A TEST FOR THE NONPARAMETRIC TWO SAMPLE SCALE PROBLEM

We propose a distribution-free test for the nonparametric two sample scale problem. Unlike the other tests for this problem, we do not assume that the two distribution functions have a common median. We assume that they have a common quantile of order a (not necessarily 1/2). The test statistic is a modification of the Sukhatme statistic for the scale problem and the Wilcoxon-Mann-Whitney statistic for stochastic dominance. It is shown that the new test is uniformly more efficient (in the Pitman sense) than the Sukhatme test and has very good efficiency when compared to the Mood test.