Obtaining evidence for no effect

Obtaining evidence that something does not exist requires knowing how big it would be were it to exist. Testing a theory that predicts an effect thus entails specifying the range of effect sizes consistent with the theory, in order to know when the evidence counts against the theory. Indeed, a theoretically relevant effect size must be specified for power calculations, equivalence testing, and Bayes factors in order that the inferential statistics test the theory. Specifying relevant effect sizes for power, or the equivalence region for equivalence testing, or the scale factor for Bayes factors, is necessary for many journal formats, such as registered reports, and should be necessary for all articles that use hypothesis testing. Yet there is little systematic advice on how to approach this problem. This article offers some principles and practical advice for specifying theoretically relevant effect sizes for hypothesis testing.