A New Bayesian Two-Sample t Test and Solution to the Behrens–Fisher Problem Based on Gaussian Mixture Modelling with Known Allocations

Abstract Testing differences between a treatment and control group is common practice in biomedical research like randomized controlled trials (RCT). The standard two-sample t test relies on null hypothesis significance testing (NHST) via p values, which has several drawbacks. Bayesian alternatives were recently introduced using the Bayes factor, its own limitations. This paper introduces an alternative to current tests by interpreting underlying model as two-component Gaussian mixture effect size quantity of interest, most relevant clinical research. Unlike values or proposed method focusses estimation under uncertainty instead explicit testing. Therefore, Gibbs sampler, posterior produced, used subsequently for either based region practical equivalence (ROPE). An illustrative example, theoretical results simulation study show usefulness method, made available R package . In sum, new provides solution Behrens–Fisher problem modelling.