On the Interpretation of Hypothesis Tests following Neyman and Pearson

Abstract

To begin with, Neyman and Pearson agreed with Fisher that the result in a hypothesis test is a measure of evidence. In their first joint paper, which was published in 1928, they declared that the level of significance (P-level) attained in a likelihood ratio test is a measure of evidence against the null hypothesis [1928, pp.28–9], and that a hypothesis test is a method with which to "accept" or "reject" the null hypothesis "..with a greater or less degree of confidence" or certainty [1928, pp.1, 67]. This was clearly an inferential interpretation.1 However, in 1933, in their celebrated joint paper to the Royal Society, they introduced the notion that a hypothesis test is simply a "rule of behavior", i.e. a rule for decision between alternate courses of action. This was Neyman's idea. Pearson, it seems, retained the position that a hypothesis test is a legitimate method for inference. Indeed, in a paper of his own published in 1955, Pearson agreed explicitly with Fisher that a test is a "means for learning" [1955, p.206]. Furthermore, in this same paper, he, disclaimed any association with Neyman's idea that tests are methods merely for "inductive behavior" or decision [1955, pp.206–7]. Moreover, there seems a commitment to inference throughout Pearson's writing. For example, consider his statement in a joint paper with Clopper [1934, pp.404–5] that some confidence interval (P1,P2) with "confidence coefficient" 1-α entails a degree of confidence or certainty (probability-,)2 of 1-α that the true paramater θ lies in the interval p 1 to p 2 , i.e. prob 1(θ∊ (p 1,p 2)=1-α.