Meta Analysis of Bayes Factors

Bayes Factors, the Bayesian tool for hypothesis testing, are receiving increasing attention in the literature. Compared to their frequentist rivals ($p$-values or test statistics), Bayes Factors have the conceptual advantage of providing evidence both for and against a null hypothesis and they can be calibrated so that they do not depend so heavily on the sample size. However, research on the synthesis of Bayes Factors arising from individual studies has received very limited attention. In this work we review and propose methods for combining Bayes Factors from multiple studies, depending on the level of information available. In the process, we provide insights with respect to the interplay between frequentist and Bayesian evidence. We also clarify why some intuitive suggestions in the literature can be misleading. We assess the performance of the methods discussed via a simulation study and apply the methods in an example from the field of psychology.