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

Sueli Mingoti and Otaviano Neves

Journal of Applied Statistics, 2003, vol. 30, issue 3, 335-341

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.

Date: 2003
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DOI: 10.1080/0266476022000030101

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