Tests for Patterned Alternatives in k-Sample Problems

Abstract This article suggests nonparametric methods of testing for a patterned alternative. As an example, suppose that we suspect that with increasing age, one's ability to perform a certain job tends to improve, but that after some point advancing age tends to mean diminishing performance. Suppose that N employees are grouped by age into k groups and employees' job performances are ranked from 1 to N. Viewing performance as the dependent variable, the particular pattern of increasing group locations followed by decreasing group locations is called an umbrella (pattern). The tests proposed herein allow the experimenter to test for this or any pattern of his choice. Given k groups, let denote the mean rank of the data in group j. Considering only statistics of the form , where Σ aj , = 0, we find a statistic having maximum asymptotic local power and greatest efficiency when the alternative hypothesis consists of a specific pattern. The case in which the researcher specifies a vague pattern is handled by ...