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Articles
DOI: 10.29303/emj.v6i1.131
Submitted: 2022-05-18
Published: 2023-06-26

The Simulation Study of Normality Test Using Kolmogorov-Smirnov, Anderson-Darling, and Shapiro-Wilk

Institut Teknologi Sepuluh Nopember
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Giatma Dwijuna Ahadi

Departemen Statistika, Fakultas Sains dan Analitika Data, Institut Teknologi Sepuluh Nopember, Surabaya
Institut Teknologi Sepuluh Nopember, Surabaya
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Neni Nur Laili Ersela Zain

Departemen Matematika, Fakultas Sains dan Analitika Data, Institut Teknologi Sepuluh Nopember, Surabaya
Normal Distribution Kolmogorov-Smirnov Anderson-Darling Shapiro-Wilk

Abstract

The normal distribution is an important assumption for many statistical methods. The t-distribution is similar to the normal distribution, but there are differences in variance and free degree depending on the sample size. Normality testing usually uses Kolmogorov-Smirnov, Anderson-Darling, and Shapiro-Wilk tests. Simulating was performed on data derived from normal distributions, t-distributions, and exponential distributions. In the N(10,2) generation data, it was found that the Shapiro-Wilk method was better than other methods, while in a large sample, it was found that the Anderson-Darling method was better than the other methods. The data for the generation of the distribution of t(1) shows that the cumulative value of rejecting  is close to 100%, meaning the data is not normally distributed. In a near-normal t(20) distribution, but not a normal data gain, Anderson-Darling and Shapiro-Wilk test performance showed good results. Meanwhile, in the t(100) generation data, the result was obtained that the most consistent cumulative value was the Anderson-Darling method. Furthermore, the Exp(1) data generator produces a cumulative value of rejecting  close to 100%, with the most consistent method being Kolmogorov-Smirnov. So it can be known that the normality test selection depends on the number of samples and the data distribution.

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How to Cite

Ahadi, G. D., & Zain, N. N. L. E. (2023). The Simulation Study of Normality Test Using Kolmogorov-Smirnov, Anderson-Darling, and Shapiro-Wilk. EIGEN MATHEMATICS JOURNAL, 6(1), 11–19. https://doi.org/10.29303/emj.v6i1.131