The most surprising discovery about today’s statistics wars is that some who set out shingles as “statistical reformers” themselves are guilty of misdefining some of the basic concepts of error statistical tests—notably power. (See my recent post on power howlers.) A major purpose of my Statistical Inference as Severe Testing: How to Get Beyond the Statistics Wars (2018, CUP) is to clarify basic notions to get beyond what I call “chestnuts” and “howlers” of tests. The only way that disputing tribes can get beyond the statistics wars is by (at least) understanding correctly the central concepts. But these misunderstandings are more common than ever, so I’m asking readers to help. Why are they more common (than before the “new reformers” of the last decade)? I suspect that at least one reason is the popularity of Bayesian variants on tests: if one is looking to find posterior probabilities of hypotheses, then error statistical ingredients may tend to look as if that’s what they supply. Continue reading
Monthly Archives: April 2022
Join me in reforming the “reformers” of statistical significance tests
Happy Birthday Neyman: What was Neyman opposing when he opposed the ‘Inferential’ Probabilists? Your weekend Phil Stat reading
Today is Jerzy Neyman’s birthday (April 16, 1894 – August 5, 1981). I’m reposting a link to a quirky, but fascinating, paper of his that explains one of the most misunderstood of his positions–what he was opposed to in opposing the “inferential theory”. The paper, fro 60 years ago,Neyman, J. (1962), ‘Two Breakthroughs in the Theory of Statistical Decision Making‘ [i] It’s chock full of ideas and arguments. “In the present paper” he tells us, “the term ‘inferential theory’…will be used to describe the attempts to solve the Bayes’ problem with a reference to confidence, beliefs, etc., through some supplementation …either a substitute a priori distribution [exemplified by the so called principle of insufficient reason] or a new measure of uncertainty” such as Fisher’s fiducial probability. It arises on p. 391 of Excursion 5 Tour III of Statistical Inference as Severe Testing: How to Get Beyond the Statistics Wars (2018, CUP). Here’s a link to the proofs of that entire tour. If you hear Neyman rejecting “inferential accounts,” you have to understand it in this very specific way: he’s rejecting “new measures of confidence or diffidence”. Here he alludes to them as “easy ways out”. He is not rejecting statistical inference in favor of behavioral performance as is typically thought. It’s amazing how an idiosyncratic use of a word 60 years ago can cause major rumblings decades later. Neyman always distinguished his error statistical performance conception from Bayesian and Fiducial probabilisms [ii]. The surprising twist here is semantical and the culprit is none other than…Allan Birnbaum. Yet Birnbaum gets short shrift, and no mention is made of our favorite “breakthrough” (or did I miss it?). You can find quite a lot on this blog searching Birnbaum. Continue reading
Power howlers return as criticisms of severity
Suppose you are reading about a statistically significant result x that just reaches a threshold p-value α from a test T+ of the mean of a Normal distribution
H0: µ ≤ 0 against H1: µ > 0
with n iid samples, and (for simplicity) known σ. The test “rejects” H0 at this level & infers evidence of a discrepancy in the direction of H1.
I have heard some people say:
A. If the test’s power to detect alternative µ’ is very low, then the just statistically significant x is poor evidence of a discrepancy (from the null) corresponding to µ’. (i.e., there’s poor evidence that µ > µ’ ). See point* on language in notes.
They will generally also hold that if POW(µ’) is reasonably high (at least .5), then the inference to µ > µ’ is warranted, or at least not problematic.
I have heard other people say:
B. If the test’s power to detect alternative µ’ is very low, then the just statistically significant x is good evidence of a discrepancy (from the null) corresponding to µ’ (i.e., there’s good evidence that µ > µ’).
They will generally also hold that if POW(µ’) is reasonably high (at least .5), then the inference to µ > µ’ is unwarranted.
Which is correct, from the perspective of the frequentist error statistical philosophy? Continue reading
Insevere Tests of Severe Testing (iv)
One does not have evidence for a claim if little if anything has been done to rule out ways the claim may be false. The claim may be said to “pass” the test, but it’s one that utterly lacks stringency or severity. On the basis of this very simple principle, I build a notion of evidence that applies to any error prone inference. In this account, data x are evidence for a claim C only if (and only to the extent that) C has passed a severe test with x. How to apply this simple idea, however, and how to use it to solve central problems of induction and statistical inference requires careful consideration of how it is to be fleshed out. (See this post on strong vs weak severity.) Continue reading
No fooling: The Statistics Wars and Their Casualties Workshop is Postponed to 22-23 September, 2022
The Statistics Wars
and Their Casualties
22-23 September 2022
London School of Economics (CPNSS)
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), Stephen Guttinger (University of Exeter), David Hand (Imperial College London), Margherita Harris (London School of Economics and Political Science), Christian Hennig (University of Bologna), Katrin Hohl *(City University London),
Daniël Lakens (Eindhoven University of Technology), Deborah Mayo (Virginia Tech), Richard Morey (Cardiff University), Stephen Senn (Edinburgh, Scotland), Jon Williamson (University of Kent) Continue reading