EQUIVALENCE AND INTERVAL TESTING FOR LEHMANNS ALTERNATIVE

Equivalence and interval tests for Lehmann's alternative that extend t he well-known Savage test for one-sided hypotheses are proposed. The p roposed tests are shown to be unbiased with a strictly unimodal power function, provided the sample sizes in both treatment groups are equal . By means of a numerical investigation of the bias in the case of une qual sample sizes that are not too far apart, the suggested tests stil l turn out to provide practicable solutions. Because the computational effort to perform the suggested tests is considerable, tables contain ing the critical values are displayed to perform these tests easily. A numerical analysis of the power function of the interval test establi shes this procedure as a powerful tool for detection of a significantl y relevant difference in the small-sample case. In contrast to the cas e of interval testing, the fact arises that the performance of a power ful equivalence study under Lehmann's alternative requires an extensiv e amount of data. Because the proposed tests are based on the locally optimal scores under Lehmann's alternative, we cannot improve the sugg ested equivalence test essentially. Therefore, we also provide the asy mptotic version of this test and display tables containing the require d numerical values.