Type I error rates for James's second‐order test and Wilcox's H m test under heteroscedasticity and non‐normality

Actual Type I error rates (τ) for James's second‐order test and Wilcox's H m test on means were estimated for various conditions in which variances were either homoscedastic or heteroscedastic and distributions were either normal or non‐normal. Actual Type I error rates for both James's second‐order and Wilcox's H m tests were affected by non‐normality. However, the two tests tended to have τ near the nominal Type I error rate (α) when applied to data sampled from symmetric non‐normal distributions. When applied to data sampled from asymmetric distributions, larger values of τ‐α occurred and τ‐α tended to increase as the degree of asymmetry increased.