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An Exhaustive Power Comparison of Normality Tests

Author

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  • Jurgita Arnastauskaitė

    (Department of Applied Mathematics, Kaunas University of Technology, 51368 Kaunas, Lithuania
    Department of Computer Sciences, Kaunas University of Technology, 51368 Kaunas, Lithuania)

  • Tomas Ruzgas

    (Department of Computer Sciences, Kaunas University of Technology, 51368 Kaunas, Lithuania)

  • Mindaugas Bražėnas

    (Department of Mathematical modelling, Kaunas University of Technology, 51368 Kaunas, Lithuania)

Abstract

A goodness-of-fit test is a frequently used modern statistics tool. However, it is still unclear what the most reliable approach is to check assumptions about data set normality. A particular data set (especially with a small number of observations) only partly describes the process, which leaves many options for the interpretation of its true distribution. As a consequence, many goodness-of-fit statistical tests have been developed, the power of which depends on particular circumstances (i.e., sample size, outlets, etc.). With the aim of developing a more universal goodness-of-fit test, we propose an approach based on an N-metric with our chosen kernel function. To compare the power of 40 normality tests, the goodness-of-fit hypothesis was tested for 15 data distributions with 6 different sample sizes. Based on exhaustive comparative research results, we recommend the use of our test for samples of size n ≥ 118 .

Suggested Citation

  • Jurgita Arnastauskaitė & Tomas Ruzgas & Mindaugas Bražėnas, 2021. "An Exhaustive Power Comparison of Normality Tests," Mathematics, MDPI, vol. 9(7), pages 1-20, April.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:7:p:788-:d:530863
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    References listed on IDEAS

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    1. Coin, Daniele, 2008. "A goodness-of-fit test for normality based on polynomial regression," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 2185-2198, January.
    2. Gel, Yulia R. & Miao, Weiwen & Gastwirth, Joseph L., 2007. "Robust directed tests of normality against heavy-tailed alternatives," Computational Statistics & Data Analysis, Elsevier, vol. 51(5), pages 2734-2746, February.
    3. Paul Zhang, 1999. "Omnibus test of normality using the Q statistic," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(4), pages 519-528.
    4. Zhang, Jin & Wu, Yuehua, 2005. "Likelihood-ratio tests for normality," Computational Statistics & Data Analysis, Elsevier, vol. 49(3), pages 709-721, June.
    5. Bonett, Douglas G. & Seier, Edith, 2002. "A test of normality with high uniform power," Computational Statistics & Data Analysis, Elsevier, vol. 40(3), pages 435-445, September.
    6. Jarque, Carlos M. & Bera, Anil K., 1980. "Efficient tests for normality, homoscedasticity and serial independence of regression residuals," Economics Letters, Elsevier, vol. 6(3), pages 255-259.
    7. M. Mahibbur Rahman & Z. Govindarajulu, 1997. "A modification of the test of Shapiro and Wilk for normality," Journal of Applied Statistics, Taylor & Francis Journals, vol. 24(2), pages 219-236.
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    Cited by:

    1. Atif Avdović & Vesna Jevremović, 2022. "Quantile-Zone Based Approach to Normality Testing," Mathematics, MDPI, vol. 10(11), pages 1-16, May.

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