Asymptotic Behavior of Two-Sample Tests Based on Powers of Ranks for Detecting Scale and Location Alternatives

Two-sample tests based on powers of ranks are considered. These tests are asymptotically optimum against either scale or location alternatives for distributions presented in this article. Specific cases among the classes of tests considered here include the Wilcoxon, sum of squared ranks, median, Ansari-Bradley and Mood two-sample rank tests. The quality of the normal approximation for these tests is indicated by obtaining each test statistic's approximate large sample skewness and kurtosis. Asymptotic comparisons are made between selected tests and best tests for detecting scale alternatives, given particular one-sided distributions commonly used in statistics.