For your delectation and delight, desultory dicta on the law of delicts.

Daubert Retrospective – Statistical Significance

January 5th, 2019

The holiday break was an opportunity and an excuse to revisit the briefs filed in the Supreme Court by parties and amici, in the Daubert case. The 22 amicus briefs in particular provided a wonderful basis upon which to reflect how far we have come, and also how far we have to go, to achieve real evidence-based fact finding in technical and scientific litigation. Twenty-five years ago, Rules 702 and 703 vied for control over errant and improvident expert witness testimony. With Daubert decided, Rule 702 emerged as the winner. Sadly, most courts seem to ignore or forget about Rule 703, perhaps because of its awkward wording. Rule 702, however, received the judicial imprimatur to support the policing and gatekeeping of dysepistemic claims in the federal courts.

As noted last week,1 the petitioners (plaintiffs) in Daubert advanced several lines of fallacious and specious argument, some of which was lost in the shuffle and page limitations of the Supreme Court briefings. The plaintiffs’ transposition fallacy received barely a mention, although it did bring forth at least a footnote in an important and overlooked amicus brief filed by American Medical Association (AMA), the American College of Physicians, and over a dozen other medical specialty organizations,2 all of which both emphasized the importance of statistical significance in interpreting epidemiologic studies, and the fallacy of interpreting 95% confidence intervals as providing a measure of certainty about the estimated association as a parameter. The language of these associations’ amicus brief is noteworthy and still relevant to today’s controversies.

The AMA’s amicus brief, like the brief filed by the National Academies of Science and the American Association for the Advancement of Science, strongly endorsed a gatekeeping role for trial courts to exclude testimony not based upon rigorous scientific analysis:

The touchstone of Rule 702 is scientific knowledge. Under this Rule, expert scientific testimony must adhere to the recognized standards of good scientific methodology including rigorous analysis, accurate and statistically significant measurement, and reproducibility.”3

Having incorporated the term “scientific knowledge,” Rule 702 could not permit anything less in expert witness testimony, lest it pollute federal courtrooms across the land.

Elsewhere, the AMA elaborated upon its reference to “statistically significant measurement”:

Medical researchers acquire scientific knowledge through laboratory investigation, studies of animal models, human trials, and epidemiological studies. Such empirical investigations frequently demonstrate some correlation between the intervention studied and the hypothesized result. However, the demonstration of a correlation does not prove the hypothesized result and does not constitute scientific knowledge. In order to determine whether the observed correlation is indicative of a causal relationship, scientists necessarily rely on the concept of “statistical significance.” The requirement of statistical reliability, which tends to prove that the relationship is not merely the product of chance, is a fundamental and indispensable component of valid scientific methodology.”4

And then again, the AMA spelled out its position, in case the Court missed its other references to the importance of statistical significance:

Medical studies, whether clinical trials or epidemiologic studies, frequently demonstrate some correlation between the action studied … . To determine whether the observed correlation is not due to chance, medical scientists rely on the concept of ‘statistical significance’. A ‘statistically significant’ correlation is generally considered to be one in which statistical analysis suggests that the observed relationship is not the result of chance. A statistically significant correlation does not ‘prove’ causation, but in the absence of such a correlation, scientific causation clearly is not proven.95

In its footnote 9, in the above quoted section of the brief, the AMA called out the plaintiffs’ transposition fallacy, without specifically citing to plaintiffs’ briefs:

It is misleading to compare the 95% confidence level used in empirical research to the 51% level inherent in the preponderance of the evidence standard.”6

Actually the plaintiffs’ ruse was much worse than misleading. The plaintiffs did not compare the two probabilities; they equated them. Some might call this ruse, an outright fraud on the court. In any event, the AMA amicus brief remains an available, citable source for opposing this fraud and the casual dismissal of the importance of statistical significance.

One other amicus brief touched on the plaintiffs’ statistical shanigans. The Product Liability Advisory Council, National Association of Manufacturers, Business Roundtable, and Chemical Manufacturers Association jointly filed an amicus brief to challenge some of the excesses of the plaintiffs’ submissions.7  Plaintiffs’ expert witness, Shanna Swan, had calculated type II error rates and post-hoc power for some selected epidemiologic studies relied upon by the defense. Swan’s complaint had been that some studies had only 20% probability (power) to detect a statistically significant doubling of limb reduction risk, with significance at p < 5%.8

The PLAC Brief pointed out that power calculations must assume an alternative hypothesis, and that the doubling of risk hypothesis had no basis in the evidentiary record. Although the PLAC complaint was correct, it missed the plaintiffs’ point that the defense had set exceeding a risk ratio of 2.0, as an important benchmark for specific causation attributability. Swan’s calculation of post-hoc power would have yielded an even lower probability for detecting risk ratios of 1.2 or so. More to the point, PLAC noted that other studies had much greater power, and that collectively, all the available studies would have had much greater power to have at least one study achieve statistical significance without dodgy re-analyses.

1 The Advocates’ Errors in Daubert” (Dec. 28, 2018).

2 American Academy of Allergy and Immunology, American Academy of Dermatology, American Academy of Family Physicians, American Academy of Neurology, American Academy of Orthopaedic Surgeons, American Academy of Pain Medicine, American Association of Neurological Surgeons, American College of Obstetricians and Gynecologists, American College of Pain Medicine, American College of Physicians, American College of Radiology, American Society of Anesthesiologists, American Society of Plastic and Reconstructive Surgeons, American Urological Association, and College of American Pathologists.

3 Brief of the American Medical Association, et al., as Amici Curiae, in Support of Respondent, in Daubert v. Merrell Dow Pharmaceuticals, Inc., U.S. Supreme Court no. 92-102, 1993 WL 13006285, at *27 (U.S., Jan. 19, 1993)[AMA Brief].

4 AMA Brief at *4-*5 (emphasis added).

5 AMA Brief at *14-*15 (emphasis added).

6 AMA Brief at *15 & n.9.

7 Brief of the Product Liability Advisory Council, Inc., National Association of Manufacturers, Business Roundtable, and Chemical Manufacturers Association as Amici Curiae in Support of Respondent, as Amici Curiae, in Support of Respondent, in Daubert v. Merrell Dow Pharmaceuticals, Inc., U.S. Supreme Court no. 92-102, 1993 WL 13006288 (U.S., Jan. 19, 1993) [PLAC Brief].

8 PLAC Brief at *21.

The Judicial Labyrinth for Scientific Evidence

October 3rd, 2018

The real Daedalus (not the musician), as every school child knows, was the creator of the Cretan Labyrinth, where the Minotaur resided. The Labyrinth had been the undoing of many Greeks and barbarians, until an Athenian, Theseus, took up the challenge of slaying the Minotaur. With the help of Ariadne’s thread, Theseus solved the labyrinthic puzzle and slayed the Minotaur.

Theseus and the Minotaur on 6th-century black-figure pottery (Wikimedia Commons 2005)

Dædalus is also the Journal of the American Academy of Arts and Sciences. The Academy has been, for over 230 years, addressing issues issues in both the humanities and in the sciences. In the fall 2018 issue of Dædalus (volume 147, No. 4), the Academy has published a dozen essays by noted scholars in the field, who report on the murky interface of science and law in the courtrooms of the United States. Several of the essays focus on sorry state of forensic “science” in the criminal justice system, which has been the subject of several critical official investigations, only to be dismissed and downplayed by both the Obama and Trump administrations. Other essays address the equally sorry state of judicial gatekeeping in civil actions, with some limited suggestions on how the process of scientific fact finding might be improved. In any event, this issue, Science & the Legal System,” is worth reading even if you do not agree with the diagnoses or the proposed therapies. There is still room for a collaboration between a modern day Daedalus and Ariadne to help us find the way out of this labyrinth.


Shari Seidman Diamond & Richard O. Lempert, “Introduction” (pp. 5–14)

Connecting Science and Law

Sheila Jasanoff, “Science, Common Sense & Judicial Power in U.S. Courts” (pp. 15-27)

Linda Greenhouse, “The Supreme Court & Science: A Case in Point,” (pp. 28–40)

Shari Seidman Diamond & Richard O. Lempert, “When Law Calls, Does Science Answer? A Survey of Distinguished Scientists & Engineers,” (pp. 41–60)

Accomodation or Collision: When Science and Law Meet

Jules Lobel & Huda Akil, “Law & Neuroscience: The Case of Solitary Confinement,” (pp. 61–75)

Rebecca S. Eisenberg & Robert Cook-Deegan, “Universities: The Fallen Angels of Bayh-Dole?” (pp. 76–89)

Jed S. Rakoff & Elizabeth F. Loftus, “The Intractability of Inaccurate Eyewitness Identification” (pp. 90–98)

Jennifer L. Mnookin, “The Uncertain Future of Forensic Science” (pp. 99–118)

Joseph B. Kadane and Jonathan J. Koehler, “Certainty & Uncertainty in Reporting Fingerprint Evidence” (pp. 119–134)

Communicating Science in Court

Nancy Gertner & Joseph Sanders, “Alternatives to Traditional Adversary Methods of Presenting Scientific Expertise in the Legal System” (pp. 135–151)

Daniel L. Rubinfeld & Joe S. Cecil, “Scientists as Experts Serving the Court” (pp. 152–163)

Valerie P. Hans and Michael J. Saks, “Improving Judge & Jury Evaluation of Scientific Evidence” (pp. 164–180)

Continuing the Dialogue

David Baltimore, David S. Tatel & Anne-Marie Mazza, “Bridging the Science-Law Divide” (pp. 181–194)

N.J. Supreme Court Uproots Weeds in Garden State’s Law of Expert Witnesses

August 8th, 2018

The United States Supreme Court’s decision in Daubert is now over 25 years old. The idea of judicial gatekeeping of expert witness opinion testimony is even older in New Jersey state courts. The New Jersey Supreme Court articulated a reliability standard before the Daubert case was even argued in Washington, D.C. See Landrigan v. Celotex Corp., 127 N.J. 404, 414 (1992); Rubanick v. Witco Chem. Corp., 125 N.J. 421, 447 (1991). Articulating a standard, however, is something very different from following a standard, and in many New Jersey trial courts, until very recently, the standard was pretty much anything goes.

One counter-example to the general rule of dog-eat-dog in New Jersey was Judge Nelson Johnson’s careful review and analysis of the proffered causation opinions in cases in which plaintiffs claimed that their use of the anti-acne medication isotretinoin (Accutane) caused Crohn’s disease. Judge Johnson, who sits in the Law Division of the New Jersey Superior Court for Atlantic County held a lengthy hearing, and reviewed the expert witnesses’ reliance materials.1 Judge Johnson found that the plaintiffs’ expert witnesses had employed undue selectivity in choosing what to rely upon. Perhaps even more concerning, Judge Johnson found that these witnesses had refused to rely upon reasonably well-conducted epidemiologic studies, while embracing unpublished, incomplete, and poorly conducted studies and anecdotal evidence. In re Accutane, No. 271(MCL), 2015 WL 753674, 2015 BL 59277 (N.J.Super. Law Div., Atlantic Cty. Feb. 20, 2015). In response, Judge Johnson politely but firmly closed the gate to conclusion-driven duplicitous expert witness causation opinions in over 2,000 personal injury cases. “Johnson of Accutane – Keeping the Gate in the Garden State” (Mar. 28, 2015).

Aside from resolving over 2,000 pending cases, Judge Johnson’s judgment was of intense interest to all who are involved in pharmaceutical and other products liability litigation. Judge Johnson had conducted a pretrial hearing, sometimes called a Kemp hearing in New Jersey, after the New Jersey Supreme Court’s opinion in Kemp v. The State of New Jersey, 174 N.J. 412 (2002). At the hearing and in his opinion that excluded plaintiffs’ expert witnesses’ causation opinions, Judge Johnson demonstrated a remarkable aptitude for analyzing data and inferences in the gatekeeping process.

When the courtroom din quieted, the trial court ruled that the proffered testimony of Dr., Arthur Kornbluth and Dr. David Madigan did not meet the liberal New Jersey test for admissibility. In re Accutane, No. 271(MCL), 2015 WL 753674, 2015 BL 59277 (N.J.Super. Law Div. Atlantic Cty. Feb. 20, 2015). And in closing the gate, Judge Johnson protected the judicial process from several bogus and misleading “lines of evidence,” which have become standard ploys to mislead juries in courthouses where the gatekeepers are asleep. Recognizing that not all evidence is on the same analytical plane, Judge Johnson gave case reports short shrift.

[u]nsystematic clinical observations or case reports and adverse event reports are at the bottom of the evidence hierarchy.”

Id. at *16. Adverse event reports, largely driven by the very litigation in his courtroom, received little credit and were labeled as “not evidentiary in a court of law.” Id. at 14 (quoting FDA’s description of FAERS).

Judge Johnson recognized that there was a wide range of identified “risk factors” for irritable bowel syndrome, such as prior appendectomy, breast-feeding as an infant, stress, Vitamin D deficiency, tobacco or alcohol use, refined sugars, dietary animal fat, fast food. In re Accutane, 2015 WL 753674, at *9. The court also noted that there were four medications generally acknowledged to be potential risk factors for inflammatory bowel disease: aspirin, nonsteroidal anti-inflammatory medications (NSAIDs), oral contraceptives, and antibiotics. Understandably, Judge Johnson was concerned that the plaintiffs’ expert witnesses preferred studies unadjusted for potential confounding co-variables and studies that had involved “cherry picking the subjects.” Id. at *18.

Judge Johnson had found that both sides in the isotretinoin cases conceded the relative unimportance of animal studies, but the plaintiffs’ expert witnesses nonetheless invoked the animal studies in the face of the artificial absence of epidemiologic studies that had been created by their cherry-picking strategies. Id.

Plaintiffs’ expert witnesses had reprised a common claimants’ strategy; namely, they claimed that all the epidemiology studies lacked statistical power. Their arguments often ignored that statistical power calculations depend upon statistical significance, a concept to which many plaintiffs’ counsel have virulent antibodies, as well as an arbitrarily selected alternative hypothesis of association size. Furthermore, the plaintiffs’ arguments ignored the actual point estimates, most of which were favorable to the defense, and the observed confidence intervals, most of which were reasonably narrow.

The defense responded to the bogus statistical arguments by presenting an extremely capable clinical and statistical expert witness, Dr. Stephen Goodman, to present a meta-analysis of the available epidemiologic evidence.

Meta-analysis has become an important facet of pharmaceutical and other products liability litigation[1]. Fortunately for Judge Johnson, he had before him an extremely capable expert witness, Dr. Stephen Goodman, to explain meta-analysis generally, and two meta-analyses he had performed on isotretinoin and irritable bowel outcomes.

Dr. Goodman explained that the plaintiffs’ witnesses’ failure to perform a meta-analysis was telling when meta-analysis can obviate the plaintiffs’ hyperbolic statistical complaints:

the strength of the meta-analysis is that no one feature, no one study, is determinant. You don’t throw out evidence except when you absolutely have to.”

In re Accutane, 2015 WL 753674, at *8.

Judge Johnson’s judicial handiwork received non-deferential appellate review from a three-judge panel of the Appellate Division, which reversed the exclusion of Kornbluth and Madigan. In re Accutane Litig., 451 N.J. Super. 153, 165 A.3d 832 (App. Div. 2017). The New Jersey Supreme Court granted the isotretinoin defendants’ petition for appellate review, and the issues were joined over the appropriate standard of appellate review for expert witness opinion exclusions, and the appropriateness of Judge Johnson’s exclusions of Kornbluth and Madigan. A bevy of amici curiae joined in the fray.2

Last week, the New Jersey Supreme Court issued a unanimous opinion, which reversed the Appellate Division’s holding that Judge Johnson had “mistakenly exercised” discretion. Applying its own precedents from Rubanick, Landrigan, and Kemp, and the established abuse-of-discretion standard, the Court concluded that the trial court’s ruling to exclude Kornbluth and Madigan was “unassailable.” In re Accutane Litig., ___ N.J. ___, 2018 WL 3636867 (2018), Slip op. at 79.3

The high court graciously acknowledged that defendants and amici had “good reason” to seek clarification of New Jersey law. Slip op. at 67. In abandoning abuse-of-discretion as its standard of review, the Appellate Division had relied upon a criminal case that involved the application of the Frye standard, which is applied as a matter of law. Id. at 70-71. The high court also appeared to welcome the opportunity to grant review and reverse the intermediate court reinforce “the rigor expected of the trial court” in its gatekeeping role. Id. at 67. The Supreme Court, however, did not articulate a new standard; rather it demonstrated at length that Judge Johnson had appropriately applied the legal standards that had been previously announced in New Jersey Supreme Court cases.4

In attempting to defend the Appellate Division’s decision, plaintiffs sought to characterize New Jersey law as somehow different from, and more “liberal” than, the United States Supreme Court’s decision in Daubert. The New Jersey Supreme Court acknowledged that it had never formally adopted the dicta from Daubert about factors that could be considered in gatekeeping, slip op. at 10, but the Court went on to note what disinterested observers had long understood, that the so-called Daubert factors simply flowed from a requirement of sound methodology, and that there was “little distinction” and “not much light” between the Landrigan and Rubanick principles and the Daubert case or its progeny. Id at 10, 80.

Curiously, the New Jersey Supreme Court announced that the Daubert factors should be incorporated into the New Jersey Rules 702 and 703 and their case law, but it stopped short of declaring New Jersey a “Daubert” jurisdiction. Slip op. at 82. In part, the Court’s hesitance followed from New Jersey’s bifurcation of expert witness standards for civil and criminal cases, with the Frye standard still controlling in the criminal docket. At another level, it makes no sense to describe any jurisdiction as a “Daubert” state because the relevant aspects of the Daubert decision were dicta, and the Daubert decision and its progeny were superseded by the revision of the controlling statute in 2000.5

There were other remarkable aspects of the Supreme Court’s Accutane decision. For instance, the Court put its weight behind the common-sense and accurate interpretation of Sir Austin Bradford Hill’s famous articulation of factors for causal judgment, which requires that sampling error, bias, and confounding be eliminated before assessing whether the observed association is strong, consistent, plausible, and the like. Slip op. at 20 (citing the Reference Manual at 597-99), 78.

The Supreme Court relied extensively on the National Academies’ Reference Manual on Scientific Evidence.6 That reliance is certainly preferable to judicial speculations and fabulations of scientific method. The reliance is also positive, considering that the Court did not look only at the problematic epidemiology chapter, but adverted also to the chapters on statistical evidence and on clinical medicine.

The Supreme Court recognized that the Appellate Division had essentially sanctioned an anything goes abandonment of gatekeeping, an approach that has been all-too-common in some of New Jersey’s lower courts. Contrary to the previously prevailing New Jersey zeitgeist, the Court instructed that gatekeeping must be “rigorous” to “prevent[] the jury’s exposure to unsound science through the compelling voice of an expert.” Slip op. at 68-9.

Not all evidence is equal. “[C]ase reports are at the bottom of the evidence hierarchy.” Slip op. at 73. Extrapolation from non-human animal studies is fraught with external validity problems, and such studies “far less probative in the face of a substantial body of epidemiologic evidence.” Id. at 74 (internal quotations omitted).

Perhaps most chilling for the lawsuit industry will be the Supreme Court’s strident denunciation of expert witnesses’ selectivity in choosing lesser evidence in the face of a large body of epidemiologic evidence, id. at 77, and their unprincipled cherry picking among the extant epidemiologic publications. Like the trial court, the Supreme Court found that the plaintiffs’ expert witnesses’ inconsistent use of methodological criteria and their selective reliance upon studies (disregarding eight of the nine epidemiologic studies) that favored their task masters was the antithesis of sound methodology. Id. at 73, citing with approval, In re Lipitor, ___ F.3d ___ (4th Cir. 2018) (slip op. at 16) (“Result-driven analysis, or cherry-picking, undermines principles of the scientific method and is a quintessential example of applying methodologies (valid or otherwise) in an unreliable fashion.”).

An essential feature of the Supreme Court’s decision is that it was not willing to engage in the common reductionism that has “all epidemiologic studies are flawed,” and which thus privileges cherry picking. Not all disagreements between expert witnesses can be framed as differences in interpretation. In re Accutane will likely stand as a bulwark against flawed expert witness opinion testimony in the Garden State for a long time.

1 Judge Nelson Johnson is also the author of Boardwalk Empire: The Birth, High Times, and Corruption of Atlantic City (2010), a spell-binding historical novel about political and personal corruption.

2 In support of the defendants’ positions, amicus briefs were filed by the New Jersey Business & Industry Association, Commerce and Industry Association of New Jersey, and New Jersey Chamber of Commerce; by law professors Kenneth S. Broun, Daniel J. Capra, Joanne A. Epps, David L. Faigman, Laird Kirkpatrick, Michael M. Martin, Liesa Richter, and Stephen A. Saltzburg; by medical associations the American Medical Association, Medical Society of New Jersey, American Academy of Dermatology, Society for Investigative Dermatology, American Acne and Rosacea Society, and Dermatological Society of New Jersey, by the Defense Research Institute; by the Pharmaceutical Research and Manufacturers of America; and by New Jersey Civil Justice Institute. In support of the plaintiffs’ position and the intermediate appellate court’s determination, amicus briefs were filed by political action committee the New Jersey Association for Justice; by the Ironbound Community Corporation; and by plaintiffs’ lawyer Allan Kanner.

3 Nothing in the intervening scientific record called question upon Judge Johnson’s trial court judgment. See, e.g., I.A. Vallerand, R.T. Lewinson, M.S. Farris, C.D. Sibley, M.L. Ramien, A.G.M. Bulloch, and S.B. Patten, “Efficacy and adverse events of oral isotretinoin for acne: a systematic review,” 178 Brit. J. Dermatol. 76 (2018).

4 Slip op. at 9, 14-15, citing Landrigan v. Celotex Corp., 127 N.J. 404, 414 (1992); Rubanick v. Witco Chem. Corp., 125 N.J. 421, 447 (1991) (“We initially took that step to allow the parties in toxic tort civil matters to present novel scientific evidence of causation if, after the trial court engages in rigorous gatekeeping when reviewing for reliability, the proponent persuades the court of the soundness of the expert’s reasoning.”).

5 The Court did acknowledge that Federal Rule of Evidence 702 had been amended in 2000, to reflect the Supreme Court’s decision in Daubert, Joiner, and Kumho Tire, but the Court did not deal with the inconsistencies between the present rule and the 1993 Daubert case. Slip op. at 64, citing Calhoun v. Yamaha Motor Corp., U.S.A., 350 F.3d 316, 320-21, 320 n.8 (3d Cir. 2003).

6 See Accutane slip op. at 12-18, 24, 73-74, 77-78. With respect to meta-analysis, the Reference Manual’s epidemiology chapter is still stuck in the 1980s and the prevalent resistance to poorly conducted, often meaningless meta-analyses. SeeThe Treatment of Meta-Analysis in the Third Edition of the Reference Manual on Scientific Evidence” (Nov. 14, 2011) (The Reference Manual fails to come to grips with the prevalence and importance of meta-analysis in litigation, and fails to provide meaningful guidance to trial judges).

P-Values: Pernicious or Perspicacious?

May 12th, 2018

Professor Kingsley R. Browne, of the Wayne State University Law School, recently published a paper that criticized the use of p-values and significance testing in discrimination litigation. Kingsley R. Browne, “Pernicious P-Values: Statistical Proof of Not Very Much,” 42 Univ. Dayton L. Rev. 113 (2017) (cited below as Browne). Browne amply documents the obvious and undeniable, that judges, lawyers, and even some ill-trained expert witnesses, are congenitally unable to describe and interpret p-values properly. Most of Browne’s examples are from the world of anti-discrimination law, but he also cites a few from health effects litigation as well. Browne also cites from many of the criticisms of p-values in the psychology and other social science literature.

Browne’s efforts to correct judicial innumeracy are welcomed, but they take a peculiar turn in this law review article. From the well-known state of affairs of widespread judicial refusal or inability to discuss statistical concepts accurately, Browne argues for what seem to be two incongruous, inconsistent responses. Rejecting the glib suggestion of former Judge Posner that evidence law is not “fussy” about evidence, Browne argues that federal evidence law requires courts to be “fussy” about evidence, and that Rule 702 requires courts to exclude expert witnesses, whose opinions fail to “employ[] in the courtroom the same level of intellectual rigor that characterizes the practice of an expert in the relevant field.” Browne at 143 (quoting from Kumho Tire Co. v. Carmichael, 526 U.S. 137, 152 (1999). Browne tells us, with apparently appropriate intellectual rigor, that “[i]f a disparity that does not provide a p-value of less than 0.05 would not be accepted as meaningful in the expert’s discipline, it is not clear that the expert should be allowed to testify – on the basis of his expertise in that discipline – that the disparity is, in fact, meaningful.” Id.

In a volte face, Browne then argues that p-values do “not tell us much,” basically because they are dependent upon sample size. Browne suggests that the quantitative disparity between expected value and observed proportion or average can be assessed without the use of p-values, and that measuring a p-value “adds virtually nothing and just muddies the water.” Id. at 152. The prevalent confusion among judges and lawyers seems sufficient in Browne’s view to justify his proposal, as well as his further suggestion that Rule 403 should be invoked to exclude p-values:

The ease with which reported p-values cause a trier of fact to slip into the transposition fallacy and the difficulty of avoiding that lapse of logic, coupled with the relatively sparse information actually provided by the p-value, make p-values prime candidates for exclusion under Federal Rule of Evidence 403. *** If judges, not to mention the statistical experts they rely on, cannot use the information without falling into fallacious reasoning, the likelihood that the jury will misunderstand the evidence is very high. Since the p-value actually provides little useful relevant information, the high risk of misleading the jury greatly exceeds its scant probative value, so it simply should not be presented to the jury.”

Id. at 152-53.

And yet, elsewhere in the same article, Browne ridicules one court and several expert witnesses who have argued in favor of conclusions that were based upon p-values up to 50%.1 The concept of p-values cannot be so flexible as to straddle the extremes of having no probative value, and yet capable of rendering an expert witness’s opinions ludicrous. P-values quantify an estimate of random error, even if that error rate varies with sample size. To be sure, the measure of random error depends upon the specified model and assumption of a null hypothesis, but the crucial point is that the estimate (whether mean, proportion, risk ratio, risk difference, etc.) is rather meaningless without some further estimate of random variability of the estimate. Of course, random error is not the only type of error, but the existence of other potential systematic errors is hardly a reason to ignore random error.

In the science of health effects, many applications of p-values have given way to the use of confidence intervals, which arguably provide more direct assessments of both sample estimates, along with ranges of potential outcomes that are reasonably compatible with the sample estimates. Remarkably, Browne never substantively discusses confidence intervals in his article.

Under the heading of other problems with p-values and significance testing, Browne advances four additional putative problems with p-values. First, Browne asserts with little to no support that “[t]he null hypothesis is unlikely a priori.” Id. at 155. He fails to tell us why the null hypothesis of no disparity is not a reasonable starting place in the absence of objective evidence of a prior estimate. Furthermore, a null hypothesis of no difference will have legal significance in claims of health effects, or of unlawful discrimination.

Second, Browne argues that significance testing will lead to “[c]onflation of statistical and practical (or legal) significance” in the minds of judges and jurors. Id. at 156-58. This charge is difficult to sustain. The actors in legal cases can probably best appreciate practical significance and its separation from statistical significance, most readily. If a large class action showed that the expected value of a minority’s proportion was 15%, and the observed proportion was 14.8%, p < 0.05, most innumerate judges and jurors would sense that this disparity was unimportant and that no employer would fine tune its discriminatory activities so closely as to achieve such a meaningless difference.

Third, Browne reminds us that the validity and the interpretation of a p-value turns on the assumption that the statistical model is perfectly specified. Id. at 158-59. His reminder is correct, but again, this aspect of p-values (or confidence intervals) is relatively easy to explain, as well as to defend or challenge. To be sure, there may be legitimate disputes about whether an appropriate model was used (say binomial versus hypergeometric), but such disputes are hardly the most arcane issues that judges and jurors will face.

Fourth, Browne claims that “the alternative hypothesis is seldom properly specified.” Id. at 159-62. Unless analysts are focused on measuring pre-test power or type II error, however, they need not advance an alternative hypothesis. Furthermore, it is hardly a flaw with significance testing that it does not account for systematic bias or confounding.

Browne does not offer an affirmative response such as urging courts to adopt a Bayesian program. A Bayesian response to prevalent blunders in interpreting statistical significance would introduce perhaps even more arcane and hard-to-discern blunders in court proceedings. Browne also leaves courts without a meaningful approach to evaluate random error other than to engage in crude comparisons between two means or proportions. The recommendations in this law review article appear to be a giant step, backwards, into an epistemic void.

1See Browne at 146, citing In re Photochromic Lens Antitrust Litig., 2014 WL 1338605 (M.D. Fla. April 3, 2014) (reversing magistrate judge’s exclusion of an expert witness who had advanced claims based upon p-value of 0.50); id. at 147 n. 116, citing In re High-Tech Employee Antitrust Litig., 2014 WL 1351040 (N.D. Cal. 2014).