues.

But what is that anomaly? 

The anomaly is that after a certain size threshold of voters in a precinct (500), there is a positive correlation between precinct size and percent Republican votes.  

Why is that an issue?

Clarkson is a QA engineer in anomaly detection mode.  She's starting from an a priori premise that precinct size should not determine results, and thus, statistically significant correlations should not exist.

Is Clarkson's analysis of the data correct?

Though disagreeing with her conclusions, I tend to view the mechanics of her analysis as correct.  In fact, I was able to replicate, using the 2010 Kansas Gubernatorial Election.  The relationship is weak statistically speaking, but statistically significant.  This indicates that something non-random is happening in the data. Regression statistics and visual plot below. (for help in interpreting regression outputs, click here)

And a scatter plot of the analysis.
The line indicates the line of best fit for the data, demonstrating Clarkson's correlation

The correlations exist, so does that mean people must be acting nefariously in those large districts?

Here we go.  Absolutely not.  And here's why: covariates.  In the real world, multiple variables often correlate with one another, causing us to find relationships that are really measuring something else.  Clarkson's comments allude to this when she talks about potentially underlying and undetermined demographic factors. 

There are many what-if's here.  What if other variables also correlate with precinct size?  Age, Race, Wealth, Urbanity, etc, etc, etc.  In these cases we could be latently measuring other factors through measuring precinct size.   Some may speculate that conservative populaces somehow push for fewer, larger precincts and less division, though there is little evidence to back up that type of conclusion.  Specifically for the demographic factors, we should keep in mind, this is a weak relationship so slight and correlated latent groups can play a relatively large role.

The author of this analysis already drop the smallest precincts as a whole, because they tend to be more rural, and thus more Republican.  By doing this, the authors tacitly admit that underlying demographic factors can impact the correlation between precinct size and voting behavior.  We haven't gone through the steps to exclude all other demographic factors, so why are we making vague accusations of fraud and garnering media attention?  


I posted twice later that month, again responding to Clarkson’s analysis, and looking at specific factors that might be amiss in her data.  It still bothered me that Clarkson had posted essentially no work in attempts to falsify demographic trends (she has not posted any attempted falsification work, to date).  I set out to look into alternate causes of Clarkson’s correlation.  Here’s a synopsis of my analysis:

  1. I changed data sets to the 2008 Presidential election.  This is valid because the correlation of interest (Republicans doing better in larger precincts) still holds up.
  2. Nearly every demographic covariate I threw at the equation was statistically significant and more important than the "number of voters" variable.  What does this mean? Demographics are certain to play in vote shares (somewhat obviously). 
  3. If I create a large predictive model, using other variables such as population density, county size, and relationships between local precincts, the number of voters voting in the precinct becomes statistically insignificant.  In essence, the underlying cause of Clarkson's correlation is a demographic profile that tends to covary with precinct size.

This means: The original analysis was looking at a very small relationship in a world where much more important relationships exist.  And if we look at the data in a way where we simultaneously account for multiple factors, the correlation from Clarkson's original commentary is simply non-existent.

First for validation of Clarkson's initial simple correlation, did it hold up?  Absolutely and here is the evidence.

Correlation between total precinct votes in 2008 and Republican share is positive and statistically significant.

But what else correlates to the percentage that votes Republican in an election?  A lot of our variables, it turns out.  Here's a correlation matrix.  Notice that size of precinct is actually the lowest absolute correlation value.  Also of note, many of them are cross-correlated with size of precinct, pointing towards multi-collinearity.

What happens if I add some of these demographic variables that a priori make sense in a model?  Number of voters in the precinct is no longer a significant predictor of vote share, but other variables end up highly significant. One variable worth noting is the percent voting.  This variable is important, because as the percent of voters voting increases, the percent Republican increases significantly.  This is partial verification of a prior concern I had regarding higher turnout in Republican districts being an underlying cause of Clarkson's correlation.

Multiple factor model at precinct level, with total votes, percent voting, land area, percent voting age, area ratio to county, and county population.

Statistical impact: The key takeaway is that the small correlation found by Clarkson and previous authors is most likely due to other correlated variables.  These variables generally measure demographic factors and precinct design concerns (and correlate conceptually with the ideas from commentors on this blog and elsewhere). We have no good a priori reason to believe that precinct size should be uncorrelated to vote share %.


Clarkson’s theory is that most precincts under 500 voters are rural and Republican leaning districts, whereas over 500 voters, she would expect the precinct size relationship to Republican percentage to level out, or become more Democrat leaning, because larger precincts would be at the urban core.  I have explained the problems with this logic in several different blog posts:  Effectively, precinct creation is not a randomized process, thus many covariates, demographic and otherwise come into play.  I even demonstrated how Clarkson's analysis withers up when we expose the data to demographic covariates.

Let's look at this through a few visual examples.

Focusing on Johnson County and Sedgwick County, I highlighted all of the precincts with 500 or more voters in the 2014 Governor's election, and then went on to classify each one by larger buckets.  After 500 voters per precinct, the smallest precincts are the ones closest to the urban core, while the largest are in the outer-rural suburbs.  This map demonstrates that relationship:

Johnson County KS, Center City to Upper Right
Additionally, for Sedgwick County KS:

Sedgwick County Kansas, Center City in Center-Right

On face, we don't necessarily know that the gentrified areas closest to the urban core are going to be the most liberal.  So I mapped this as well, validating that the areas closest to the urban core tend to be the most liberal, with the most conservative areas outside of the 435 loop, to the south and west of the inner urban core. 
Johnson County KS, Vote % by Party

Sedgwick County also shows a very obvious pattern, with the most democratic areas in the central city area, moving more Republican towards the suburbs.

Sedgwick County Kansas, Vote % by Party

What does this mean?  Two concepts are validated
  • Precinct creation is not random, and the larger precincts within Johnson County and Sedgwick County do not lie closest to the "democrat" urban core, or randomly throughout the region, but instead in rural and near-urban suburbs-in direct opposition to Clarkson's hypothesis.
  • Those suburban areas (outside of the 435-loop in JoCo, suburban non-core areas in  SGCO) tend to also be more conservative.

In essence, the primary hypothesis of Clarkson's analysis is flawed, because these a priori relationships exist.  In this case, it appears that the patterns of suburbanization over time have led to this scenario: in large cities, the largest precincts are not at the urban core, but instead lie in the ring suburban areas which have gradually developed over the past 50 years.  (In Wichita, a large portion of new-development ring-suburban area lies inside city limits). 

Clarkson's theory is based on a broken a priori notion:  after 500 voters, there should be no correlation between precinct size and percent that vote Republican.  The specific reason her theory is broken is that the precinct creation was not random, and in fact suburbanization caused the largest of the precincts to be in whiter, richer, and more Republican leaning areas.  


I have now demonstrated this for Sedgwick and Johnson Counties, how much do those two counties actually matter to overall Kansas results?


Let's take a deeper look into large precincts.  An easy way is to break precincts into buckets by size, and talk about them in this way.  Here are the size buckets I am using:

  • Regular Precincts: 0-500 voters (Clarkson ignored these)
  • Large Precincts: 500-1000 voters
  • Super-Large Precincts: 1000+ voters

First, how does Brownback perform by each size-grouping of precincts?  Here's a chart:

This chart actually verifies Clarkson's correlation.  Effectively, Brownback did best in regular and super-large precincts.  The fact that he did better in super-large precincts than large precincts is the exact correlation that Clarkson cited in her original work.  This is just another validation that the correlation exists, but NOT of Clarkson's interpretation of this finding as evidence of fraud.

But how much do suburbanization patterns in Johnson and Sedgwick County matter in this?  A lot.   First, Johnson and Sedgwick counties make up only 12% of the regular sized precincts. But they make up almost two thirds of large precincts, and 70% of the super-large precincts.  Sedgwick county has more than 2/3rds of the super-large precincts statewide, and a higher ratio of super large::large precincts.  

A quick aside, because the independent variable in Clarkson's correlation is "precinct size" this means that Sedgwick County can create a correlation simply by  1.being more conservative than Johnson County  and 2. having larger precincts than Johnson County.  More on that below though.

If we look at Clarkson's analysis, over 2/3rds of the sample can be attributed to Johnson or Sedgwick counties, where we know that her a priori assertion is broken.  Moreover, when we run the vote count to Republican percent correlation on the other 1/3rd we see no correlation.  The effect is only observable in urban/suburban counties (where demographically significant suburbanization processes have occurred).  Thus Sedgwick and Johnson counties are all that matter to the observed correlation and we don't need to explore additional counties.  Here's an R output for the other 101 counties:

One more thing.  There's another factor that increases correlation when we aggregate results.  Because the majority of super large precincts are in Sedgwick County, it gives leverage to Sedgwick County over Johnson County.  And because generally Wichita is a more conservative region than Johnson County, that leverage serves to increase the correlation, though due to no nefarious or unexplained phenomena.  

The concept of leverage, or "mix" (i.e., the mix of counties), can easily be shown graphically.  Luckily, this is easy in the ggplot2 R library.  Here is a scatter of Clarkson's correlation with counties color coded.  In this you notice the more liberal counties tend to have mid-large precincts (Wyandotte, Douglas, even Johnson county) while more conservative Counties (Sedgwick, Other Rural) make up a majority of the largest precincts (also, bar chart above demonstrates this).  This enhances Clarkson's correlation when counties are combined, simply due to the mix of counties, not in-county nefarious action by voting machines or bad actors at precincts.

This analysis demonstrates that a portion of the correlation at the statewide level for Kansas is due to relative conservative ratios in separate urban areas. In essence, it's not surprising that we would see 


I am not the only person working on this issue.  A political scientist named Mark Lindeman, (also mentioned in the Fries'dat and Sampietro paper) explored the same correlations Clarkson and I have reviewed, but analyzing different dimensions of the data.  Specifically, his work draws the correlation back to original voter registration data, and demonstrates that the correlation doesn't start at the ballot box (link to Lindeman's most recent paper)

What does that mean?  Party affiliation at registration is also correlated with total number of voters, long before we get to the voting machine.  That means that Clarkson’s correlation exists prior to the voting system, and in fact the correlation between large precincts and Republican registration occurs effectively in nature.  What could cause this to exist in nature? A few things, demographic effects and patterns of suburbanization included.  I suggest reading his work, and I also validated his work using Johnson County data in 2004, see chart below, first validating Clarkson's correlation, then replicating Lindeman's  correlation to registration patterns. 


A few months after my initial post, Esquire magazine’s online version ran a quick piece of Clarkson’s work.   I wrote some text with links to my work in the comments section of the article.  Beth Clarkson herself later responded and we had an engaged conversation about her work.  Here is Clarkson's final statement to me on Esquire forums:

We seem to be in agreement that the null in my case isn't true. I disagree that it invalidates my work because I feel the cause is what is under debate. Your suggestion of assuming a particular prior distribution may or may not be appropriate. I haven't looked at it deeply enough to know for sure. In short, I'm agreeing that you could well be right about that. That our electronic voting machines are eminately hackable and have no post-election audit procedures in place are established facts and are equally concerning to me. Do you diagree about that aspect? Are you satisfied with assuming a distribution that fits the pattern? Or do you agree that our voting system should be (but isn't) transparent enough for citizens to feel confident that the results are accurate?

Here's my response one by one:
  1. On the NULL case not being true.  I agree with Clarkson that we can "reject the NULL hypothesis", in fact in my first post on the subject (and above in this post) I replicated her results.  But all Clarkson is saying here by claiming the null case is false is that she found a non-zero correlation.  I agree, there is a non-zero positive correlation, but if we dive deeper why are we testing a null hypothesis?  And if we can reject it, have we done the research to say that there aren't reasonable alternate explanations (I have, and there are)?  Keep in mind my prior work on this subject, that show demographic and precinct creation reasons create this correlation.  In essence rejecting the null hypothesis here is in no way meaningful because it is only testing the false assumption that there should not be a correlation.  That has been the point of this blog's work on the subject, that the null hypothesis is irrelevant.
  2. On her admission that she hasn't looked deeply into this.  She concedes that I may be right. A lot of thoughts here.  She has been threatening lawsuits and doing newspaper interviews over something she hasn't deeply reviewed.  She also said earlier in her comments that she hasn't had access to demographic or mapping data.  I have been able to compile that data, usually in a matter minutes, whenever I have wanted to look at it.  Access to data is easy, and it's the job of a modern statistician or data scientist to acquire it and test your work, due diligence.  Effectively here, she admits she's done less work on the subject than I have, and concedes I may be right.
  3. On open government concerns.  I have always agreed with her on this concern, on this blog, and publicly, multiple times.  I have also offered to help, if I can, should she get access to that data.  At this point this is a silly rhetorical ploy. Clarkson has conceded she hasn't done due diligence on her work on intellectual grounds, and has started making vague allusions to things that sound appealing to everyone.  Overall, this is largely a diversionary tactic from the real issue at hand, the failing of her theories.


In late July of this summer, a paper was published that cited Clarkson’s work and served as an attempted critique of my and Mark Lindeman’s work.  As reviewers of this paper I spoke to stated, this is not a publishable paper, and the statistical work is over-simplistic, especially for complex elections, in a demographically influenced, multi-dimensional world.  As I stated earlier, responding to this paper is probably not worth my time.  However, in the context of a highly contested national election, I feel obliged to respond.

Point 1:The authors punt on actually critiquing models.
Outside of Clarkson’s attempt to invalidate my model (I rebut below), the totality of criticism of both myself and Mark Lindeman was rhetorical, and not pointed at specific issues of the model.  One outright untruth in the paper is that Lindeman fails to deliver any data, which he has repeatedly done in other public places (in fact, the report links to Lindeman's data and code).  The authors also suggest I don’t use the right statistical model, but fail to point out why it is statistically invalid. 

Effectively, the authors are delivering a debate critique of simply standing up and yelling *wrong*, without delivering a critique of the actual data, statistics, methods, or underlying theory. The critique doesn’t work largely because it’s non-existent.  This paper would struggle to stand up to peer review required by reputable publications.  Their paper also doesn't explain why the data is weak, and as I have responded, line by line, with each of their actual concerns, I consider Clarkson, Fries’dat, and Sampietro to be thoroughly disproven.      

But the concept that Lindeman doesn’t deliver any substantive data is still troubling to me, because he certainly does, and I actually proved that previously in this post.  Actually, Lindeman’s work tends to make my work somewhat irrelevant (as it demonstrates the nearest root cause to Clarkson’s correlation).  Let’s revisit his theory: that we can prove that Clarkson’s relationship exists prior to the voting machines, and in fact, that more Republicans register in larger districts than smaller.  Can this be demonstrated once again?  Yes. Once again, in the 2010 Kansas Governor's Election.

First, beyond 500 voters, Republican registration correlates with precinct size:

Second, once we account for voter registration patterns in our model that relationship disappears:

To summarize, the paper’s (Fries’dat  and Sampietro) critique is insufficient, and fails to address any of the work of Lindeman and Bowles.  Here I have once again replicated Lindeman’s work which is a statistical proof of his hypothesis: that Clarkson’s correlation isn’t unexpected, but it in fact follows voter registration patterns.

Point 2: The Concept of Suburbanization Over Time

To quote the authors:
"Bowles’ critique does not provide an explanation for the appearance of the pattern since the year 2000. Precincts have never been randomly created districts. So why wasn’t this pattern present in earlier elections?"

A few reasons why this is also false:
  1. Their evidence for the pattern not existing prior to 2000 is simply “Phil Evans told us.” In the section of the paper addressing my work they state “didn’t exist prior to 2000” as fact.  This claim is mentioned throughout the paper as fact, but there is only one apparent citation, which is on page 24, where they declare that “Phil Evans Told Us” (PAGE 24)  Citing what someone said (hearsay, effectively)  rather than actual statistical evidence is not sufficient, especially when you’re trying to prove that something wasn’t observed before a prior date (proving an absence).  In this case you need a fairly exhaustive analysis, looking across multiple regions and time horizons to prove.  Traditionally, large meta-analysis study would be required before this type of claim (absence) should be made in an academic setting.  
  2. The pattern DID appear before the year 2000.   In fact I found it in the first race prior to 2000 I analyzed, Dole/Kemp v Clinton/Gore, 1996, Sedgwick County (here I replicated the graphing method from the Fries'dat and Sampietro paper).
  3. The theory accounts for over-time effects. It also seems that the authors fail to account for "time" in "suburbanization over time.".  The point of my overall theory is that suburbanization patterns that occur *over time* would lead to a scenario where more Republican suburbs would have large, high-turnout precincts, whereas inner cities created prior would have smaller, old created precincts.  The process of suburbanization has occurred *over time* (specifically, from the 1950s to present) and thus we would expect two things:
    1. At some point in time, during the process of suburbanization, the relationship would become statistically significant.
    2. The relationship would generally increase in strength over time.

Point 3: Wichita is not 100% inner-city.

The authors of the study include a graph that says 
“Fig. 19 — 2014 Kansas Senate race - the increase of a candidate’s percentage in the large precincts is only seen in the inner city precincts, not the suburban precincts”  

This claim is problematic for several reasons:
  • They misunderstand the concept of suburbanization over time.  In this case Clarkson created an overall simplistic model binarizing the world into “urban” versus “rural.”  Because suburbanization has been a long gradual process over time, binarizing into two lines (urban versus rural) doesn’t appropriately account for this long-time effect.  In fact, we would expect the correlation to exist at subunits, especially in large cities with new-developing suburban areas inside city limits (like Wichita, Kansas).  The two new maps below demonstrate this graduated standard.  The effect of large precincts and a priori suburbanization exist inside city limits.
  • Once again in misunderstanding the theory, Clarkson has validated our analysis. In this case, the test is actually further validation of our patterns of suburbanization, because the city of Wichita  includes large suburban outer-ring precincts (still fully inside city limits) where we would expect the correlation to exist.  The other test, "the rural line on her chart" actually becomes a test of rural-country versus “rural-towns” read: towns that exist inside vast suburban areas.  This second line, thus, correlates with population density, and with the traditional theory that less-rural people tend to be more liberal. (why < 500 voter precincts are generally excluded)

Let’s dive deeper, shall we?  Now that we’ve disproven Clarkson’s critique on prima facie theoretical grounds, we should dive in for a deeper understanding of theories of suburbanization.  Let’s start with Wichita, Kansas presidential election 2008.

The maps demonstrate the trends at hand in precinct size.  First map is Wichita Kansas only (mirrors Clarkson’s analysis) and shows a significant increase in size as we move away from the city center, marked with black dot.  Because Wichita grew from this city center, this shows that higher vote total precincts tend to exist further from the center city, validating the first part of my processes of suburban precinct creation theory.  

But is this a statistically significant relationship?  We can test that using a regression analysis for large precincts.  This analysis demonstrates that the distance from center city (calculated via haversines method) is a positive, statistically significant predictor of number of voters.  This is important, because it is confirmatory of my initial theory, of precinct creation in near-suburban areas being key to understanding the functional basis of Clarkson’s theory. 

But distance from center city is also very good predictor of Republican vote share, validating the original hypothesis that ceteris paribus, we would expect, inside a large city, that larger precincts would relate strongly to large Republican vote shares.  We prove this out, in what’s actually a quite predictive model (R-squared = .45).  This is important as well, because it demonstrates (though logical) that inside a city, suburban areas tend to vote substantially more Republican than inner-city districts.

This creates an initial framework for our theoretical basis: precincts larger become in size as we move from inner-city to the suburban areas and also suburban areas tend to vote more Republican.  But how does this relate to Clarkson’s correlation?

The same analysis can be conducted for Johnson County, Kansas, which shows a very strong
"Clarkson's" correlation for multiple, consecutive elections. Though Johnson County Kansas didn’t develop in the same center-city method of Wichita, we can still estimate a model that accounts for these factors.  In this case we have to consider both the root of growth (area closest to Kansas City Missouri) and indicators of center micro-cities in Johnson County  (Lenexa, Shawnee, Overland Park, Olathe) and the best demographic proxy for these small-precinct old-center-cities: percent Hispanic.  In the map below the black dot represents center of growth for county:

Validation of the relative strength and existence for Clarkson’s calculation, in Johnson County for 2008 is below.

The output below validates that we can predict precinct size by looking at distance from center city  plus percentage Hispanic, proving that voters in a precinct is correlated with underlying demographics.

Also though a corollary point, that the relationship isn't just at the voter level, but also that distance to center city is predictive of population of a precinct.  This means that we aren't just talking about who shows up to vote, or potentially that votes were added to some districts, but that in fact the precincts are larger from a census-population perspective.

We then create a secondary analysis, where we try to estimate Clarkson’s correlation, controlling for known demographic patterns that impact voting factors.  In this case we see that Clarkson’s correlation fully disappears after accounting for these two factors (distance to center city, percent hispanic).

To bring this full circle (a bit for my own amusement) we can also predict Lindeman’s voter registration percentages, looking at distance to center city, as well as Hispanic percentages.

Point 4: State variation in models demonstrate same underlying process.

The authors contend that precinct creation varies by state, each having their own system of rules and and strategies.  This may be true, but all systems of precincts are in reactions to underlying population growth trends, and thus the underlying theory of precinct interaction with population demographics holds up.  This isn’t so much of an argument, as the authors granting my Kansas analysis.  Similar analysis has discovered similar findings in other states regarding relative demographics of suburbs and precinct construction.  It also ignores the confirmatory analysis from Mark Lindeman (which he has conducted, for many other states) where we know that the Clarkson correlation begins at registration NOT at the voting machine.


Throughout this paper I’ve outlined Clarkson’s original analysis, its drawbacks, and my critique.  Furthermore, I’ve created a detailed analysis and response to the Fries'dat and Sampietro paper that serves as a basis going forward.  In summary:
  • Clarkson offers a correlation which she claims may be voter fraud without providing further falsifying demographic or alternate cause analysis.
  • Lindeman and I have spent a good deal of time and effort analyzing the underlying cause of the correlation. These demographic and initial registration factors easily explain the correlation on two grounds:
    • The correlation is traceable back to the initial registration.
    • The underlying reason for the correlation relates to underlying demographics, specifically the impact of suburban/urban divides in large cities.
  • The Fries'dat and Sampietro paper is an insufficient critique of the theory, as there are no substantive critical points in the paper and those that do exist are easily refuted through a deep look and underlying theoretical constructs and data.

A final thought on the methods and issues at hand.  There is a further effort to validate the upcoming election, and Clarkson is leading the charge.  I was sent the image below seeking volunteers for a “citizen exit poll”… putting aside the validity of “citizen exit polls” as a mechanism for validating election results (it’s not).  The image is a clinic in how to bias results in studies, mainly by soliciting volunteers who will be motivated by the “rigged” headline.   This poster reiterates the reason it was important for me to respond: there will likely be information coming from dubious sources after this election claiming that the result was rigged. As social and demographic data is highly dimensional and *soft* we will need to be very rigorous in our analysis and acceptance of those sources.  That said-I would welcome a statistically valid and rigorous post audit to validate the results of the 2016 presidential election.

Wednesday, October 19, 2016

A Layperson's Guide to Multivariate Regression Outputs

Multivariate regression is a common technique used to predict a single outcome (dependent variable) using many predictors (independent variables).  For data scientists, multivariate regression is often the first statistical predictive technique to learn, and the easiest to understand and describe mathematically.  

For a lay person, the math of multivariate regression can seem daunting.  However, the general concepts can be described using knowledge of high school algebra and geometry.  Essentially, multivariate regression is the process of determining the line that best fits a set of data across multiple factors.  We can easily visualize this when we think about a two-dimensional problem, such as the pace in the Boston Marathon by age: 

The blue line represents the mathematically determined line of best fit.  As this looks like a coordinate plane from high school algebra, we can describe this line (and thus, the mean relationship between age and pace) using a y=mx+b equation.  Here that relationship looks like:

pace =  0.029 X [age]  +   8.06
This concept is easy to understand in two dimensions, but the "multi" in multivariate regression refers to multiple predictive variables.  In this case, the line now extends into multiple dimensions, and instead of our simple high school y=mx+b we now have something like:

 y=m1x1 + m2x2+m3x3+m4x4..+b
This sounds complex, and it certainly can be. The complex outputs that authors sometimes post in conjunction with the analyses do not help a non-statistical reader understand what the analysis means.  Below I will describe how to interpret multivariate regression outputs and what they mean in terms of describing the world, without having to understand advanced statistics.  I created a simple regression, predicting Boston Marathon pace by age and gender, and printed the output below:  

Here's what each element means one-by-one (elements 4,7 and 11, are all you really need to understand):
  1. Formula: shows what predictive elements went into the equation, and what is being predicted, separated by the ~ symbol.
  2. Residuals: tells us statistics about the "error" in the equation, essentially how far each of our data points are from our final predicted line.
  3. Variables: a list of all the predictive variables placed in the equation plus the "intercept," or the high school "b" from our predictive equation.
  4. Coefficient Estimate: this is the "m" from our high school equation, and tells the slope of the line between each independent variable and the dependent variable.  For instance, the data above tells us that pace tends to increase with age (coefficient is positive) at a rate of about 0.03 minutes per year.
  5. Standard Error: we can think about this as the standard deviation of data around our coefficient estimates.  Essentially, how much variation do we believe could exist in all of our "m" elements in the equation?
  6. t-value: this is the t statistical value, which is calculated by dividing the coefficient (4) by the standard error (5).  The interpretation isn't straight forward, so as a non-statistical person you can largely ignore this.
  7. P: the p-value is calculated from our t value (you can look it up in a table).  There two definitions we can use:
    1. (dumb statistical definition, skip) The value represents the probability of observing the coefficient and standard error values at least this extreme, assuming that the NULL hypothesis is correct. 
    2. This is tells you if an independent variable is statistically significant, meaning, if it is likely to have a non-random predictive relationship with the dependent variable.  In essence: does the independent variable have a meaning relationship with the dependent variable?  The lower this is the more likely the relationship is significant, with values below 0.05 being "significant" under common statistical standards.
  8. Asterisks: the asterisks represent at what level of significance each variable is significant in the model, redundant to (7).
  9. Sig Codes: these serve as a key for (8) above, and are derived from the P-value, (7).
  10. Residual error: this can largely be ignored, though the "degrees of freedom" tells us how many rows were used in the dataset.
  11. Multiple-R-Square: this is a measure of the quality of the model, expressed in how much variance is "explained" in the dependent variable. Using the prior example, if we were going to predict the pace of runners in the Boston Marathon, and knew nothing except average times for past finishers, our best predictive strategy would be to just guess the average for each competitor (R-squared = 0).  But if we know the age and gender of the competitor, we can create a linear model to represent their relationships to pace, and use those to inform our predictions (model above, R-squared is 0.086).  If we had prior paces for each finisher, we may be able to  improve our predictive model, and could measure that improvement by the R-squared value. This value runs from 0 to 1, and gets continuously "better" as it increases. 
  12. F-statistic: This one can also largely be ignored, though the p-value tells whether the regression as a whole is statistically significant.

And a test!  For the regression below I've added a single factor to the equation.  The variable e_a is a categorically indicator (assumes values 0 or 1) and indicates that the runner is or isn't part of some group.  Mail your answers to, to these questions (no prizes, only knowing you're right):

  1. What group of runners do you think the variable e_a represent? (hint: e_a is an acronym)
  2. How did the addition of this variable impact the model in terms of quality and other variables?