On Bayes factors for hypothesis tests.

Abstract

We develop alternative families of Bayes factors for use in hypothesis tests as alternatives to the popular default Bayes factors. The alternative Bayes factors are derived for the statistical analyses most commonly used in psychological research - one-sample and two-sample t tests, regression, and ANOVA analyses. They possess the same desirable theoretical and practical properties as the default Bayes factors and satisfy additional theoretical desiderata while mitigating against two features of the default priors that we consider implausible. They can be conveniently computed via an R package that we provide. Furthermore, hypothesis tests based on Bayes factors and those based on significance tests are juxtaposed. This discussion leads to the insight that default Bayes factors as well as the alternative Bayes factors are equivalent to test-statistic-based Bayes factors as proposed by Johnson. Journal of the Royal Statistical Society Series B: Statistical Methodology, 67, 689-701. (2005). We highlight test-statistic-based Bayes factors as a general approach to Bayes-factor computation that is applicable to many hypothesis-testing problems for which an effect-size measure has been proposed and for which test power can be computed.