Harold Jeffreys's default Bayes factor hypothesis tests: Explanation, extension, and application in psychology

Harold Jeffreys pioneered the development of default Bayes factor hypothesis tests for standard statistical problems. Using Jeffreys's Bayes factor hypothesis tests, researchers can grade the decisiveness of the evidence that the data provide for a point null hypothesis H0 versus a composite alternative hypothesis H1. Consequently, Jeffreys's tests are of considerable theoretical and practical relevance for empirical researchers in general and for experimental psychologists in particular. To highlight this relevance and to facilitate the interpretation and use of Jeffreys's Bayes factor tests we focus on two common inferential scenarios: testing the nullity of a normal mean (i.e., the Bayesian equivalent of the t-test) and testing the nullity of a correlation. For both Bayes factor tests, we explain their development, we extend them to one-sided problems, and we apply them to concrete examples from experimental psychology.