Precedence Test and Maximal Precedence Test

In this paper, we first describe the precedence test for testing the hypothesis that two distribution functions are equal. We examine the power properties of this precedence test under a location shift between the two populations using Monte Carlo simulations, and compare them with those of Wilcoxon’s rank sum test. After noting that a ‘masking effect’ affects the performance of the precedence test, we next propose a maximal precedence test. We then examine the power properties of this maximal precedence test under a location shift, and compare them with those of the precedence test and Wilcoxon’s rank-sum test. Finally, we describe some possible extensions of the test procedures described here.