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

Abstract

For the c-sample location problem with ordered alternatives the test of Jonckheere (1954) and Terpstra (1952) is a well-known competitor to the parametric test introduced by Barlow et al. (1972, p. 184). Generalizations of the Jonckheere-Terpstra test are proposed e.g., by Puri (1965), Tryon and Hettmansperger (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 substatistics. For the case of a specified alternative these weights are determined to obtain maximal efficacies. It is shown that the maximal achievable efficacies in the defined classes of generalized Jonckheere-type tests and Tryon -Hettmansperger-type tests always are equal.

Keywords:

• Asymptotic relative efficiency
• Jonckheere-Terpstra test
• Jonckheere-type test
• Puri-type test
• Tryon-Hcttmanspcrger-type test

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