.
After some wrestling with the Zenodo system of uploading, my paper “Sir David Cox’s Statistical Philosophy and its Relevance to Today’s Statistical Controversies” is now published (open access) in the JSM 2023 Proceedings (link).
Abstract
I discuss Sir David Cox’s views of the nature and importance of statistical foundations and their relevance to today’s controversies about statistical inference, particularly in using statistical significance tests. A central theme in Cox’s statistical philosophy is the importance of calibrating methods by considering their behavior in (actual or hypothetical) repeated sampling. Two key questions are open to philosophical controversy:
How can the frequentist calibration be used as an evidential or inferential assessment? How can we ensure that the hypothetical long-run used in calibration is relevant to the specific data?
I will discuss the answers that emerge from Cox’s work and our jointly written papers, Mayo and Cox (2006) and Cox and Mayo (2010) on statistical significance testing, objectivity in statistics, and conditioning.
Key Words: calibration, conditioning, Sir David R. Cox, statistical foundations, statistical philosophy, statistical significance tests
Cox tended to take Fisher’s side in the Fisher-Neyman wars. However, when we worked on Mayo and Cox 2006, he was open-minded enough to read some applied papers of Neyman that deviated from the usual caricatures. This is reflected somewhat in Mayo and Cox 2006, and in a footnote in his 2006 Principles of Statistical Inference (CUP), which I only stumbled across a few years ago:
Section 3.4. The contrast made here between the calculation of p-values as measures of evidence of consistency and the more decision-focused emphasis on accepting and rejecting hypotheses might be taken as one characteristic difference between the Fisherian and the Neyman-Pearson formulations of statistical theory. While this is in some respects the case, the actual practice in specific applications as between Fisher and Neyman was almost the reverse. Neyman often in effect reported p-values whereas some of Fisher’s use of tests in applications was much more dichotomous. For a discussion of the notion of severity of tests, and the circumstances when consistency with H0 might be taken as positive support for H0, see Mayo (1996). (43-4)
Please share your questions and comments in the Comments to this blog post.
Reference (with link):
Mayo, D.G. (2023). Sir David Cox’s Statistical Philosophy and its Relevance to Today’s Statistical Controversies. JSM 2023 Proceedings, DOI: https://zenodo.org/records/10028243.
Error Statistics Philosophy 
Thank you for posting your paper. I have a question. As you are no doubt aware, Birnbaum’s (1962) formulation of the conditionality principle involved an equivalence relation rather than a direction to replace unconditional frames of reference with conditional frames of reference when certain conditions apply. He later noted that “It was the adoption of an unqualified equivalence formulation of conditionality, and related concepts, which led, in my 1962 paper, to the monster of the likelihood axiom” (Biometrika (1975), p.263.)
Cox’s versions of the conditionality principle (Cox and Hinkley (1974); Reid and Cox (2014)) do not involve equivalence relations. Similarly, unlike other weak conditionality principles, the weak conditionality principle in your Cox and Mayo (2010) paper also does not involve an equivalence relation. Are you able to relate any insights about David’s view of the inappropriateness of Birnbaum’s version or about using the equivalence approach in conditionality principles?
Grahambornholt:
thanks for your comment. As you’ll see if you look at Mayo (2014), I do formulate WCP as an equivalence–as the only equivalence that holds true. See also the discussion in my response to David. You can find a link to the Statistical Science paper, discussion and response on this blog.
Thanks for your reply. I was just wondering if Cox had indicated to you what he thought of the various equivalence formulations used in some conditionality principles.