A new nonparametric test for the ordered alternative problem

Abstract

Abstract This paper proposes a new nonparametric test for detecting nondecreasing ordered alternatives. The exact mean and variance of the null distribution are derived and it is shown that this distribution is asymptotically normal. The test is designed to help alleviate some of the problems that existing tests have with high powers when the assumed a priori ordering among the parameters is incorrect. For example, a simulation study indicates that the proposed test has higher powers than the general alternative Kruskal-Wallis test when the assumed ordering is correct, and much lower powers than existing nonparametric tests for ordered alternatives when the location parameters differ, but do not follow a nondecreasing pattern. Some actual data examples are also discussed. Keywords: Asymptotic DistributionJonckheere-Terpstra TestOrdered AlternativeNonparametric TestPower Comparisons