A Monte Carlo simulation study for Kolmogorov-Smirnov two-sample test under the precondition of heterogeneity : upon the changes on the probabilities of statistical power and type I error rates with respect to skewness measure

摘要

Skewnessand kurtosis are adopted by many statisticians as the contraventions ofparametric statistics. Therefore, using nonparametric tests would give moreproper results for skewed and kurtic series. Many observations also suggestthat skewness provokes the loss of power for statistical tests. This paper aimsto investigate the impact of skewness on statistical power. For this purpose,the paper takes hold of nine different distributions on Fleishman’s powerfunction when skewness measures are 1,75, 1,50, 1,25, 1,00, 0,75, 0,50, 0,25,0,00, -0,25 and kurtosis measure is 3,75, simultaneously. The investigationconcentrates on Kolmogorov-Smirnov two-sample test and considers thesignificance level (α)as 0,05. This paper runs totally 32 representative sample size simulationalternatives, involving four small and equal; twelve small and different; fourlarge and equal; and twelve large and different sample sizes. The Monte Carlosimulation study takes standard deviation ratios as 2, 3 and 4 under theprecondition of heterogeneity. According to the results of equal sample sizes,no significant change are observed on the possibility of Type I error forKolmogorov-Smirnov tests, when the skewness measures decrease from 1,75 to-0,25. For both small and large small sizes, the power of the correspondingtest decreases when the coefficient of skewness decreases.