A Default Bayesian Hypothesis Test for ANOVA Designs

This article presents a Bayesian hypothesis test for analysis of variance (ANOVA) designs. The test is an application of standard Bayesian methods for variable selection in regression models. We illustrate the effect of various <italic>g</italic>-priors on the ANOVA hypothesis test. The Bayesian test for ANOVA designs is useful for empirical researchers and for students; both groups will get a more acute appreciation of Bayesian inference when they can apply it to practical statistical problems such as ANOVA. We illustrate the use of the test with two examples, and we provide R code that makes the test easy to use.