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A modified Kolmogorov-Smirnov test for normality

Author

Listed:
  • Drezner, Zvi
  • Turel, Ofir
  • Zerom, Dawit

Abstract

In this paper we propose an improvement of the Kolmogorov-Smirnov test for normality. In the current implementation of the Kolmogorov-Smirnov test, a sample is compared with a normal distribution where the sample mean and the sample variance are used as parameters of the distribution. We propose to select the mean and variance of the normal distribution that provide the closest fit to the data. This is like shifting and stretching the reference normal distribution so that it fits the data in the best possible way. If this shifting and stretching does not lead to an acceptable fit, the data is probably not normal. We also introduce a fast easily implementable algorithm for the proposed test. A study of the power of the proposed test indicates that the test is able to discriminate between the normal distribution and distributions such as uniform, bi-modal, beta, exponential and log-normal that are different in shape, but has a relatively lower power against the student t-distribution that is similar in shape to the normal distribution. In model settings, the former distinction is typically more important to make than the latter distinction. We demonstrate the practical significance of the proposed test with several simulated examples.

Suggested Citation

  • Drezner, Zvi & Turel, Ofir & Zerom, Dawit, 2008. "A modified Kolmogorov-Smirnov test for normality," MPRA Paper 14385, University Library of Munich, Germany, revised 30 Mar 2009.
    • Handle: RePEc:pra:mprapa:14385
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    File URL: https://mpra.ub.uni-muenchen.de/14385/1/MPRA_paper_14385.pdf
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    References listed on IDEAS

    as
    1. 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.
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    Cited by:

    1. Mohd Effendi @ Ewan Mohd Matore* & Ahmad Zamri Khairani, 2018. "Comparison of Rasch Model Logits and Likert Mean Score in Testing the Normality Assumption," The Journal of Social Sciences Research, Academic Research Publishing Group, pages 75-82:6.

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    More about this item

    Keywords

    Closest fit; Kolmogorov-Smirnov; Normal distribution;
    All these keywords.

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics

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