How to use and report Bayesian hypothesis tests

This article provides guidance on interpreting and reporting Bayesian hypothesis tests, to aid their understanding. To use and report a Bayesian hypothesis test, predicted effect sizes must be specified. The article will provide guidance in specifying effect sizes of interest (which also will be of relevance to those using frequentist statistics). First, if a minimally interesting effect size can be specified, a null interval is defined as the effects smaller in magnitude than the minimally interesting effect. Then the proportion of the posterior distribution that falls in the null interval indicates the plausibility of the null interval hypothesis. Second, if a rough scale of effect can be determined, a Bayes factor can indicate evidence for a model representing that scale of effect versus a model of the null hypothesis. Both methods allow data to count against a theory that predicts a difference. By contrast, nonsignificance does not count against such a theory. Various examples are provided including the suitability of Bayesian analyses for demonstrating the absence of conscious perception under putative subliminal conditions, and its presence in supraliminal conditions.