Detection of Non-Normality in Data Sets and Comparison between Different Normality Tests

O. Emmanuel, Biu and T. Maureen, Nwakuya and Wonu, Nduka (2020) Detection of Non-Normality in Data Sets and Comparison between Different Normality Tests. Asian Journal of Probability and Statistics, 5 (4). pp. 1-20. ISSN 2582-0230

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Abstract

The paper provides five tests of data normality at different sample sizes. The tests are the Shapiro-Wilk (SW) test, Anderson-Darling (AD) test, Kolmogorov-Smirnov (KS) test, Ryan-Joiner (RJ) test, and Jarque-Bera (JB) test. These tests were used to test for normality for two secondary data sets with sample size (155) for large and (40) for small; and then test the simulated scenario with standard normal “N(0,1)” data sets; where the large samples of sizes (150, 140, 130, 130, 110 and 100) and small samples of sizes (40. 35, 30, 25, 20, 15 and 10) are considered at two levels of significance (5% and 10%). However, the aim of this paper is to detect and compare the performance of the different normality tests considered. The normality test results shows Kolmogorov-Smirnov (KS) test is a most powerful test than other tests since it detect the simulated large sample data sets do not follow a normal distribution at 5%, while for small sample sizes at 5% level of significance; the results showed the Jarque-Bera (JB) test is a most powerful test than other tests since it detects that the simulated small sample data do not follow a normal distribution at 5%. This paper recommended JB test for normality test when the sample size is small and KS test when the sample size is large at 5% level of significance.

Item Type: Article
Subjects: Science Global Plos > Mathematical Science
Depositing User: Unnamed user with email support@science.globalplos.com
Date Deposited: 24 Apr 2023 07:15
Last Modified: 06 Feb 2024 04:24
URI: http://ebooks.manu2sent.com/id/eprint/552

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