P-values

Deconstructing “A World Beyond P-values”

.A world beyond p-values?

I was asked to write something explaining the background of my slides (posted here) in relation to the recent ASA “A World Beyond P-values” conference. I took advantage of some long flight delays on my return to jot down some thoughts:

The contrast between the closing session of the conference “A World Beyond P-values,” and the gist of the conference itself, shines a light on a pervasive tension within the “Beyond P-Values” movement. Two very different debates are taking place. First there’s the debate about how to promote better science. This includes welcome reminders of the timeless demands of rigor and integrity required to avoid deceiving ourselves and others–especially crucial in today’s world of high-powered searches and Big Data. That’s what the closing session was about. [1]

The second debate is a contemporary version of long-standing, but unresolved, disagreements on statistical philosophy: degrees of belief vs. error control, frequentist vs. Bayesian, testing vs. confidence intervals, etc. That’s what most of the conference revolved around. The opening talk by Steve Goodman was “Why is Eliminating P-values so Hard?”. Admittedly there were concurrent sessions, so my view is selective. True, bad statistics–perverse incentives, abuses of significance tests, publication biases and the resulting irreplicability–have given a new raison d’etre for (re)fighting the old, and tackling newer, statistics wars. And, just to be clear, let me say that I think these battles should be reexamined, but taking into account the more sophisticated variants of the methods, on all sides. Yet the conference, by and large, presumed the main war was already over, and the losers were tests of the statistical significance of differences–not merely abuses of the tests, the entire statistical method! [2]

Under the revolutionary rubric of “The Radical Prescription for Change”, we heard, in the final session, eminently sensible recommendations for doing good science–the first interpretation in my deconstruction. Marcia McNutt provided a terrific overview of what Science, Nature, and key agencies are doing to uplift scientific rigor and sound research. She listed statistical issues: file drawer problems, p-hacking, poor experimental design, model misspecification; and empirical ones: unidentified variables, outliers and data gaps, problems with data smoothing, and so on. In an attempt at “raising the bar”, she tells us, 80 editors agreed on the importance of preregistration, randomization and blindness. Excellent! Gelman recommended that p-values be just one piece of information rather than a rigid rod by which, once jumped over, publication ensues. Decisions should be holistic and take into account background information and questions of measurement. The ways statisticians can help scientists, Gelman proposed, is (1) by changing incentives so that it’s harder to cheat and (2) helping them determine the frequency properties of their tools (e.g., their abilities to reveal or avoid magnitude and sign errors). Meng, in his witty and sagacious manner, suggested punishing researchers by docking their salary if they’re wrong–using some multiple of their p-values. The one I like best is his recommendation that researchers ask themselves whether they’d ever dream of using the results of their work on themselves or a loved one. I totally agree!

Thus, in the interpretation represented by the closing session, “A World Beyond P-values” refers to a world beyond cookbook, and other modes of, bad statistics. A second reading, however, has it refer to statistical inference where significance tests, if permitted at all, are to be compelled to wear badges of shame–use them at your peril. Never mind that these are the very tools relied upon to reveal lack of replication, to show adulteration by cherry-picking and other biasing selection effects, and to test assumptions. From that vantage point, it made sense that participants began by offering up alternative or modified statistical tools–and there were many. Why fight the battle–engage the arguments–if the enemy is already down? Using the suffix “cide”, (killer), we might call it statistical testicide.

I’m certainly not defending the crude uses of tests long lampooned. Even when used correctly, they’re just a part of what I call error statistics: tools that employ sampling distributions to assess and control the capabilities of methods to avoid erroneous interpretations of data (error probabilities).[3] My own work in philosophy of statistics has been to reformulate statistical tests to avoid fallacies and arrive at an evidential interpretation of error probabilities in scientific contexts (to assess and control well-testedness).

Given my sense of the state of play, I decided that the best way to tackle the question of “What are the Best Uses For P-Values?”–the charge for our session–was to supply the key existing responses to criticisms of significance tests. Typically hidden from view (at least in these circles), these should now serve as handy retorts for the significance test user. The starting place for future significance test challengers should no longer be to just rehearse the criticisms, but to grapple with these responses and the arguments behind them.[4]

So to the question on my first slide: What contexts ever warrant the use of statistical tests of significance? The answer is: Precisely those you’d find yourself in if you’re struggling to get to a “World Beyond P-values” in the first sense–namely, battling bad statistical science.

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[1] Andrew Gelman, Columbia University; Marcia McNutt, National Academy of Sciences; Xiao-Li Meng, Harvard University.

[2] Please correct me with info from other sessions. I’m guessing one of the policy-oriented session might have differed. Naturally, I’m excluding ours.

[3] proper subset of error statistics uses these capabilities to assess how severely claims have passed.

[4] Please search this blog for details behind each, e.g., likelihood principle, p-values exaggerate, error probabilities, power, law of likelihood, p-value madness, etc.

Some related blogposts:

The ASA Document on P-values: One Year On

Statistical Reforms Without Philosophy Are Blind

Saturday Night Brainstorming and Task Forces (spoof)

On the Current State of Play in the Crisis of Replication in Psychology: Some Heresies

 

Categories: P-values, Philosophy of Statistics, reforming the reformers | 1 Comment

Statistical skepticism: How to use significance tests effectively: 7 challenges & how to respond to them

Here are my slides from the ASA Symposium on Statistical Inference : “A World Beyond p < .05”  in the session, “What are the best uses for P-values?”. (Aside from me,our session included Yoav Benjamini and David Robinson, with chair: Nalini Ravishanker.)

7 QUESTIONS

  • Why use a tool that infers from a single (arbitrary) P-value that pertains to a statistical hypothesis H0 to a research claim H*?
  • Why use an incompatible hybrid (of Fisher and N-P)?
  • Why apply a method that uses error probabilities, the sampling distribution, researcher “intentions” and violates the likelihood principle (LP)? You should condition on the data.
  • Why use methods that overstate evidence against a null hypothesis?
  • Why do you use a method that presupposes the underlying statistical model?
  • Why use a measure that doesn’t report effect sizes?
  • Why do you use a method that doesn’t provide posterior probabilities (in hypotheses)?

 

Categories: P-values, spurious p values, statistical tests, Statistics | Leave a comment

New venues for the statistics wars

I was part of something called “a brains blog roundtable” on the business of p-values earlier this week–I’m glad to see philosophers getting involved.

Next week I’ll be in a session that I think is intended to explain what’s right about P-values at an ASA Symposium on Statistical Inference : “A World Beyond p < .05”.

Our session, “What are the best uses for P-values?“, I take it, will discuss the value of frequentist (error statistical) testing more generally, as is appropriate. (Aside from me, it includes Yoav Benjamini and David Robinson.)

One of the more baffling things about today’s statistics wars is their tendency to readily undermine themselves. One example is how they lead to relinquishing the strongest criticisms against findings that have been based on fishing expeditions. In the interest of promoting a statistical account that downplays error probabilities (Bayes Factors), it becomes difficult to lambast a researcher for engaging in practices on grounds that they violate error probabilities (cherry-picking, multiple testing, trying and trying again, post-data selection effects). You can’t condemn a researcher for engaging in practices on grounds that they violate error probabilities, if you reject error probabilities. The direct criticism has been lost. The criticism is redirected to finding the cherry picked hypothesis improbable. But now the cherry picker is free to discount the criticism as something a Bayesian can always do to counter a statistically significant finding–and they do this very effectively![1] Moreover, cherry picked hypotheses are often believable, that’s what makes things like post-data subgroups so seductive. Finally, in an adequate account, the improbability of a claim must be distinguished from its having been poorly tested. (You need to be able to say things like, “it’s plausible, but that’s a lousy test of it.”)

Now I realize error probabilities are often criticized as relevant only for long-run error control, but that’s a mistake. Ask yourself: what bothers you when cherry pickers selectively report favorable findings, and then claim to have good evidence of an effect? You’re not concerned that making a habit out of this would yield poor long-run performance–even though it would. What bothers you, and rightly so, is they haven’t done a good job in ruling out spurious findings in the case at hand. You need a principle to explain this epistemological standpoint–something frequentists have only hinted at. To state it informally:

I haven’t been given evidence for a claim C by dint of a method that had little if any capability to reveal specific flaws in C, even if they are present.

It’s a minimal requirement for evidence; I call it the severity requirement, but it doesn’t matter what its called. The stronger form says:

Data provide evidence for C only to the extent C has been subjected to and passes a reasonably severe test–one that probably would have found flaws in C, if present.

To many, “a world beyond p <.05” suggests a world without error statistical testing. So if you’re to use such a test in the best way, you’ll need to say why. Why use a statistical test of significance for your context and problem rather than some other tool? What type of context would ever make statistical (significance) testing just the ticket? Since the right use of these methods cannot be divorced from responding to expected critical challenges, I’ve decided to focus my remarks on giving those responses. However, I’m still working on it. Feel free to share thoughts.

Anyone who follows this blog knows I’ve been speaking about these things for donkey’s years–search terms of interest on this blog. I’ve also just completed a book, Statistical Inference as Severe Testing: How to Get Beyond the Statistics Wars (CUP 2018).

[1] The inference to denying the weight of the finding lacks severity; it can readily be launched by simply giving high enough prior weight to the null hypothesis.

Mayo, D. 2018, Statistical Inference as Severe Testing: How to Get Beyond the Statistics Wars (Cambridge, 2018)

Categories: Announcement, Bayesian/frequentist, P-values | 3 Comments

Thieme on the theme of lowering p-value thresholds (for Slate)

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Here’s an article by Nick Thieme on the same theme as my last blogpost. Thieme, who is Slate’s 2017 AAAS Mass Media Fellow, is the first person to interview me on p-values who (a) was prepared to think through the issue for himself (or herself), and (b) included more than a tiny fragment of my side of the exchange.[i]. Please share your comments.

Will Lowering P-Value Thresholds Help Fix Science? P-values are already all over the map, and they’re also not exactly the problem.

 

 

Illustration by Slate

                 Illustration by Slate

Last week a team of 72 scientists released the preprint of an article attempting to address one aspect of the reproducibility crisis, the crisis of conscience in which scientists are increasingly skeptical about the rigor of our current methods of conducting scientific research.

Their suggestion? Change the threshold for what is considered statistically significant. The team, led by Daniel Benjamin, a behavioral economist from the University of Southern California, is advocating that the “probability value” (p-value) threshold for statistical significance be lowered from the current standard of 0.05 to a much stricter threshold of 0.005. Continue reading

Categories: P-values, reforming the reformers, spurious p values | 14 Comments

“A megateam of reproducibility-minded scientists” look to lowering the p-value

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Having discussed the “p-values overstate the evidence against the null fallacy” many times over the past few years, I leave it to readers to disinter the issues (pro and con), and appraise the assumptions, in the most recent rehearsal of the well-known Bayesian argument. There’s nothing intrinsically wrong with demanding everyone work with a lowered p-value–if you’re so inclined to embrace a single, dichotomous standard without context-dependent interpretations, especially if larger sample sizes are required to compensate the loss of power. But lowering the p-value won’t solve the problems that vex people (biasing selection effects), and is very likely to introduce new ones (see my comment). Kelly Servick, a reporter from Science, gives the ingredients of the main argument given by “a megateam of reproducibility-minded scientists” in an article out today: Continue reading

Categories: Error Statistics, highly probable vs highly probed, P-values, reforming the reformers | 55 Comments

3 YEARS AGO (JULY 2014): MEMORY LANE

3 years ago...

3 years ago…

MONTHLY MEMORY LANE: 3 years ago: July 2014. I mark in red 3-4 posts from each month that seem most apt for general background on key issues in this blog, excluding those reblogged recently[1]. Posts that are part of a “unit” or a group count as one. This month there are three such groups: 7/8 and 7/10; 7/14 and 7/23; 7/26 and 7/31.

July 2014

  • (7/7) Winner of June Palindrome Contest: Lori Wike
  • (7/8) Higgs Discovery 2 years on (1: “Is particle physics bad science?”)
  • (7/10) Higgs Discovery 2 years on (2: Higgs analysis and statistical flukes)
  • (7/14) “P-values overstate the evidence against the null”: legit or fallacious? (revised)
  • (7/23) Continued:”P-values overstate the evidence against the null”: legit or fallacious?
  • (7/26) S. Senn: “Responder despondency: myths of personalized medicine” (Guest Post)
  • (7/31) Roger Berger on Stephen Senn’s “Blood Simple” with a response by Senn (Guest Posts)

[1] Monthly memory lanes began at the blog’s 3-year anniversary in Sept, 2014.

 

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Categories: 3-year memory lane, Higgs, P-values | Leave a comment

If you’re seeing limb-sawing in P-value logic, you’re sawing off the limbs of reductio arguments

images-2I was just reading a paper by Martin and Liu (2014) in which they allude to the “questionable logic of proving H0 false by using a calculation that assumes it is true”(p. 1704).  They say they seek to define a notion of “plausibility” that

“fits the way practitioners use and interpret p-values: a small p-value means H0 is implausible, given the observed data,” but they seek “a probability calculation that does not require one to assume that H0 is true, so one avoids the questionable logic of proving H0 false by using a calculation that assumes it is true“(Martin and Liu 2014, p. 1704).

Questionable? A very standard form of argument is a reductio (ad absurdum) wherein a claim C  is inferred (i.e., detached) by falsifying ~C, that is, by showing that assuming ~C entails something in conflict with (if not logically contradicting) known results or known truths [i]. Actual falsification in science is generally a statistical variant of this argument. Supposing Hin p-value reasoning plays the role of ~C. Yet some aver it thereby “saws off its own limb”! Continue reading

Categories: P-values, reforming the reformers, Statistics | 13 Comments

Er, about those other approaches, hold off until a balanced appraisal is in

I could have told them that the degree of accordance enabling the ASA’s “6 principles” on p-values was unlikely to be replicated when it came to most of the “other approaches” with which some would supplement or replace significance tests– notably Bayesian updating, Bayes factors, or likelihood ratios (confidence intervals are dual to hypotheses tests). [My commentary is here.] So now they may be advising a “hold off” or “go slow” approach until some consilience is achieved. Is that it? I don’t know. I was tweeted an article about the background chatter taking place behind the scenes; I wasn’t one of people interviewed for this. Here are some excerpts, I may add more later after it has had time to sink in. (check back later)

“Reaching for Best Practices in Statistics: Proceed with Caution Until a Balanced Critique Is In”

J. Hossiason

“[A]ll of the other approaches*, as well as most statistical tools, may suffer from many of the same problems as the p-values do. What level of likelihood ratio in favor of the research hypothesis will be acceptable to the journal? Should scientific discoveries be based on whether posterior odds pass a specific threshold (P3)? Does either measure the size of an effect (P5)?…How can we decide about the sample size needed for a clinical trial—however analyzed—if we do not set a specific bright-line decision rule? 95% confidence intervals or credence intervals…offer no protection against selection when only those that do not cover 0, are selected into the abstract (P4). (Benjamini, ASA commentary, pp. 3-4)

What’s sauce for the goose is sauce for the gander right?  Many statisticians seconded George Cobb who urged “the board to set aside time at least once every year to consider the potential value of similar statements” to the recent ASA p-value report. Disappointingly, a preliminary survey of leaders in statistics, many from the original p-value group, aired striking disagreements on best and worst practices with respect to these other approaches. The Executive Board is contemplating a variety of recommendations, minimally, that practitioners move with caution until they can put forward at least a few agreed upon principles for interpreting and applying Bayesian inference methods. The words we heard ranged from “go slow” to “moratorium [emphasis mine]. Having been privy to some of the results of this survey, we at Stat Report Watch decided to contact some of the individuals involved. Continue reading

Categories: P-values, reforming the reformers, Statistics | 6 Comments

The ASA Document on P-Values: One Year On

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I’m surprised it’s a year already since posting my published comments on the ASA Document on P-Values. Since then, there have been a slew of papers rehearsing the well-worn fallacies of tests (a tad bit more than the usual rate). Doubtless, the P-value Pow Wow raised people’s consciousnesses. I’m interested in hearing reader reactions/experiences in connection with the P-Value project (positive and negative) over the past year. (Use the comments, share links to papers; and/or send me something slightly longer for a possible guest post.)
Some people sent me a diagram from a talk by Stephen Senn (on “P-values and the art of herding cats”). He presents an array of different cat commentators, and for some reason Mayo cat is in the middle but way over on the left side,near the wall. I never got the key to interpretation.  My contribution is below: 

Chart by S.Senn

“Don’t Throw Out The Error Control Baby With the Bad Statistics Bathwater”

D. Mayo*[1]

The American Statistical Association is to be credited with opening up a discussion into p-values; now an examination of the foundations of other key statistical concepts is needed. Continue reading

Categories: Bayesian/frequentist, P-values, science communication, Statistics, Stephen Senn | 14 Comments

Hocus pocus! Adopt a magician’s stance, if you want to reveal statistical sleights of hand

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Here’s the follow-up post to the one I reblogged on Feb 3 (please read that one first). When they sought to subject Uri Geller to the scrutiny of scientists, magicians had to be brought in because only they were sufficiently trained to spot the subtle sleight of hand shifts by which the magician tricks by misdirection. We, too, have to be magicians to discern the subtle misdirections and shifts of meaning in the discussions of statistical significance tests (and other methods)—even by the same statistical guide. We needn’t suppose anything deliberately devious is going on at all! Often, the statistical guidebook reflects shifts of meaning that grow out of one or another critical argument. These days, they trickle down quickly to statistical guidebooks, thanks to popular articles on the “statistics crisis in science”. The danger is that their own guidebooks contain inconsistencies. To adopt the magician’s stance is to be on the lookout for standard sleights of hand. There aren’t that many.[0]

I don’t know Jim Frost, but he gives statistical guidance at the minitab blog. The purpose of my previous post is to point out that Frost uses the probability of a Type I error in two incompatible ways in his posts on significance tests. I assumed he’d want to clear this up, but so far he has not. His response to a comment I made on his blog is this: Continue reading

Categories: frequentist/Bayesian, P-values, reforming the reformers, S. Senn, Statistics | 39 Comments

The “P-values overstate the evidence against the null” fallacy

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The allegation that P-values overstate the evidence against the null hypothesis continues to be taken as gospel in discussions of significance tests. All such discussions, however, assume a notion of “evidence” that’s at odds with significance tests–generally Bayesian probabilities of the sort used in Jeffrey’s-Lindley disagreement (default or “I’m selecting from an urn of nulls” variety). Szucs and Ioannidis (in a draft of a 2016 paper) claim “it can be shown formally that the definition of the p value does exaggerate the evidence against H0” (p. 15) and they reference the paper I discuss below: Berger and Sellke (1987). It’s not that a single small P-value provides good evidence of a discrepancy (even assuming the model, and no biasing selection effects); Fisher and others warned against over-interpreting an “isolated” small P-value long ago.  But the formulation of the “P-values overstate the evidence” meme introduces brand new misinterpretations into an already confused literature! The following are snippets from some earlier posts–mostly this one–and also includes some additions from my new book (forthcoming). 

Categories: Bayesian/frequentist, fallacy of rejection, highly probable vs highly probed, P-values, Statistics | 47 Comments

Szucs & Ioannidis Revive the Limb-Sawing Fallacy

 

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When logical fallacies of statistics go uncorrected, they are repeated again and again…and again. And so it is with the limb-sawing fallacy I first posted in one of my “Overheard at the Comedy Hour” posts.* It now resides as a comic criticism of significance tests in a paper by Szucs and Ioannidis (posted this week),  Here’s their version:

“[P]aradoxically, when we achieve our goal and successfully reject Hwe will actually be left in complete existential vacuum because during the rejection of HNHST ‘saws off its own limb’ (Jaynes, 2003; p. 524): If we manage to reject H0then it follows that pr(data or more extreme data|H0) is useless because H0 is not true” (p.15).

Here’s Jaynes (p. 524):

“Suppose we decide that the effect exists; that is, we reject [null hypothesis] H0. Surely, we must also reject probabilities conditional on H0, but then what was the logical justification for the decision? Orthodox logic saws off its own limb.’ 

Ha! Ha! By this reasoning, no hypothetical testing or falsification could ever occur. As soon as H is falsified, the grounds for falsifying disappear! If H: all swans are white, then if I see a black swan, H is falsified. But according to this criticism, we can no longer assume the deduced prediction from H! What? Continue reading

Categories: Error Statistics, P-values, reforming the reformers, Statistics | 14 Comments

“Tests of Statistical Significance Made Sound”: excerpts from B. Haig

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I came across a paper, “Tests of Statistical Significance Made Sound,” by Brian Haig, a psychology professor at the University of Canterbury, New Zealand. It hits most of the high notes regarding statistical significance tests, their history & philosophy and, refreshingly, is in the error statistical spirit! I’m pasting excerpts from his discussion of “The Error-Statistical Perspective”starting on p.7.[1]

The Error-Statistical Perspective

An important part of scientific research involves processes of detecting, correcting, and controlling for error, and mathematical statistics is one branch of methodology that helps scientists do this. In recognition of this fact, the philosopher of statistics and science, Deborah Mayo (e.g., Mayo, 1996), in collaboration with the econometrician, Aris Spanos (e.g., Mayo & Spanos, 2010, 2011), has systematically developed, and argued in favor of, an error-statistical philosophy for understanding experimental reasoning in science. Importantly, this philosophy permits, indeed encourages, the local use of ToSS, among other methods, to manage error. Continue reading

Categories: Bayesian/frequentist, Error Statistics, fallacy of rejection, P-values, Statistics | 12 Comments

Glymour at the PSA: “Exploratory Research is More Reliable Than Confirmatory Research”

psa-homeI resume my comments on the contributions to our symposium on Philosophy of Statistics at the Philosophy of Science Association. My earlier comment was on Gerd Gigerenzer’s talk. I move on to Clark Glymour’s “Exploratory Research Is More Reliable Than Confirmatory Research.” His complete slides are after my comments.

GLYMOUR’S ARGUMENT (in a nutshell):Glymour_2006_IMG_0965

“The anti-exploration argument has everything backwards,” says Glymour (slide #11). While John Ioannidis maintains that “Research findings are more likely true in confirmatory designs,” the opposite is so, according to Glymour. (Ioannidis 2005, Glymour’s slide #6). Why? To answer this he describes an exploratory research account for causal search that he has been developing:

exploratory-research-is-more-reliable-than-confirmatory-research-13-1024(slide #5)

What’s confirmatory research for Glymour? It’s moving directly from rejecting a null hypothesis with a low P-value to inferring a causal claim. Continue reading

Categories: fallacy of rejection, P-values, replication research | 20 Comments

Gigerenzer at the PSA: “How Fisher, Neyman-Pearson, & Bayes Were Transformed into the Null Ritual”: Comments and Queries (ii)

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Gerd Gigerenzer, Andrew Gelman, Clark Glymour and I took part in a very interesting symposium on Philosophy of Statistics at the Philosophy of Science Association last Friday. I jotted down lots of notes, but I’ll limit myself to brief reflections and queries on a small portion of each presentation in turn, starting with Gigerenzer’s “Surrogate Science: How Fisher, Neyman-Pearson, & Bayes Were Transformed into the Null Ritual.” His complete slides are below my comments. I may write this in stages, this being (i).

SLIDE #19

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  1. Good scientific practice–bold theories, double-blind experiments, minimizing measurement error, replication, etc.–became reduced in the social science to a surrogate: statistical significance.

I agree that “good scientific practice” isn’t some great big mystery, and that “bold theories, double-blind experiments, minimizing measurement error, replication, etc.” are central and interconnected keys to finding things out in error prone inquiry. Do the social sciences really teach that inquiry can be reduced to cookbook statistics? Or is it simply that, in some fields, carrying out surrogate science suffices to be a “success”? Continue reading

Categories: Fisher, frequentist/Bayesian, Gigerenzer, Gigerenzer, P-values, spurious p values, Statistics | 11 Comments

For Statistical Transparency: Reveal Multiplicity and/or Just Falsify the Test (Remark on Gelman and Colleagues)

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Gelman and Loken (2014) recognize that even without explicit cherry picking there is often enough leeway in the “forking paths” between data and inference so that by artful choices you may be led to one inference, even though it also could have gone another way. In good sciences, measurement procedures should interlink with well-corroborated theories and offer a triangulation of checks– often missing in the types of experiments Gelman and Loken are on about. Stating a hypothesis in advance, far from protecting from the verification biases, can be the engine that enables data to be “constructed”to reach the desired end [1].

[E]ven in settings where a single analysis has been carried out on the given data, the issue of multiple comparisons emerges because different choices about combining variables, inclusion and exclusion of cases…..and many other steps in the analysis could well have occurred with different data (Gelman and Loken 2014, p. 464).

An idea growing out of this recognition is to imagine the results of applying the same statistical procedure, but with different choices at key discretionary junctures–giving rise to a multiverse analysis, rather than a single data set (Steegen, Tuerlinckx, Gelman, and Vanpaemel 2016). One lists the different choices thought to be plausible at each stage of data processing. The multiverse displays “which constellation of choices corresponds to which statistical results” (p. 797). The result of this exercise can, at times, mimic the delineation of possibilities in multiple testing and multiple modeling strategies. Continue reading

Categories: Bayesian/frequentist, Error Statistics, Gelman, P-values, preregistration, reproducibility, Statistics | 9 Comments

If you think it’s a scandal to be without statistical falsification, you will need statistical tests (ii)

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1. PhilSci and StatSci. I’m always glad to come across statistical practitioners who wax philosophical, particularly when Karl Popper is cited. Best of all is when they get the philosophy somewhere close to correct. So, I came across an article by Burnham and Anderson (2014) in Ecology:

While the exact definition of the so-called ‘scientific method’ might be controversial, nearly everyone agrees that the concept of ‘falsifiability’ is a central tenant [sic] of empirical science (Popper 1959). It is critical to understand that historical statistical approaches (i.e., P values) leave no way to ‘test’ the alternative hypothesis. The alternative hypothesis is never tested, hence cannot be rejected or falsified!… Surely this fact alone makes the use of significance tests and P values bogus. Lacking a valid methodology to reject/falsify the alternative science hypotheses seems almost a scandal.” (Burnham and Anderson p. 629)

Well I am (almost) scandalized by this easily falsifiable allegation! I can’t think of a single “alternative”, whether in a “pure” Fisherian or a Neyman-Pearson hypothesis test (whether explicit or implicit) that’s not falsifiable; nor do the authors provide any. I grant that understanding testability and falsifiability is far more complex than the kind of popularized accounts we hear about; granted as well, theirs is just a short paper.[1] But then why make bold declarations on the topic of the “scientific method and statistical science,” on falsifiability and testability? Continue reading

Categories: P-values, Severity, statistical tests, Statistics, StatSci meets PhilSci | 22 Comments

Mayo & Parker “Using PhilStat to Make Progress in the Replication Crisis in Psych” SPSP Slides

Screen Shot 2016-06-19 at 12.53.32 PMHere are the slides from our talk at the Society for Philosophy of Science in Practice (SPSP) conference. I covered the first 27, Parker the rest. The abstract is here:

Categories: P-values, reforming the reformers, replication research, Statistics, StatSci meets PhilSci | Leave a comment

“So you banned p-values, how’s that working out for you?” D. Lakens exposes the consequences of a puzzling “ban” on statistical inference

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I came across an excellent post on a blog kept by Daniel Lakens: “So you banned p-values, how’s that working out for you?” He refers to the journal that recently banned significance tests, confidence intervals, and a vague assortment of other statistical methods, on the grounds that all such statistical inference tools are “invalid” since they don’t provide posterior probabilities of some sort (see my post). The editors’ charge of “invalidity” could only hold water if these error statistical methods purport to provide posteriors based on priors, which is false. The entire methodology is based on methods in which probabilities arise to qualify the method’s capabilities to detect and avoid erroneous interpretations of data [0]. The logic is of the falsification variety found throughout science. Lakens, an experimental psychologist, does a great job delineating some of the untoward consequences of their inferential ban. I insert some remarks in black. Continue reading

Categories: frequentist/Bayesian, Honorary Mention, P-values, reforming the reformers, science communication, Statistics | 45 Comments

My Slides: “The Statistical Replication Crisis: Paradoxes and Scapegoats”

Below are the slides from my Popper talk at the LSE today (up to slide 70): (post any questions in the comments)

 

Categories: P-values, replication research, reproducibility, Statistics | 11 Comments

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