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I will continue to post mementos and, at times, short excerpts following the pace of one “Tour” a week, in sync with some book clubs reading Statistical Inference as Severe Testing: How to Get Beyond the Statistics Wars (SIST or Statinfast 2018, CUP), e.g., Lakens. This puts us at Excursion 2 Tour I, but first, here’s a quick Souvenir (Souvenir C) from Excursion 1 Tour II:

Souvenir C: A Severe Tester’s Translation Guide

Just as in ordinary museum shops, our souvenir literature often probes treasures that you didn’t get to visit at all. Here’s an example of that, and you’ll need it going forward. There’s a confusion about what’s being done when the significance tester considers the set of all of the outcomes leading to a d(x) greater than or equal to 1.96, i.e., {x: d(x) ≥ 1.96}, or just d(x) ≥ 1.96. This is generally viewed as throwing away the particular x, and lumping all these outcomes together. What’s really happening, according to the severe tester, is quite different. What’s actually being signified is that we are interested in the method, not just the particular outcome. Those who embrace the LP make it very plain that data-dependent selections and stopping rules drop out. To get them to drop in, we signal an interest in what the test procedure would have yielded. This is a counterfactual and is altogether essential in expressing the properties of the method, in particular, the probability it would have yielded some nominally significant outcome or other. Continue reading →

severe testing or severe sabotage? [not a book review]

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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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)

Continue reading →

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 →