Statistical Power Comparisons For Equal Skewness Different Kurtosis And Equal Kurtosis Different Skewness Coefficients In Nonparametric Tests

Mann-Whitney and Kolmogorov-Smirnov two-sample tests are the most appropriate tests when the data, which are obtained from independent two-sample, are asked for testing by the help of nonparametric tests. Both Mann-Whitney and Kolmogorov-Smirnov two-sample tests are nonparametric statistics tests which are used to determine whether independent two-sample belongs to the same or similar populations. In this study, the statistical powers of these two tests are compared by analyzing the change in kurtosis coefficients under the assumption of equal skewness coefficients and analyzing the change in skewness coefficients under the assumption of equal kurtosis coefficients. Variances are assumed as heterogeneous for both situations and variance ratios 2, 3, 4, 1/2, 1/3 and 1/4 are used. Also, equal sample sizes of 4, 5, 8, 10, 12, 15, 16 and 20 are used as small and equal sample sizes. The results of the analyses revealed that Mann-Whitney test is more powerful between small and equal sample sizes of 4 to 10, and Kolmogorov-Smirnov two-sample test is more powerful between small and equal sample sizes of 12 to 20.