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. Research on the synthesis of Bayes Factors arising from individual studies has received increasing attention, mostly for the fixed effects model for meta-analysis. In this work, we review and propose methods for combining Bayes Factors from multiple studies, depending on the level of information available, focusing on the common effect model. In the process, we provide insights with respect to the interplay between frequentist and Bayesian evidence. We assess the performance of the methods discussed via a simulation study and apply the methods in an example from the field of positive psychology.

翻译：贝叶斯因子作为贝叶斯假设检验工具，正日益受到学界关注。相较于频率学派的竞争方法（$p$值或检验统计量），贝叶斯因子具有概念上的优势：既能提供支持原假设的证据，也能提供反对原假设的证据，且可通过校准使其对样本量的依赖性显著降低。针对单项研究产生的贝叶斯因子进行合成的相关研究日益增多，目前主要集中在元分析中的固定效应模型。本研究系统回顾并提出了根据可用信息水平整合多项研究贝叶斯因子的方法，重点关注公共效应模型。在此过程中，我们深入探讨了频率学派证据与贝叶斯证据之间的相互作用关系。通过模拟研究评估了所讨论方法的性能，并将这些方法应用于积极心理学领域的实证案例。