The Mann-Whitney (MW) test and the Kolmogrov-Smirnov two sample test (KS-2) are nonparametric statistical tests used to detect whether there is a general difference between two samples when the two underlying population distributions are distribution-free. The focus of this study was to examine and compare Type I error rates and statistical power between the MW and the KS-2 tests when the two samples had different population variances or various degrees of kurtosis and skewness. This study also compared Type I error rates and power with applicable different sizes between two samples. SAS program was used for simulations. Findings and conclusions from the simulations for Type I error rates and statistical power between the MW and the KS-2 tests were discussed. Theoretical and practical implications, limitations of the study, are discussed, as well as recommendations for future research.