On the Neyman–Pearson Theory of Testing

Abstract

4 Likelihoods. 5 Summary. I INTRODUCTION Spielman [1973] presents 'A Refutation of the Neyman-Pearson Theory of Testing'. He states at the outset [p. 202],1 'I intend to show that NPT is inadequate on its own terms'. We have had great difficulty in following his argument because he never quite states exactly what Neyman-Pearson Theory (NPT) is to him, and because his objections are not relevant to our conception of NPT. As we understand Spielman's criticism, it amounts to saying that NPT is inadequate because it is neither Bayesian nor reasoning based on the likelihood principle. We find this roughly equivalent to saying he is going to criticise Hebrew theology on its own terms, and then basing his entire argument on the New Testament. We hope to establish below that (i) Neyman and Pearson considered a Bayesian approach and reasoning based directly on likelihoods, and deliberately excluded both from their theory giving reasons for this exclusion and (2) the procedure Spielman would employ in any of the examples he discussed or cited--given the constraints of the problem-is exactly the one that Neyman and Pearson would recommend. There are differences between Neyman-Pearson and Bayesian Theory, but these differences are not relevant to the examples and the issues Spielman discusses.