Application of RSS design with rank-sum precedence tests for early decision on equality of two distributions

In this article, we utilize Wilcoxon's rank-sum statistic into the precedence test based on ranked set sample (RSS) and propose three different statistics for testing the equality of two distributions. The exact null distributions of the proposed test statistics are derived, critical values are tabulated for set size up to 8, and number of RSS cycles up to 9. The exact power functions of the proposed test statistics under the Lehmann alternative are derived. Then, the power values of these tests and some of their competitors are compared exactly under the Lehmann alternative and also through Monte Carlo simulations under a location-shift alternative. Finally, a real data is conducted to illustrate the proposed test statistics.