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Use of Statistical Analysis in Supreme Court Election Case

  • 1.  Use of Statistical Analysis in Supreme Court Election Case

    Posted 12-09-2020 09:25

    The recently filed case of Texas v. Pennsylvania, filed in the Supreme Court's original jurisdiction, included a declaration by Dr. Charles J. Cicchetti, PhD, concerning a statistical analysis of election results. Dr. Cicchetti compared the 2020 election results in the four swing states being sued. (See the appendix in the first link below). He concluded, not surprisingly, I think, that the increase in Democratic votes between the election reflected a real difference in populations, and the probablility of such a difference arising by sampling error from the same population was extremely small.

    He similarly compared ballots received on election day with later mail-in ballots and likewise found the probability of their arising by chance from the same population as extremely low: earlier and later ballots came from different populations. 

    The Supreme Court filing took these results and presented them as evidence that something was wrong with the election. As they said in their main filing (the 2nd link below), "Expert analysis using a commonly accepted statistical test further raises serious questions as to the integrity of this election.)

    In their motion for expedition (the first link), they presented Dr. Cicchetti's results as showing that "the probability of former Vice President Biden winning the popular vote in the four defendent states" was astronomically low. 

    Dr. Cicchetti's declaration doesn't contain a conclusion that the integrity of the election was questionable. It merely shows that in both analyses, the results very likely came from two different populations. The declaration even says that there are many possible reasons why this might be the case. The declaration also presents Dr. Cicchetti as an economist, not a statistician. 


    But what can or should a statistician, as distinct from  some other kind of quantitative professional, ethically do in this situation?

    My understanding is that a statistician has an ethical obligation not merely to provide a report of analyses that does not contain misleading conclusions. Rather, if results from that report are published or presented to the public or key decision makers, a statistician has an ethical obligation to ensure that their name is not associated with incorrect or misleading inferences and conclusions.


    And I would also think a Supreme Court brief, or indeed any court filing, would count as a publication Thus, I would think a professional statistician would have some obligation to have their name taken off such a brief and not allow their work to support such an inference, and if necessary to write the Supreme Court that their name was used without their permission.  


    What do you think? What would you have done in this case? What are a statistician's ethical obligations here?

    The views in this post are mine only, and do not reflect my employer.

    Motion for Expedition with declaration:
    https://www.supremecourt.gov/DocketPDF/22/22O155/163048/20201208132827887_TX-v-State-ExpedMot%202020-12-07%20FINAL.pdf

    Main Brief (Motion for Leave):
    https://www.supremecourt.gov/DocketPDF/22/22O155/162953/20201207234611533_TX-v-State-Motion-2020-12-07%20FINAL.pdf


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    Jonathan Siegel
    Director Clinical Statistics

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  • 2.  RE: Use of Statistical Analysis in Supreme Court Election Case

    Posted 12-09-2020 13:45
    Edited by Brittany Alexander 12-09-2020 20:18
    I would have never taken the job as an expert for this. It should have been clear that they wanted an expert to come up with some statistical evidence that could suggest fraud.  Why else would it be important to examine how likely the election results are. I think Dr. Cicchetti likely knew how his analysis would be used and it doesn't appear that he has publicly denounced the conclusion in the brief. Not only are the conclusions not communicated well, but the analysis is also just plain wrong.  A z-test with a binomial approximation is not appropriate since there isn't a constant proportion, votes aren't independent, and the election results are a population and not a sample.  He estimates the variance (pg. 22 of motion for the expedition) using N*(1-p) which is not the proper variance.   I do believe that we have an obligation as statisticians to present our analysis in a clear way that non-experts can understand and fight back if our analysis is being misconstrued.  This is also not the first election lawsuit this cycle to use statistically unsound analysis to show "evidence" of fraud.  I think statistical experts have an obligation to clearly explain the conclusion of the analysis and why they used the model they used. Dr. Cichetti didn't do that in my opinion, because he failed to clearly state that this analysis is not sufficient to prove  or even suggest fraud.

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    Brittany Alexander
    3rd Year Statistics Ph.D. Student
    Texas A&M University
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  • 3.  RE: Use of Statistical Analysis in Supreme Court Election Case

    Posted 12-10-2020 10:11
    I haven't been able to find the expert's report in an appendix at the first link. Can someone give me the page numbers? I'd like to use it as an illustration of bad interpretation after a correct calculation in my methods class.
    Lynne Stokes
    Dept. of Statistical Science
    Southern Methodist University

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    S. Stokes
    Southern Methodist University
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  • 4.  RE: Use of Statistical Analysis in Supreme Court Election Case

    Posted 12-10-2020 12:38
    It's in page 22 of this link.  Right after the marking for footnote 2, he mentions his formula for the variance (N*(1-p)) which is wrong.  I also calculated some of the z-scores myself using the same data in case that was a typo and they didn't match. Both the calculation and interpretation are wrong.

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    Brittany Alexander
    3rd Year Statistics Ph.D. Student
    Pre-Doctoral Research Associate at the Institute for Science, Technology, and Public Policy
    Texas A&M University
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  • 5.  RE: Use of Statistical Analysis in Supreme Court Election Case

    Posted 12-11-2020 11:58
    Is there no room for ASA to present a formal statement regarding just what the test of difference of two proportions (when performed correctly) really means? NO need to attack x or y. Just state that a test of two proportions just tests whether or not those two proportions are the same? That it does not test the source, the change of heart or opinion or probability of voting for the same people again?  Just to state that such test does not mean what it was portrayed to mean?
    Or is it maybe that we should not even dignify such interpretation with a response?

    Again it does not need to be confrontational, just like the statement on p values was, it can be an informational statement.

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    Alberto Nettel-Aguirre
    Associate Professor
    University of Calgary
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  • 6.  RE: Use of Statistical Analysis in Supreme Court Election Case

    Posted 12-14-2020 09:57

    Alberto Nettel-Aguirre asks "Is there no room for ASA to present a formal statement"?

    I think there may be room, but I don't see a mechanism. Who would write such a statement?  Who would choose which statements to write? How would they be vetted and approved? 


    There are are a statistical experts in the relevant fields who are quite capable of responding. The ASA strongly supports, fosters, and supports education on statistical practices - even holding an annual conference on it, of which I presently serve as Vice Chair. The question here is not one of concern or desire but rather one of agency: from my own individual perspective, I see neither a mechanism nor desire for the ASA, as an organization, to police statistical practice. 

    For my own part, from the perspective of an ethicist and an advocate for statistical best practice, I would like to see the ASA do more to address malpractice as in done in some other professional societies. A first step might be to develop a clear statement of what the ASA considers to be unacceptable. However, the ASA has neither the means nor mandate to police all of statistical usage. The many extremely capable experts in the many areas of practice are able to write op-ed pieces to address this need. 

    Please do not misunderstand me! I find this misuse deplorable. People need to write and and speak out, and the ASA can and does encourage recognized experts to do so. The response you seek is being provided by individuals who experts in the field. 



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    David J Corliss, PhD
    Director, Peace-Work www.peace-work.org
    davidjcorliss@peace-work.org
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  • 7.  RE: Use of Statistical Analysis in Supreme Court Election Case

    Posted 12-10-2020 18:40
    Thanks for sharing these links. The thought that comes to my mind is Mark Twain's words: "there are 3 kinds of lies: lies, damned lies and statistics",  The z-scores, p-values and probabilities are based on a sampling distribution assumption that has no role in this context. Consequently, it's no more than a defective calculation disguised as a cogent statistical argument  It should be seen for what it is: hogwash and deplorable.  Any objective third party would see right through it. Mark Twain were he alive, would be wagging his finger at Dr. Cicchetti.

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    Stan Altan
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  • 8.  RE: Use of Statistical Analysis in Supreme Court Election Case

    Posted 12-12-2020 13:35
    Brittany, the variance formula is correct: mean X prob of not getting a vote is Np X (1-p).  The hypothesis seems silly though.  Stan, Twain didn't claim to have originated "lies, damned lies and statistics".  He attributed it to Disraeli, but this hasn't been verified.

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    Allan Stewart-Oaten
    Emeritus, Ecology and Statistics
    University of California, Santa Barbara
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  • 9.  RE: Use of Statistical Analysis in Supreme Court Election Case

    Posted 12-14-2020 09:25
    Yes indeed,
    Twain didn't claim to have originated "lies, damned lies and statistics". He attributed it to Disraeli, but this hasn't been verified.

    According to Wikipedia the true originator is not Twain, it can't be found in Disraeli at all, and its originator is not known with certainty: Lies, damned lies, and statistics
    Relevant to the present discussion, the History section ends with
    Robert Giffen (1837–1910), Walter Bagehot's assistant editor at The Economist and President of the Statistical Society from 1882 to 1884, was a further early writer to have connected the expression regarding statistics to the expression regarding experts. Writing in the Economic Journal in 1892, he stated: "An old jest runs to the effect that there are three degrees of comparison among liars. There are liars, there are outrageous liars, and there are scientific experts. This has lately been adapted to throw dirt upon statistics. There are three degrees of comparison, it is said, in lying. There are lies, there are outrageous lies, and there are statistics."


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    Sander Greenland
    Department of Epidemiology and Department of Statistics
    University of California, Los Angeles
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  • 10.  RE: Use of Statistical Analysis in Supreme Court Election Case

    Posted 12-14-2020 16:26
    I don't think I was clear about his variance assumption. The variance of X of a binomial distribution is Np(1-p).  However Dr. Cicchetti is doing a binomial approximation inside a z-test which gives the proportion a  
    variance of (p(1-p))/N but he used a variance of N(1-p). Note that this is not even the variance of a binomial because it is missing a p.

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    Brittany Alexander
    3rd Year Statistics Ph.D. Student
    Pre-Doctoral Research Associate at the Institute for Science, Technology, and Public Policy
    Texas A&M University
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  • 11.  RE: Use of Statistical Analysis in Supreme Court Election Case

    Posted 12-14-2020 15:20

    On Friday, a second "supplemental declaration" from Dr. Cicchetti was filed as an appendix to the State of Texas' reply brief. In his second declaration, Dr. Cicchetti clarified his findings and comments and the inferences he believed should be drawn from them, and responded directly to critics who had called his analysis "nonsense."

    in my previous email, I had been careful to distinguish between the findings and conclusions reported  by Dr. Cicchetti's himself in his own report, and the statement made by Texas' lawyers aboit his report in their briefs. In doing so, I gave Dr. Cicchetti a certain benefit of the doubt in limiting his responsibility for what the lawyers said about his work. 


    Dr. Cicchetti's second declaration, unfortunately, removes some of the distinction between his and the lawyers' comments, bringing his position closer to the lawyers. I must therefore regretfully report that, in choosing to speak up and not to remain, Dr. Cicchetti has removed some of the benefit of the doubt I had previously accorded him. 

    Dr. Cicchetti's second declaration characterizes Biden's win as an "unusual statistical anomaly" and states that "further investigation and audits should be consucted before finalizing the outcome" of the election.  Thus, this second declaration makes clear that itiz Dr. Cicchetti himself, and not just the lawyers, who is characterizing his findings as evidence that there is something fishy about the election results warranting Texas' request for the Suprme Court to halt finalization the results pending further investigation and audits. 


    Dr. Ciccetti also presents additional evidence in support of these conclusions, including evidence of shifts in support in various aubgroups between the 2016 and 2020 elections. 


    I must therefore report that my concern here lies not just with Dr. Cicchetti's silence regarding the lawyers use of his statements, but his affirmative statements.

    I had previously spoken regarding what I had perceived as ethical issues raised bu Dr. Cicchetti's silence regarding the use of his research by others. "Qui tacit consentire," Robert Bolt's Sir Thomas More informs us, "Silence gives consent." While this is so, there is still room for ethical doubt. The ethical person may, in extreme circumstances, sometimes have need to use the cover of silence, and rest in the shelter of the shadow of doubt it casts, as More's case well illustrates. Sometimes silence is the better part of valor. 

    But here Dr. Cicchetti has spoken. All doubt, sadly, has been removed. 

    As before, my opinion here is strictly my own.

    Here is the link to the second declaration. It begins on p. 31 of the pdf, labeled p. 152a:

    https://www.supremecourt.gov/DocketPDF/22/22O155/163497/20201211110907446_TX-v-State-LeaveReply-2020-12-11.pdf

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    Jonathan Siegel
    Director Clinical Statistics
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  • 12.  RE: Use of Statistical Analysis in Supreme Court Election Case

    Posted 12-15-2020 14:34

    Having served as a statistics expert witness, I have some thoughts.  The emphasis of this discussion seems to be on the fact that a microscopic p-value is consistent with a difference in populations but doesn't indicate that election cheating is the explanation.  Of course, this is true.  Also true is that lawyers on both sides are advocates who will choose to use words harmonious with client interest.  Attorneys gladly point out that it is not their duty to make the other side's case, but there is a duty to point out when the attorney or expert witness for the other side over-reaches with an explanation.  My experience in several age, race and sex discrimination suits, and in cases in which students are suspected of having cheated on multiple choice exams is that there almost always is both statistical and non-statistical evidence to be weighed as a package in order to render a verdict. The one exception I recall is an age discrimination suit in which the p-value associated with the fact that only workers aged 60 or over had been terminated from the workforce was .000000000088 for an age-neutral process.  The day after I presented the analysis in a deposition, the plaintiffs' lawyer told me that the case was over – settled out-of-court – because the company didn't want the p-value to be aired in court.



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    [Mick] [Norton]
    [Professor Emeritus]
    [College of Charleston][]
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