stat wars and their casualties

Upcoming Workshop: The Statistics Wars and Their Casualties workshop

The Statistics Wars
and Their Casualties

22-23 September 2022
15:00-18:00 pm London Time*
(London School of Economics, CPNSS)

To register for the  workshop,
please fill out the registration form here.

For schedules and updated details, please see the workshop webpage:

*These will be sessions 1 & 2, there will be two more
online sessions (3 & 4) on December 1 & 8.

While the field of statistics has a long history of passionate foundational controversy, the last decade has, in many ways, been the most dramatic. Misuses of statistics, biasing selection effects, and high-powered methods of big-data analysis, have helped to make it easy to find impressive-looking but spurious results that fail to replicate. As the crisis of replication has spread beyond psychology and social sciences to biomedicine, genomics, machine learning and other fields, the need for critical appraisal of proposed reforms is growing. Many are welcome (transparency about data, eschewing mechanical uses of statistics); some are quite radical. The experts do not agree on the best ways to promote trustworthy results, and these disagreements often reflect philosophical battles–old and new– about the nature of inductive-statistical inference and the roles of probability in statistical inference and modeling. Intermingled in the controversies about evidence are competing social, political, and economic values. If statistical consumers are unaware of assumptions behind rival evidence-policy reforms, they cannot scrutinize the consequences that affect them. What is at stake is a critical standpoint that we may increasingly be in danger of losing. Critically reflecting on proposed reforms and changing standards requires insights from statisticians, philosophers of science, psychologists, journal editors, economists and practitioners from across the natural and social sciences. This workshop will bring together these interdisciplinary insights–from speakers as well as attendees.


Yoav Benjamini (Tel Aviv University), Alexander Bird (University of Cambridge), Mark Burgman (Imperial College London),  Daniele Fanelli (London School of Economics and Political Science), Roman Frigg (London School of Economics and Political Science), Stephan Guttinger (University of Exeter), David Hand (Imperial College London), Margherita Harris  (London School of Economics and Political Science), Christian Hennig (University of Bologna), Daniël Lakens (Eindhoven University of Technology), Deborah Mayo (Virginia Tech), Richard Morey (Cardiff University), Stephen Senn (Edinburgh, Scotland), Jon Williamson (University of Kent)


The Foundation for the Study of Experimental Reasoning, Reliability, and the Objectivity and Rationality of Science (E.R.R.O.R.S.); Centre for Philosophy of Natural and Social Science (CPNSS), London School of Economics; Virginia Tech Department of Philosophy

Organizers: D. Mayo, R. Frigg and M. Harris
(chief logistics and contact person): Jean Miller
Executive Planning Committee: Y. Benjamini, D. Hand, D. Lakens, S. Senn

To register for the workshop,
please fill out the registration form here. 

Categories: Announcement, stat wars and their casualties | 1 Comment

D. Lakens responds to confidence interval crusading journal editors


In what began as a guest commentary on my 2021 editorial in Conservation Biology, Daniël Lakens recently published a response to a recommendation against using null hypothesis significance tests by journal editors from the International Society of Physiotherapy Journal. Here are some excerpts from his full article, replies (‘response to Lakens‘), links and a few comments of my own. Continue reading

Categories: stat wars and their casualties, statistical significance tests | 12 Comments

Paul Daniell & Yu-li Ko commentaries on Mayo’s ConBio Editorial

I had been posting commentaries daily from January 6, 2022 (on my editorial “The Statistics Wars and Intellectual conflicts of Interest”, Conservation Biology) until Sir David Cox died on January 18, at which point I switched to some memorial items. These two commentaries from what Daniell calls my ‘birthday festschrift’ were left out, and I put them up now. (Links to others are below.)

Continue reading

Categories: Mayo editorial, stat wars and their casualties | 1 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 | 3 Comments

Bayesian philosophers vs Bayesian statisticians: Remarks on Jon Williamson

While I would agree that there are differences between Bayesian statisticians and Bayesian philosophers, those differences don’t line up with the ones drawn by Jon Williamson in his presentation to our Phil Stat Wars Forum (May 20 slides). I hope Bayesians (statisticians, or more generally, practitioners, and philosophers) will weigh in on this. 

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Categories: Phil Stat Forum, stat wars and their casualties

April 22 “How an information metric could bring truce to the statistics wars” (Daniele Fanelli)

The eighth meeting of our Phil Stat Forum*:

The Statistics Wars
and Their Casualties

22 April 2021

TIME: 15:00-16:45 (London); 10:00-11:45 (New York, EST)

For information about the Phil Stat Wars forum and how to join, click on this link.

“How an information metric could bring truce to the statistics wars

Daniele Fanelli Continue reading

Categories: Phil Stat Forum, replication crisis, stat wars and their casualties

Aris Spanos: Modeling vs. Inference in Frequentist Statistics (guest post)


Aris Spanos
Wilson Schmidt Professor of Economics
Department of Economics
Virginia Tech

The following guest post (link to updated PDF) was written in response to C. Hennig’s presentation at our Phil Stat Wars Forum on 18 February, 2021: “Testing With Models That Are Not True”. Continue reading

Categories: misspecification testing, Spanos, stat wars and their casualties

JSM 2020 Panel on P-values & “Statistical Significance”

All: On July 30 (10am EST) I will give a virtual version of my JSM presentation, remotely like the one I will actually give on Aug 6 at the JSM. Co-panelist Stan Young may as well. One of our surprise guests tomorrow (not at the JSM) will be Yoav Benjamini!  If you’re interested in attending our July 30 practice session* please follow the directions here. Background items for this session are in the “readings” and “memos” of session 5.

*unless you’re already on our LSE Phil500 list

JSM 2020 Panel Flyer (PDF)
JSM online program w/panel abstract & information): Continue reading

Categories: Announcement, JSM 2020, significance tests, stat wars and their casualties

On Some Self-Defeating Aspects of the ASA’s (2019) Recommendations on Statistical Significance Tests (ii)


“Before we stood on the edge of the precipice, now we have taken a great step forward”


What’s self-defeating about pursuing statistical reforms in the manner taken by the American Statistical Association (ASA) in 2019? In case you’re not up on the latest in significance testing wars, the 2016 ASA Statement on P-Values and Statistical Significance, ASA I, arguably, was a reasonably consensual statement on the need to avoid some well-known abuses of P-values–notably if you compute P-values, ignoring selective reporting, multiple testing, or stopping when the data look good, the computed P-value will be invalid. (Principle 4, ASA I) But then Ron Wasserstein, executive director of the ASA, and co-editors, decided they weren’t happy with their own 2016 statement because it “stopped just short of recommending that declarations of ‘statistical significance’ be abandoned” altogether. In their new statement–ASA II(note)–they announced: “We take that step here….Statistically significant –don’t say it and don’t use it”.

Why do I say it is a mis-take to have taken the supposed next “great step forward”? Why do I count it as unsuccessful as a piece of statistical science policy? In what ways does it make the situation worse? Let me count the ways. The first is in this post. Others will come in following posts, until I become too disconsolate to continue.[i] Continue reading

Categories: P-values, stat wars and their casualties, statistical significance tests

Hardwicke and Ioannidis, Gelman, and Mayo: P-values: Petitions, Practice, and Perils (and a question for readers)


The October 2019 issue of the European Journal of Clinical Investigations came out today. It includes the PERSPECTIVE article by Tom Hardwicke and John Ioannidis, an invited editorial by Gelman and one by me:

Petitions in scientific argumentation: Dissecting the request to retire statistical significance, by Tom Hardwicke and John Ioannidis

When we make recommendations for scientific practice, we are (at best) acting as social scientists, by Andrew Gelman

P-value thresholds: Forfeit at your peril, by Deborah Mayo

I blogged excerpts from my preprint, and some related posts, here.

All agree to the disagreement on the statistical and metastatistical issues: Continue reading

Categories: ASA Guide to P-values, P-values, stat wars and their casualties

(Excerpts from) ‘P-Value Thresholds: Forfeit at Your Peril’ (free access)


A key recognition among those who write on the statistical crisis in science is that the pressure to publish attention-getting articles can incentivize researchers to produce eye-catching but inadequately scrutinized claims. We may see much the same sensationalism in broadcasting metastatistical research, especially if it takes the form of scapegoating or banning statistical significance. A lot of excitement was generated recently when Ron Wasserstein, Executive Director of the American Statistical Association (ASA), and co-editors A. Schirm and N. Lazar, updated(note) the 2016 ASA Statement on P-Values and Statistical Significance (ASA I). In their 2019 interpretation, ASA I “stopped just short of recommending that declarations of ‘statistical significance’ be abandoned,” and in their new statement (ASA II)(note) announced: “We take that step here….’statistically significant’ –don’t say it and don’t use it”. To herald the ASA II(note), and the special issue “Moving to a world beyond ‘p < 0.05’”, the journal Nature requisitioned a commentary from Amrhein, Greenland and McShane “Retire Statistical Significance” (AGM). With over 800 signatories, the commentary received the imposing title “Scientists rise up against significance tests”! Continue reading

Categories: ASA Guide to P-values, P-values, stat wars and their casualties

The Statistics Wars: Errors and Casualties


Had I been scheduled to speak later at the 12th MuST Conference & 3rd Workshop “Perspectives on Scientific Error” in Munich, rather than on day 1, I could have (constructively) illustrated some of the errors and casualties by reference to a few of the conference papers that discussed significance tests. (Most gave illuminating discussions of such topics as replication research, the biases that discredit meta-analysis, statistics in the law, formal epistemology [i]). My slides follow my abstract. Continue reading

Categories: slides, stat wars and their casualties | Tags:

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