Statistics

History of statistics sleuths out there? “Ideas came into my head as I sat on a gate overlooking an experimental blackcurrant plot”–No wait, it was apples, probably

E.S.Pearson on Gate

E.S.Pearson on a Gate, Mayo sketch

Here you see my scruffy sketch of Egon drawn 20 years ago for the frontispiece of my book, “Error and the Growth of Experimental Knowledge” (EGEK 1996). The caption is

“I might recall how certain early ideas came into my head as I sat on a gate overlooking an experimental blackcurrant plot… –E.S Pearson, “Statistical Concepts in Their Relation to Reality”.

He is responding to Fisher to “dispel the picture of the Russian technological bogey”. [i]

So, as I said in my last post, just to make a short story long, I’ve recently been scouring around the history and statistical philosophies of Neyman, Pearson and Fisher for purposes of a book soon to be completed, and I discovered a funny little error about this quote. Only maybe 3 or 4 people alive would care, but maybe someone out there knows the real truth.

OK, so I’d been rereading Constance Reid’s great biography of Neyman, and in one place she interviews Egon about the sources of inspiration for their work. Here’s what Egon tells her:

One day at the beginning of April 1926, down ‘in the middle of small samples,’ wandering among apple plots at East Malling, where a cousin was director of the fruit station, he was ‘suddenly smitten,’ as he later expressed it,with a ‘doubt’ about the justification for using Student’s ratio (the t-statistic) to test a normal mean (Quotes are from Pearson in Reid, p. 60).

Soon after, Egon contacted Neyman and their joint work began.

I assumed the meanderings over apple plots was a different time, and that Egon just had a habit of conducting his deepest statistical thinking while overlooking fruit. Yet it shared certain unique features with the revelation when gazing over at the blackcurrant plot, as in my picture, if only in the date and the great importance he accorded it (although I never recall his saying he was “smitten” before). I didn’t think more about it. Then, late one night last week I grabbed a peculiar book off my shelf that contains a smattering of writings by Pearson for a work he never completed: “Student: A Statistical Biography of William Sealy Gosset” (1990, edited and augmented by Plackett and Barnard, Clarendon, Oxford). The very first thing I open up to is a note by Egon Pearson:

I cannot recall now what was the form of the doubt which struck me at East Malling, but it would naturally have arisen when discussing there the interpretation of results derived from small experimental plots. I seem to visualize myself sitting alone on a gate thinking over the basis of ‘small sample’ theory and ‘mathematical statistics Mark II’ [i.e., Fisher]. When nearly thirty years later (JRSS B, 17, 204 1955), I wrote refuting the suggestion of R.A.F. [Fisher] that the Neyman-Pearson approach to testing statistical hypotheses had arisen in industrial acceptance procedures, the plot which the gate was overlooking had through the passage of time become a blackcurrant one! (Pearson 1990 p. 81)

What? This is weird. So that must mean it wasn’t blackcurrants after all, and Egon is mistaken in the caption under the picture I drew 20 years ago. Yet, he doesn’t say here that it was apples either, only that it had “become a blackcurrant” plot in a later retelling. So, not blackcurrant, so, it must have been apple, putting this clue together with what he told Constance Reid. So it appears I can no longer quote that “blackcurrant” statement, at least not without explaining that, in all likelihood, it was really apples. If any statistical sleuths out there can corroborate that it was apples, or knows the correct fruit that Egon was gazing at (and, come to think of it, why couldn’t it have been both?) I’d be very grateful to know [ii]. I will happily cite you. I know this is a bit of minutia–don’t say I didn’t warn you [iii]. By contrast, the Pearson paper replying to Fisher is extremely important (and very short). It’s entitled “Statistical Concepts in Their Relation to Reality”. You can read the paper HERE.

 

[i] Some of the previous lines, and 6 following words:

There was no question of a difference in point of view having ‘originated’ when Neyman ‘re-interpreted’ Fisher’s early work on tests of significance ‘in terms of that technological and commercial apparatus which is known as an acceptance procedure’. …
Indeed, to dispel the picture of the Russian technological bogey, I might recall how certain early ideas came into my head as I sat on a gate overlooking an experimental blackcurrant plot at the East Malling Research Station!E.S Pearson, “Statistical Concepts in Their Relation to Reality” 

[ii] As Erich Lehmann put it in his EGEK review, Pearson is “the hero of Mayo’s story” because I found in his work, if only in brief discussions, hints, and examples, the key elements for an “inferential” or “evidential” interpretation of Neyman. So I should get the inspirational fruit correct.

[iii] I’m not saying I know the answer isn’t in the book on Student, or someplace else.

Fisher 1955 “Scientific Methods and Scientific Induction” .

Pearson E.S., 1955 “Statistical Methods in Their Relation to Reality”.

Reid, C. 1998, Neyman–From Life. Springer.

Categories: E.S. Pearson, phil/history of stat, Statistics | 1 Comment

Performance or Probativeness? E.S. Pearson’s Statistical Philosophy

egon pearson

E.S. Pearson (11 Aug, 1895-12 June, 1980)

This is a belated birthday post for E.S. Pearson (11 August 1895-12 June, 1980). It’s basically a post from 2012 which concerns an issue of interpretation (long-run performance vs probativeness) that’s badly confused these days. I’ve recently been scouring around the history and statistical philosophies of Neyman, Pearson and Fisher for purposes of a book soon to be completed. I recently discovered a little anecdote that calls for a correction in something I’ve been saying for years. While it’s little more than a point of trivia, it’s in relation to Pearson’s (1955) response to Fisher (1955)–the last entry in this post.  I’ll wait until tomorrow or the next day to share it, to give you a chance to read the background. 

 

Are methods based on error probabilities of use mainly to supply procedures which will not err too frequently in some long run? (performance). Or is it the other way round: that the control of long run error properties are of crucial importance for probing the causes of the data at hand? (probativeness). I say no to the former and yes to the latter. This, I think, was also the view of Egon Sharpe (E.S.) Pearson. 

Cases of Type A and Type B

“How far then, can one go in giving precision to a philosophy of statistical inference?” (Pearson 1947, 172)

Continue reading

Categories: 4 years ago!, highly probable vs highly probed, phil/history of stat, Statistics | Tags: | Leave a comment

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 | 20 Comments

S. Senn: “Painful dichotomies” (Guest Post)

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Stephen Senn
Head of  Competence Center for Methodology and Statistics (CCMS)
Luxembourg Institute of Health
Twitter @stephensenn

Painful dichotomies

The tweet read “Featured review: Only 10% people with tension-type headaches get a benefit from paracetamol” and immediately I thought, ‘how would they know?’ and almost as quickly decided, ‘of course they don’t know, they just think they know’. Sure enough, on following up the link to the Cochrane Review in the tweet it turned out that, yet again, the deadly mix of dichotomies and numbers needed to treat had infected the brains of researchers to the extent that they imagined that they had identified personal response. (See Responder Despondency for a previous post on this subject.)

The bare facts they established are the following:

The International Headache Society recommends the outcome of being pain free two hours after taking a medicine. The outcome of being pain free or having only mild pain at two hours was reported by 59 in 100 people taking paracetamol 1000 mg, and in 49 out of 100 people taking placebo.

and the false conclusion they immediately asserted is the following

This means that only 10 in 100 or 10% of people benefited because of paracetamol 1000 mg.

To understand the fallacy, look at the accompanying graph. Continue reading

Categories: junk science, PhilStat/Med, Statistics, Stephen Senn | 27 Comments

3 YEARS AGO (JULY 2013): MEMORY LANE

3 years ago...

3 years ago…

MONTHLY MEMORY LANE: 3 years ago: July 2013. I mark in red three posts that seem most apt for general background on key issues in this blog, excluding those reblogged recently [1], and in green up to 3 others I’d recommend[2].  Posts that are part of a “unit” or a group of “U-Phils”(you [readers] philosophize) count as one.

July 2013

  • (7/3) Phil/Stat/Law: 50 Shades of gray between error and fraud
  • (7/6) Bad news bears: ‘Bayesian bear’ rejoinder–reblog mashup
  • (7/10) PhilStatLaw: Reference Manual on Scientific Evidence (3d ed) on Statistical Significance (Schachtman)
  • (7/11) Is Particle Physics Bad Science? (memory lane)
  • (7/13) Professor of Philosophy Resigns over Sexual Misconduct (rejected post)
  • (7/14) Stephen Senn: Indefinite irrelevance
  • (7/17) Phil/Stat/Law: What Bayesian prior should a jury have? (Schachtman)
  • (7/19) Msc Kvetch: A question on the Martin-Zimmerman case we do not hear
  • (7/20) Guest Post: Larry Laudan. Why Presuming Innocence is Not a Bayesian Prior
  • (7/23) Background Knowledge: Not to Quantify, But To Avoid Being Misled By, Subjective Beliefs
  • (7/26) New Version: On the Birnbaum argument for the SLP: Slides for JSM talk

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

[2] New Rule, July 30, 2016.

 

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Categories: 3-year memory lane, Error Statistics, Statistics | Leave a comment

“Nonsignificance Plus High Power Does Not Imply Support for the Null Over the Alternative.”

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Seeing the world through overly rosy glasses

Taboos about power nearly always stem from misuse of power analysis. Sander Greenland (2012) has a paper called “Nonsignificance Plus High Power Does Not Imply Support for the Null Over the Alternative.”  I’m not saying Greenland errs; the error would be made by anyone who interprets power analysis in a manner giving rise to Greenland’s objection. So what’s (ordinary) power analysis?

(I) Listen to Jacob Cohen (1988) introduce Power Analysis

“PROVING THE NULL HYPOTHESIS. Research reports in the literature are frequently flawed by conclusions that state or imply that the null hypothesis is true. For example, following the finding that the difference between two sample means is not statistically significant, instead of properly concluding from this failure to reject the null hypothesis that the data do not warrant the conclusion that the population means differ, the writer concludes, at least implicitly, that there is no difference. The latter conclusion is always strictly invalid, and is functionally invalid as well unless power is high. The high frequency of occurrence of this invalid interpretation can be laid squarely at the doorstep of the general neglect of attention to statistical power in the training of behavioral scientists. Continue reading

Categories: Cohen, Greenland, power, Statistics | 46 Comments

3 YEARS AGO (JUNE 2013): MEMORY LANE

3 years ago...

3 years ago…

MONTHLY MEMORY LANE: 3 years ago: June 2013. I mark in red three posts 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 of “U-Phils”(you [readers] philosophize) count as one. Here I grouped 6/5 and 6/6.

June 2013

  • (6/1) Winner of May Palindrome Contest
  • (6/1) Some statistical dirty laundry*(recently reblogged)
  • (6/5) Do CIs Avoid Fallacies of Tests? Reforming the Reformers :(6/5 and6/6 are paired as one)
  • (6/6) PhilStock: Topsy-Turvy Game
  • (6/6) Anything Tests Can do, CIs do Better; CIs Do Anything Better than Tests?* (reforming the reformers cont.)
  • (6/8) Richard Gill: “Integrity or fraud… or just questionable research practices?*(recently reblogged)
  • (6/11) Mayo: comment on the repressed memory research [How a conceptual criticism, requiring no statistics, might go.]
  • (6/14) P-values can’t be trusted except when used to argue that p-values can’t be trusted!
  • (6/19) PhilStock: The Great Taper Caper
  • (6/19) Stanley Young: better p-values through randomization in microarrays
  • (6/22) What do these share in common: m&ms, limbo stick, ovulation, Dale Carnegie? Sat night potpourri*(recently reblogged)
  • (6/26) Why I am not a “dualist” in the sense of Sander Greenland
  • (6/29) Palindrome “contest” contest
  • (6/30) Blog Contents: mid-year

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

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Categories: 3-year memory lane, Error Statistics, Statistics | Leave a comment

A. Birnbaum: Statistical Methods in Scientific Inference (May 27, 1923 – July 1, 1976)

Allan Birnbaum: May 27, 1923- July 1, 1976

Allan Birnbaum died 40 years ago today. He lived to be only 53 [i]. From the perspective of philosophy of statistics and philosophy of science, Birnbaum is best known for his work on likelihood, the Likelihood Principle [ii], and for his attempts to blend concepts of likelihood with error probability ideas to arrive at what he termed “concepts of statistical evidence”. Failing to find adequate concepts of statistical evidence, Birnbaum called for joining the work of “interested statisticians, scientific workers and philosophers and historians of science”–an idea I have heartily endorsed. While known for a result that the (strong) Likelihood Principle followed from sufficiency and conditionality principles (a result that Jimmy Savage deemed one of the greatest breakthroughs in statistics), a few years after publishing it, he turned away from it, perhaps discovering gaps in his argument. A post linking to a 2014 Statistical Science issue discussing Birnbaum’s result is here. Reference [5] links to the Synthese 1977 volume dedicated to his memory. The editors describe it as their way of “paying homage to Professor Birnbaum’s penetrating and stimulating work on the foundations of statistics”. Ample weekend reading! Continue reading

Categories: Birnbaum, Likelihood Principle, phil/history of stat, Statistics | Tags: | 62 Comments

Richard Gill: “Integrity or fraud… or just questionable research practices?” (Is Gill too easy on them?)

Professor Gill

Professor Gill

Professor Richard Gill
Statistics Group
Mathematical Institute
Leiden University

It was statistician Richard Gill who first told me about Diederik Stapel (see an earlier post on Diederik). We were at a workshop on Error in the Sciences at Leiden in 2011. I was very lucky to have Gill be assigned as my commentator/presenter—he was excellent! As I was explaining some data problems to him, he suddenly said, “Some people don’t bother to collect data at all!” That’s when I learned about Stapel.

Committees often turn to Gill when someone’s work is up for scrutiny of bad statistics or fraud, or anything in between. Do you think he’s being too easy on researchers when he says, about a given case:

“data has been obtained by some combination of the usual ‘questionable research practices’ [QRPs] which are prevalent in the field in question. Everyone does it this way, in fact, if you don’t, you’d never get anything published. …People are not deliberately cheating: they honestly believe in their theories and believe the data is supporting them.”

Isn’t that the danger in relying on deeply felt background beliefs?  Have our attitudes changed (toward QRPs) over the past 3 years (harsher or less harsh)? Here’s a talk of his I blogged 3 years ago (followed by a letter he allowed me to post). I reflect on the pseudoscientific nature of the ‘recovered memories’ program in one of the Geraerts et al. papers in a later post. Continue reading

Categories: 3-year memory lane, junk science, Statistical fraudbusting, Statistics | 4 Comments

What do these share in common: m&ms, limbo stick, ovulation, Dale Carnegie? Are we lowering the bar?

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For entertainment only

In a post 3 years ago (“What do these share in common: m&m’s, limbo stick, ovulation, Dale Carnegie? Sat night potpourri”), I expressed doubts about expending serious effort to debunk the statistical credentials of studies that most readers without any statistical training would regard as “for entertainment only,” dubious, or pseudoscientific quackery. It needn’t even be that the claim is implausible, what’s implausible is that it has been well probed in the experiment at hand. Given the attention being paid to such examples by some leading statisticians, and scores of replication researchers over the past 3 years–attention that has been mostly worthwhile–maybe the bar has been lowered. What do you think? Anyway, this is what I blogged 3 years ago. (Oh, I decided to put in a home-made cartoon!) Continue reading

Categories: junk science, replication research, Statistics | 2 Comments

Some statistical dirty laundry: have the stains become permanent?

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Right after our session at the SPSP meeting last Friday, I chaired a symposium on replication that included Brian Earp–an active player in replication research in psychology (Replication and Evidence: A tenuous relationship p. 80). One of the first things he said, according to my notes, is that gambits such as cherry picking, p-hacking, hunting for significance, selective reporting, and other QRPs, had been taught as acceptable become standard practice in psychology, without any special need to adjust p-values or alert the reader to their spuriousness [i]. (He will correct me if I’m wrong[2].) It shocked me to hear it, even though it shouldn’t have, given what I’ve learned about statistical practice in social science. It was the Report on Stapel that really pulled back the curtain on this attitude toward QRPs in social psychology–as discussed in this blogpost 3 years ago. (If you haven’t read Section 5 of the report on flawed science, you should.) Many of us assumed that QRPs, even if still committed, were at least recognized to be bad statistical practices since the time of Morrison and Henkel’s (1970) Significance Test Controversy. A question now is this: have all the confessions of dirty laundry, the fraudbusting of prominent researchers, the pledges to straighten up and fly right, the years of replication research, done anything to remove the stains? I leave the question open for now. Here’s my “statistical dirty laundry” post from 2013: Continue reading

Categories: junk science, reproducibility, spurious p values, Statistics | 4 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

“A sense of security regarding the future of statistical science…” Anon review of Error and Inference

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Aris Spanos, my colleague (in economics) and co-author, came across this anonymous review of our Error and Inference (2010) [E & I]. Interestingly, the reviewer remarks that “The book gives a sense of security regarding the future of statistical science and its importance in many walks of life.” We’re not sure what the reviewer means–but it’s appreciated regardless. This post was from yesterday’s 3-year memory lane and was first posted here.

2010 American Statistical Association and the American Society for Quality

TECHNOMETRICS, AUGUST 2010, VOL. 52, NO. 3, Book Reviews, 52:3, pp. 362-370.

Error and Inference: Recent Exchanges on Experimental Reasoning, Reliability, and the Objectivity and Rationality of Science, edited by Deborah G. MAYO and Aris SPANOS, New York: Cambridge University Press, 2010, ISBN 978-0-521-88008-4, xvii+419 pp., $60.00.

This edited volume contemplates the interests of both scientists and philosophers regarding gathering reliable information about the problem/question at hand in the presence of error, uncertainty, and with limited data information.

The volume makes a significant contribution in bridging the gap between scientific practice and the philosophy of science. The main contribution of this volume pertains to issues of error and inference, and showcases intriguing discussions on statistical testing and providing alternative strategy to Bayesian inference. In words, it provides cumulative information towards the philosophical and methodological issues of scientific inquiry at large.

The target audience of this volume is quite general and open to a broad readership. With some reasonable knowledge of probability theory and statistical science, one can get the maximum benefit from most of the chapters of the volume. The volume contains original and fascinating articles by eminent scholars (nine, including the editors) who range from names in statistical science to philosophy, including D. R. Cox, a name well known to statisticians. Continue reading

Categories: 3-year memory lane, Review of Error and Inference, Statistics | 3 Comments

3 YEARS AGO (MAY 2013): MEMORY LANE

3 years ago...

3 years ago…

MONTHLY MEMORY LANE: 3 years ago: May 2013. I mark in red three posts that seem most apt for general background on key issues in this blog [1].  Some of the May 2013 posts blog the conference we held earlier that month: “Ontology and Methodology”.  I highlight in burgundy a post on Birnbaum that follows up on my last post in honor of his birthday. New questions or comments can be placed on this post.

May 2013

  • (5/3) Schedule for Ontology & Methodology, 2013
  • (5/6) Professorships in Scandal?
  • (5/9) If it’s called the “The High Quality Research Act,” then ….
  • (5/13) ‘No-Shame’ Psychics Keep Their Predictions Vague: New Rejected post
  • (5/14) “A sense of security regarding the future of statistical science…” Anon review of Error and Inference
  • (5/18) Gandenberger on Ontology and Methodology (May 4) Conference: Virginia Tech
  • (5/19) Mayo: Meanderings on the Onto-Methodology Conference
  • (5/22) Mayo’s slides from the Onto-Meth conference
  • (5/24) Gelman sides w/ Neyman over Fisher in relation to a famous blow-up
  • (5/26) Schachtman: High, Higher, Highest Quality Research Act
  • (5/27) A.Birnbaum: Statistical Methods in Scientific Inference
  • (5/29) K. Staley: review of Error & Inference

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

Categories: 3-year memory lane, Statistics | Leave a comment

Allan Birnbaum: Foundations of Probability and Statistics (27 May 1923 – 1 July 1976)

27 May 1923-1 July 1976

27 May 1923-1 July 1976

Today is Allan Birnbaum’s birthday. In honor of his birthday this year, I’m posting the articles in the Synthese volume that was dedicated to his memory in 1977. The editors describe it as their way of  “paying homage to Professor Birnbaum’s penetrating and stimulating work on the foundations of statistics”. I paste a few snippets from the articles by Giere and Birnbaum. If you’re interested in statistical foundations, and are unfamiliar with Birnbaum, here’s a chance to catch up.(Even if you are,you may be unaware of some of these key papers.)

HAPPY BIRTHDAY ALLAN!

Synthese Volume 36, No. 1 Sept 1977: Foundations of Probability and Statistics, Part I

Editorial Introduction:

This special issue of Synthese on the foundations of probability and statistics is dedicated to the memory of Professor Allan Birnbaum. Professor Birnbaum’s essay ‘The Neyman-Pearson Theory as Decision Theory; and as Inference Theory; with a Criticism of the Lindley-Savage Argument for Bayesian Theory’ was received by the editors of Synthese in October, 1975, and a decision was made to publish a special symposium consisting of this paper together with several invited comments and related papers. The sad news about Professor Birnbaum’s death reached us in the summer of 1976, but the editorial project could nevertheless be completed according to the original plan. By publishing this special issue we wish to pay homage to Professor Birnbaum’s penetrating and stimulating work on the foundations of statistics. We are grateful to Professor Ronald Giere who wrote an introductory essay on Professor Birnbaum’s concept of statistical evidence and who compiled a list of Professor Birnbaum’s publications.

THE EDITORS

Continue reading

Categories: Birnbaum, Error Statistics, Likelihood Principle, Statistics, strong likelihood principle | 7 Comments

Frequentstein: What’s wrong with (1 – β)/α as a measure of evidence against the null? (ii)

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In their “Comment: A Simple Alternative to p-values,” (on the ASA P-value document), Benjamin and Berger (2016) recommend researchers report a pre-data Rejection Ratio:

It is the probability of rejection when the alternative hypothesis is true, divided by the probability of rejection when the null hypothesis is true, i.e., the ratio of the power of the experiment to the Type I error of the experiment. The rejection ratio has a straightforward interpretation as quantifying the strength of evidence about the alternative hypothesis relative to the null hypothesis conveyed by the experimental result being statistically significant. (Benjamin and Berger 2016, p. 1)

The recommendation is much more fully fleshed out in a 2016 paper by Bayarri, Benjamin, Berger, and Sellke (BBBS 2016): Rejection Odds and Rejection Ratios: A Proposal for Statistical Practice in Testing Hypotheses. Their recommendation is:

…that researchers should report the ‘pre-experimental rejection ratio’ when presenting their experimental design and researchers should report the ‘post-experimental rejection ratio’ (or Bayes factor) when presenting their experimental results. (BBBS 2016, p. 3)….

The (pre-experimental) ‘rejection ratio’ Rpre , the ratio of statistical power to significance threshold (i.e., the ratio of the probability of rejecting under H1 and H0 respectively), is shown to capture the strength of evidence in the experiment for Hover H0. (ibid., p. 2)

But in fact it does no such thing! [See my post from the FUSION conference here.] J. Berger, and his co-authors, will tell you the rejection ratio (and a variety of other measures created over the years) are entirely frequentist because they are created out of frequentist error statistical measures. But a creation built on frequentist measures doesn’t mean the resulting animal captures frequentist error statistical reasoning. It might be a kind of Frequentstein monster! [1] Continue reading

Categories: J. Berger, power, reforming the reformers, S. Senn, Statistical power, Statistics | 36 Comments

Fallacies of Rejection, Nouvelle Cuisine, and assorted New Monsters

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Jackie Mason

Whenever I’m in London, my criminologist friend Katrin H. and I go in search of stand-up comedy. Since it’s Saturday night (and I’m in London), we’re setting out in search of a good comedy club (I’ll complete this post upon return). A few years ago we heard Jackie Mason do his shtick, a one-man show billed as his swan song to England.  It was like a repertoire of his “Greatest Hits” without a new or updated joke in the mix.  Still, hearing his rants for the nth time was often quite hilarious. It turns out that he has already been back doing another “final shtick tour” in England, but not tonight.

A sample: If you want to eat nothing, eat nouvelle cuisine. Do you know what it means? No food. The smaller the portion the more impressed people are, so long as the food’s got a fancy French name, haute cuisine. An empty plate with sauce!

As one critic wrote, Mason’s jokes “offer a window to a different era,” one whose caricatures and biases one can only hope we’ve moved beyond:

But it’s one thing for Jackie Mason to scowl at a seat in the front row and yell to the shocked audience member in his imagination, “These are jokes! They are just jokes!” and another to reprise statistical howlers, which are not jokes, to me. This blog found its reason for being partly as a place to expose, understand, and avoid them. I had earlier used this Jackie Mason opening to launch into a well-known fallacy of rejection using statistical significance tests. I’m going to go further this time around. I began by needling some leading philosophers of statistics: Continue reading

Categories: reforming the reformers, science-wise screening, Statistical power, statistical tests, Statistics | Tags: , , , , | 5 Comments

Excerpts from S. Senn’s Letter on “Replication, p-values and Evidence”

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I first blogged this letter here. Below the references are some more recent blog links of relevance to this issue. 

 Dear Reader:  I am typing in some excerpts from a letter Stephen Senn shared with me in relation to my April 28, 2012 blogpost.  It is a letter to the editor of Statistics in Medicine  in response to S. Goodman. It contains several important points that get to the issues we’ve been discussing. You can read the full letter here. Sincerely, D. G. Mayo

 STATISTICS IN MEDICINE, LETTER TO THE EDITOR

From: Stephen Senn*

Some years ago, in the pages of this journal, Goodman gave an interesting analysis of ‘replication probabilities’ of p-values. Specifically, he considered the possibility that a given experiment had produced a p-value that indicated ‘significance’ or near significance (he considered the range p=0.10 to 0.001) and then calculated the probability that a study with equal power would produce a significant result at the conventional level of significance of 0.05. He showed, for example, that given an uninformative prior, and (subsequently) a resulting p-value that was exactly 0.05 from the first experiment, the probability of significance in the second experiment was 50 per cent. A more general form of this result is as follows. If the first trial yields p=α then the probability that a second trial will be significant at significance level α (and in the same direction as the first trial) is 0.5. Continue reading

Categories: 4 years ago!, reproducibility, S. Senn, Statistics | Tags: , , , | 3 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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