The efficacy of some c-sample rank tests of homogeneity against ordered alternatives

For the c-sample location problem with ordered alternatives the test of Jon ckheere (1954) and Terpstra (1952) is a well-known competitor to the parame tric test introduced by Barlow et al. (1972, p. 184). Generalizations of th e Jonckheere-Terpstra test are proposed e.g., by Purl (1965), Tryon and Het tmansperger (1973) and Buning and Kossler (1996). All these tests are based on the pairwise ranking method. In the present paper their efficacies are compared. The Jonckheere-type and Tryon-Hettmansperger-type test statistics can be further generalized by introducing weight coefficients to the subst atistics. For the case of a specified alternative these weights are determi ned to obtain maximal efficacies. It is shown that the maximal achievable e fficacies in the defined classes of generalized Jonckheere-type tests and T ryon-Hettmansperger-type tests always are equal.