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.