Bayes factor usually models the distribution of the observed data under the alternative hypothesis H1 over that under the null hypothesis Ho, It has also been used to model the distribution of a test statistic under H1 over that under Ho.We consider a Bayes factor, which models an approximate distribution of a maximum statistic under H0 over that under H0.The resulting Bayes factor involves singlefold integrations and can be evaluated easily.The results are applied to case-control genetic association studies.