Increasing physicians' awareness of the impact of statistics on research outcomes: Comparative power of the t-test and Wilcoxon rank-sum test in small samples applied research

To effectively evaluate medical literature, practicing physicians and medic al researchers must understand the impact of statistical tests on research outcomes. Applying inefficient statistics not only increases the need for r esources, but more importantly increases the probability of committing a Ty pe I or Type II error. The t-test is one of the most prevalent tests used i n the medical field and is the uniformally most powerful unbiased test (UMP U) under normal curve theory. But does it maintain its UMPU properties when assumptions of normality are violated? A Monte Carlo investigation evaluat es the comparative power of the independent samples t-test and its nonparam etric counterpart, the Wilcoxon Rank-Sum (WRS) test, to violations from pop ulation normality, using three commonly occurring distributions and small s ample sizes. The t-test was more powerful under relatively symmetric distri butions, although the magnitude of the differences was moderate. Under dist ributions with extreme skews, the WRS held large power advantages. When dis tributions consist of heavier tails or extreme skews, the WRS should be the test of choice. In rum, when population characteristics are unknown, the W RS is recommended, based on the magnitude of these power differences in ext reme skews, and the modest variation in symmetric distributions. J CLIN EPI DEMIOL 52;3:229-235, 1999. (C) 1999 Elsevier Science Inc.