Removing skewness and kurtosis by transformation when testing for mean equality

Abstract

A transformation of the Welch statistic to compare means is proposed to correct skewness and kurtosis of parent populations. The results show that this transformation seems to improve the performance of the test in heavy-tailed distributions more than other transformations focused only on skewness. The proposed test outperforms the Welch test in asymmetric heavy-tailed distributions with high heteroscedasticity and it behaves better than the Johnson’s transformation trimmed mean Welch test in normal, near-normal and light-tailed distributions. It may also be a better option when some of the distributions are heavy-tailed and some light-tailed.