We compared three tests for mean equality: the Welch (1938) heteroscedastic statistic, the Zhou et al. (1997) test, derived to be used with skewed lognormal data, and Yuen's (1974) procedure which uses robust estimators of central tendency and variability with the Welch test in order to combat the combined effects of nonnormality and variance heterogeneity. Over the 162 conditions of nonnormality and variance heterogeneity we investigated, only the Yuen procedure reliably controlled its rate of Type I error.
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Keselman et al. (2002) studied this question.
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