The two-means problem—a secondarily Bayes approach

Abstract

The two-means problem is that of comparing the means of samples from two Gaussian distributions with unknown variances. Since the distribution of the Behrens-Fisher statistic depends upon the ratio of the population variances, a prior distribution may be specified for this ratio and the posterior distribution of the Behrens-Fisher statistic found conditional upon the ratio of the sample variances. The effect on the critical values caused by varying the prior is studied.