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.
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)
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:
- 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.