Asymptotic expansion of the non null distribution of the two-sample t-statistic under non normality with application in power comparison

This article studies the non null distribution of the two-sample t-statistic, or Welch statistic, under non normality. The asymptotic expansion of the non null distribution is derived up to n-1, where n is the pooled sample size, under general conditions. It is used to compare the power with that obtained by normal theory method. A simple technique is recommended to achieve more power through a monotone transformation in practice.