  In practical situations, most experimental designs often yield unbalanced
data which have different numbers of observations per unit because of cost
constraints, or missing data, etc. In this paper, we consider the Bayesian
approach to hypothesis testing or model selection under the one-way unbalanced
fixed-effects ANOVA model. We adopt Zellner's g-prior with the beta-prime
distribution for g, which results in an explicit closed-form expression of the
Bayes factor without integral representation. Furthermore, we investigate the
model selection consistency of the Bayes factor under three different
asymptotic scenarios: either the number of units goes to infinity, the number
of observations per unit goes to infinity, or both go to infinity. The results
presented extend some existing ones of the Bayes factor for the balanced ANOVA
models in the literature.
