Proposed tests for location and scale for an umbrella alternative

Abstract

Three nonparametric tests are proposed for a CRD design with k populations to test for the umbrella alternative with known peak, p, for both location and scale parameters. The tests are combinations of the Mack-Wolfe test (Mack and Wolfe, 1981) and a Moses modified Mack-Wolfe test based on the Moses technique (Moses, 1963). A simulation study was implemented to see if the proposed tests maintained their significant levels. Also, the tests proposed were compared based on estimated powers for different sample sizes, for changes in location parameters only, for changes in scale parameters only, and for changes in both location and scale parameters. Finally, recommendations as to which test is better are given.