Deborah G. Mayo Did Pearson Reject the Neyman-pearson Philosophy of Statistics?*

I document some of the main evidence showing that E. S. Pearson rejected the key features of the behavioral-decision philosophy that became associated with the Neyman-Pearson Theory of statistics (NPT). I argue that NPT principles arose not out of behavioral aims, where the concern is solely with behaving correctly sufficiently often in some long run, but out of the epistemological aim of learning about causes of experimental results (e.g., distinguishing genuine from spurious effects). The view Pearson did hold gives a deeper understanding of NPT tests than their typical formulation as 'acceptreject routines', against which criticisms of NPT are really directed. The 'Pearsonian' view that emerges suggests how NPT tests may avoid these criticisms while still retaining what is central to these methods: the control of error probabilities. , 2 1. I N T R O D U C T I O N The Neyman-Pearson Theory of statistics (NPT), often referred to as 'standard' or 'orthodox' statistical theory, is the generally-received view in university departments of statistics, and it underlies common statistical reports. Strictly speaking, NPT procedures of hypotheses testing and estimation are only a part of the full collection of methods referred to as 'sampling theory', which also includes methods of experimental design and data analysis, But it is this part on which philosophical critics of 'standard' or 'orthodox' statistical theory have generally concentrated. Egon S. Pearson (not to be confused with his father, Karl'), although one of the two founders of NPT, rejected the statistical philosophy that ultimately became associated with NPT, or so I shall argue. Because specific citations are important for my case, I shall quote throughout at some length. Another reason for doing so is to put these remarks largely overlooked in discussions of the philosophy of statistics together in one place. Understanding Pearson's rejection of the NPT philosophy is of more than merely historical interest. It is also highly relevant to the allegations of many philosophers of statistics Fetzer (1981), Hacking (1965) (but compare Hacking (1980)), Howson and Urbach (1989), Kyburg (1971, 1974), Levi (1980), Rosenkrantz (1977), Seidenfeld (1979), Spielman (1973), and of several statisticians as well that NPT, Synthese 90: 233-262, 1992. © 1992 Kluwer Academic Publishers. Printed in the Netherlands. 234 D E B O R A H G. MAYO despite its widespread use, is inappropriate for statistical inference in science. In statistical practice as well, there continues to be a lively debate over the use of NPT methods, with their seeming rigidities, in the face of the vicissitudes of actual experimental data (e.g., in clinical trials and risk assessments). Many of these contemporary criticisms mirror, I claim, Pearson's own reasons for rejecting the philosophy typically associated with NPT. Extricating the view Pearson did hold, I think, gives a much deeper understanding of NPT principles than that found in statistics texts, against which criticisms of NPT are really directed. Such an understanding suggests how NPT may avoid some of these criticisms while still retaining what is central to sampling theory methods: the fundamental importance of error probabilities. Finally, the 'Pearsonian' view of statistical inference that emerges seems to offer a promising avenue for using statistical reasoning to accomplish the task at which 'inductive logics' fell short: illuminating the nature and rationale of experimental learning in science. 2. NEYMAN--PEARSON THEORY OF STATISTICAL TESTS