On a generalization of the Behrens-Fisher problem

Abstract

Suppose that there are two sets of normal populations, the first set consisting of populations N (μ i , σ 1 2 ) (i = 1,…, p ) and the second set consisting of populations N (μ 1 * , σ 2 2 ) ( i = 1,…, p ) and suppose that we are interested in testing the hypothesis H o :μ i = μ i * ( i = 1, … p ), or in testing H o 1 : μ 1 −μ 1 * = μ 2 −μ 2 * =… = μ p − p * . For testing these hypotheses we give two types of test procedures designed to control the size of the tests below a preassigned level α under variance heterogeneity.