Some Nonparametric Tests Based on the Order Stratification Method for the Two-Sample Problem

In this paper several rank order statistics for the univariate two-sample testing problem are proposed and their asymptotic relative efficiencies (ARE's) w. r. t. the Wilcoxon test in the location problem and also w. r. t. the Mood test in the scale problem for important symmetric distributions are investigated. The ARE's of our tests w. r. t. the Wilcoxon test for the exponential and the gamma alternatives are also investigated in the scale case. Our statistics are constructed with the aid of the idea of McIntyre [5] and of Takahashi and Wakimoto [9], which may be called the order stratification method. When the order of the magnitude of the observations between a small member is intuitively found without measurement by e. g. a visual inspection and the measurement is costly, our test statistics are available and we can conclude that the tests based on only a half or a third of the samples have high ARE's. Furthermore even if we use all the samples our method is powerful especially in the scale and the scale slippage model.