Supplementary data for the paper "Neither the t-test nor Welch’s test: a case for robust alternatives in two-sample comparisons with non-ideal data"
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Student’s t -test and Welch’s t -test are the most common defaults for comparing two independent samples, but each rests on often-violated assumptions. We compared the two tests in simulations varying sample-size imbalance, variances, and skewness, plus an empirical sampling study of gender differences on two psychological scales; further simulations compared both classical tests with the Yuen-Welch test, the t -test on ranks, Welch’s t -test on ranks, a permutation-based Welch test, the Brunner-Munzel test, the Kolmogorov–Smirnov test, and the Anderson–Darling test. Under unequal sample sizes, the t -test failed to maintain nominal Type I error when standard deviations also differed (the classical Welch motivation), while Welch’s test inflated Type I error when distributions were skewed, with the false positive rate reaching approximately 6%, 7.5%, and 9% at population skewness 1, 2, and 3 (nominal 5%). When sample sizes were equal, both classical tests held nominal Type I error; under unequal sample sizes with skewness, both lost power to robust alternatives, so the t -test was no remedy for Welch’s inflation. Among the alternatives, the permutation-based Welch test held the …
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