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With the advent of so-called default Bayesian hypothesis tests, scientists inapplied fields have gained access to a powerful and principled method fortesting hypotheses. However, such default tests usually come with a compromise,requiring the analyst to accept a one-size-fits-all approach to hypothesistesting. Further, such tests may not have the flexibility to test problems thescientist really cares about. In this tutorial, I demonstrate a flexibleapproach to generalizing one specific default test (the JZS t-test; Rouder etal., 2009) that is becoming increasingly popular in the social and behavioralsciences. The approach uses two theoretical results, the Savage-Dickey densityratio (Dickey and Lientz, 1980) and the technique of encompassing priors(Klugkist et al., 2005) in combination with MCMC sampling via an easy-to-useprobabilistic modeling package for R called Greta. Through a comprehensivemathematical description of the techniques as well as illustrative examples,the reader is presented with a general, flexible workflow that can be extendedto solve problems relevant to his or her own work.

A tutorial on generalizing the default Bayesian t-test via posterior sampling and encompassing priors