A class of distribution-free tests for testing homogeneity against ordered alternatives (Q1095532)

A class of distribution-free tests for homogeneity of several populations against ordered alternatives is proposed. These are particularly useful when testing time is expensive so that an early termination of an experiment is desirable. The Pitman efficacy is derived and the optimal member of the class, the one with maximum efficacy, is identified. This optimal test is then compared with some other popular tests in terms of the asymptotic relative efficiency. A modification of the proposed test is considered when no additional information about the alternatives is available so that the optimal test can not be used. The modified test is compared to the optimal test through asymptotic relative efficiency.