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A note on the Zhang omnibus test for normality based on the Q statistic

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  • Sueli Mingoti
  • Otaviano Neves

Abstract

A discussion about the estimators proposed by Zhang (1999) for the true standard deviation C of a normal distribution is presented. Those estimators, called by Zhang q 1 and q 2 , are functions of the expected values of the order statistics from a standard normal distribution and they were the basis of the Q statistic used in the derivation of a new test for normality proposed by Zhang. Although the type I error and the power of the test was discussed by Zhang, no study was performed to test the reliability of q 1 and q 2 as estimators of C . In this paper, it is shown that q 1 is a very poor estimator for C especially when C is large. On the other hand, the estimator q 2 has a performance very similar to the well-known sample standard deviation S. When some correlation is introduced among the sample units it can be seen that the estimator q 1 is much more affected than the estimators q 2 and S.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:japsta:v:30:y:2003:i:3:p:335-341
    DOI: 10.1080/0266476022000030101
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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. Paul Zhang, 1999. "Omnibus test of normality using the Q statistic," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(4), pages 519-528.
    3. Nien Fan Zhang, 1998. "Estimating process capability indexes for autocorrelated data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 25(4), pages 559-574.
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