A Tutorial on Testing Hypotheses Using the Bayes Factor

Learning about hypothesis evaluation using the Bayes factor could enhance psychological research. In contrast to null-hypothesis significance testing it renders the evidence in favor of each of the hypotheses under consideration (it can be used to quantify support for the null-hypothesis) instead of a dichotomous reject/do-not-reject decision; it can straightforwardly be used for the evaluation of multiple hypotheses without having to bother about the proper manner to account for multiple testing; and it allows continuous reevaluation of hypotheses after additional data have been collected (Bayesian updating). This tutorial addresses researchers considering to evaluate their hypotheses by means of the Bayes factor. The focus is completely applied and each topic discussed is illustrated using Bayes factors for the evaluation of hypotheses in the context of an ANOVA model, obtained using the R package bain. Readers can execute all the analyses presented while reading this tutorial if they download bain and the R-codes used. It will be elaborated in a completely nontechnical manner: what the Bayes factor is, how it can be obtained, how Bayes factors should be interpreted, and what can be done with Bayes factors. After reading this tutorial and executing the associated code, researchers will be able to use their own data for the evaluation of hypotheses by means of the Bayes factor, not only in the context of ANOVA models, but also in the context of other statistical models. Translational Abstract Learning about hypothesis evaluation using the Bayes factor could enhance psychological research. The Bayes factor quantifies the support in the data for two competing hypotheses. These may be the traditional null and alternative hypotheses, but these may also be informative hypotheses like m1 > m2 > m3 and (m1 ― m2) > (m2 ― m3) where m1, m2, and m3 denote the means in three experimental groups. Bayesian hypotheses evaluation offers options such as quantifying evidence in favor of the null-hypothesis, simultaneous evaluation of multiple hypotheses, and Bayesian updating, that is, recomputation of the Bayes factor after additional data have been collected. In this tutorial it is elaborated how researchers can use the Bayes factor for the analysis of their own data. The focus is completely applied and each topic discussed is illustrated using Bayes factors for the evaluation of hypotheses in the context of an ANOVA model, obtained using the R package bain. Readers can execute all the analyses presented while reading this tutorial if they download bain and the R-codes used from the bain website. It will be elaborated in a completely nontechnical manner: what the Bayes factor is, how it can be obtained, how Bayes factors should be interpreted, and what can be done with Bayes factors. After reading this tutorial and executing the associated code, researchers will be able to use their own data for the evaluation of hypotheses by means of the Bayes factor, not only in the context of ANOVA models, but also in the context of other statistical models.