Author Archives: Mayo

New Version: On the Birnbaum argument for the SLP: Slides for my JSM talk

Posted on July 26, 2013 by Mayo

Picture 216 1mayo In my latest formulation of the controversial Birnbaum argument for the strong likelihood principle (SLP), I introduce a new symbol \Rightarrow  to represent a function from a given experiment-outcome pair, (E,z) to a generic inference implication.  This should clarify my argument (see my new paper).

(E,z) \Rightarrow InfrE(z) is to be read “the inference implication from outcome z in experiment E” (according to whatever inference type/school is being discussed).

A draft of my slides for the Joint Statistical Meetings JSM in Montreal next week are right after the abstract. Comments are very welcome.

Interested readers may search this blog for quite a lot of discussion of the SLP (e.g., here and here) including links to the central papers, “U-Phils” by others (e.g., here, here, and here), and amusing notes (e.g., Don’t Birnbaumize that experiment my friend, and Midnight with Birnbaum).

On the Birnbaum Argument for the Strong Likelihood Principle

Abstract

An essential component of inference based on familiar frequentist notions p-values, significance and confidence levels, is the relevant sampling distribution (hence the term sampling theory). This feature results in violations of a principle known as the strong likelihood principle (SLP), the focus of this paper. In particular, if outcomes x* and y* from experiments E1 and E2 (both with unknown parameter θ), have different probability models f1, f2, then even though f1(x*; θ) = cf2(y*; θ) for all θ, outcomes x* and y* may have different implications for an inference about θ. Although such violations stem from considering outcomes other than the one observed, we argue, this does not require us to consider experiments other than the one performed to produce the data. David Cox (1958) proposes the Weak Conditionality Principle (WCP) to justify restricting the space of relevant repetitions. The WCP says that once it is known which Ei produced the measurement, the assessment should be in terms of the properties of the particular Ei.      

The surprising upshot of Allan Birnbaum’s (1962) argument is that the SLP appears to follow from applying the WCP in the case of mixtures, and so uncontroversial a principle as sufficiency (SP). But this would preclude the use of sampling distributions. The goal of this article is to provide a new clarification and critique of Birnbaum’s argument. Although his argument purports that [(WCP and SP) entails SLP], we show how data may violate the SLP while holding both the WCP and SP. Such cases directly refute [WCP entails SLP].

Comments, questions, errors are welcome.

Full paper can be found here: http://arxiv-web3.library.cornell.edu/abs/1302.7021

Categories: Error Statistics, Statistics, strong likelihood principle | 20 Comments

Background Knowledge: Not to Quantify, But To Avoid Being Misled By, Subjective Beliefs

Posted on July 23, 2013 by Mayo

drapery6A low-powered statistical analysis of this blog—nearing its 2-year anniversary!—reveals that the topic to crop up most often—either front and center, or lurking in the bushes–is that of “background information”. The following was one of my early posts, back in Oct.30, 2011:

October 30, 2011 (London). Increasingly, I am discovering that one of the biggest sources of confusion about the foundations of statistics has to do with what it means or should mean to use “background knowledge” and “judgment” in making statistical and scientific inferences. David Cox and I address this in our “Conversation” in RMM (2011); it is one of the three or four topics in that special volume that I am keen to take up.

Insofar as humans conduct science and draw inferences, and insofar as learning about the world is not reducible to a priori deductions, it is obvious that “human judgments” are involved. True enough, but too trivial an observation to help us distinguish among the very different ways judgments should enter according to contrasting inferential accounts. When Bayesians claim that frequentists do not use or are barred from using background information, what they really mean is that frequentists do not use prior probabilities of hypotheses, at least when those hypotheses are regarded as correct or incorrect, if only approximately. So, for example, we would not assign relative frequencies to the truth of hypotheses such as (1) prion transmission is via protein folding without nucleic acid, or (2) the deflection of light is approximately 1.75” (as if, as Pierce puts it, “universes were as plenty as blackberries”). How odd it would be to try to model these hypotheses as themselves having distributions: to us, statistical hypotheses assign probabilities to outcomes or values of a random variable.

However, quite a lot of background information goes into designing, carrying out, and analyzing inquiries into hypotheses regarded as correct or incorrect. For a frequentist, that is where background knowledge enters. There is no reason to suppose that the background required in order sensibly to generate, interpret, and draw inferences about H should—or even can—enter through prior probabilities for H itself! Of course, presumably, Bayesians also require background information in order to determine that “data x” have been observed, to determine how to model and conduct the inquiry, and to check the adequacy of statistical models for the purposes of the inquiry. So the Bayesian prior only purports to add some other kind of judgment, about the degree of belief in H. It does not get away from the other background judgments that frequentists employ.

This relates to a second point that came up in our conversation when Cox asked, “Do we want to put in a lot of information external to the data, or as little as possible?” Continue reading →

Categories: Background knowledge, Error Statistics | Tags: , | Leave a comment

Guest Post: Larry Laudan. Why Presuming Innocence is Not a Bayesian Prior

Posted on July 20, 2013 by Mayo

DSCF3726“Why presuming innocence has nothing to do with assigning low prior probabilities to the proposition that defendant didn’t commit the crime”

by Professor Larry Laudan
Philosopher of Science*

Several of the comments to the July 17 post about the presumption of innocence suppose that jurors are asked to believe, at the outset of a trial, that the defendant did not commit the crime and that they can legitimately convict him if and only if they are eventually persuaded that it is highly likely (pursuant to the prevailing standard of proof) that he did in fact commit it. Failing that, they must find him not guilty. Many contributors here are conjecturing how confident jurors should be at the outset about defendant’s material innocence.

That is a natural enough Bayesian way of formulating the issue but I think it drastically misstates what the presumption of innocence amounts to.  In my view, the presumption is not (or at least should not be)  an instruction about whether jurors believe defendant did or did not commit the crime.  It is, rather, an instruction about their probative attitudes.wavy capital

There are three reasons for thinking this:

a). asking a juror to begin a trial believing that defendant did not commit a crime requires a doxastic act that is probably outside the jurors’ control.  It would involve asking jurors  to strongly believe an empirical assertion for which they have no evidence whatsoever.  It is wholly unclear that any of us has the ability to talk ourselves into resolutely believing x if we have no empirical grounds for asserting x. By contrast, asking juries to believe that they have seen as yet no proof of defendant’s guilt is an easy belief to acquiesce in since it is obviously true. Continue reading →

Categories: frequentist/Bayesian, PhilStatLaw, Statistics | 28 Comments

Msc Kvetch: A question on the Martin-Zimmerman case we do not hear

Posted on July 19, 2013 by Mayo

questionmark pinkThis is off topic, but a question I don’t hear people ask in regard to the Zimmerman case is: why didn’t any of the several people hearing screams intervene to stop the brawl? Never mind who was screaming, no one felt an obligation to intervene. Eye-witness John Good came out and said something like “stop” but then immediately ran back inside. Others could be heard saying, “don’t go out there”. I don’t say they should have joined the fight, but if a few people had gone outside and screamed or blew a whistle it probably would have been effective.

(I’ve been in such situations twice.)

Categories: msc kvetch | 5 Comments

Phil/Stat/Law: What Bayesian prior should a jury have? (Schachtman)

Posted on July 17, 2013 by Mayo

wavy capitalNathan Schachtman, Esq., PC* emailed me the following interesting query a while ago:

NAS-3When I was working through some of the Bayesian in the law issues with my class, I raised the problem of priors of 0 and 1 being off “out of bounds” for a Bayesian analyst.  I didn’t realize then that the problem had a name:  Cromwell’s Rule.

My point was then, and more so now, what is the appropriate prior the jury should have when it is sworn?  When it hears opening statements?  Just before the first piece of evidence is received?

Do we tell the jury that the defendant is presumed innocent, which means that it’s ok to entertain a very, very small prior probability of guilt, say no more than 1/N, where N is the total population of people? This seems wrong as a matter of legal theory.  But if the prior = 0, then no amount of evidence can move the jury off its prior.

*Schachtman’s legal practice focuses on the defense of product liability suits, with an emphasis on the scientific and medico-legal issues.  He teaches a course in statistics in the law at the Columbia Law School, NYC. He also has a legal blog here.

Categories: PhilStatLaw, Statistics | Tags: | 27 Comments

Stephen Senn: Indefinite irrelevance

Posted on July 14, 2013 by Mayo
Stephen SennStephen Senn
Head, Methodology and Statistics Group,
Competence Center for Methodology and Statistics (CCMS),
Luxembourg

At a workshop on randomisation I attended recently I was depressed to hear what I regard as hackneyed untruths treated as if they were important objections. One of these is that of indefinitely many confounders. The argument goes that although randomisation may make it probable that some confounders are reasonably balanced between the arms, since there are indefinitely many of these, the chance that at least some are badly confounded is so great as to make the procedure useless.

This argument is wrong for several related reasons. The first is to do with the fact that the total effect of these indefinitely many confounders is bounded. This means that the argument put forward is analogously false to one in which it were claimed that the infinite series ½, ¼,⅛ …. did not sum to a limit because there were infinitely many terms. The fact is that the outcome value one wishes to analyse poses a limit on the possible influence of the covariates. Suppose that we were able to measure a number of covariates on a set of patients prior to randomisation (in fact this is usually not possible but that does not matter here). Now construct principle components, C1, C2… .. based on these covariates. We suppose that each of these predict to a greater or lesser extent the outcome, Y  (say).  In a linear model we could put coefficients on these components, k1, k2… (say). However one is not free to postulate anything at all by way of values for these coefficients, since it has to be the case for any set of m such coefficients that inequality (2)where  V(  ) indicates variance of. Thus variation in outcome bounds variation in prediction. This total variation in outcome has to be shared between the predictors and the more predictors you postulate there are, the less on average the influence per predictor.

The second error is to ignore the fact that statistical inference does not proceed on the basis of signal alone but also on noise. It is the ratio of these that is important. If there are indefinitely many predictors then there is no reason to suppose that their influence on the variation between treatment groups will be bigger than their variation within groups and both of these are used to make the inference. Continue reading →

Categories: RCTs, Statistics, Stephen Senn | 15 Comments

Professor of Philosophy Resigns over Sexual Misconduct (rejected post)

Posted on July 13, 2013 by Mayo

Unknown-1My field (philosophy) is not known for the kinds of data frauds and retractions we’ve discussed on this blog, but scandals revolving around sexual harassment by male faculty are not rare, though I can’t think of another with a senior faculty resigning, at least not in recent times. This article is from 

A Few Words on the McGinn Imbroglio from the philosophy smoker blog (June 4, 2013)

As I guess we [in philosophy] all know, Colin McGinn has chosen to resign from the University of Miami rather than allow the University to proceed with an investigation into allegations of sexual misconduct involving a research assistant. The article at the Chronicle of Higher Ed is here (paywalled); Sally Haslanger has posted a PDF of the whole thing here. Discussion at NewApps here, here, here, and here; discussion at Feminist Philosophers here; discussion at Leiter here and here.

Briefly, what seems to have happened is this: McGinn had a Research Assistant who was a female graduate student. Last spring, the RA started feeling uncomfortable with McGinn. Then, last April, McGinn allegedly started sending her sexually explicit email messages, including one in which, according to the RA’s boyfriend and two unnamed faculty members, “McGinn wrote that he had been thinking about the student while masturbating.”* Wowza.

The RA then contacted the Office of Equality Administration. According to CHE, “after the university’s Office of Equality Administration and the vice provost for faculty affairs conducted an investigation, Mr. McGinn was given the option of agreeing to resign or having an investigation into the allegations against him continue in a public setting, several of the philosopher’s colleagues said.”

It’s hard to know exactly what to make of this. On one obvious interpretation, there’s a clearly implied threat: if you don’t resign, we’re going to publicly drag your name through the mud. And I’m not sure how normal the prospect of a “public” investigation is in this kind of circumstance. For example, if I recall correctly, the Oregon case from a couple of years ago involved an investigation that was supposed to have been kept private, and was made public only in violation of the University’s procedures. But procedures vary from institution to institution, and I don’t have any expertise here. I don’t really have any idea whether this is unusual or not, although my suspicion is that it is at least a little unusual.

It therefore seems reasonable to worry about whether the procedures Miami followed here were respectful of McGinn’s right to due process. But it’s worth emphasizing that the CHE article is not very clear about precisely what happened—for example, Leiter says that McGinn had legal representation and was acting on his lawyer’s advice, but the CHE doesn’t mention it. It is also worth emphasizing that the account in the CHE comes from unnamed “colleagues,” not McGinn or his representatives or any official source at the University. And this comment at Feminist Philosophers, the veracity of which I am not in a position to verify, makes the meeting seem at least a little less troubling. On that account, it was more like, we’ve got some pretty compelling, well-documented evidence of misconduct, which we are duty-bound to pursue; but we’d like to give you the opportunity to resign now and save us both a big headache.

Harrassment occurs between professors, and not just between professors and students, but without the obvious professor-student taboo, it is not taken especially seriously, in my experience. Naturally philosophers, being philosophers, some of them, will engage in deep philosophical discussion of the philosophical nature and justification of the infractions and even how it might have grown out of a legitimate philosophical research on the topic of the evolutionary development of the hand, in relation to its physical functions. Continue reading →

Categories: Rejected Posts, Uncategorized | 2 Comments

Is Particle Physics Bad Science? (memory lane)

Posted on July 11, 2013 by Mayo

Memory Lane: reblog July 11, 2012 (+ updates at the end). 

I suppose[ed] this was somewhat of a joke from the ISBA, prompted by Dennis Lindley, but as I [now] accord the actual extent of jokiness to be only ~10%, I’m sharing it on the blog [i].  Lindley (according to O’Hagan) wonders why scientists require so high a level of statistical significance before claiming to have evidence of a Higgs boson.  It is asked: “Are the particle physics community completely wedded to frequentist analysis?  If so, has anyone tried to explain what bad science that is?”

Bad science?   I’d really like to understand what these representatives from the ISBA would recommend, if there is even a shred of seriousness here (or is Lindley just peeved that significance levels are getting so much press in connection with so important a discovery in particle physics?)

Well, read the letter and see what you think.

On Jul 10, 2012, at 9:46 PM, ISBA Webmaster wrote:

Dear Bayesians,

A question from Dennis Lindley prompts me to consult this list in search of answers.

We’ve heard a lot about the Higgs boson.  The news reports say that the LHC needed convincing evidence before they would announce that a particle had been found that looks like (in the sense of having some of the right characteristics of) the elusive Higgs boson.  Specifically, the news referred to a confidence interval with 5-sigma limits.

Now this appears to correspond to a frequentist significance test with an extreme significance level.  Five standard deviations, assuming normality, means a p-value of around 0.0000005.  A number of questions spring to mind.

1.  Why such an extreme evidence requirement?  We know from a Bayesian  perspective that this only makes sense if (a) the existence of the Higgs  boson (or some other particle sharing some of its properties) has extremely small prior probability and/or (b) the consequences of erroneously announcing its discovery are dire in the extreme.  Neither seems to be the case, so why  5-sigma?

2.  Rather than ad hoc justification of a p-value, it is of course better to do a proper Bayesian analysis.  Are the particle physics community completely wedded to frequentist analysis?  If so, has anyone tried to explain what bad science that is? Continue reading →

Categories: philosophy of science, Statistics | Tags: , , , , , | Leave a comment

PhilStatLaw: Reference Manual on Scientific Evidence (3d ed) on Statistical Significance (Schachtman)

Posted on July 10, 2013 by Mayo

Memory Lane: One Year Ago on error statistics.com

A quick perusal of the “Manual” on Nathan Schachtman’s legal blog shows it to be chock full of revealing points of contemporary legal statistical philosophy.  The following are some excerpts, read the full blog here.   I make two comments at the end.

July 8th, 2012

Nathan Schachtman

How does the new Reference Manual on Scientific Evidence (RMSE3d 2011) treat statistical significance?  Inconsistently and at times incoherently.

Professor Berger’s Introduction

In her introductory chapter, the late Professor Margaret A. Berger raises the question of the role statistical significance should play in evaluating a study’s support for causal conclusions:

“What role should statistical significance play in assessing the value of a study? Epidemiological studies that are not conclusive but show some increased risk do not prove a lack of causation. Some courts find that they therefore have some probative value, 62 at least in proving general causation. 63”

Margaret A. Berger, “The Admissibility of Expert Testimony,” in RMSE3d 11, 24 (2011).

This seems rather backwards.  Berger’s suggestion that inconclusive studies do not prove lack of causation seems nothing more than a tautology.  And how can that tautology support the claim that inconclusive studies “therefore ” have some probative value? This is a fairly obvious logical invalid argument, or perhaps a passage badly in need of an editor.

…………

Chapter on Statistics

The RMSE’s chapter on statistics is relatively free of value judgments about significance probability, and, therefore, a great improvement upon Berger’s introduction.  The authors carefully describe significance probability and p-values, and explain:

“Small p-values argue against the null hypothesis. Statistical significance is determined by reference to the p-value; significance testing (also called hypothesis testing) is the technique for computing p-values and determining statistical significance.”

David H. Kaye and David A. Freedman, “Reference Guide on Statistics,” in RMSE3d 211, 241 (3ed 2011).  Although the chapter confuses and conflates Fisher’s interpretation of p-values with Neyman’s conceptualization of hypothesis testing as a dichotomous decision procedure, this treatment is unfortunately fairly standard in introductory textbooks.

Kaye and Freedman, however, do offer some important qualifications to the untoward consequences of using significance testing as a dichotomous outcome:

“Artifacts from multiple testing are commonplace. Because research that fails to uncover significance often is not published, reviews of the literature may produce an unduly large number of studies finding statistical significance.111 Even a single researcher may examine so many different relationships that a few will achieve statistical significance by mere happenstance. Almost any large data set—even pages from a table of random digits—will contain some unusual pattern that can be uncovered by diligent search. Having detected the pattern, the analyst can perform a statistical test for it, blandly ignoring the search effort. Statistical significance is bound to follow.

There are statistical methods for dealing with multiple looks at the data, which permit the calculation of meaningful p-values in certain cases.112 However, no general solution is available, and the existing methods would be of little help in the typical case where analysts have tested and rejected a variety of models before arriving at the one considered the most satisfactory (see infra Section V on regression models). In these situations, courts should not be overly impressed with claims that estimates are significant. Instead, they should be asking how analysts developed their models.113 ”

Id. at 256 -57.  This qualification is omitted from the overlapping discussion in the chapter on epidemiology, where it is very much needed. Continue reading →

Categories: P-values, PhilStatLaw, significance tests | Tags: , , , , | 6 Comments

Bad news bears: ‘Bayesian bear’ rejoinder-reblog mashup

Posted on July 6, 2013 by Mayo

Oh No! It’s those mutant bears again. To my dismay, I’ve been sent, for the third time, that silly, snarky, adolescent, clip of those naughty “what the p-value” bears (first posted on Aug 5, 2012), who cannot seem to get a proper understanding of significance tests into their little bear brains. So apparently some people haven’t seen my rejoinder which, as I said then, practically wrote itself. So since it’s Saturday night here at the Elbar Room, let’s listen in to a mashup of both the clip and my original rejoinder (in which p-value bears are replaced with hypothetical Bayesian bears). 

These stilted bear figures and their voices are sufficiently obnoxious in their own right, even without the tedious lampooning of p-values and the feigned horror at learning they should not be reported as posterior probabilities.

Mayo’s Rejoinder:

Bear #1: Do you have the results of the study?

Bear #2:Yes. The good news is there is a .996 probability of a positive difference in the main comparison.

Bear #1: Great. So I can be well assured that there is just a .004 probability that such positive results would occur if they were merely due to chance.

Bear #2: Not really, that would be an incorrect interpretation. Continue reading →

Categories: Bayesian/frequentist, Comedy, P-values, Statistics | Tags: , , , | 13 Comments

Phil/Stat/Law: 50 Shades of gray between error and fraud

Posted on July 3, 2013 by Mayo

500x307-embo-reports-vol-73-meeting-report-fig-1-abcAn update on the Diederik Stapel case: July 2, 2013, The Scientist, “Dutch Fraudster Scientist Avoids Jail”.

Two years after being exposed by colleagues for making up data in at least 30 published journal articles, former Tilburg University professor Diederik Stapel will avoid a trial for fraud. Once one of the Netherlands’ leading social psychologists, Stapel has agreed to a pre-trial settlement with Dutch prosecutors to perform 120 hours of community service.

According to Dutch newspaper NRC Handeslblad, the Dutch Organization for Scientific Research awarded Stapel $2.8 million in grants for research that was ultimately tarnished by misconduct. However, the Dutch Public Prosecution Service and the Fiscal Information and Investigation Service said on Friday (June 28) that because Stapel used the grant money for student and staff salaries to perform research, he had not misused public funds. …

In addition to the community service he will perform, Stapel has agreed not to make a claim on 18 months’ worth of illness and disability compensation that he was due under his terms of employment with Tilburg University. Stapel also voluntarily returned his doctorate from the University of Amsterdam and, according to Retraction Watch, retracted 53 of the more than 150 papers he has co-authored.

“I very much regret the mistakes I have made,” Stapel told ScienceInsider. “I am happy for my colleagues as well as for my family that with this settlement, a court case has been avoided.”

No surprise he’s not doing jail time, but 120 hours of community service?  After over a decade of fraud, and tainting 14 of 21 of the PhD theses he supervised?  Perhaps the “community service” should be to actually run the experiments he had designed?  What about his innocence of misusing public funds? Continue reading →

Categories: PhilStatLaw, spurious p values, Statistics | 13 Comments

Blog Contents: mid-year

Posted on June 30, 2013 by Mayo

Error Statistics Philosophy BLOG: Table of Contents 2013 (January-June)*

img_02443January 2013

(1/2) Severity as a ‘Metastatistical’ Assessment
(1/4) Severity Calculator
(1/6) Guest post: Bad Pharma? (S. Senn)
(1/9) RCTs, skeptics, and evidence-based policy
(1/10) James M. Buchanan
(1/11) Aris Spanos: James M. Buchanan: a scholar, teacher and friend
(1/12) Error Statistics Blog: Table of Contents
(1/15) Ontology & Methodology: Second call for Abstracts, Papers
(1/18) New Kvetch/PhilStock
(1/19) Saturday Night Brainstorming and Task Forces: (2013) TFSI on NHST
(1/22) New PhilStock
(1/23) P-values as posterior odds?
(1/26) Coming up: December U-Phil Contributions….
(1/27) U-Phil: S. Fletcher & N. Jinn
(1/30) U-Phil: J. A. Miller: Blogging the SLP Continue reading →

Categories: Metablog, Statistics | Leave a comment

Palindrome “contest” contest

Posted on June 29, 2013 by Mayo

 metablog old fashion typewriterWant to win one of these books? You may not have noticed that since May, the palindrome rules have gotten trivially easy. So since it’s Saturday night, and I’m giving a time extension to 14 July – Le Quatorze juillet—have some fun coming up with a palindrome. It only needs to include “Elba” and the word “contest”. For full bibiographies and complete rules, see palindrome page:

 .EGEK CoverSend your candidates to me at error@vt.edu. One of the winners under the older, much harder, rules is here.

Previous palindrome contests included:

runs test, omnibus, cycle, dominate, editor, data, Model, sample, random, probable, Bayes, confident, likely, error, decision, variable, integrate, maximal, median (comedian), interpret, action, code, predict, luck, assess, model, simple, null, bootstrap,minimum, wrong, prefer, dogma, (s)exist, email

with variations.

Categories: Announcement, Palindrome | Leave a comment

Why I am not a “dualist” in the sense of Sander Greenland

Posted on June 26, 2013 by Mayo

Janus--2face

This post picks up, and continues, an exchange that began with comments on my June 14 blogpost (between Sander Greenland, Nicole Jinn, and I). My new response is at the end. The concern is how to expose and ideally avoid some of the well known flaws and foibles in statistical inference, thanks to gaps between data and statistical inference, and between statistical inference and substantive claims. I am not rejecting the use of multiple methods in the least (they are highly valuable when one method is capable of detecting or reducing flaws in one or more others). Nor am I speaking of classical dualism in metaphysics (which I also do not espouse). I begin with Greenland’s introduction of this idea in his comment… (For various earlier comments, see the post.)

Sander Greenland 

…. I sense some confusion of criticism of the value of tests as popular tools vs. criticism of their logical foundation. I am a critic in the first, practical category, who regards the adoption of testing outside of narrow experimental programs as an unmitigated disaster, resulting in publication bias, prosecutor-type fallacies, and affirming the consequent fallacies throughout the health and social science literature. Even though testing can in theory be used soundly, it just hasn’t done well in practice in these fields. This could be ascribed to human failings rather than failings of received testing theories, but I would require any theory of applied statistics to deal with human limitations, just as safety engineering must do for physical products. I regard statistics as having been woefully negligent of cognitive psychology in this regard. In particular, widespread adoption and vigorous defense of a statistical method or philosophy is no more evidence of its scientific value than widespread adoption and vigorous defense of a religion is evidence of its scientific value. 
That should bring us to alternatives. I am aware of no compelling data showing that other approaches would have done better, but I do find compelling the arguments that at least some of the problems would have been mitigated by teaching a dualist approach to statistics, in which every procedure must be supplied with both an accurate frequentist and an accurate Bayesian interpretation, if only to reduce prevalent idiocies like interpreting a two-sided P-value as “the” posterior probability of a point null hypothesis.

 Nicole Jinn
 (to Sander Greenland)

 What exactly is this ‘dualist’ approach to teaching statistics and why does it mitigate the problems, as you claim? (I am increasingly interested in finding more effective ways to teach/instruct others in various age groups about statistics.)
I have a difficult time seeing how effective this ‘dualist’ way of teaching could be for the following reason: the Bayesian and frequentist approaches are vastly different in their aims and the way they see statistics being used in (natural or social) science, especially when one looks more carefully at the foundations of each methodology (e.g., disagreements about where exactly probability enters into inference, or about what counts as relevant information). Hence, it does not make sense (to me) to supply both types of interpretation to the same data and the same research question! Instead, it makes more sense (from a teaching perspective) to demonstrate a Bayesian interpretation for one experiment, and a frequentist interpretation for another experiment, in the hopes of getting at the (major) differences between the two methodologies.

Mayo

Sander. Thanks for your comment. 
Interestingly, I think the conglomeration of error statistical tools are the ones most apt at dealing with human limitations and foibles: they give piecemeal methods to ask one question at a time (e.g., would we be mistaken to suppose there is evidence of any effect at all? mistaken about how large? about iid assumptions? about possible causes? about implications for distinguishing any theories?). The standard Bayesian apparatus requires setting out a complete set of hypotheses that might arise, plus prior probabilities in each of them (or in “catchall” hypotheses), as well as priors in the model…and after this herculean task is complete, there is a purely deductive update: being deductive it never goes beyond the givens. Perhaps the data will require a change in your prior—this is what you must have believed before, since otherwise you find your posterior unacceptable—thereby encouraging the very self-sealing inferences we all claim to deplore. Continue reading →

Categories: Bayesian/frequentist, Error Statistics, P-values, Statistics | 21 Comments

What do these share in common: m&ms, limbo stick, ovulation, Dale Carnegie? Sat night potpourri

Posted on June 22, 2013 by Mayo
images-2

For entertainment only

I had said I would label as pseudoscience or questionable science any enterprise that regularly permits the kind of ‘verification biases’ in the laundry list of my June 1 post.  How regularly? (I’ve been asked)

Well, surely if it’s as regular as, say, much of social psychology, it goes over the line. But it’s not mere regularity, it’s the nature of the data, the type of inferences being drawn, and the extent of self-scrutiny and recognition of errors shown (or not shown). The regularity is just a consequence of the methodological holes. My standards may be considerably more stringent than most, but quite aside from statistical issues, I simply do not find hypotheses well-tested if they are based on “experiments” that consist of giving questionnaires. At least not without a lot more self-scrutiny and discussion of flaws than I ever see. (There may be counterexamples.)

Attempts to recreate phenomena of interest in typical social science “labs” leave me with the same doubts. Huge gaps often exist between elicited and inferred results. One might locate the problem under “external validity” but to me it is just the general problem of relating statistical data to substantive claims.

Experimental economists (expereconomists) take lab results plus statistics to warrant sometimes ingenious inferences about substantive hypotheses.  Vernon Smith (of the Nobel Prize in Econ) is rare in subjecting his own results to “stress tests”.  I’m not withdrawing the optimistic assertions he cites from EGEK (Mayo 1996) on Duhem-Quine (e.g., from “Rhetoric and Reality” 2001, p. 29). I’d still maintain, “Literal control is not needed to attribute experimental results correctly (whether to affirm or deny a hypothesis). Enough experimental knowledge will do”.  But that requires piece-meal strategies that accumulate, and at least a little bit of “theory” and/or a decent amount of causal understanding.[1]

I think the generalizations extracted from questionnaires allow for an enormous amount of “reading into” the data. Suddenly one finds the “best” explanation. Questionnaires should be deconstructed for how they may be misinterpreted, not to mention how responders tend to guess what the experimenter is looking for. (I’m reminded of the current hoopla over questionnaires on breadwinners, housework and divorce rates!) I respond with the same eye-rolling to just-so story telling along the lines of evolutionary psychology.

I apply the “Stapel test”: Even if Stapel had bothered to actually carry out the data-collection plans that he so carefully crafted, I would not find the inferences especially telling in the least. Take for example the planned-but-not-implemented study discussed in the recent New York Times article on Stapel:

 Stapel designed one such study to test whether individuals are inclined to consume more when primed with the idea of capitalism. He and his research partner developed a questionnaire that subjects would have to fill out under two subtly different conditions. In one, an M&M-filled mug with the word “kapitalisme” printed on it would sit on the table in front of the subject; in the other, the mug’s word would be different, a jumble of the letters in “kapitalisme.” Although the questionnaire included questions relating to capitalism and consumption, like whether big cars are preferable to small ones, the study’s key measure was the amount of M&Ms eaten by the subject while answering these questions….Stapel and his colleague hypothesized that subjects facing a mug printed with “kapitalisme” would end up eating more M&Ms.

Stapel had a student arrange to get the mugs and M&Ms and later load them into his car along with a box of questionnaires. He then drove off, saying he was going to run the study at a high school in Rotterdam where a friend worked as a teacher.

Stapel dumped most of the questionnaires into a trash bin outside campus. At home, using his own scale, he weighed a mug filled with M&Ms and sat down to simulate the experiment. While filling out the questionnaire, he ate the M&Ms at what he believed was a reasonable rate and then weighed the mug again to estimate the amount a subject could be expected to eat. He built the rest of the data set around that number. He told me he gave away some of the M&M stash and ate a lot of it himself. “I was the only subject in these studies,” he said.

He didn’t even know what a plausible number of M&Ms consumed would be! But never mind that, observing a genuine “effect” in this silly study would not have probed the hypothesis. Would it? Continue reading →

Categories: junk science, Statistics | 5 Comments

Stanley Young: better p-values through randomization in microarrays

Posted on June 19, 2013 by Mayo

I wanted to locate some uncluttered lounge space for one of the threads to emerge in comments from 6/14/13. Thanks to Stanley Young for permission to post this. 

YoungPhoto2008 S. Stanley Young, PhD
Assistant Director for Bioinformatics
National Institute of Statistical Sciences
Research Triangle Park, NC

There is a relatively unknown problem with microarray experiments, in addition to the multiple testing problems. Samples should be randomized over important sources of variation; otherwise p-values may be flawed. Until relatively recently, the microarray samples were not sent through assay equipment in random order. Clinical trial statisticians at GSK insisted that the samples go through assay in random order. Rather amazingly the data became less messy and p-values became more orderly. The story is given here:
http://blog.goldenhelix.com/?p=322
Essentially all the microarray data pre-2010 is unreliable. For another example, Mass spec data was analyzed Petrocoin. The samples were not randomized that claims with very small p-values failed to replicate. See K.A. Baggerly et al., “Reproducibility of SELDI-TOF protein patterns in serum: comparing datasets from different experiments,” Bioinformatics, 20:777-85, 2004. So often the problem is not with p-value technology, but with the design and conduct of the study.

experim_design6

Please check other comments on microarrays from 6/14/13.

Categories: P-values, Statistics | Tags: , , | 9 Comments

PhilStock: The Great Taper Caper

Posted on June 19, 2013 by Mayo

stock picture smaillSee Rejected Posts.

Categories: PhilStock, Rejected Posts | Leave a comment

P-values can’t be trusted except when used to argue that P-values can’t be trusted!

Posted on June 14, 2013 by Mayo

images-1Have you noticed that some of the harshest criticisms of frequentist error-statistical methods these days rest on methods and grounds that the critics themselves purport to reject? Is there a whiff of inconsistency in proclaiming an “anti-hypothesis-testing stance” while in the same breath extolling the uses of statistical significance tests and p-values in mounting criticisms of significance tests and p-values? I was reminded of this in the last two posts (comments) on this blog (here and here) and one from Gelman from a few weeks ago (“Interrogating p-values”).

Gelman quotes from a note he is publishing:

“..there has been a growing sense that psychology, biomedicine, and other fields are being overwhelmed with errors … . In two recent series of papers, Gregory Francis and Uri Simonsohn and collaborators have demonstrated too-good-to-be-true patterns of p-values in published papers, indicating that these results should not be taken at face value.”

But this fraudbusting is based on finding statistically significant differences from null hypotheses (e.g., nulls asserting random assignments of treatments)! If we are to hold small p-values untrustworthy, we would be hard pressed to take them as legitimating these criticisms, especially those of a career-ending sort.

…in addition to the well-known difficulties of interpretation of p-values…,…and to the problem that, even when all comparisons have been openly reported and thus p-values are mathematically correct, the ‘statistical significance filter’ ensures that estimated effects will be in general larger than true effects, with this discrepancy being well over an order of magnitude in settings where the true effects are small… (Gelman 2013)

But surely anyone who believed this would be up in arms about using small p-values as evidence of statistical impropriety. Am I the only one wondering about this?*

CLARIFICATION (6/15/13): Corey’s comment today leads me to a clarification, lest anyone misunderstand my point. I am sure that Francis, Simonsohn and others would never be using p-values and associated methods in the service of criticism if they did not regard the tests as legitimate scientific tools. I wasn’t talking about them. I was alluding to critics of tests who point to their work as evidence the statistical tools are not legitimate. Now maybe Gelman only intends to say, what we know and agree with, that tests can be misused and misinterpreted. But in these comments, our exchanges, and elsewhere, it is clear he is saying something much stronger. In my view, the use of significance tests by debunkers should have been taken as strong support for the value of the tools, correctly used. In short, I thought it was a success story! and I was rather perplexed to see somewhat the reverse.

______________________

*This just in: If one wants to see a genuine quack extremist** who was outed long ago***, see Ziliac’s article declaring the Higgs physicists are pseudoscientists for relying on significance levels!( in the Financial Post 6/12/13).

**I am not placing the critics referred to above under this umbrella in the least.

***For some reviews of Ziliac and McCloskey, see widgets on left. For their flawed testimony on the Matrixx case, please search this blog.

Categories: reforming the reformers, Statistical fraudbusting, Statistics | 43 Comments

Mayo: comment on the repressed memory research

Posted on June 11, 2013 by Mayo

freud mirror espHere are some reflections on the repressed memory articles from Richard Gill’s post, focusing on Geraerts, et.al.,(2008).

1. Richard Gill reported that “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 and are just doing their best to make this as clear as possible to everyone.”

This remark is very telling. I recommend we just regard those cases as illustrating a theory one believes, rather than providing evidence for that theory. If we could mark them as such, we can stop blaming significance tests for playing a role in what are actually only illustrative attempts, or to strengthen someone’s beliefs about a theory.

2. I was surprised the examples had to do with recovered memories. Wasn’t that entire area dubbed a pseudoscience way back (at least 15-25 years ago?) when “therapy induced” memories of childhood sexual abuse (CSA) were discovered to be just that—therapy induced and manufactured? After the witch hunts that ensued (the very accusation sufficing for evidence), I thought the field of “research” had been put out of its and our misery. So, aside from having used the example in a course on critical thinking, I’m not up on this current work at all. But, as these are just blog comments, let me venture some off-the-cuff skeptical thoughts. They will have almost nothing to do with the statistical data analysis, by the way…

3. Geraerts, et.al., (2008, 22) admit at the start of the article that therapy-recovered CSA memories are unreliable, and the idea of automatically repressing a traumatic event like CSA implausible. Then mightn’t it seem the entire research program should be dropped? Not to its adherents! As with all theories that enjoy the capacity of being sufficiently flexible to survive anomaly (Popper’s pseudosciences), there’s some life left here too. Maybe , its adherents reason, it’s not necessary for those who report “spontaneously recovered” CSA memories to be repressors, instead they merely be “suppressors” who are good at blocking out negative events. If so, they didn’t automatically repress but rather deliberately suppressed: “Our findings may partly explain why people with spontaneous CSA memories have the subjective impression that they have ‘repressed’ their CSA memories for many years.” (ibid., 22).

4. Shouldn’t we stop there? I would. We have a research program growing out of an exemplar of pseudoscience being kept alive by ever-new “monster-barring” strategies (as Lakatos called them). (I realize they’re not planning to go out to the McMartin school, but still…) If a theory T is flexible enough so that any observations can be interpreted through it, and thereby regarded as confirming T, then it is no surprise that this is still true when the instances are dressed up with statistics. It isn’t that theories of repressed memories are implausible or improbable (in whatever sense one takes those terms). It is the ever-flexibility of these theories that renders the research program pseudoscience (along with, in this case, a history of self-sealing data interpretations). Continue reading →

Categories: junk science, Statistical fraudbusting, Statistics | 7 Comments

Richard Gill: “Integrity or fraud… or just quesionable research practices?”

Posted on June 8, 2013 by Mayo
Professor Gill

Professor Gill

Professor Richard Gill
Statistics Group
Mathematical Institute
Leiden University
http://www.math.leidenuniv.nl/~gill/

I am very grateful to Richard Gill for permission to post an e-mail from him (after my “dirty laundry” post) along with slides from his talk, “Integrity or fraud… or just questionable research practices?” and associated papers. I record my own reflections on the pseudoscientific nature of the program in one of the Geraerts et.al., papers in a later post.

I certainly have been thinking about these issues a lot in recent months. I got entangled in intensive scientific and media discussions – mainly confined to the Netherlands  – concerning the cases of social psychologist Dirk Smeesters and of psychologist Elke Geraerts.  See: http://www.math.leidenuniv.nl/~gill/Integrity.pdf

And I recently got asked to look at the statistics in some papers of another … [researcher] ..but this one is still confidential ….

The verdict on Smeesters was that he like Stapel actually faked data (though he still denies this).

The Geraerts case is very much open, very much unclear. The senior co-authors Merckelbach, McNally of the attached paper, published in the journal “Memory”, have asked the journal editors for it to be withdrawn because they suspect the lead author, Elke Geraerts, of improper conduct. She denies any impropriety. It turns out that none of the co-authors have the data. Legally speaking it belongs to the University of Maastricht where the research was carried out and where Geraerts was a promising postdoc in Merckelbach’s group. She later got a chair at Erasmus University Rotterdam and presumably has the data herself but refuses to share it with her old co-authors or any other interested scientists. Just looking at the summary statistics in the paper one sees evidence of “too good to be true”. Average scores in groups supposed in theory to be similar are much closer to one another than one would expect on the basis of the within group variation (the paper reports averages and standard deviations for each group, so it is easy to compute the F statistic for equality of the three similar groups and use its left tail probability as test statistic. Continue reading →

Categories: junk science, Statistical fraudbusting, Statistics | 5 Comments

Blog at WordPress.com.