Sir David Cox: Significance tests: rethinking the controversy (September 5, 2018 RSS keynote)

Sir David Cox speaking at the RSS meeting in a session: “Significance Tests: Rethinking the Controversy” on 5 September 2018.

We were part of a session:

Keynote 4 – Significance Tests: Rethinking the Controversy Assembly Room

Sir David Cox, Nuffield College, Oxford
Deborah Mayo, Virginia Tech
Richard Morey, Cardiff University
Aris Spanos, Virginia Tech

All 4 talks are on this post:

RSS 2018 – Significance Tests: Rethinking the Controversy

It was the same day and conference that my book, Statistical Inference as Severe Testing: How to Get Beyond the Statistics Wars (2018, CUP) first made its physical appearance:

Blurb for session:

Intermingled in today’s statistical controversies are some long-standing, but unresolved, disagreements on the nature and principles of statistical methods and the roles for probability in statistical inference and modelling. In reaction to the so-called “replication crisis” in the sciences, some reformers suggest significance tests as a major culprit. To understand the ramifications of the proposed reforms, there is a pressing need for a deeper understanding of the source of the problems in the sciences and a balanced critique of the alternative methods being proposed to supplant significance tests. In this session speakers offer perspectives on significance tests from statistical science, econometrics, experimental psychology and philosophy of science. There will be also be panel discussion.



Categories: Sir David Cox, statistical significance tests | Tags: | Leave a comment

Sir David Cox

         July 15, 1924-January 18, 2022




Categories: Error Statistics | 1 Comment

Nathan Schactman: Of Significance, Error, Confidence, and Confusion – In the Law and In Statistical Practice (Guest Post)


Nathan Schachtman,  Esq., J.D.
Legal Counsel for Scientific Challenges

Of Significance, Error, Confidence, and Confusion – In the Law and In Statistical Practice

The metaphor of law as an “empty vessel” is frequently invoked to describe the law generally, as well as pejoratively to describe lawyers. The metaphor rings true at least in describing how the factual content of legal judgments comes from outside the law. In many varieties of litigation, not only the facts and data, but the scientific and statistical inferences must be added to the “empty vessel” to obtain a correct and meaningful outcome.

Once upon a time, the expertise component of legal judgments came from so-called expert witnesses, who were free to opine about the claims of causality solely by showing that they had more expertise than the lay jurors. In Pennsylvania, for instance, the standard to qualify witnesses to give “expert opinions” was to show that they had “a reasonable pretense to expertise on the subject.”

In the 19th and the first half of the 20th century, causal claims, whether of personal injuries, discrimination, or whatever, virtually always turned on a conception of causation as necessary and sufficient to bring about the alleged harm. In discrimination claims, plaintiffs pointed to the “inexorable zero,” in cases in which no Black citizen was ever seated on a grand jury, in a particular county, since the demise of Reconstruction. In health claims, the mode of reasoning usually followed something like Koch’s postulates.

The second half of the 20th century was marked by the rise of stochastic models in our understanding of the world. The consequence is that statistical inference made its way into the empty vessel. The rapid introduction of statistical thinking into the law did not always go well. In a seminal discrimination case, Casteneda v. Partida, 430 U.S. 432 (1977), in an opinion by Associate Justice Blackmun, the court calculated a binomial probability for observing the sample result (rather than a result at least as extreme as such a result), and mislabeled the measurement “standard deviations” rather than standard errors:

“As a general rule for such large samples, if the difference between the expected value and the observed number is greater than two or three standard deviations, then the hypothesis that the jury drawing was random would be suspect to a social scientist.  The 11-year data here reflect a difference between the expected and observed number of Mexican-Americans of approximately 29 standard deviations. A detailed calculation reveals that the likelihood that such a substantial departure from the expected value would occur by chance is less than I in 10140.” Id. at 430 U.S. 482, 496 n.17 (1977). Justice Blackmun was graduated from Harvard College, summa cum laude, with a major in mathematics.

Despite the extreme statistical disparity in the 11-year run of grand juries, Justice Blackmun’s opinion provoked a robust rejoinder, not only on the statistical analysis, but on the Court’s failure to account for obvious omitted confounding variables in its simplistic analysis. And then there were the inconvenient facts that Mr. Partida was a rapist, indicted by a grand jury (50% with “Hispanic” names), which was appointed by jury commissioners (3/5 Hispanic). Partida was convicted by a petit jury (7/12 Hispanic), in front a trial judge who was Hispanic, and he was denied a writ of habeas court by Judge Garza, who went on to be a member of the Court of Appeals. In any event, Justice Blackmun’s dictum about “two or three” standard deviations soon shaped the outcome of many thousands of discrimination cases, and was translated into a necessary p-value of 5%.

Beginning in the early 1960s, statistical inference became an important feature of tort cases that involved claims based upon epidemiologic evidence. In such health-effects litigation, the judicial handling of concepts such as p-values and confidence intervals often went off the rails.  In 1989, the United States Court of Appeals for the Fifth Circuit resolved an appeal involving expert witnesses who relied upon epidemiologic studies by concluding that it did not have to resolve questions of bias and confounding because the studies relied upon had presented their results with confidence intervals.[1] Judges and expert witnesses persistently interpreted single confidence intervals from one study as having a 95 percent probability of containing the actual parameter.[2] Similarly, many courts and counsel committed the transposition fallacy in interpreting p-values as posterior probabilities for the null hypothesis.[3]

Against this backdrop of mistaken and misrepresented interpretation of p-values, the American Statistical Association’s p-value statement was a helpful and understandable restatement of basic principles.[4] Within a few weeks, however, citations to the p-value Statement started to show up in the briefs and examinations of expert witnesses, to support contentions that p-values (or any procedure to evaluate random error) were unimportant, and should be disregarded.[5]

In 2019, Ronald Wasserstein, the ASA executive director, along with two other authors wrote an editorial, which explicitly called for the abandonment of using “statistical significance.”[6] Although the piece was labeled “editorial,” the journal provided no disclaimer that Wasserstein was not speaking ex cathedra.

The absence of a disclaimer provoked a great deal of confusion. Indeed, Brian Turran, the editor of Significancepublished jointly by the ASA and the Royal Statistical Society, wrote an editorial interpreting the Wasserstein editorial as an official ASA “recommendation.” Turran ultimately retracted his interpretation, but only in response to a pointed letter to the editor.[7] Turran adverted to a misleading press release from the ASA as the source of his confusion. Inquiring minds might wonder why the ASA allowed such a press release to go out.

In addition to press releases, some people in the ASA started to send emails to journal editors, to nudge them to abandon statistical significance testing on the basis of what seemed like an ASA recommendation. For the most part, this campaign was unsuccessful in the major biomedical journals.[8]

While this controversy was unfolding, then President Karen Kafadar of the ASA stepped into the breach to state definitively that the Executive Director was not speaking for the ASA.[9] In November 2019, the ASA board of directors approved a motion to create a “Task Force on Statistical Significance and Replicability.”[8] Its charge was “to develop thoughtful principles and practices that the ASA can endorse and share with scientists and journal editors. The task force will be appointed by the ASA President with advice and participation from the ASA Board.”

Professor Mayo’s editorial has done the world of statistics, as well as the legal world of judges, lawyers, and legal scholars, a service in calling attention to the peculiar intellectual conflicts of interest that played a role in the editorial excesses of some of  the ASA’s leadership. From a lawyer’s perspective, it is clear that courts have been misled, and distracted by, some of the ASA officials who seem to have worked to undermine a consensus position paper on p-values.[10]

Curiously, the task force’s report did not find a home in any of the ASA’s several scholarly publications. Instead “The ASA President’s Task Force Statement on Statistical Significance and Replicability[11] appeared in the The Annals of Applied  Statistics, where it is accompanied by an editorial by ASA former President Karen Kafadar.[12] In November 2021, the ASA’s official “magazine,” Chance, also published the Task Force’s Statement.[13]

Judges and litigants who must navigate claims of statistical inference need guidance on the standard of care scientists and statisticians should use in evaluating such claims. Although the Taskforce did not elaborate, it advanced five basic propositions, which had been obscured by many of the recent glosses on the ASA 2016 p-value statement, and the 2019 editorial discussed above:

  1. “Capturing the uncertainty associated with statistical summaries is critical.”
  2. “Dealing with replicability and uncertainty lies at the heart of statistical science. Study results are replicable if they can be verified in further studies with new data.”
  3. “The theoretical basis of statistical science offers several general strategies for dealing with uncertainty.”
  4. “Thresholds are helpful when actions are required.”
  5. “P-values and significance tests, when properly applied and interpreted, increase the rigor of the conclusions drawn from data.”

Although the Task Force’s Statement will not end the debate or the “wars,” it will go a long way to correct the contentions made in court about the insignificance of significance testing, while giving courts a truer sense of the professional standard of care with respect to statistical inference in evaluating claims of health effects.


[1] Brock v. Merrill Dow Pharmaceuticals, Inc., 874 F.2d 307, 311-12 (5th Cir. 1989).

[2] Richard W. Clapp & David Ozonoff, “Environment and Health: Vital Intersection or Contested Territory?” 30 Am. J. L. & Med. 189, 210 (2004) (“Thus, a RR [relative risk] of 1.8 with a confidence interval of 1.3 to 2.9 could very likely represent a true RR of greater than 2.0, and as high as 2.9 in 95 out of 100 repeated trials.”) (Both authors testify for claimants cases involving alleged environmental and occupational harms.); Schachtman, “Confidence in Intervals and Diffidence in the Courts” (Mar. 4, 2012) (collecting numerous examples of judicial offenders).

[3] See, e.g., In re Ephedra Prods. Liab. Litig., 393 F.Supp. 2d 181, 191, 193 (S.D.N.Y. 2005) (Rakoff, J.) (credulously accepting counsel’s argument that the use of a critical value of less than 5% of significance probability increased the “more likely than not” burden of proof upon a civil litigant). The decision has been criticized in the scholarly literature, but it is still widely cited without acknowledging its error. See Michael O. Finkelstein, Basic Concepts of Probability and Statistics in the Law 65 (2009).

[4] Ronald L. Wasserstein & Nicole A. Lazar, “The ASA’s Statement on p-Values: Context, Process, and Purpose,” 70 The Am. Statistician 129 (2016); see “The American Statistical Association’s Statement on and of Significance” (March 17, 2016). The commentary beyond the “bold faced” principles was at times less helpful in suggesting that there was something inherently inadequate in using p-values. With the benefit of hindsight, this commentary appears to represent editorizing by the authors, and not the sense of the expert committee that agreed to the six principles.

[5] Schachtman, “The American Statistical Association Statement on Significance Testing Goes to Court, Part I” (Nov. 13, 2018), “Part II” (Mar. 7, 2019).

[6] Ronald L. Wasserstein, Allen L. Schirm, and Nicole A. Lazar, “Editorial: Moving to a World Beyond ‘p < 0.05’,” 73 Am. Statistician S1, S2 (2019); see Schachtman,“Has the American Statistical Association Gone Post-Modern?” (Mar. 24, 2019).

[7] Brian Tarran, “THE S WORD … and what to do about it,” Significance (Aug. 2019); Donald Macnaughton, “Who Said What,” Significance 47 (Oct. 2019).

[8] See, e.g., David Harrington, Ralph B. D’Agostino, Sr., Constantine Gatsonis, Joseph W. Hogan, David J. Hunter, Sharon-Lise T. Normand, Jeffrey M. Drazen, and Mary Beth Hamel, “New Guidelines for Statistical Reporting in the Journal,” 381 New Engl. J. Med. 285 (2019); Jonathan A. Cook, Dean A. Fergusson, Ian Ford, Mithat Gonen, Jonathan Kimmelman, Edward L. Korn, and Colin B. Begg, “There is still a place for significance testing in clinical trials,” 16 Clin. Trials 223 (2019).

[9] Karen Kafadar, “The Year in Review … And More to Come,” AmStat News 3 (Dec. 2019); see also Kafadar, “Statistics & Unintended Consequences,” AmStat News 3,4 (June 2019).

[10] Deborah Mayo, “The statistics wars and intellectual conflicts of interest,” 36 Conservation Biology (2022) (in-press, online Dec. 2021).

[11] Yoav Benjamini, Richard D. DeVeaux, Bradly Efron, Scott Evans, Mark Glickman, Barry Braubard, Xuming He, Xiao Li Meng, Nancy Reid, Stephen M. Stigler, Stephen B. Vardeman, Christopher K. Wikle, Tommy Wright, Linda J. Young, and Karen Kafadar, “The ASA President’s Task Force Statement on Statistical Significance and Replicability,” 15 Annals of Applied Statistics (2021) (in press)

[12] Karen Kafadar, “Editorial: Statistical Significance, P-Values, and Replicability,” 15 Annals of Applied Statistics (2021).

[13] Yoav Benjamini, Richard D. De Veaux, Bradley Efron, Scott Evans, Mark Glickman, Barry I. Graubard, Xuming He, Xiao-Li Meng, Nancy M. Reid, Stephen M. Stigler, Stephen B. Vardeman, Christopher K. Wikle, Tommy Wright, Linda J. Young & Karen Kafadar, “ASA President’s Task Force Statement on Statistical Significance and Replicability,” 34 Chance 10 (2021).

Previous commentaries on my editorial (more to come*)

Ionides and Ritov

*Let me know if you wish to write one

Categories: ASA Guide to P-values, ASA Task Force on Significance and Replicability, PhilStat Law, Schachtman | 2 Comments

John Park: Poisoned Priors: Will You Drink from This Well?(Guest Post)


John Park, MD
Radiation Oncologist
Kansas City VA Medical Center

Poisoned Priors: Will You Drink from This Well?

As an oncologist, specializing in the field of radiation oncology, “The Statistics Wars and Intellectual Conflicts of Interest”, as Prof. Mayo’s recent editorial is titled, is one of practical importance to me and my patients (Mayo, 2021). Some are flirting with Bayesian statistics to move on from statistical significance testing and the use of P-values. In fact, what many consider the world’s preeminent cancer center, MD Anderson, has a strong Bayesian group that completed 2 early phase Bayesian studies in radiation oncology that have been published in the most prestigious cancer journal —The Journal of Clinical Oncology (Liao et al., 2018 and Lin et al, 2020). This brings about the hotly contested issue of subjective priors and much ado has been written about the ability to overcome this problem. Specifically in medicine, one thinks about Spiegelhalter’s classic 1994 paper mentioning reference, clinical, skeptical, or enthusiastic priors who also uses an example from radiation oncology (Spiegelhalter et al., 1994) to make his case. This is nice and all in theory, but what if there is ample evidence that the subject matter experts have major conflicts of interests (COIs) and biases so that their priors cannot be trusted?  A debate raging in oncology, is whether non-invasive radiation therapy is as good as invasive surgery for early stage lung cancer patients. This is a not a trivial question as postoperative morbidity from surgery can range from 19-50% and 90-day mortality anywhere from 0–5% (Chang et al., 2021). Radiation therapy is highly attractive as there are numerous reports hinting at equal efficacy with far less morbidity. Unfortunately, 4 major clinical trials were unable to accrue patients for this important question. Why could they not enroll patients you ask? Long story short, if a patient is referred to radiation oncology and treated with radiation, the surgeon loses out on the revenue, and vice versa. Dr. David Jones, a surgeon at Memorial Sloan Kettering, notes there was no “equipoise among enrolling investigators and medical specialties… Although the reasons are multiple… I believe the primary reason is financial” (Jones, 2015). I am not skirting responsibility for my field’s biases. Dr. Hanbo Chen, a radiation oncologist, notes in his meta-analysis of multiple publications looking at surgery vs radiation that overall survival was associated with the specialty of the first author who published the article (Chen et al, 2018). Perhaps the pen is mightier than the scalpel!

Currently, there is one surgery vs radiation trial that is accruing well, the VALOR study, a Veterans Affairs (VA) only trial. Although only 9 VA medical centers were involved in 2020, it had enrolled more participants than all previous major (phase 3) trials combined (Moghanaki and Hagan, 2020). I do not believe it is too bold to say that a major portion of this success is due to the fact there are no financial incentives for the surgeons or radiation therapists at the VA (i.e. VA physicians are salaried and do not receive payment per patient).

Here are some clear examples of what I call “poisoned priors” due to COIs. Whether financial or for prestige (would you want to be known as the inferior treatment modality for one of the most common cancers?), the COIs loom large. Many of the specialists in question are highly biased, with exposed COIs. Are we to trust priors constructed from them? Will the errors really be contained within the posteriors from these biased priors? In order to overcome this, you say that you want to use an uninformative or weakly informative prior as a statistical method to judge incoming data? Then what’s the point of having prior knowledge, in this case the surgeons’ and radiation oncologists’ priors who are the subject matter experts, if you are not willing to use them? Indeed as Prof. Mayo notes “It may be retorted that implausible inferences will indirectly be blocked by appropriate prior degrees of belief (informative priors), but this misses the crucial point. The key function of statistical tests is to constrain the human tendency to selectively favor views they believe” (Mayo, 2021). If this statement holds for appropriate prior degrees of belief, how much more is it relevant when we can show that those involved have inappropriate prior degrees belief?

These types of poisoned priors are ubiquitous in medicine and must be taken into account — we haven’t even dealt with “Big Pharma” (and don’t get me started)! We must not give up the apparatus of the phase 3 randomized trial, with its randomization, blinding, multiplicity control, and preregistered statistical thresholds for type I and II error control, which is the best form of severe testing we have for our patients.


  • Chang JY, Mehran RJ, Feng L, et al. Stereotactic ablative radiotherapy for operable stage I non-small-cell lung cancer (revised STARS): long-term results of a single-arm, prospective trial with prespecified comparison to surgery. The Lancet Oncology. 2021;22(10):1448-1457. doi:10.1016/S1470-2045(21)00401-0
  • Chen H, Laba JM, Boldt RG, et al. Stereotactic Ablative Radiation Therapy Versus Surgery in Early Lung Cancer: A Meta-analysis of Propensity Score Studies. Int J Radiat Oncol Biol Phys. 2018;101(1):186-194. doi:10.1016/j.ijrobp.2018.01.064
  • Jones DR. Do we know bad science when we see it? The Journal of Thoracic and Cardiovascular Surgery. 2015;150(3):472-473. doi:10.1016/j.jtcvs.2015.07.032
  • Liao Z, Lee JJ, Komaki R, et al. Bayesian Adaptive Randomization Trial of Passive Scattering Proton Therapy and Intensity-Modulated Photon Radiotherapy for Locally Advanced Non-Small-Cell Lung Cancer. J Clin Oncol. 2018;36(18):1813-1822. doi:10.1200/JCO.2017.74.0720
  • Lin SH, Hobbs BP, Verma V, et al. Randomized Phase IIB Trial of Proton Beam Therapy Versus Intensity-Modulated Radiation Therapy for Locally Advanced Esophageal Cancer. J Clin Oncol. 2020;38(14):1569-1579. doi:10.1200/JCO.19.02503
  • Mayo DG. The statistics wars and intellectual conflicts of interest. Conserv Biol. Published online December 6, 2021. doi:10.1111/cobi.13861
  • Moghanaki D, Hagan M. Strategic Initiatives for Veterans with Lung Cancer. Fed Pract. 2020;37(Suppl 4):S76-S80. doi:10.12788/fp.0019
  • Razi, S. S., Kodia, K., Alnajar, A., Block, M. I., Tarrazzi, F., Nguyen, D., & Villamizar, N. (2020). Lobectomy Versus Stereotactic Body Radiotherapy In Healthy Octogenarians With Stage I Lung Cancer. The Annals of Thoracic Surgery, S000349752031448X.
  • Spiegelhalter DJ, Freedman LS, Parmar MKB. Bayesian Approaches to Randomized Trials. Journal of the Royal Statistical Society Series A (Statistics in Society). 1994;157(3):357-416. doi:10.2307/2983527

Previous commentaries on Mayo (2021) editorial (more to come*)
Ionides and Ritov

(*if you wish to contribute a commentary, let me know)

Categories: ASA Task Force on Significance and Replicability, Bayesian priors, PhilStat/Med, statistical significance tests | Tags: | 2 Comments

Brian Dennis: Journal Editors Be Warned:  Statistics Won’t Be Contained (Guest Post)


Brian Dennis

Professor Emeritus
Dept Fish and Wildlife Sciences,
Dept Mathematics and Statistical Science
University of Idaho


Journal Editors Be Warned:  Statistics Won’t Be Contained

I heartily second Professor Mayo’s call, in a recent issue of Conservation Biology, for science journals to tread lightly on prescribing statistical methods (Mayo 2021).  Such prescriptions are not likely to be constructive;  the issues involved are too vast.

The science of ecology has long relied on innovative statistical thinking.  Fisher himself, inventor of P values and a considerable portion of other statistical methods used by generations of ecologists, helped ecologists quantify patterns of biodiversity (Fisher et al. 1943) and understand how genetics and evolution were connected (Fisher 1930).  G. E. Hutchinson, the “founder of modern ecology” (and my professional grandfather), early on helped build the tradition of heavy consumption of mathematics and statistics in ecological research (Slack 2010). Continue reading

Categories: ecology, editors, Likelihood Principle, Royall | Tags: | 2 Comments

Philip Stark (guest post): commentary on “The Statistics Wars and Intellectual Conflicts of Interest” (Mayo Editorial)


Philip B. Stark
Department of Statistics
University of California, Berkeley

I enjoyed Prof. Mayo’s comment in Conservation Biology Mayo, 2021 very much, and agree enthusiastically with most of it. Here are my key takeaways and reflections.

Error probabilities (or error rates) are essential to consider. If you don’t give thought to what the data would be like if your theory is false, you are not doing science. Some applications really require a decision to be made. Does the drug go to market or not? Are the girders for the bridge strong enough, or not? Hence, banning “bright lines” is silly. Conversely, no threshold for significance, no matter how small, suffices to prove an empirical claim. In replication lies truth. Abandoning P-values exacerbates moral hazard for journal editors, although there has always been moral hazard in the gatekeeping function. Absent any objective assessment of evidence, publication decisions are even more subject to cronyism, “taste”, confirmation bias, etc. Throwing away P-values because many practitioners don’t know how to use them is perverse. It’s like banning scalpels because most people don’t know how to perform surgery. People who wish to perform surgery should be trained in the proper use of scalpels, and those who wish to use statistics should be trained in the proper use of P-values. Throwing out P-values is self-serving to statistical instruction, too: we’re making our lives easier by teaching less instead of teaching better. Continue reading

Categories: ASA Task Force on Significance and Replicability, editorial, multiplicity, P-values | 4 Comments

Kent Staley: Commentary on “The statistics wars and intellectual conflicts of interest” (Guest Post)


Kent Staley

Department of Philosophy
Saint Louis University


Commentary on “The statistics wars and intellectual conflicts of interest” (Mayo editorial)

In her recent Editorial for Conservation Biology, Deborah Mayo argues that journal editors “should avoid taking sides” regarding “heated disagreements about statistical significance tests.” Particularly, they should not impose bans suggested by combatants in the “statistics wars” on statistical methods advocated by the opposing side, such as Wasserstein et al.’s (2019) proposed ban on the declaration of statistical significance and use of p value thresholds. Were journal editors to adopt such proposals, Mayo argues, they would be acting under a conflict of interest (COI) of a special kind: an “intellectual” conflict of interest.

Conflicts of interest are worrisome because of the potential for bias. Researchers will no doubt be all too familiar with the institutional/bureaucratic requirement of declaring financial interests. Whether such disclosures provide substantive protections against bias or simply satisfy a “CYA” requirement of administrators, the rationale is that assessment of research outcomes can incorporate information relevant to the question of whether the investigators have arrived at a conclusion that overstates (or even fabricates) the support for a claim, when the acceptance of that claim would financially benefit them. This in turn ought to reduce the temptation of investigators to engage in such inflation or fabrication of support. The idea obviously applies quite naturally to editorial decisions as well as research conclusions. Continue reading

Categories: conflicts of interest, editors, intellectual COI, significance tests, statistical tests | 5 Comments

Yudi Pawitan: Behavioral aspects in the statistical significance war-game(Guest Post)



Yudi Pawitan
Department of Medical Epidemiology and Biostatistics
Karolinska Institutet, Stockholm


Behavioral aspects in the statistical significance war-game

I remember with fondness the good old days when the only ‘statistical war’-game was fought between the Bayesian and the frequentist. It was simpler – except when the likelihood principle is thrown in, always guaranteed to confound the frequentist – and the participants were for the most part collegial. Moreover, there was a feeling that it was a philosophical debate. Even though the Bayesian-frequentist war is not fully settled, we can see areas of consensus, for example in objective Bayesianism or in conditional inference. However, on the P-value and statistical significance front, the war looks less simple as it is about statistical praxis; it is no longer Bayesian vs frequentist, with no consensus in sight and with wide implications affecting the day-to-day use of statistics. Typically, a persistent controversy between otherwise sensible and knowledgeable people – thus excluding anti-vaxxers and conspiracy theorists – might indicate we are missing some common perspectives or perhaps the big picture. In complex issues there can be genuinely distinct aspects about which different players disagree and, at some point, agree to disagree. I am not sure we have reached that point yet, with each side still working to persuade the other side the faults of their position. For now, I can only concur with Mayo (2021)’s appeal that at least the umpires – journals editors – recognize (a) the issue at hand and (b) that genuine debates are still ongoing, so it is not yet time to take sides. Continue reading

Categories: Error Statistics | 5 Comments

January 11: Phil Stat Forum (remote): Statistical Significance Test Anxiety

Special Session of the (remote)
Phil Stat Forum:

11 January 2022

“Statistical Significance Test Anxiety”

TIME: 15:00-17:00 (London, GMT); 10:00-12:00 (EST)

Presenters: Deborah Mayo (Virginia Tech) &
Yoav Benjamini (Tel Aviv University)

Moderator: David Hand (Imperial College London)

Deborah Mayo       Yoav Benjamini        David Hand

Continue reading

Categories: Announcement, David Hand, Phil Stat Forum, significance tests, Yoav Benjamini | Leave a comment

The ASA controversy on P-values as an illustration of the difficulty of statistics


Christian Hennig
Department of Statistical Sciences
University of Bologna

The ASA controversy on P-values as an illustration of the difficulty of statistics

“I work on Multidimensional Scaling for more than 40 years, and the longer I work on it, the more I realise how much of it I don’t understand. This presentation is about my current state of not understanding.” (John Gower, world leading expert on Multidimensional Scaling, on a conference in 2009)

“The lecturer contradicts herself.” (Student feedback to an ex-colleague for teaching methods and then teaching what problems they have)

1 Limits of understanding

Statistical tests and P-values are widely used and widely misused. In 2016, the ASA issued a statement on significance and P-values with the intention to curb misuse while acknowledging their proper definition and potential use. In my view the statement did a rather good job saying things that are worthwhile saying while trying to be acceptable to those who are generally critical on P-values as well as those who tend to defend their use. As was predictable, the statement did not settle the issue. A “2019 editorial” by some of the authors of the original statement (recommending “to abandon statistical significance”) and a 2021 ASA task force statement, much more positive on P-values, followed, showing the level of disagreement in the profession. Continue reading

Categories: ASA Task Force on Significance and Replicability, Mayo editorial, P-values | 3 Comments

E. Ionides & Ya’acov Ritov (Guest Post) on Mayo’s editorial, “The Statatistics Wars and Intellectual Conflicts of Interest”


Edward L. Ionides


Director of Undergraduate Programs and Professor,
Department of Statistics, University of Michigan

Ya’acov Ritov Professor
Department of Statistics, University of Michigan


Thanks for the clear presentation of the issues at stake in your recent Conservation Biology editorial (Mayo 2021). There is a need for such articles elaborating and contextualizing the ASA President’s Task Force statement on statistical significance (Benjamini et al, 2021). The Benjamini et al (2021) statement is sensible advice that avoids directly addressing the current debate. For better or worse, it has no references, and just speaks what looks to us like plain sense. However, it avoids addressing why there is a debate in the first place, and what are the justifications and misconceptions that drive different positions. Consequently, it may be ineffective at communicating to those swing voters who have sympathies with some of the insinuations in the Wasserstein & Lazar (2016) statement. We say “insinuations” here since we consider that their 2016 statement made an attack on p-values which was forceful, indirect and erroneous. Wasserstein & Lazar (2016) started with a constructive discussion about the uses and abuses of p-values before moving against them. This approach was good rhetoric: “I have come to praise p-values, not to bury them” to invert Shakespeare’s Anthony. Good rhetoric does not always promote good science, but Wasserstein & Lazar (2016) successfully managed to frame and lead the debate, according to Google Scholar. We warned of the potential consequences of that article and its flaws (Ionides et al, 2017) and we refer the reader to our article for more explanation of these issues (it may be found below). Wasserstein, Schirm and Lazar (2019) made their position clearer, and therefore easier to confront. We are grateful to Benjamini et al (2021) and Mayo (2021) for rising to the debate. Rephrasing Churchill in support of their efforts, “Many forms of statistical methods have been tried, and will be tried in this world of sin and woe. No one pretends that the p-value is perfect or all-wise. Indeed (noting that its abuse has much responsibility for the replication crisis) it has been said that the p-value is the worst form of inference except all those other forms that have been tried from time to time”. Continue reading

Categories: ASA Task Force on Significance and Replicability, editors, P-values, significance tests | 2 Comments

B. Haig on questionable editorial directives from Psychological Science (Guest Post)


Brian Haig, Professor Emeritus
Department of Psychology
University of Canterbury
Christchurch, New Zealand


What do editors of psychology journals think about tests of statistical significance? Questionable editorial directives from Psychological Science

Deborah Mayo’s (2021) recent editorial in Conservation Biology addresses the important issue of how journal editors should deal with strong disagreements about tests of statistical significance (ToSS). Her commentary speaks to applied fields, such as conservation science, but it is relevant to basic research, as well as other sciences, such as psychology. In this short guest commentary, I briefly remark on the role played by the prominent journal, Psychological Science (PS), regarding whether or not researchers should employ ToSS. PS is the flagship journal of the Association for Psychological Science, and two of its editors-in-chief have offered explicit, but questionable, advice on this matter. Continue reading

Categories: ASA Task Force on Significance and Replicability, Brian Haig, editors, significance tests | Tags: | 1 Comment

D. Lakens (Guest Post): Averting journal editors from making fools of themselves


Daniël Lakens

Associate Professor
Human Technology Interaction
Eindhoven University of Technology

Averting journal editors from making fools of themselves

In a recent editorial, Mayo (2021) warns journal editors to avoid calls for authors guidelines to reflect a particular statistical philosophy, and not to go beyond merely enforcing the proper use of significance tests. That such a warning is needed at all should embarrass anyone working in statistics. And yet, a mere three weeks after Mayo’s editorial was published, the need for such warnings was reinforced when a co-editorial by journal editors from the International Society of Physiotherapy (Elkins et al., 2021) titled “Statistical inference through estimation: recommendations from the International Society of Physiotherapy Journal Editors” stated: “[This editorial] also advises researchers that some physiotherapy journals that are members of the International Society of Physiotherapy Journal Editors (ISPJE) will be expecting manuscripts to use estimation methods instead of null hypothesis statistical tests.” Continue reading

Categories: D. Lakens, significance tests | 3 Comments

Midnight With Birnbaum (Remote, Virtual Happy New Year 2021)!


.For the second year in a row, unlike the previous 9 years that I’ve been blogging, it’s not feasible to actually revisit that spot in the road, looking to get into a strange-looking taxi, to head to “Midnight With Birnbaum”.  Because of the extended pandemic, I am not going out this New Year’s Eve again, so the best I can hope for is a zoom link of the sort I received last year, not long before midnight– that will link me to a hypothetical party with him. (The pic on the left is the only blurry image I have of the club I’m taken to.) I just keep watching my email, to see if a zoom link arrives. My book Statistical Inference as Severe Testing: How to Get Beyond the Statistics Wars (CUP, 2018)  doesn’t include the argument from my article in Statistical Science (“On the Birnbaum Argument for the Strong Likelihood Principle”), but you can read it at that link along with commentaries by A. P. David, Michael Evans, Martin and Liu, D. A. S. Fraser (who sadly passed away in 2021), Jan Hannig, and Jan Bjornstad  but there’s much in it that I’d like to discuss with him. The (Strong) Likelihood Principle (LP or SLP)–whether or not it is named–remains at the heart of many of the criticisms of Neyman-Pearson (N-P) statistics and statistical significance testing in general. Continue reading

Categories: Birnbaum, Birnbaum Brakes, strong likelihood principle | Tags: , , , | 1 Comment

“This is the moment” to discount a positive Covid test (after 5 days) (i)


This week’s big controversy concerns the CDC’s deciding to cut recommended days for isolation for people infected with Covid. CDC director Walensky was all over the news explaining that this “was the moment” for a cut, given the whopping number of new Covid cases (over 400,000 on Dec. 28, exceeding the previous record which was in the 300,000’s).

“In the context of the fact that we were going to have so many more cases — many of those would be asymptomatic or mildly symptomatic — people would feel well enough to be at work, they would not necessarily tolerate being home, and that they may not comply with being home, this was the moment that we needed to make that decision,” Walensky told CNN.

The CDC had already explained last week that “health care workers’ isolation period could be cut to five days, or even fewer, in the event of severe staffing shortages at U.S. hospitals”.

Then, on Monday, the CDC announced that individuals who test positive for Covid-19 and are asymptomatic need to isolate for only five days, not 10 days, citing increasing evidence that people are most infectious in the initial days after developing symptoms.

What’s really causing alarm among many health experts is that the new policy has no requirement for a negative test result, with a rapid test, before ending isolation. Even if you test positive on day 5, the CDC says, you can go about your business. So long as you’re asymptomatic or mildly symptomatic or your “symptoms are resolving” and you wear a mask. I don’t suppose the new looser guidance would result in any pressure being put on a pilot or other worker to get back to work even with some mild brain fog or coughing that seemed to be resolving.[1] Continue reading

Categories: covid-19 | 5 Comments

January 11: Phil Stat Forum (remote)

Special Session of the (remote)
Phil Stat Forum:

11 January 2022

“Statistical Significance Test Anxiety”

TIME: 15:00-17:00 (London, GMT); 10:00-12:00 (EST)

Presenters: Deborah Mayo (Virginia Tech) &
Yoav Benjamini (Tel Aviv University)

Moderator: David Hand (Imperial College London)

Deborah Mayo       Yoav Benjamini        David Hand

Focus of the Session: 

Continue reading

Categories: Announcement, David Hand, Phil Stat Forum, significance tests, Yoav Benjamini | Leave a comment

The Statistics Wars and Intellectual Conflicts of Interest


My editorial in Conservation Biology is published (open access): “The Statistical Wars and Intellectual Conflicts of Interest”. Share your comments, here and/or send a separate item (to Error), if you wish, for possible guest posting*. (All readers are invited to a special January 11 Phil Stat Session with Y. Benjamini and D. Hand described here.) Here’s most of the editorial:

The Statistics Wars and Intellectual Conflicts of Interest

How should journal editors react to heated disagreements about statistical significance tests in applied fields, such as conservation science, where statistical inferences often are the basis for controversial policy decisions? They should avoid taking sides. They should also avoid obeisance to calls for author guidelines to reflect a particular statistical philosophy or standpoint. The question is how to prevent the misuse of statistical methods without selectively favoring one side.

The statistical‐significance‐test controversies are well known in conservation science. In a forum revolving around Murtaugh’s (2014) “In Defense of P values,” Murtaugh argues, correctly, that most criticisms of statistical significance tests “stem from misunderstandings or incorrect interpretations, rather than from intrinsic shortcomings of the P value” (p. 611). However, underlying those criticisms, and especially proposed reforms, are often controversial philosophical presuppositions about the proper uses of probability in uncertain inference. Should probability be used to assess a method’s probability of avoiding erroneous interpretations of data (i.e., error probabilities) or to measure comparative degrees of belief or support? Wars between frequentists and Bayesians continue to simmer in calls for reform.

Consider how, in commenting on Murtaugh (2014), Burnham and Anderson (2014 : 627) aver that “P‐values are not proper evidence as they violate the likelihood principle (Royall, 1997).” This presupposes that statistical methods ought to obey the likelihood principle (LP), a long‐standing point of controversy in the statistics wars. The LP says that all the evidence is contained in a ratio of likelihoods (Berger & Wolpert, 1988). Because this is to condition on the particular sample data, there is no consideration of outcomes other than those observed and thus no consideration of error probabilities. One should not write this off because it seems technical: methods that obey the LP fail to directly register gambits that alter their capability to probe error. Whatever one’s view, a criticism based on presupposing the irrelevance of error probabilities is radically different from one that points to misuses of tests for their intended purpose—to assess and control error probabilities.

Error control is nullified by biasing selection effects: cherry‐picking, multiple testing, data dredging, and flexible stopping rules. The resulting (nominal) p values are not legitimate p values. In conservation science and elsewhere, such misuses can result from a publish‐or‐perish mentality and experimenter’s flexibility (Fidler et al., 2017). These led to calls for preregistration of hypotheses and stopping rules–one of the most effective ways to promote replication (Simmons et al., 2012). However, data dredging can also occur with likelihood ratios, Bayes factors, and Bayesian updating, but the direct grounds to criticize inferences as flouting error probability control is lost. This conflicts with a central motivation for using p values as a “first line of defense against being fooled by randomness” (Benjamini, 2016). The introduction of prior probabilities (subjective, default, or empirical)–which may also be data dependent–offers further flexibility.

Signs that one is going beyond merely enforcing proper use of statistical significance tests are that the proposed reform is either the subject of heated controversy or is based on presupposing a philosophy at odds with that of statistical significance testing. It is easy to miss or downplay philosophical presuppositions, especially if one has a strong interest in endorsing the policy upshot: to abandon statistical significance. Having the power to enforce such a policy, however, can create a conflict of interest (COI). Unlike a typical COI, this one is intellectual and could threaten the intended goals of integrity, reproducibility, and transparency in science.

If the reward structure is seducing even researchers who are aware of the pitfalls of capitalizing on selection biases, then one is dealing with a highly susceptible group. For a journal or organization to take sides in these long-standing controversies—or even to appear to do so—encourages groupthink and discourages practitioners from arriving at their own reflective conclusions about methods.

The American Statistical Association (ASA) Board appointed a President’s Task Force on Statistical Significance and Replicability in 2019 that was put in the odd position of needing to “address concerns that a 2019 editorial [by the ASA’s executive director (Wasserstein et al., 2019)] might be mistakenly interpreted as official ASA policy” (Benjamini et al., 2021)—as if the editorial continues the 2016 ASA Statement on p-values (Wasserstein & Lazar, 2016). That policy statement merely warns against well‐known fallacies in using p values. But Wasserstein et al. (2019) claim it “stopped just short of recommending that declarations of ‘statistical significance’ be abandoned” and announce taking that step. They call on practitioners not to use the phrase statistical significance and to avoid p value thresholds. Call this the no‐threshold view. The 2016 statement was largely uncontroversial; the 2019 editorial was anything but. The President’s Task Force should be commended for working to resolve the confusion (Kafadar, 2019). Their report concludes: “P-values are valid statistical measures that provide convenient conventions for communicating the uncertainty inherent in quantitative results” (Benjamini et al., 2021). A disclaimer that Wasserstein et al., 2019 was not ASA policy would have avoided both the confusion and the slight to opposing views within the Association.

The no‐threshold view has consequences (likely unintended). Statistical significance tests arise “to test the conformity of the particular data under analysis with [a statistical hypothesis] H0 in some respect to be specified” (Mayo & Cox, 2006: 81). There is a function D of the data, the test statistic, such that the larger its value (d), the more inconsistent are the data with H0. The p value is the probability the test would have given rise to a result more discordant from H0 than d is were the results due to background or chance variability (as described in H0). In computing p, hypothesis H0 is assumed merely for drawing out its probabilistic implications. If even larger differences than d are frequently brought about by chance alone (p is not small), the data are not evidence of inconsistency with H0. Requiring a low pvalue before inferring inconsistency with H0 controls the probability of a type I error (i.e., erroneously finding evidence against H0).

Whether interpreting a simple Fisherian or an N‐P test, avoiding fallacies calls for considering one or more discrepancies from the null hypothesis under test. Consider testing a normal mean H0: μ ≤ μ0 versus H1: μ > μ0. If the test would fairly probably have resulted in a smaller p value than observed, if μ = μ1 were true (where μ1 = μ0 + γ, for γ > 0), then the data provide poor evidence that μ exceeds μ1. It would be unwarranted to infer evidence of μ > μ1. Tests do not need to be abandoned when the fallacy is easily avoided by computing p values for one or two additional benchmarks (Burgman, 2005; Hand, 2021; Mayo, 2018; Mayo & Spanos, 2006).

The same is true for avoiding fallacious interpretations of nonsignificant results. These are often of concern in conservation, especially when interpreted as no risks exist. In fact, the test may have had a low probability to detect risks. But nonsignificant results are not uninformative. If the test very probably would have resulted in a more statistically significant result were there a meaningful effect, say μ > μ1 (where μ1 = μ0 + γ, for γ > 0), then the data are evidence that μ < μ1. (This is not to infer μ ≤ μ0.) “Such an assessment is more relevant to specific data than is the notion of power” (Mayo & Cox, 2006: 89). This also matches inferring that μ is less than the upper bound of the corresponding confidence interval (at the associated confidence level) or a severity assessment (Mayo, 2018). Others advance equivalence tests (Lakens, 2017; Wellek, 2017). An N‐P test tells one to specify H0 so that the type I error is the more serious (considering costs); that alone can alleviate problems in the examples critics adduce (H0would be that the risk exists).

Many think the no‐threshold view merely insists that the attained p value be reported. But leading N‐P theorists already recommend reporting p, which “gives an idea of how strongly the data contradict the hypothesis…[and] enables others to reach a verdict based on the significance level of their choice” (Lehmann & Romano, 2005: 63−64). What the no‐threshold view does, if taken strictly, is preclude testing. If one cannot say ahead of time about any result that it will not be allowed to count in favor of a claim, then one does not test that claim. There is no test or falsification, even of the statistical variety. What is the point of insisting on replication if at no stage can one say the effect failed to replicate? One may argue for approaches other than tests, but it is unwarranted to claim by fiat that tests do not provide evidence. (For a discussion of rival views of evidence in ecology, see Taper & Lele, 2004.)

Many sign on to the no‐threshold view thinking it blocks perverse incentives to data dredge, multiple test, and p hack when confronted with a large, statistically nonsignificant p value. Carefully considered, the reverse seems true. Even without the word significance, researchers could not present a large (nonsignificant) p value as indicating a genuine effect. It would be nonsensical to say that even though more extreme results would frequently occur by random variability alone that their data are evidence of a genuine effect. The researcher would still need a small value, which is to operate with a threshold. However, it would be harder to hold data dredgers culpable for reporting a nominally small p value obtained through data dredging. What distinguishes nominal p values from actual ones is that they fail to meet a prespecified error probability threshold.


While it is well known that stopping when the data look good inflates the type I error probability, a strict Bayesian is not required to adjust for interim checking because the posterior probability is unaltered. Advocates of Bayesian clinical trials are in a quandary because “The [regulatory] requirement of Type I error control for Bayesian [trials] causes them to lose many of their philosophical advantages, such as compliance with the likelihood principle” (Ryan etal., 2020: 7).

It may be retorted that implausible inferences will indirectly be blocked by appropriate prior degrees of belief (informative priors), but this misses the crucial point. The key function of statistical tests is to constrain the human tendency to selectively favor views they believe in. There are ample forums for debating statistical methodologies. There is no call for executive directors or journal editors to place a thumb on the scale. Whether in dealing with environmental policy advocates, drug lobbyists, or avid calls to expel statistical significance tests, a strong belief in the efficacy of an intervention is distinct from its having been well tested. Applied science will be well served by editorial policies that uphold that distinction.

For the acknowledgments and references, see the full editorial here.

I will cite as many (constructive) readers’ views as I can at the upcoming forum with Yoav Benjamini and David Hand on January 11 on zoom (see this post). *Authors of articles I put up as guest posts or cite at the Forum will get a free copy of my Statistical Inference as Severe Testing: How to Get Beyond the Statistics Wars (CUP, 2018).

Categories: significance tests, spurious p values, stat wars and their casualties, strong likelihood principle | 2 Comments

Bickel’s defense of significance testing on the basis of Bayesian model checking


In my last post, I said I’d come back to a (2021) article by David Bickel, “Null Hypothesis Significance Testing Defended and Calibrated by Bayesian Model Checking” in The American Statistician. His abstract begins as follows:


Significance testing is often criticized because p-values can be low even though posterior probabilities of the null hypothesis are not low according to some Bayesian models. Those models, however, would assign low prior probabilities to the observation that the p-value is sufficiently low. That conflict between the models and the data may indicate that the models needs revision. Indeed, if the p-value is sufficiently small while the posterior probability according to a model is insufficiently small, then the model will fail a model check….(from Bickel 2021)

Continue reading

Categories: Bayesian/frequentist, D. Bickel, Fisher, P-values | 3 Comments

P-values disagree with posteriors? Problem is your priors, says R.A. Fisher

What goes around…

How often do you hear P-values criticized for “exaggerating” the evidence against a null hypothesis? If your experience is like mine, the answer is ‘all the time’, and in fact, the charge is often taken as one of the strongest cards in the anti-statistical significance playbook. The argument boils down to the fact that the P-value accorded to a point null H0 can be small while its Bayesian posterior probability high–provided a high enough prior is accorded to H0. But why suppose P-values should match Bayesian posteriors? And what justifies the high (or “spike”) prior to a point null? While I discuss this criticism at considerable length in Statistical Inference as Severe Testing: How to get beyond the statistics wars (CUP, 2018), I did not quote an intriguing response by R.A. Fisher to disagreements between P-values and posteriors’s (in Statistical Methods and Scientific Inference, Fisher 1956); namely, that such a prior probability assignment would itself be rejected by the observed small P-value–if the prior were itself regarded as a hypothesis to test. Or so he says. I did mention this response by Fisher in an encyclopedia article from way back in 2006 on “philosophy of statistics”: Continue reading

Categories: Bayesian/frequentist, Fisher, P-values | 7 Comments

Memory Lane (4 years ago): Why significance testers should reject the argument to “redefine statistical significance”, even if they want to lower the p-value*


An argument that assumes the very thing that was to have been argued for is guilty of begging the question; signing on to an argument whose conclusion you favor even though you cannot defend its premises is to argue unsoundly, and in bad faith. When a whirlpool of “reforms” subliminally alter  the nature and goals of a method, falling into these sins can be quite inadvertent. Start with a simple point on defining the power of a statistical test. Continue reading

Categories: Bayesian/frequentist, fallacy of rejection, P-values, reforming the reformers, spurious p values | 3 Comments

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