A Remark on the Zhang Omnibus Test for Normality

Zhang (1999) proposed a novel test statistic Q for testing normality based on the ratio of two unbiased standard deviation estimators, q₁ and q₂, for the true population standard deviation σ. Mingoti & Neves (2003) discussed some properties of q₁ and q₂ and showed that the variance of q₁ increases as the true population variance increases. In this paper, we show that the distribution of q₁ is not normal. As a result, normality percentage points for Q are not appropriate. In this paper, percentage points of Q are obtained using simulations. Monte Carlo simulations are provided to evaluate the performance of the new method and Zhang's method.