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

Authors

  • Süleyman Demir Sakarya University

Keywords:

Normal distribution, Skewness, Kurtosis, Normality tests

Abstract

The aim of this study is to compare normality tests in terms of different sample sizes in data with normal distribution under different kurtosis and skewness coefficients obtained simulatively. For this purpose, firstly, simulative data were produced using the MATLAB program for the conditions that coefficients of skewness and kurtosis were (-0.50, -0.25, 0, 0.25, 0.50) and in different sample sizes (N=10, 20, 30, 40, 50, 100, 200, 300, 400, 500, 900). The normality analysis of each datum was conducted using MATLAB program and 10 different normality tests (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 DAgostino & Pearson Test). As a result of the analysis made according to 10 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 were affected by the sample size, and normality tests tend to give significant results, especially for n>200.

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Published

2022-06-19

How to Cite

Demir, S. (2022). Comparison of Normality Tests in Terms of Sample Sizes under Different Skewness and Kurtosis Coefficients. International Journal of Assessment Tools in Education, 9(2), 397-409. Retrieved from https://ijate.net/index.php/ijate/article/view/53

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