Proposed tests for location and scale in a nondecreasing ordered alternative

Abstract

Six nonparametric tests are proposed for the nondecreasing ordered alternative when testing for a difference in either location or scale. The six tests are various combinations of a well-known ordered alternative test for location and a technique that Moses used to convert a scale testing problem into a location testing problem by transforming the data. A simulation study is conducted to determine how well the proposed tests maintain their significance levels. Powers are estimated for the proposed tests under a variety of conditions for three, four and five populations. Several types of variable parameters are considered: when the location parameters are different and the scale parameters are equal; when the location parameters are equal and the scale parameters are different; when the location and scale parameters are both different. Equal and unequal sample sizes of 18 and 30 are considered. Subgroup sizes of 3 and 6 are both used when applying the Moses technique. Recommendations are given.