Aggregating evidence from conceptual replication studies using the product Bayes factor

The product Bayes factor (PBF) can synthesize evidence for an informative hypothesis across heterogeneous replication studies. It is particularly useful when the number of studies is relatively low and conventional assumptions about between-studies heterogeneity are likely violated. The present paper introduces a user-friendly implementation of the PBF in the bain R-package. The method was validated in a simulation study that manipulated sample size, number of replication samples, and reliability. Several tutorial examples demonstrate the use of the method in distinct use cases. Results of the simulation study show that PBF had a higher overall accuracy when benchmarked against other evidence synthesis methods, including random-effects meta-analysis (RMA). This was primarily due to PBF’s greater sensitivity in detecting a true effect. However, PBF had relatively lower specificity. The PBF showed increasing sensitivity and specificity with increasing sample size. With an increasing number of samples, lower sensitivity was traded for greater specificity. Although PBF's overall performance was less susceptible to reliability than the other algorithms, this masked a trade-off between reliability and specificity. PBF thus appears to be a promising method for meta-analysis of heterogeneous conceptual replication studies. Nonetheless, users should be aware of its lower specificity, and the fact that the Bayesian approach to inference addresses a qualitatively different research question than other evidence synthesis methods.