Testing homogeneity of several normal population means based on an interval hypothesis

Testing the homogeneity of k normal population means usually refers to testing the standard null hypothesis that all mean values are equal. In this paper, we investigate the testing of interval hypothesis H-0,H-delta : vertical bar mu(i) - mu(j)vertical bar <= delta for all 1 <= i, j <= k for some delta > 0. We show that the associated likelihood ratio tests have either noncentral chi-square distribution or noncentral F distribution. The tests proposed in this work are natural extensions of the chi-square and the F-tests for exact homogeneity. Based on the least favorable parameters associated with the envelope, we also consider tests based on bootstrap techniques. Numerical studies based both on synthetic and on real data are used to evaluate and compare the proposed tests.