Informed Bayesian t-Tests

Across the empirical sciences, few statistical procedures rival the of the frequentist t-test. In contrast, the Bayesian versions of the-test have languished in obscurity. In recent years, however, the theoretical practical advantages of the Bayesian t-test have become increasingly and various Bayesian t-tests have been proposed, both objective ones (based on general desiderata) and subjective ones (based on expert knowledge). we propose a flexible t-prior for standardized effect size that allows of the Bayes factor by evaluating a single numerical integral. This contains previous objective and subjective t-test Bayes factors special cases. Furthermore, we propose two measures for informed prior that quantify the departure from the objective Bayes factor of predictive matching and information consistency. We illustrate use of informed prior distributions based on an expert prior elicitation.