Comparison of Normality Tests in Terms of Sample Sizes under Different Skewness and Kurtosis Coefficients

Abstract

This study aims to compare normality tests in different sample sizes in data with normal distribution under different kurtosis and skewness coefficients obtained simulatively. To this end, firstly, simulative data were produced using the MATLAB program for different skewness/kurtosis coefficients and different sample sizes. The normality analysis of each data type was conducted using the MATLAB program and ten different normality tests; namely, (Kolmogorov Smirnov (KS) Test, KS Stephens Modification, KS Marsaglia, KS Lilliefors Modification, Anderson-Darling Test, Cramer- Von Mises Test, Shapiro-Wilk Test, Shapiro-Francia Test, Jarque-Bera Test, and D’Agostino & Pearson Test). As a result of the analyses conducted according to ten different normality tests, it was found that normality tests were not affected by the sample size when the skewness and kurtosis coefficients were equal to or close to zero; however, in cases where the skewness and kurtosis coefficients moved away from zero, it was found that normality tests are affected by the sample size, and such tests tend to give significant results. Therefore, in large samples, it may be suggested that critical values for skewness and kurtosis coefficients’ z-scores as proposed by Kim (2013) and Mayers (2013) or the histogram graphs be used.