Minimum Message Length T-Test.

The frequentist two-sample t-test for comparison of two means is one of the most widely used hypothesis tests in practice. Recently, several Bayesian alternatives to the t-test were derived and shown to have some advantages, such as incorporation of prior expert knowledge, over the standard methodology. This manuscript introduces a new Bayesian t-test based on the minimum message length (MML) principle of inductive inference. The aim of the manuscript is to introduce the general reader to MML and demonstrate how MML can be applied to a problem of central importance in statistics.