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Omnibus test of normality using the Q statistic

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  • Paul Zhang

Abstract

A new statistical procedure for testing normality is proposed. The Q statistic is derived as the ratio of two linear combinations of the ordered random observations. The coefficients of the linear combinations are utilizing the expected values of the order statistics from the standard normal distribution. This test is omnibus to detect the deviations from normality that result from either skewness or kurtosis. The statistic is independent of the origin and the scale under the null hypothesis of normality, and the null distribution of Q can be very well approximated by the Cornish-Fisher expansion. The powers for various alternative distributions were compared with several other test statistics by simulations.

Suggested Citation

  • Paul Zhang, 1999. "Omnibus test of normality using the Q statistic," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(4), pages 519-528.
    • Handle: RePEc:taf:japsta:v:26:y:1999:i:4:p:519-528
    DOI: 10.1080/02664769922395
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    References listed on IDEAS

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    1. J. P. Royston, 1982. "An Extension of Shapiro and Wilk's W Test for Normality to Large Samples," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 31(2), pages 115-124, June.
    2. C. S. Davis & M. A. Stephens, 1978. "Approximating the Covariance Matrix of Normal Order Statistics," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 27(2), pages 206-212, June.
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    Cited by:

    1. Steven Garren & Richard Smith & Walter Piegorsch, 2001. "Bootstrap goodness-of-fit test for the beta-binomial model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 28(5), pages 561-571.
    2. Jurgita Arnastauskaitė & Tomas Ruzgas & Mindaugas Bražėnas, 2021. "An Exhaustive Power Comparison of Normality Tests," Mathematics, MDPI, vol. 9(7), pages 1-20, April.
    3. Sueli Mingoti & Otaviano Neves, 2003. "A note on the Zhang omnibus test for normality based on the Q statistic," Journal of Applied Statistics, Taylor & Francis Journals, vol. 30(3), pages 335-341.
    4. Ardian Harri & Keith H. Coble, 2011. "Normality testing: two new tests using L-moments," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(7), pages 1369-1379, May.
    5. Hwang, Yi-Ting & Wei, Peir Feng, 2006. "A novel method for testing normality in a mixed model of a nested classification," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 1163-1183, November.

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