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Article

Open Access

A Statistical Power Comparison of the Kolmogorov-Smirnov Two-Sample Test and the Wald Wolfowitz Test in Terms of Fixed Skewness and Fixed Kurtosis in Large Sample Sizes

Author(s)

Ötüken SENGER

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DOI:10.17265/1537-1506/2013.07.003

Affiliation(s)

Ötüken SENGER, Ph.D., Assistant Professor, Department of Numerical Methods, Faculty of Economic and Administrative Sciences, Kafkas University.

ABSTRACT

In this study, the statistical powers of Kolmogorov-Smirnov two-sample (KS-2) and Wald Wolfowitz (WW) tests, non-parametric tests used in testing data from two independent samples, have been compared in terms of fixed skewness and fixed kurtosis by means of Monte Carlo simulation. This comparison has been made when the ratio of variance is two as well as with equal and different sample sizes for large sample volumes. The sample used in the study is: (25, 25), (25, 50), (25, 75), (25, 100), (50, 25), (50, 50), (50, 75), (50, 100), (75, 25), (75, 50), (75, 75), (75, 100), (100, 25), (100, 50), (100, 75), and (100, 100). According to the results of the study, it has been observed that the statistical power of both tests decreases when the coefficient of kurtosis is held fixed and the coefficient of skewness is reduced while it increases when the coefficient of skewness is held fixed and the coefficient of kurtosis is reduced. When the ratio of skewness is reduced in the case of fixed kurtosis, the WW test is stronger in sample volumes (25, 25), (25, 50), (25, 75), (25, 100), (50, 75), and (50, 100) while KS-2 test is stronger in other sample volumes. When the ratio of kurtosis is reduced in the case of fixed skewness, the statistical power of WW test is stronger in volume samples (25, 25), (25, 75), (25, 100), and (75, 25) while KS-2 test is stronger in other sample volumes.

KEYWORDS

Kolmogorov-Smirnov Two-Sample (KS-2) test, Wald Wolfowitz (WW) test, statistical power, skewness, kurtosis

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