Impact of skewness on statistical power

Abstract

In this study, in order to research the effect of skewness on statistical power, four different distributions are handled in power function of Fleishman in which the kurtosis value is 0.00 and the skewness values are 0.75, 0.50, 0.25 and 0.00. In the study, Kolmogorov-Smirnov two sample tests are taken benefit of and the importance level of a is taken as 0.05. The sample sizes used in the study are the equal and small sample sizes from (2, 2) to (20, 20); additionally, in this study the mean ratio of the samples are taken as 0:0.5, 0:1, 0:1.5, 0:2, 0:2.5 and 0:3. As per the results obtained from the study, when the kurtosis coefficient in the same sample size is maintained fixed and taken as 0, and when the skewness coefficient is increased from 0 to 0.25, big scale of changes do not occur in the statistical power. When the skewness ratio is increased from 0.25 to 0.50; while the ratio of the means are 0:0.5, 0:1 and 0:1.5; decrease is viewed in the statistical power, and when the ratio of the means are 0:2, 0:2.5 and 0:3; increase is viewed in the statistical power. And when the kurtosis coefficient is increased from 0.50 to 0.75 it is viewed that almost in all of the ratios mean the statistical power is increasing. It is concluded that the statistical power increases as the ratio of the means is increasing for all of the sample sizes.