Abstract

The p value is the probability under the null hypothesis of obtaining an experimental result that is at least as extreme as the one that we have actually obtained. That probability plays a crucial role in frequentist statistical inferences. But if we take the word ‘extreme’ to mean ‘improbable’, then we can show that this type of inference can be very problematic. In this paper, I argue that it is a mistake to make such an interpretation. Under minimal assumptions about the alternative hypothesis, I explain why ‘extreme’ means ‘outside the most precise predicted range of experimental outcomes for a given upper bound probability of error’. Doing so, I rebut recent formulations of recurrent criticisms against the frequentist approach in statistics and underscore the importance of random variables.