A measure of skewness for testing departures from normality
  We propose a new skewness test statistic for normality based on the Pearson measure of skewness. We 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 $S_{U}$ system. Finally the performance of the proposed statistic is shown by comparing the powers of several skewness test statistics against some alternative hypotheses. 
Shigekazu Nakagawa, Hiroki Hashiguchi and Naoto Niki
stat.CO math.ST stat.TH