A tutorial on aggregating evidence from conceptual replication studies using the product Bayes factor

The product Bayes factor (PBF) synthesizes evidence for an informative hypothesis across heterogeneous replication studies. It can be used when fixed- or random effects meta-analysis fall short. For example, when effect sizes are incomparable and cannot be pooled, or when studies diverge significantly in the populations, study designs, and measures used. PBF shines as a solution for small sample meta-analyses, where the number of between-study differences is often large relative to the number of studies, precluding the use of meta-regression to account for these differences. Users should be mindful of the fact that the PBF answers a qualitatively different research question than other evidence synthesis methods. For example, whereas fixed-effect meta-analysis estimates the size of a population effect, the PBF quantifies to what extent an informative hypothesis is supported in all included studies. This tutorial paper showcases the user-friendly PBF functionality within the bain R-package. This new implementation of an existing method was validated using a simulation study, available in an Online Supplement. Results showed that PBF had a high overall accuracy, due to greater sensitivity and lower specificity, compared to random-effects meta-analysis, individual participant data meta-analysis, and vote counting. Tutorials demonstrate applications of the method on meta-analytic and individual participant data. The example datasets, based on published research, are included in bain so readers can reproduce the examples and apply the code to their own data. The PBF is a promising method for synthesizing evidence for informative hypotheses across conceptual replications that are not suitable for conventional meta-analysis.