Monte Carlo Study - Two Nonparametric Statistics with Comparisons of Type I Error Rates and Power

The Mann-Whitney (MW) test and the Kolmogrov-Smirnov twosample test (KS-2) are nonparametric statistical tests used todetect whether there is a general difference between two sampleswhen the two underlying population distributions aredistribution-free. The focus of this study was to examine andcompare Type I error rates and statistical power between the MW andthe KS-2 tests when the two samples had different populationvariances or various degrees of kurtosis and skewness. This studyalso compared Type I error rates and power, if applicable, when thetwo samples were of different sizes. Simulations in SAS programwere conducted to simulate various conditions to examine Type Ierror rates and statistical powers for these two nonparametricstatistical tests. The study revealed that the KS-2 test is smallerthan the MW test in comparisons of the type I error rates inunequal sample sets. The MW test had slightly more statisticalpower the KS-2 test under the condition of small and equal-sizedsamples. Moreover, when population variances vary between twosamples, the KS-2 test has more statistical power than the MW test.Furthermore, the power of the KS-2 test exceeded the power of theMW test in large sample settings when either one of the followingconditions existed: (1) The difference in the Skewness ratoss inpopulations between the two samples was more than 0.5 with the samekurtosis and variance. (2) The difference in the Kurtosis ratios inpopulations between the two samples was more than 2.0 with the sameskewness and variance. Theoretical and practical implications,limitations of the study, are discussed, as well as recommendationsfor future research.