Equally sized samples were drawn from exponential, uniform, and normal distributions. The two-sample
t test was conducted if either both samples (Strategy I) or the collapsed set of residuals from both samples
(Strategy II) had passed the preliminary Shapiro-Wilk test for normality; otherwise, Mann-Whitney’s U test was
conducted. By simulation, we separately estimated the conditional Type I error probabilities for the parametric and
nonparametric part of the two-stage procedure. Finally, we assessed the overall Type I error rate and the power of
the two-stage procedure as a whole.