Misplaced Criticisms of Neyman-Pearson Testing in the Case of Two Simple Hypotheses ∗ Aris Spanos Department of Economics, Virginia Tech, Blacksburg, VA 24061 aris@vt.edu February 2011 Abstract The main aim of this note is to revisit the widely-used Bayesian criticism that in the case of simple vs. simple hypotheses Neyman-Pearson (N-P) test- ing gives rise to fallacious results. Using a particular example in Berger and Wolpert (1988) the paper argues that the Bayesian criticism is based on inade- quate understanding of N-P testing and an erroneous intuition stemming from Bayesian reasoning. In particular, their premise that when one is interested in only two values of the parameter in question the rest of the parameter values are irrelevant is false; in N-P testing all parameter values are relevant for sta- tistical purposes. Moreover, their claim that rejecting the null in a N-P test provides evidence for a particular alternative is a classic example of the well- known fallacy of rejection. This fallacy can be easily addressed in frequentist testing using a post-data evaluation of the accept/reject rules based on severity reasoning. This latter is also used to show that the invoked Bayesian intuition is clearly false. Key words: Neyman-Pearson testing; power of a test; fallacy of rejection; post-data severity evaluation; Bayes factor; warranted discrepancy from the null. ∗ Published in Advances and Applications in Statistical Science, 6: 229-242, 2011. 1