Statistics

Gelman at the PSA: “Confirmationist and Falsificationist Paradigms in Statistical Practice”: Comments & Queries

screen-shot-2016-10-26-at-10-23-07-pmTo resume sharing some notes I scribbled down on the contributions to our Philosophy of Science Association symposium on Philosophy of Statistics (Nov. 4, 2016), I’m up to Gelman. Comments on Gigerenzer and Glymour are here and here. Gelman didn’t use slides but gave a very thoughtful, extemporaneous presentation on his conception of “falsificationist Bayesianism”, its relation to current foundational issues, as well as to error statistical testing. My comments follow his abstract.

Confirmationist and Falsificationist Paradigms in Statistical Practice

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Andrew Gelman

There is a divide in statistics between classical frequentist and Bayesian methods. Classical hypothesis testing is generally taken to follow a falsificationist, Popperian philosophy in which research hypotheses are put to the test and rejected when data do not accord with predictions. Bayesian inference is generally taken to follow a confirmationist philosophy in which data are used to update the probabilities of different hypotheses. We disagree with this conventional Bayesian-frequentist contrast: We argue that classical null hypothesis significance testing is actually used in a confirmationist sense and in fact does not do what it purports to do; and we argue that Bayesian inference cannot in general supply reasonable probabilities of models being true. The standard research paradigm in social psychology (and elsewhere) seems to be that the researcher has a favorite hypothesis A. But, rather than trying to set up hypothesis A for falsification, the researcher picks a null hypothesis B to falsify, which is then taken as evidence in favor of A. Research projects are framed as quests for confirmation of a theory, and once confirmation is achieved, there is a tendency to declare victory and not think too hard about issues of reliability and validity of measurements.

Instead, we recommend a falsificationist Bayesian approach in which models are altered and rejected based on data. The conventional Bayesian confirmation view blinds many Bayesians to the benefits of predictive model checking. The view is that any Bayesian model necessarily represents a subjective prior distribution and as such could never be tested. It is not only Bayesians who avoid model checking. Quantitative researchers in political science, economics, and sociology regularly fit elaborate models without even the thought of checking their fit. We can perform a Bayesian test by first assuming the model is true, then obtaining the posterior distribution, and then determining the distribution of the test statistic under hypothetical replicated data under the fitted model. A posterior distribution is not the final end, but is part of the derived prediction for testing. In practice, we implement this sort of check via simulation.

Posterior predictive checks are disliked by some Bayesians because of their low power arising from their allegedly “using the data twice”. This is not a problem for us: it simply represents a dimension of the data that is virtually automatically fit by the model. What can statistics learn from philosophy? Falsification and the notion of scientific revolutions can make us willing to check our model fit and to vigorously investigate anomalies rather than treat prediction as the only goal of statistics. What can the philosophy of science learn from statistical practice? The success of inference using elaborate models, full of assumptions that are certainly wrong, demonstrates the power of deductive inference, and posterior predictive checking demonstrates that ideas of falsification and error statistics can be applied in a fully Bayesian environment with informative likelihoods and prior distributions.

Mayo Comments:

(a) I welcome Gelman’s arguments against all Bayesian probabilisms, and am intrigued with Gelman and Shalizi’s (2013) ‘meeting of the minds’ (which I regard as a kind of error statistical Bayesianism) [1]. As I say in my concluding remark on their paper:

The authors have provided a radical and important challenge to the foundations of current Bayesian statistics, in a way that reflects current practice. Their paper points to interesting new research problems for advancing what is essentially a dramatic paradigm change in Bayesian foundations. …I hope that [it]…will motivate Bayesian epistemologists in philosophy to take note of foundational problems in Bayesian practice, and that it will inspire philosophically-minded frequentist error statisticians to help craft a new foundation for using statistical tools – one that will afford a series of error probes that, taken together, enable stringent or severe testing.

I’ve been trying to understand the workings of the approach well enough to illuminate its philosophical foundations–more on that in a later post [2].

(b) Going back to my symposium chicken-scratching, I wrote: “Gelman says p-values aren’t falsificationist, but confirmationist–[he’s referring to] that abusive animal” whereby a statistically significant result is taken as evidence in favor of a research claim H taken to entail the observed effect. This is also how Glymour characterized confirmatory research in his talk (see the slide I discuss). In one of my own slides from the PSA, I describe p-value reasoning, given an apt test statistic T:

controversy-over-the-significance-test-controversy-10-1024

From inferring a genuine discrepancy from a test hypothesis, you can’t go directly to a genuine falsification of, or discrepancy from, the test hypothesis, but you can once you’ve shown a significant result rarely fails to be brought about (as Fisher required). The next stages may lead to a revised model or hypothesis being warranted with severity; later still, a falsification of a research claim may be well-corroborated. Once the statistical (relativistic) light-bending effect was vouchsafed (by means of statistically rejecting Newtonian null hypotheses), it falsified the Newtonian prediction (of a 0 or half the Einstein deflection effect) and, together with other statistical inferences, led to passing the Einstein effect severely. The large randomized, controlled trials of Hormone Replacement Therapy in 2002 revealed statistically significant increased risks of heart disease. They falsified, first, the nulls of the RCTs, and second, the widely accepted claim (from observational studies) that HRT helps prevent heart disease. I’m skimming details, but the gist is clear. How else is Gelman’s own statistical falsification program supposed to work?  Posterior predictive p-values follow essentially the same error statistical testing reasoning.

Share your thoughts.

[1] Another relevant, short, and clear paper is Gelman’s (2011) “Induction and Deduction in Bayesian Data Analysis” (2011).

[2] You can search this blog for quite a lot on Gelman and our exchanges.

REFERENCES

Fisher, R. A. 1947. The Design of Experiments (4th ed.). Edinburgh: Oliver and Boyd.

Gelman, A. 2011. ‘Induction and Deduction in Bayesian Data Analysis’, in  Error and Inference: Recent Exchanges on Experimental Reasoning, Reliability, and the Objectivity and Rationality of Science, Mayo, D., Spanos, A. and Staley, K. (eds.), pp. 67-78. Cambridge: Cambridge University Press.

Gelman, A. and Shalizi, C. 2013. ‘Philosophy and the Practice of Bayesian Statistics’ and ‘Rejoinder’, British Journal of Mathematical and Statistical Psychology 66(1): 8–38; 76-80.

Mayo, D. G. (2013) “Comments on A. Gelman and C. Shalizi:“Philosophy and the Practice of Bayesian Statistics”, commentary on A. Gelman and C. Shalizi “Philosophy and the Practice of Bayesian Statistics” (with discussion), British Journal of Mathematical and Statistical Psychology 66(1): 5-64.

Categories: Bayesian/frequentist, Gelman, Shalizi, Statistics | 50 Comments

3 YEARS AGO (NOVEMBER 2013): MEMORY LANE

3 years ago...

3 years ago…

MONTHLY MEMORY LANE: 3 years ago: November 2013. I mark in red three posts from each month 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 count as one. Here I’m counting 11/9, 11/13, and 11/16 as one

November 2013

  • (11/2) Oxford Gaol: Statistical Bogeymen
  • (11/4) Forthcoming paper on the strong likelihood principle
  • (11/9) Null Effects and Replication (cartoon pic)
  • (11/9) Beware of questionable front page articles warning you to beware of questionable front page articles (iii)
  • (11/13) T. Kepler: “Trouble with ‘Trouble at the Lab’?” (guest post)
  • (11/16) PhilStock: No-pain bull
  • (11/16) S. Stanley Young: More Trouble with ‘Trouble in the Lab’ (Guest post)
  • (11/18) Lucien Le Cam: “The Bayesians hold the Magic”
  • (11/20) Erich Lehmann: Statistician and Poet
  • (11/23) Probability that it is a statistical fluke [i]
  • (11/27)The probability that it be a statistical fluke” [iia]
  • (11/30) Saturday night comedy at the “Bayesian Boy” diary (rejected post*)

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

[2] New Rule, July 30, 2016-very convenient.

 

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

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

gigerenzer-slide-19

  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

3 YEARS AGO (OCTOBER 2013): MEMORY LANE

3 years ago...

3 years ago…

MONTHLY MEMORY LANE: 3 years ago: October 2013. I mark in red three posts from each month 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 pair count as one.

October 2013

  • (10/3) Will the Real Junk Science Please Stand Up? (critical thinking)
     
  • (10/5) Was Janina Hosiasson pulling Harold Jeffreys’ leg?
  • (10/9) Bad statistics: crime or free speech (II)? Harkonen update: Phil Stat / Law /Stock
  • (10/12) Sir David Cox: a comment on the post, “Was Hosiasson pulling Jeffreys’ leg?”(10/5 and 10/12 are a pair)
     
  • (10/19) Blog Contents: September 2013
  • (10/19) Bayesian Confirmation Philosophy and the Tacking Paradox (iv)*
  • (10/25) Bayesian confirmation theory: example from last post…(10/19 and 10/25 are a pair)
  • (10/26) Comedy hour at the Bayesian (epistemology) retreat: highly probable vs highly probed (vs what ?)
  • (10/31) WHIPPING BOYS AND WITCH HUNTERS (interesting to see how things have changed and stayed the same over the past few years, share comments)

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

[2] New Rule, July 30, 2016-very convenient.

 

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Categories: 3-year memory lane, Error Statistics, Statistics | 22 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

A new front in the statistics wars? Peaceful negotiation in the face of so-called ‘methodological terrorism’

images-30I haven’t been blogging that much lately, as I’m tethered to the task of finishing revisions on a book (on the philosophy of statistical inference!) But I noticed two interesting blogposts, one by Jeff Leek, another by Andrew Gelman, and even a related petition on Twitter, reflecting a newish front in the statistics wars: When it comes to improving scientific integrity, do we need more carrots or more sticks? 

Leek’s post, from yesterday, called “Statistical Vitriol” (29 Sep 2016), calls for de-escalation of the consequences of statistical mistakes:

Over the last few months there has been a lot of vitriol around statistical ideas. First there were data parasites and then there were methodological terrorists. These epithets came from established scientists who have relatively little statistical training. There was the predictable backlash to these folks from their counterparties, typically statisticians or statistically trained folks who care about open source.
Continue reading

Categories: Anil Potti, fraud, Gelman, pseudoscience, Statistics | 15 Comments

G.A. Barnard’s 101st Birthday: The Bayesian “catch-all” factor: probability vs likelihood

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G. A. Barnard: 23 Sept 1915-30 July, 2002

Today is George Barnard’s 101st birthday. In honor of this, I reblog an exchange between Barnard, Savage (and others) on likelihood vs probability. The exchange is from pp 79-84 (of what I call) “The Savage Forum” (Savage, 1962).[i] Six other posts on Barnard are linked below: 2 are guest posts (Senn, Spanos); the other 4 include a play (pertaining to our first meeting), and a letter he wrote to me. 

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BARNARD:…Professor Savage, as I understand him, said earlier that a difference between likelihoods and probabilities was that probabilities would normalize because they integrate to one, whereas likelihoods will not. Now probabilities integrate to one only if all possibilities are taken into account. This requires in its application to the probability of hypotheses that we should be in a position to enumerate all possible hypotheses which might explain a given set of data. Now I think it is just not true that we ever can enumerate all possible hypotheses. … If this is so we ought to allow that in addition to the hypotheses that we really consider we should allow something that we had not thought of yet, and of course as soon as we do this we lose the normalizing factor of the probability, and from that point of view probability has no advantage over likelihood. This is my general point, that I think while I agree with a lot of the technical points, I would prefer that this is talked about in terms of likelihood rather than probability. I should like to ask what Professor Savage thinks about that, whether he thinks that the necessity to enumerate hypotheses exhaustively, is important. Continue reading

Categories: Barnard, highly probable vs highly probed, phil/history of stat, Statistics | 14 Comments

Peircean Induction and the Error-Correcting Thesis (Part I)

C. S. Peirce: 10 Sept, 1839-19 April, 1914

C. S. Peirce: 10 Sept, 1839-19 April, 1914

Today is C.S. Peirce’s birthday. He’s one of my all time heroes. You should read him: he’s a treasure chest on essentially any topic, and he anticipated several major ideas in statistics (e.g., randomization, confidence intervals) as well as in logic. I’ll reblog the first portion of a (2005) paper of mine. Links to Parts 2 and 3 are at the end. It’s written for a very general philosophical audience; the statistical parts are pretty informal. Happy birthday Peirce.

Peircean Induction and the Error-Correcting Thesis
Deborah G. Mayo
Transactions of the Charles S. Peirce Society: A Quarterly Journal in American Philosophy, Volume 41, Number 2, 2005, pp. 299-319

Peirce’s philosophy of inductive inference in science is based on the idea that what permits us to make progress in science, what allows our knowledge to grow, is the fact that science uses methods that are self-correcting or error-correcting:

Induction is the experimental testing of a theory. The justification of it is that, although the conclusion at any stage of the investigation may be more or less erroneous, yet the further application of the same method must correct the error. (5.145)

Continue reading

Categories: Bayesian/frequentist, C.S. Peirce, Error Statistics, Statistics | 18 Comments

All She Wrote (so far): Error Statistics Philosophy: 5 years on

metablog old fashion typewriter

D.G. Mayo with her  blogging typewriter

Error Statistics Philosophy: Blog Contents (5 years) [i]
By: D. G. Mayo

Dear Reader: It’s hard to believe I’ve been blogging for five years (since Sept. 3, 2011)! A big celebration is taking place at the Elbar Room this evening. If you’re in the neighborhood, stop by for some Elba Grease.

Amazingly, this old typewriter not only still works; one of the whiz kids on Elba managed to bluetooth it to go directly from my typewriter onto the blog (I never got used to computer keyboards.) I still must travel to London to get replacement ribbons for this klunker.

Please peruse the offerings below, and take advantage of some of the super contributions and discussions by guest posters and readers! I don’t know how much longer I’ll continue blogging, but at least until the publication of my book on statistical inference. After that I plan to run conferences, workshops, and ashrams on PhilStat and PhilSci, and will invite readers to take part! Keep reading and commenting. Sincerely, D. Mayo

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September 2011

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Categories: blog contents, Metablog, Statistics | 11 Comments

TragiComedy hour: P-values vs posterior probabilities vs diagnostic error rates

Did you hear the one about the frequentist significance tester when he was shown the nonfrequentist nature of p-values?

Critic: I just simulated a long series of tests on a pool of null hypotheses, and I found that among tests with p-values of .05, at least 22%—and typically over 50%—of the null hypotheses are true!

Frequentist Significance Tester: Scratches head: But rejecting the null with a p-value of .05 ensures erroneous rejection no more than 5% of the time!

Raucous laughter ensues!

(Hah, hah… “So funny, I forgot to laugh! Or, I’m crying and laughing at the same time!) Continue reading

Categories: Bayesian/frequentist, Comedy, significance tests, Statistics | 8 Comments

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: Continue reading

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 | 22 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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“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?

images-2

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

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