Detecting Mediation Effects With the Bayes Factor: Performance Evaluation and Tools for Sample Size Determination

Testing the presence of mediation effects is important in social science research. Recently, Bayesian hypothesis testing with Bayes factors (BFs) has become increasingly popular. However, the use of BFs for testing mediation effects is still under-studied, despite the growing literature on Bayesian mediation analysis. In this study, we systematically examine the performance of the BF for testing the presence versus absence of a mediation effect. Our results showed that the false and/or true positive rates of detecting mediation with the BF can be impacted by the prior specification, including the prior odds of the presence of each path (treatment-mediator path or mediator-outcome path) used in the design stage for data generation and in the analysis stage for calculating the BF of the mediation effect. Based on our examination, we developed an R function and a web application to determine sample sizes for testing mediation effects with the BF. Our study provides insights on the performance of the BF for testing mediation effects and adds to researchers' toolbox of sample size determination for mediation studies.