Specialized tests for detecting treatment effects in the two-sample problem

Nonparametric and robust statistics (those using trimmed means and Winsorized variances) were compared for their ability to detect treatment effects in the 2-sample case. In particular, 2 specialized tests, tests designed to be sensitive to treatment effects when the distributions of the data are skewed to the right, were compared with 2 nonspecialized nonparametric (Wilcoxon-Mann-Whitney; Mann & Whitney, 1947; Wilcoxon, 1949) and trimmed (Yuen, 1974) tests for 6 nonnormal distributions that varied according to their measures of skewness and kurtosis. As expected, the specialized tests provided more power to detect treatment effects, particularly for the nonparametric comparison. However, when distributions were symmetric, the nonspecialized tests were more powerful; therefore, for all the distributions investigated, power differences did not favor the specialized tests. Consequently, the specialized tests are not recommended; researchers would have to know the shapes of the distributions that they work with in order to benefit from specialized tests. In addition, the nonparametric approach resulted in more power than the trimmed-means approach did.