On the robustness and johnson's modification of the one sample T-Statistic

Cicchitelli (1989) conducted an extensive Monte Carlo study to investigate the robustness of the one sample T-statistic under non-normal parent populations. He considered a rich family of distributions, viz., the generalized λ-distribution which was introduced by Ramberg et al. (1979), as the family of parent populations. We shall address and reinforce his empirical findings by means of Edgeworth expansion of the T-statistic. As the skewness of the parent population affects the T-statistic more than the kurtosis, Johnson (1978) suggested a modification to the T-statistic to reduce the effect of skewness. We investigate the performance of this modified T-statistic under the same family of distributions as Cicchitelli considered by means of a Monte Carlo study and give some recommendations on its use.