Asymptotic properties of ANOVA Bayes factors

We study Bayes factors for testing the null hypothesis of no group differences in the one-way ANOVA model. A commonly-used Bayes factor due to Spiegelhalter ands Smith (1982), developed using vague prior distributions, is shown to be the limit of Bayes factors obtained from suitably defined proper prior distributions. This Bayes factor is compared with a new one that we develop. The two Bayes factors we consider are generic, requiring little or no a priori input. Comparisons between our proposed Bayes factor and that of Smith and Spiegelhalter are given and their consistency properties are evaluated. We find dramatic differences in terms of asymptotic performance, favoring the proposed form.