The American Statistical Association Statement on Significance Testing Goes to Court – Part I

It has been two and one-half years since the American Statistical Association (ASA) issued its statement on statistical significance. Ronald L. Wasserstein & Nicole A. Lazar, “The ASA’s Statement on p-Values: Context, Process, and Purpose,” 70 The American Statistician 129 (2016) [ASA Statement]. When the ASA Statement was published, I commended it as a needed counterweight to the exaggerated criticisms of significance testing.1 Lawyers and expert witnesses for the litigation industry had routinely poo-poohed the absence of statistical significance, but over-endorsed its presence in poorly designed and biased studies. Courts and lawyers from all sides routinely misunderstand, misstated, and misrepresented the meaning of statistical significance.2

The ASA Statement had potential to help resolve judicial confusion. It is written in non-technical language, which is easily understood by non-statisticians. Still, the Statement has to be read with care. The principle of charity led me to believe that lawyers and judges would read the Statement carefully, and that it would improve judicial gatekeeping of expert witnesses’ opinion testimony that involved statistical evidence. I am less sanguine now about the prospect of progress.

No sooner had the ASA issued its Statement than the spinning started. One scientist, and an editor PLoS Biology, blogged that “the ASA notes, the importance of the p-value has been greatly overstated and the scientific community has become over-reliant on this one – flawed – measure.”3 Lawyers for the litigation industry were even less restrained in promoting wild misrepresentations about the Statement, with claims that the ASA had condemned the use of p-values, significance testing, and significance probabilities, as “flawed.”4 And yet, no where in the ASA’s statement does the group suggest that the the p-value was a “flawed” measure.

Criminal Use of the ASA Statement

Where are we now, two plus years out from the ASA Statement? Not surprisingly, the Statement has made its way into the legal arena. The Statement has been used in any number of depositions, relied upon in briefs, and cited in at least a couple of judicial decisions, in the last two years. The empirical evidence of how the ASA Statement has been used, or might be used in the future, is still sparse. Just last month, the ASA Statement was cited by the Washington State Supreme Court, in a ruling that held the death penalty unconstitutional. State of Washington v. Gregory, No. 88086-7, (Wash. S.Ct., Oct. 11, 2018) (en banc). Mr. Gregory, who was facing the death penalty, after being duly convicted or rape, robbery, and murder. The prosecution was supported by DNA matches, fingerprint identification, and other evidence. Mr. Gregory challenged the constitutionality of his imposed punishment, not on per se grounds of unconstitutionality, but on race disparities in the imposition of the death penalty. On this claim, the Washington Supreme Court commented on the empirical evidence marshalled on Mr. Gregory’s behalf:

The most important consideration is whether the evidence shows that race has a meaningful impact on imposition of the death penalty. We make this determination by way of legal analysis, not pure science. At the very most, there is an 11 percent chance that the observed association between race and the death penalty in Beckett’s regression analysis is attributed to random chance rather than true association. Commissioner’s Report at 56-68 (the p-values range from 0.048-0.111, which measures the probability that the observed association is the result of random chance rather than a true association).[8] Just as we declined to require ‘precise uniformity’ under our proportionality review, we decline to require indisputably true social science to prove that our death penalty is impermissibly imposed based on race.

Id. (internal citations omitted).

Whatever you think of the death penalty, or how it is imposed in the United States, you will have to agree that the Court’s discussion of statistics is itself criminal. In the above quotation from the Court’s opinion, the Court badly misinterpreted the p-values generated in various regression analyses that were offered to support claims of race disparity. The Court’s equating statistically significant evidence of race disparity in these regression analyses with “indisputably true social science” also reflects a rhetorical strategy that imputes ridiculously high certainty (indisputably true) to social science conclusions in order to dismiss the need for them in order to accept a causal race disparity claim on empirical evidence.5

Gregory’s counsel had briefed the Washington Court on statistical significance, and raised the ASA Statement as excuse and justification for not presenting statistically significant empirical evidence of race disparity.6 Footnote 8, in the above quote from the Gregory decision shows that the Court was aware of the ASA Statement, which makes the Court’s errors even more unpardonable: 

[8] The most common p-value used for statistical significance is 0.05, but this is not a bright line rule. The American Statistical Association (ASA) explains that the ‘mechanical “bright-line” rules (such as “p < 0.05”) for justifying scientific claims or conclusions can lead to erroneous beliefs and poor decision making’.”7

Conveniently, Gregory’s counsel did not cite to other parts of the ASA Statement, which would have called for a more searching review of the statistical regression analyses:

“Good statistical practice, as an essential component of good scientific practice, emphasizes principles of good study design and conduct, a variety of numerical and graphical summaries of data, understanding the phenomenon under study, interpretation of results in context, complete reporting and proper logical and quantitative understanding of what data summaries mean. No single index should substitute for scientific reasoning.”8

The Supreme Court of Washington first erred in its assessment of what scientific evidence requires in terms of a burden of proof. It then accepted spurious arguments to excuse the absence of statistical significance in the statistical evidence before it, on the basis of a distorted representation of the ASA Statement. Finally, the Court erred in claiming support from social science evidence, by ignoring other methodological issues in Gregory’s empirical claims. Ironically, the Court had made significance testing the end all and be all of its analysis, and when it dispatched statistical significance as a consideration, the Court jumped to the conclusion it wanted to reach. Clearly, the intended message of the ASA Statement had been subverted by counsel and the Court.

2 See, e.g., In re Ephedra Prods. Liab. Litig., 393 F.Supp. 2d 181, 191 (S.D.N.Y. 2005). See alsoConfidence in Intervals and Diffidence in the Courts” (March 4, 2012); “Scientific illiteracy among the judiciary” (Feb. 29, 2012).

5 Moultrie v. Martin, 690 F.2d 1078, 1082 (4th Cir. 1982) (internal citations omitted) (“When a litigant seeks to prove his point exclusively through the use of statistics, he is borrowing the principles of another discipline, mathematics, and applying these principles to the law. In borrowing from another discipline, a litigant cannot be selective in which principles are applied. He must employ a standard mathematical analysis. Any other requirement defies logic to the point of being unjust. Statisticians do not simply look at two statistics, such as the actual and expected percentage of blacks on a grand jury, and make a subjective conclusion that the statistics are significantly different. Rather, statisticians compare figures through an objective process known as hypothesis testing.”).

6 Supplemental Brief of Allen Eugene Gregory, at 15, filed in State of Washington v. Gregory, No. 88086-7, (Wash. S.Ct., Jan. 22, 2018).

7 State of Washington v. Gregory, No. 88086-7, (Wash. S.Ct., Oct. 11, 2018) (en banc) (internal citations omitted).

8 ASA Statement at 132.

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