Abstract
For testing marginal homogeneity of a square contingency table under the restricted alternative that either is stochastically larger than the other, approximately somewhere most powerful tests are studied. The Mann-Whitney test is included in them. Among the approximately somewhere most powerful tests, an optimal one is derived by the most stringent principle and compared with the Mann-Whitney test and the Stuart's test with respect to their asymptotic powers. Simulation study indicates that the Mann-Whitney and most stringent tests both have consistently higher powers, compared with the Stuart's test for detecting the locational shifts when a bivariate continuous distribution is assumed as an underlying distribution. It is indicated that the Mann-Whitney test competes well with the approximately most stringent somewhere most powerful test, but the latter is more reliable than the former.
