A Bayes Factor for Replications of ANOVA Results

With an increasing number of replication studies performed in psychological science, the question of how to evaluate the outcome of a replication attempt deserves careful consideration. Bayesian approaches allow to incorporate uncertainty and prior information into the analysis of the replication attempt by their design. The Replication Bayes factor, introduced by Verhagen and Wagenmakers (2014), provides quantitative, relative evidence in favor or against a successful replication. In previous work by Verhagen and Wagenmakers (2014), it was limited to the case of <i>t</i>-tests. In this article, the Replication Bayes factor is extended to <i>F</i>-tests in multigroup, fixed-effect ANOVA designs. Simulations and examples are presented to facilitate the understanding and to demonstrate the usefulness of this approach. Finally, the Replication Bayes factor is compared to other Bayesian and frequentist approaches and discussed in the context of replication attempts. R code to calculate Replication Bayes factors and to reproduce the examples in the article is available at https://osf.io/jv39h/.

随着心理科学领域重复研究的数量不断攀升，如何评估重复研究尝试的结果这一问题，值得审慎考量。贝叶斯方法凭借其设计特性，可将不确定性与先验信息纳入重复研究的分析流程。由Verhagen与Wagenmakers（2014）提出的复制贝叶斯因子（Replication Bayes factor），能够提供支持或反对重复研究成功与否的量化相对证据。在Verhagen与Wagenmakers（2014）的早期研究中，该方法仅局限于t检验场景。本文将复制贝叶斯因子拓展至多组固定效应方差分析（ANOVA）设计中的F检验场景。文中通过模拟实验与实例分析，助力读者理解该方法并展现其应用价值。最后，本文将复制贝叶斯因子与其他贝叶斯方法及频率学派方法进行对比，并结合重复研究的场景展开讨论。用于计算复制贝叶斯因子以及复现本文示例的R代码可通过https://osf.io/jv39h/获取。