We propose a new skewness test statistic for normality based on the Pearson measure of skewness and obtain asymptotic first four moments of the null distribution for this statistic by using a computer algebra system and its normalizing transformation based on the Johnson  system. Finally, the performance of the proposed statistic is shown by comparing the powers of several skewness test statistics against some alternative hypotheses.

Pearson measure of skewness, normalizing transformation, powers.