Egon Sharpe (E.S.) Pearson’s birthday was August 11. This slightly belated birthday discussion is directly connected to the question of the uses to which frequentist methods may be put in inquiry. Are they limited to supplying procedures which will not err too frequently in some vast long run? Or are these long run results of crucial importance for understanding and learning about the underlying causes in the case at hand? I say no to the former and yes to the latter. This was also the view of Egon Pearson (of Neyman and Pearson).
(i) Cases of Type A and Type B
“How far then, can one go in giving precision to a philosophy of statistical inference?” (Pearson 1947, 172)
Pearson considers the rationale that might be given to N-P tests in two types of cases, A and B:
“(A) At one extreme we have the case where repeated decisions must be made on results obtained from some routine procedure…
(B) At the other is the situation where statistical tools are applied to an isolated investigation of considerable importance…?” (ibid., 170)
In cases of type A, long-run results are clearly of interest, while in cases of type B, repetition is impossible and may be irrelevant:
“In other and, no doubt, more numerous cases there is no repetition of the same type of trial or experiment, but all the same we can and many of us do use the same test rules to guide our decision, following the analysis of an isolated set of numerical data. Why do we do this? What are the springs of decision? Is it because the formulation of the case in terms of hypothetical repetition helps to that clarity of view needed for sound judgment? Read more