a road through the jungle
In my talk yesterday at the Philosophy Department at Virginia Tech, I introduced my new book: Statistical Inference as Severe Testing: How to Get Beyond the Statistics Wars (Cambridge 2018). I began with my preface (explaining the meaning of my title), and turned to the Statistics Wars, largely from Excursion 1 of the book. After the sum-up at the end, I snuck in an example from the replication crisis in psychology. Here are the slides.
StatSci/PhilSci Museum
Where you are in the Journey* We’ll move from the philosophical ground floor to connecting themes from other levels, from Popperian falsification to significance tests, and from Popper’s demarcation to current-day problems of pseudoscience and irreplication. An excerpt from our Museum Guide gives a broad-brush sketch of the first few sections of Tour II:
Karl Popper had a brilliant way to “solve” the problem of induction: Hume was right that enumerative induction is unjustified, but science is a matter of deductive falsification. Science was to be demarcated from pseudoscience according to whether its theories were testable and falsifiable. A hypothesis is deemed severely tested if it survives a stringent attempt to falsify it. Popper’s critics denied he could sustain this and still be a deductivist …
Popperian falsification is often seen as akin to Fisher’s view that “every experiment may be said to exist only in order to give the facts a chance of disproving the null hypothesis” (1935a, p. 16). Though scientists often appeal to Popper, some critics of significance tests argue that they are used in decidedly non-Popperian ways. Tour II explores this controversy.
While Popper didn’t make good on his most winning slogans, he gives us many seminal launching-off points for improved accounts of falsification, corroboration, science versus pseudoscience, and the role of novel evidence and predesignation. These will let you revisit some thorny issues in today’s statistical crisis in science. Continue reading
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My new book, Statistical Inference as Severe Testing: How to Get Beyond the Statistics Wars,” you might have discovered, includes Souvenirs throughout (A-Z). But there are some highlights within sections that might be missed in the excerpts I’m posting. One such “keepsake” is a quote from Fisher at the very end of Section 2.1.
These are some of the first clues we’ll be collecting on a wide difference between statistical inference as a deductive logic of probability, and an inductive testing account sought by the error statistician. When it comes to inductive learning, we want our inferences to go beyond the data: we want lift-off. To my knowledge, Fisher is the only other writer on statistical inference, aside from Peirce, to emphasize this distinction.
In deductive reasoning all knowledge obtainable is already latent in the postulates. Rigour is needed to prevent the successive inferences growing less and less accurate as we proceed. The conclusions are never more accurate than the data. In inductive reasoning we are performing part of the process by which new knowledge is created. The conclusions normally grow more and more accurate as more data are included. It should never be true, though it is still often said, that the conclusions are no more accurate than the data on which they are based. (Fisher 1935b, p. 54)
How do you understand this remark of Fisher’s? (Please share your thoughts in the comments.) My interpretation, and its relation to the “lift-off” needed to warrant inductive inferences, is discussed in an earlier section, 1.2, posted here. Here’s part of that.
StatSci/PhilSci Museum
Where you are in the Journey*
Cox: [I]n some fields foundations do not seem very important, but we both think that foundations of statistical inference are important; why do you think that is?
Mayo: I think because they ask about fundamental questions of evidence, inference, and probability … we invariably cross into philosophical questions about empirical knowledge and inductive inference. (Cox and Mayo 2011, p. 103)
Contemporary philosophy of science presents us with some taboos: Thou shalt not try to find solutions to problems of induction, falsification, and demarcating science from pseudoscience. It’s impossible to understand rival statistical accounts, let alone get beyond the statistics wars, without first exploring how these came to be “lost causes.” I am not talking of ancient history here: these problems were alive and well when I set out to do philosophy in the 1980s. I think we gave up on them too easily, and by the end of Excursion 2 you’ll see why. Excursion 2 takes us into the land of “Statistical Science and Philosophy of Science” (StatSci/PhilSci). Our Museum Guide gives a terse thumbnail sketch of Tour I. Here’s a useful excerpt:
Once the Problem of Induction was deemed to admit of no satisfactory, non-circular solutions (~1970s), philosophers of science turned to building formal logics of induction using the deductive calculus of probabilities, often called Confirmation Logics or Theories. A leader of this Confirmation Theory movement was Rudolf Carnap. A distinct program, led by Karl Popper, denies there is a logic of induction, and focuses on Testing and Falsification of theories by data. At best a theory may be accepted or corroborated if it fails to be falsified by a severe test. The two programs have analogues to distinct methodologies in statistics: Confirmation theory is to Bayesianism as Testing and Falsification are to Fisher and Neyman–Pearson.
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Error Statistics Philosophy: Blog Contents (7 years) [i]
By: D. G. Mayo
Dear Reader: I began this blog 7 years ago (Sept. 3, 2011)! A big celebration is taking place at the Elbar Room this evening, both for the blog and the appearance of my new book: Statistical Inference as Severe Testing: How to Get Beyond the Statistics Wars (CUP). While a special rush edition made an appearance on Sept 3, in time for the RSS meeting in Cardiff, it was decided to hold off on the festivities until copies of the book were officially available (yesterday)! If you’re in the neighborhood, stop by for some Elba Grease
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Many of the discussions in the book were importantly influenced (corrected and improved) by reader’s comments on the blog over the years. I thank readers for their input. Please peruse the offerings below, taking advantage of the discussions by guest posters and readers! I posted the first 3 sections of Tour I (in Excursion i) here, here, and here.
This blog will return to life, although I’m not yet sure of exactly what form it will take. Ideas are welcome. The tone of a book differs from a blog, so we’ll have to see what voice emerges here.Sincerely,
D. Mayo Continue reading
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How can a discipline, central to science and to critical thinking, have two methodologies, two logics, two approaches that frequently give substantively different answers to the same problems? … Is complacency in the face of contradiction acceptable for a central discipline of science? (Donald Fraser 2011, p. 329)
We [statisticians] are not blameless … we have not made a concerted professional effort to provide the scientific world with a unified testing methodology. (J. Berger 2003, p. 4)
From the aerial perspective of a hot-air balloon, we may see contemporary statistics as a place of happy multiplicity: the wealth of computational ability allows for the application of countless methods, with little handwringing about foundations. Doesn’t this show we may have reached “the end of statistical foundations”? One might have thought so. Yet, descending close to a marshy wetland, and especially scratching a bit below the surface, reveals unease on all sides. The false dilemma between probabilism and long-run performance lets us get a handle on it. In fact, the Bayesian versus frequentist dispute arises as a dispute between probabilism and performance. This gets to my second reason for why the time is right to jump back into these debates: the “statistics wars” present new twists and turns. Rival tribes are more likely to live closer and in mixed neighborhoods since around the turn of the century. Yet, to the beginning student, it can appear as a jungle.
Statistics Debates: Bayesian versus Frequentist
These days there is less distance between Bayesians and frequentists, especially with the rise of objective [default] Bayesianism, and we may even be heading toward a coalition government. (Efron 2013, p. 145)
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
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:
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.
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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
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
[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).
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
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”.
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.
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
[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).
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
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
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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
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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.
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)
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
Experts convene to explore new philosophy of statistics field
Error Statistics Philosophy 