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The effect of nonnormality on the Welch approximate degrees of freedom t test is demonstrated. A two-sample trimmed t statistic for unequal population variances is proposed and its performance is also evaluated in comparison to the Welch t test under normality and under long-tailed distributions. If the underlying distribution is long-tailed or contaminated with outliers, the trimmed t is strongly recommended.
Karen K. Yuen (Tue,) studied this question.