Excursion 1 Tour I (2nd stop): Probabilism, Performance, and Probativeness (1.2)

Posted on September 11, 2018 by Mayo

1.2

I shall be concerned with the foundations of the subject. But in case it should be thought that this means I am not here strongly concerned with practical applications, let me say right away that confusion about the foundations of the subject is responsible, in my opinion, for much of the misuse of the statistics that one meets in fields of application such as medicine, psychology, sociology, economics, and so forth. (George Barnard 1985, p. 2)

While statistical science (as with other sciences) generally goes about its business without attending to its own foundations, implicit in every statistical methodology are core ideas that direct its principles, methods, and interpretations. I will call this its statistical philosophy. To tell what’s true about statistical inference, understanding the associated philosophy (or philosophies) is essential. Discussions of statistical foundations tend to focus on how to interpret probability, and much less on the overarching question of how probability ought to be used in inference. Assumptions about the latter lurk implicitly behind debates, but rarely get the limelight. If we put the spotlight on them, we see that there are two main philosophies about the roles of probability in statistical inference: We may dub them performance (in the long run) and probabilism. Continue reading →

Categories: Statistical Inference as Severe Testing | 3 Comments

Excursion 1 Tour I: Beyond Probabilism and Performance: Severity Requirement (1.1)

Posted on September 8, 2018 by Mayo

The cruise begins…

I’m talking about a specific, extra type of integrity that is [beyond] not lying, but bending over backwards to show how you’re maybe wrong, that you ought to have when acting as a scientist. (Feynman 1974/1985, p. 387)

It is easy to lie with statistics. Or so the cliché goes. It is also very difficult to uncover these lies without statistical methods – at least of the right kind. Self- correcting statistical methods are needed, and, with minimal technical fanfare, that’s what I aim to illuminate. Since Darrell Huff wrote How to Lie with Statistics in 1954, ways of lying with statistics are so well worn as to have emerged in reverberating slogans:

  • Association is not causation.
  • Statistical significance is not substantive significamce
  • No evidence of risk is not evidence of no risk.
  • If you torture the data enough, they will confess.

Exposés of fallacies and foibles ranging from professional manuals and task forces to more popularized debunking treatises are legion. New evidence has piled up showing lack of replication and all manner of selection and publication biases. Even expanded “evidence-based” practices, whose very rationale is to emulate experimental controls, are not immune from allegations of illicit cherry picking, significance seeking, P-hacking, and assorted modes of extra- ordinary rendition of data. Attempts to restore credibility have gone far beyond the cottage industries of just a few years ago, to entirely new research programs: statistical fraud-busting, statistical forensics, technical activism, and widespread reproducibility studies. There are proposed methodological reforms – many are generally welcome (preregistration of experiments, transparency about data collection, discouraging mechanical uses of statistics), some are quite radical. If we are to appraise these evidence policy reforms, a much better grasp of some central statistical problems is needed.

Continue reading →

Categories: Statistical Inference as Severe Testing, Statistics | 9 Comments

The Physical Reality of My New Book! Here at the RSS Meeting

Posted on September 4, 2018 by Mayo

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Categories: SIST | 3 Comments

RSS 2018 – Significance Tests: Rethinking the Controversy

Posted on August 30, 2018 by Mayo

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Day 2, Wednesday 05/09/2018:

The 2018 Meeting of the Royal Statistical Society (Cardiff)

11:20 – 13:20

Keynote 4 – Significance Tests: Rethinking the Controversy Assembly Room

Speakers:
Sir David Cox, Nuffield College, Oxford
Deborah Mayo, Virginia Tech
Richard Morey, Cardiff University
Aris Spanos, Virginia Tech

Intermingled in today’s statistical controversies are some long-standing, but unresolved, disagreements on the nature and principles of statistical methods and the roles for probability in statistical inference and modelling. In reaction to the so-called “replication crisis” in the sciences, some reformers suggest significance tests as a major culprit. To understand the ramifications of the proposed reforms, there is a pressing need for a deeper understanding of the source of the problems in the sciences and a balanced critique of the alternative methods being proposed to supplant significance tests. In this session speakers offer perspectives on significance tests from statistical science, econometrics, experimental psychology and philosophy of science. There will be also be panel discussion.

Cox

Mayo

Morey

Spanos

Categories: Error Statistics | 2 Comments

3 YEARS AGO (AUGUST 2015): MEMORY LANE

Posted on August 17, 2018 by Mayo
3 years ago...

3 years ago…

MONTHLY MEMORY LANE: 3 years ago: August 2015. I mark in red 3-4 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 of relevance to philosophy of statistics [2]. Posts that are part of a “unit” or a group count as one.

August 2015

  • 08/05 Neyman: Distinguishing tests of statistical hypotheses and tests of significance might have been a lapse of someone’s pen
  • 08/08  Statistical Theater of the Absurd: “Stat on a Hot Tin Roof”
  • 08/11 A. Spanos: Egon Pearson’s Neglected Contributions to Statistics (recently reblogged)
  • 08/14 Performance or Probativeness? E.S. Pearson’s Statistical Philosophy
  • 08/15  Severity in a Likelihood Text by Charles Rohde
  • 08/19 Statistics, the Spooky Science
  • 08/20 How to avoid making mountains out of molehills, using power/severity
  • 08/24 3 YEARS AGO (AUGUST 2012): MEMORY LANE
  • 08/31 The Paradox of Replication, and the vindication of the P-value (but she can go deeper) 9/2/15 update (ii)

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

[2] New Rule, July 30, 2016, March 30,2017 -a very convenient way to allow data-dependent choices (note why it’s legit in selecting blog posts, on severity grounds).

 

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A. Spanos: Egon Pearson’s Neglected Contributions to Statistics

Posted on August 13, 2018 by Mayo

Continuing with the discussion of E.S. Pearson in honor of his birthday:

Egon Pearson’s Neglected Contributions to Statistics

by Aris Spanos

    Egon Pearson (11 August 1895 – 12 June 1980), is widely known today for his contribution in recasting of Fisher’s significance testing into the Neyman-Pearson (1933) theory of hypothesis testing. Occasionally, he is also credited with contributions in promoting statistical methods in industry and in the history of modern statistics; see Bartlett (1981). What is rarely mentioned is Egon’s early pioneering work on:

(i) specification: the need to state explicitly the inductive premises of one’s inferences,

(ii) robustness: evaluating the ‘sensitivity’ of inferential procedures to departures from the Normality assumption, as well as

(iii) Mis-Specification (M-S) testing: probing for potential departures from the Normality  assumption.

Arguably, modern frequentist inference began with the development of various finite sample inference procedures, initially by William Gosset (1908) [of the Student’s t fame] and then Fisher (1915, 1921, 1922a-b). These inference procedures revolved around a particular statistical model, known today as the simple Normal model: Continue reading →

Categories: E.S. Pearson, Egon Pearson, Statistics | 1 Comment

Egon Pearson’s Heresy

Posted on August 11, 2018 by Mayo

E.S. Pearson: 11 Aug 1895-12 June 1980.

Today is Egon Pearson’s birthday. In honor of his birthday, I am posting “Statistical Concepts in Their Relation to Reality” (Pearson 1955). I’ve posted it several times over the years, but always find a new gem or two, despite its being so short. E. Pearson rejected some of the familiar tenets that have come to be associated with Neyman and Pearson (N-P) statistical tests, notably the idea that the essential justification for tests resides in a long-run control of rates of erroneous interpretations–what he termed the “behavioral” rationale of tests. In an unpublished letter E. Pearson wrote to Birnbaum (1974), he talks about N-P theory admitting of two interpretations: behavioral and evidential:

“I think you will pick up here and there in my own papers signs of evidentiality, and you can say now that we or I should have stated clearly the difference between the behavioral and evidential interpretations. Certainly we have suffered since in the way the people have concentrated (to an absurd extent often) on behavioral interpretations”.

Continue reading →

Categories: phil/history of stat, Philosophy of Statistics, Statistics | Tags: , , | 2 Comments

For Popper’s Birthday: Reading from Conjectures and Refutations (+ self-test)

Posted on July 28, 2018 by Mayo
images-10

28 July 1902 – 17 September 1994

Today is Karl Popper’s birthday. I’m linking to a reading from his Conjectures and Refutations[i] along with: Popper Self-Test Questions. It includes multiple choice questions, quotes to ponder, an essay, and thumbnail definitions at the end[ii].

Blog Readers who wish to send me their answers will have their papers graded [use the comments or error@vt.edu.] An A- or better earns a signed copy of my forthcoming book: Statistical Inference as Severe Testing: How to Get Beyond the Statistics Wars. [iii]

[i] Popper reading from Conjectures and Refutations
[ii] I might note the “No-Pain philosophy” (3 part) Popper posts on this blog: parts 1, 2, and 3.

[iii] I posted this once before, but now I have a better prize.

HAPPY BIRTHDAY POPPER!

REFERENCE:

Popper, K. (1962). Conjectures and Refutations: The Growth of Scientific Knowledge. New York: Basic Books.

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Categories: Popper | 1 Comment

3 YEARS AGO (JULY 2015): MEMORY LANE

Posted on July 21, 2018 by Mayo
3 years ago...

3 years ago…

MONTHLY MEMORY LANE: 3 years ago: July 2015. I mark in red 3-4 posts from each month that seem most apt for general background on key issues in this blog, excluding those reblogged recently[1], and in green up to 3 others of general relevance to philosophy of statistics [2].  Posts that are part of a “unit” or a group count as one.

July 2015

  • 07/03 Larry Laudan: “When the ‘Not-Guilty’ Falsely Pass for Innocent”, the Frequency of False Acquittals (guest post)
  • 07/09  Winner of the June Palindrome contest: Lori Wike
  • 07/11 Higgs discovery three years on (Higgs analysis and statistical flukes)-reblogged recently
  • 07/14  Spot the power howler: α = ß?
  • 07/17  “Statistical Significance” According to the U.S. Dept. of Health and Human Services (ii)
  • 07/22 3 YEARS AGO (JULY 2012): MEMORY LANE
  • 07/24 Stephen Senn: Randomization, ratios and rationality: rescuing the randomized clinical trial from its critics
  • 07/29  Telling What’s True About Power, if practicing within the error-statistical tribe

 

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

[2] New Rule, July 30, 2016, March 30,2017 -a very convenient way to allow data-dependent choices (note why it’s legit in selecting blog posts, on severity grounds).

 

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S. Senn: Personal perils: are numbers needed to treat misleading us as to the scope for personalised medicine? (Guest Post)

Posted on July 11, 2018 by Mayo

Personal perils: are numbers needed to treat misleading us as to the scope for personalised medicine?

A common misinterpretation of Numbers Needed to Treat is causing confusion about the scope for personalised medicine.

Stephen Senn
Consultant Statistician,
Edinburgh

Introduction

Thirty years ago, Laupacis et al1 proposed an intuitively appealing way that physicians could decide how to prioritise health care interventions: they could consider how many patients would need to be switched from an inferior treatment to a superior one in order for one to have an improved outcome. They called this the number needed to be treated. It is now more usually referred to as the number needed to treat (NNT).

Within fifteen years, NNTs were so well established that the then editor of the British Medical Journal, Richard Smith could write:  ‘Anybody familiar with the notion of “number needed to treat” (NNT) knows that it’s usually necessary to treat many patients in order for one to benefit’2. Fifteen years further on, bringing us up to date,  Wikipedia makes a similar point ‘The NNT is the average number of patients who need to be treated to prevent one additional bad outcome (e.g. the number of patients that need to be treated for one of them to benefit compared with a control in a clinical trial).’3

This common interpretation is false, as I have pointed out previously in two blogs on this site: Responder Despondency and  Painful Dichotomies. Nevertheless, it seems to me the point is worth making again and the thirty-year anniversary of NNTs provides a good excuse. Continue reading →

Categories: personalized medicine, PhilStat/Med, S. Senn | 7 Comments

Statistics and the Higgs Discovery: 5-6 yr Memory Lane

Posted on July 4, 2018 by Mayo

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I’m reblogging a few of the Higgs posts at the 6th anniversary of the 2012 discovery. (The first was in this post.) The following, was originally “Higgs Analysis and Statistical Flukes: part 2″ (from March, 2013).[1]

Some people say to me: “This kind of [severe testing] reasoning is fine for a ‘sexy science’ like high energy physics (HEP)”–as if their statistical inferences are radically different. But I maintain that this is the mode by which data are used in “uncertain” reasoning across the entire landscape of science and day-to-day learning (at least, when we’re trying to find things out)[2] Even with high level theories, the particular problems of learning from data are tackled piecemeal, in local inferences that afford error control. Granted, this statistical philosophy differs importantly from those that view the task as assigning comparative (or absolute) degrees-of-support/belief/plausibility to propositions, models, or theories.  Continue reading →

Categories: Higgs, highly probable vs highly probed, P-values | 1 Comment

Replication Crises and the Statistics Wars: Hidden Controversies

Posted on June 23, 2018 by Mayo

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Below are the slides from my June 14 presentation at the X-Phil conference on Reproducibility and Replicability in Psychology and Experimental Philosophy at University College London. What I think must be examined seriously are the “hidden” issues that are going unattended in replication research and related statistics wars. An overview of the “hidden controversies” are on slide #3. Although I was presenting them as “hidden”, I hoped they wouldn’t be quite as invisible as I found them through the conference. (Since my talk was at the start, I didn’t know what to expect–else I might have noted some examples that seemed to call for further scrutiny). Exceptions came largely (but not exclusively) from a small group of philosophers (me, Machery and Fletcher). Then again,there were parallel sessions, so I missed some.  However, I did learn something about X-phil, particularly from the very interesting poster session [1]. This new area should invite much, much more scrutiny of statistical methodology from philosophers of science.

[1] The women who organized and ran the conference did an excellent job: Lara Kirfel, a psychology PhD student at UCL, and Pascale Willemsen from Ruhr University.

Categories: Philosophy of Statistics, replication research, slides | Leave a comment

Your data-driven claims must still be probed severely

Posted on June 4, 2018 by Mayo

Vagelos Education Center

Below are the slides from my talk today at Columbia University at a session, Philosophy of Science and the New Paradigm of Data-Driven Science, at an American Statistical Association Conference on Statistical Learning and Data Science/Nonparametric Statistics. Todd was brave to sneak in philosophy of science in an otherwise highly mathematical conference.

Philosophy of Science and the New Paradigm of Data-Driven Science : (Room VEC 902/903)
Organizer and Chair: Todd Kuffner (Washington U)

  1. Deborah Mayo (Virginia Tech) “Your Data-Driven Claims Must Still be Probed Severely”
  2.  Ian McKeague (Columbia) “On the Replicability of Scientific Studies”
  3.  Xiao-Li Meng (Harvard) “Conducting Highly Principled Data Science: A Statistician’s Job and Joy

 

Categories: slides, Statistics and Data Science | 5 Comments

“Intentions (in your head)” is the code word for “error probabilities (of a procedure)”: Allan Birnbaum’s Birthday

Posted on May 27, 2018 by Mayo
27 May 1923-1 July 1976

27 May 1923-1 July 1976

Today is Allan Birnbaum’s Birthday. Birnbaum’s (1962) classic “On the Foundations of Statistical Inference,” in Breakthroughs in Statistics (volume I 1993), concerns a principle that remains at the heart of today’s controversies in statistics–even if it isn’t obvious at first: the Likelihood Principle (LP) (also called the strong likelihood Principle SLP, to distinguish it from the weak LP [1]). According to the LP/SLP, given the statistical model, the information from the data are fully contained in the likelihood ratio. Thus, properties of the sampling distribution of the test statistic vanish (as I put it in my slides from this post)! But error probabilities are all properties of the sampling distribution. Thus, embracing the LP (SLP) blocks our error statistician’s direct ways of taking into account “biasing selection effects” (slide #10). [Posted earlier here.] Interesting, as seen in a 2018 post on Neyman, Neyman did discuss this paper, but had an odd reaction that I’m not sure I understand. (Check it out.) Continue reading →

Categories: Birnbaum, Birnbaum Brakes, frequentist/Bayesian, Likelihood Principle, phil/history of stat, Statistics | 7 Comments

The Meaning of My Title: Statistical Inference as Severe Testing: How to Get Beyond the Statistics Wars

Posted on May 19, 2018 by Mayo

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Excerpts from the Preface:

The Statistics Wars: 

Today’s “statistics wars” are fascinating: They are at once ancient and up to the minute. They reflect disagreements on one of the deepest, oldest, philosophical questions: How do humans learn about the world despite threats of error due to incomplete and variable data? At the same time, they are the engine behind current controversies surrounding high-profile failures of replication in the social and biological sciences. How should the integrity of science be restored? Experts do not agree. This book pulls back the curtain on why. Continue reading →

Categories: Announcement, SIST | 2 Comments

Getting Up to Speed on Principles of Statistics

Posted on May 13, 2018 by Mayo

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“If a statistical analysis is clearly shown to be effective … it gains nothing from being … principled,” according to Terry Speed in an interesting IMS article (2016) that Harry Crane tweeted about a couple of days ago [i]. Crane objects that you need principles to determine if it is effective, else it “seems that a method is effective (a la Speed) if it gives the answer you want/expect.” I suspected that what Speed was objecting to was an appeal to “principles of inference” of the type to which Neyman objected in my recent post. This turns out to be correct. Here are some excerpts from Speed’s article (emphasis is mine): Continue reading →

Categories: Likelihood Principle, Philosophy of Statistics | 5 Comments

3 YEARS AGO (May 2015): Monthly Memory Lane

Posted on May 1, 2018 by Mayo
3 years ago...               3 years ago…

MONTHLY MEMORY LANE: 3 years ago: May 2015. I mark in red 3-4 posts from each month that seem most apt for general background on key issues in this blog, excluding those reblogged recently[1]. Posts that are part of a “unit” or a group count as one, as in the case of 5/16, 5/19 and 5/24.

May 2015

  • 05/04 Spurious Correlations: Death by getting tangled in bedsheets and the consumption of cheese! (Aris Spanos)
  • 05/08 What really defies common sense (Msc kvetch on rejected posts)
  • 05/09 Stephen Senn: Double Jeopardy?: Judge Jeffreys Upholds the Law (sequel to the pathetic P-value)
  • 05/16 “Error statistical modeling and inference: Where methodology meets ontology” A. Spanos and D. Mayo
  • 05/19 Workshop on Replication in the Sciences: Society for Philosophy and Psychology: (2nd part of double header)
  • 05/24 From our “Philosophy of Statistics” session: APS 2015 convention
  • 05/27 “Intentions” is the new code word for “error probabilities”: Allan Birnbaum’s Birthday
  • 05/30 3 YEARS AGO (MAY 2012): Saturday Night Memory Lane

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

I regret being away from blogging as of late (yes, the last bit of proofing on the book): I shall return soon! Send me stuff to post of yours or items of interest in the mean time.

 

Categories: 3-year memory lane | 1 Comment

Neyman vs the ‘Inferential’ Probabilists continued (a)

Posted on April 16, 2018 by Mayo

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Today is Jerzy Neyman’s Birthday (April 16, 1894 – August 5, 1981).  I am posting a brief excerpt and a link to a paper of his that I hadn’t posted before: Neyman, J. (1962), ‘Two Breakthroughs in the Theory of Statistical Decision Making‘ [i] It’s chock full of ideas and arguments, but the one that interests me at the moment is Neyman’s conception of “his breakthrough”, in relation to a certain concept of “inference”.  “In the present paper” he tells us, “the term ‘inferential theory’…will be used to describe the attempts to solve the Bayes’ problem with a reference to confidence, beliefs, etc., through some supplementation …either a substitute a priori distribution [exemplified by the so called principle of insufficient reason] or a new measure of uncertainty” such as Fisher’s fiducial probability. Now Neyman always distinguishes his error statistical performance conception from Bayesian and Fiducial probabilisms [ii]. The surprising twist here is semantical and the culprit is none other than…Allan Birnbaum. Yet Birnbaum gets short shrift, and no mention is made of our favorite “breakthrough” (or did I miss it?). [iii] I’ll explain in later stages of this post & in comments…(so please check back); I don’t want to miss the start of the birthday party in honor of Neyman, and it’s already 8:30 p.m in Berkeley!

Note: In this article,”attacks” on various statistical “fronts” refers to ways of attacking problems in one or another statistical research program. HAPPY BIRTHDAY NEYMAN! Continue reading →

Categories: Bayesian/frequentist, Error Statistics, Neyman, Statistics | Leave a comment

3 YEARS AGO (APRIL 2015): MEMORY LANE

Posted on April 6, 2018 by Mayo
3 years ago...

3 years ago…

MONTHLY MEMORY LANE: 3 years ago: April 2015. I mark in red 3-4 posts from each month that seem most apt for general background on key issues in this blog, excluding those reblogged recently[1], and in green up to 3 others of general relevance to philosophy of statistics (in months where I’ve blogged a lot)[2].  Posts that are part of a “unit” or a group count as one.

April 2015

  • 04/01 Are scientists really ready for ‘retraction offsets’ to advance ‘aggregate reproducibility’? (let alone ‘precautionary withdrawals’)
  • 04/04 Joan Clarke, Turing, I.J. Good, and “that after-dinner comedy hour…”
  • 04/08 Heads I win, tails you lose? Meehl and many Popperians get this wrong (about severe tests)!
  • 04/13 Philosophy of Statistics Comes to the Big Apple! APS 2015 Annual Convention — NYC
  • 04/16 A. Spanos: Jerzy Neyman and his Enduring Legacy
  • 04/18 Neyman: Distinguishing tests of statistical hypotheses and tests of significance might have been a lapse of someone’s pen
  • 04/22 NEYMAN: “Note on an Article by Sir Ronald Fisher” (3 uses for power, Fisher’s fiducial argument)
  • 04/24 “Statistical Concepts in Their Relation to Reality” by E.S. Pearson
  • 04/27 3 YEARS AGO (APRIL 2012): MEMORY LANE
  • 04/30 96% Error in “Expert” Testimony Based on Probability of Hair Matches: It’s all Junk!

 

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

[2] New Rule, July 30,2016, March 30,2017 -a very convenient way to allow data-dependent choices (note why it’s legit in selecting blog posts, on severity grounds).

 

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New Warning: Proceed With Caution Until the “Alt Stat Approaches” are Evaluated

Posted on April 1, 2018 by Mayo

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

“Restoring Credibility in Statistical Science: Proceed with Caution Until a Balanced Critique Is In”

J. Hossiason Continue reading →

Categories: Announcement | 3 Comments

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