Abstract

Heterogeneity of variance is a persistent concern in independent-samples t tests, raising questions about the robustness of Bayesian hypothesis testing when the equal-variance assumption is violated. The Jeffreys-Zellner-Siow (JZS) prior, commonly used as the default in Bayesian t tests, inherently assumes homoscedasticity. The present study examines the implications of this assumption by comparing a homoscedastic Bayesian t test based on the JZS prior with a heteroscedastic alternative that allows group-specific variances, the Girón-del Castillo (BFGC) model. An extensive simulation study was conducted to investigate how Bayes factors behave across varying combinations of variance ratios, sample size ratios, standardized effect sizes, and total sample sizes. Particular attention was given to conditions in which sample size imbalance interacted with variance heterogeneity. The results showed that the two models exhibit qualitatively different patterns of evidence accumulation under heteroscedasticity. Specifically, the JZS-based Bayes factor tended to provide weaker support for the true hypothesis when the group with the larger variance also had the larger sample size, whereas the BFGC-based Bayes factor showed the opposite pattern, yielding weaker support when the larger-variance group had the smaller sample size. These findings highlight that variance assumptions in Bayesian t tests can systematically influence the interpretation of Bayes factors, especially in the presence of sample size imbalance. When heteroscedasticity is plausible, adopting a heteroscedastic Bayesian model such as BFGC may therefore lead to more reliable Bayesian inference than reliance on the default JZS specification.