Note: I find this to be an intriguing, if perhaps little-known, discussion, long before the conflicts reflected in the three articles (the “triad”) below, Here Fisher links his tests to the Neyman and Pearson lemma in terms of power. I invite your deconstructions/comments.
by R.A. Fisher, F.R.S.
Proceedings of the Royal Society, Series A, 144: 285-307 (1934)
To Thomas Bayes must be given the credit of broaching the problem of using the concepts of mathematical probability in discussing problems of inductive inference, in which we argue from the particular to the general; or, in statistical phraselogy, argue from the sample to the population, from which, ex hypothesi, the sample was drawn. Bayes put forward, with considerable caution, a method by which such problems could be reduced to the form of problems of probability. His method of doing this depended essentially on postulating a priori knowledge, not of the particular population of which our observations form a sample, but of an imaginary population of populations from which this population was regarded as having been drawn at random. Clearly, if we have possession of such a priori knowledge, our problem is not properly an inductive one at all, for the population under discussion is then regarded merely as a particular case of a general type, of which we already possess exact knowledge, and are therefore in a position to draw exact deductive inferences.