An adaptive two-sample test based on modified Wilcoxon scores

An adaptive two-sample test is proposed which uses the tail lengths of the empirical distribution to determine the appropriate rank scores. The tail lengths are functions of the sample percentiles that are estimated from the combined samples. Monte Carlo methods were used to estimate the size and power of the proposed test and several other tests. Fifteen distributions having five levels of skewness and three levels of kurtosis were used in these simulations. Sample sizes varied from 12 to 800 in each group. The proposed test has greater power than the t-test, the Wilcoxon test, and the normal scores test for skewed data, and has power that is approximately equal to those tests for symmetric data.