P-values as Frequentist Measures

Working on the last two chapters of my book on philosophy of statistical inference, I’m revisiting such topics as weak conditioning, Birnbaum, likelihood principle, etc., and was reading from the Proceedings of the Berkeley Conference in Honor of Jerzy Neyman and Jack Kiefer (1985)[i]. In a paper I had not seen (or had forgotten), Jim Berger “The Frequentist Viewpoint and Conditioning,” writes that the quoting of a P-value “may be felt to be a frequentist procedure by some, since it involves an averaging over the sample space. The reporting of P-values can be given no long-run frequency interpretation [in any of the set-ups generally considered].  A P-value actually lies closer to conditional (Bayesian) measures than to frequentist measures.” (Berger 1985, 23). These views are echoed in Berger’s more recent “Could Fisher,Jeffreys and Neyman Have Agreed on Testing?”(2003). This is at odds with what Fisher, N-P, Cox, Lehmann, etc. have held, and if true, would also seem to entail that a severity assessment had no frequentist interpretation!  The flaw lies in that all-too-common behavioristic, predesignated conception…

Among related posts:



[i] Also because of Peter Gruenwald’s recent mention of Kiefer’s work, read long ago.

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