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

, ,
American Statistician
Safe Bayesian Inference: A Theory of Misspecification based on Statistical Learning
Centrum Wiskunde & Informatica, Amsterdam (CWI), The Netherlands

Gronau, Q., Ly, A., & Wagenmakers, E.-J. (2020). Informed Bayesian t-Tests. American Statistician, 74(2), 137–143. doi:10.1080/00031305.2018.1562983