  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.
