Testing equality of means after a preliminary test of equality of variances

Abstract

In testing equality of means of two Normal populations Student's t -test is not generally applicable when the variances of the two populations may be unequal and their ratio is unknown. In the present paper several procedures are considered whereby a preliminary test is performed to ascertain whether or not the variances may be regarded as equal. On the basis of the outcome of this preliminary test one proceeds to test for equality of means. The optimal choice of the level of the preliminary test is made on the basis of controlling the size of the combined test in the sense of keeping it close to a pre-assigned level of significance. Tables of size and power are included to indicate the behaviour of the proposed tests.