An Exact Bayesian Model for Meta-Analysis of the Standardized Mean Difference with Its Simultaneous Credible Intervals

While Bayesian methodology is increasingly favored in behavioral research for its clear probabilistic inference and model structure, its widespread acceptance as a standard meta-analysis approach remains limited. Although some conventional Bayesian hierarchical models are frequently used for analysis, their performance has not been thoroughly examined. This study evaluates two commonly used Bayesian models for meta-analysis of standardized mean difference and identifies significant issues with these models. In response, we introduce a new Bayesian model equipped with novel features that address existing model concerns and a broader limitation of the current Bayesian meta-analysis. Furthermore, we introduce a simple computational approach to construct simultaneous credible intervals for the summary effect and between-study heterogeneity, based on their joint posterior samples. This fully captures the joint uncertainty in these parameters, a task that is challenging or impractical with frequentist models. Through simulation studies rooted in a joint Bayesian/frequentist paradigm, we compare our model's performance against existing ones under conditions that mirror realistic research scenarios. The results reveal that our new model outperforms others and shows enhanced statistical properties. We also demonstrate the practicality of our models using real-world examples, highlighting how our approach strengthens the robustness of inferences regarding the summary effect.