Printed in Great Britain On the Behrens-Fisher problem

A brief survey of the recent literature leads to the conclusion that approximately similar tests for the Behrens-Fisher problem retain their practical relevance. The asymptotic ex-pansion of the power function of Welch's test is compared with the asymptotic expansion of the power functions of other asymptotically similar tests. Finally, it is shown that in the class of all translation invariant tests the Welch test is asymptotically uniformly most powerful against one-sided alternatives