This evaluation was additionally motivated by the anticipation that, although the observed conditional
Type I error rates of both the main parametric test and the nonparametric test were seriously altered by screening
for normality, these results will rarely occur in practice because the Shapiro-Wilk test is very powerful in
large samples. Again, pairs of samples were generated from exponential, uniform, and normal distributions.
Depending on whether the preliminary Shapiro-Wilk test was significant or not, Mann-Whitney’s U test or
Student’s t test was conducted in the main analysis.
Table 3 outlines the estimated unconditional Type I error rates. In line with this expectation, the results
show that the two-stage procedure as a whole can be considered robust with respect to the unconditional
Type I error rate. This holds true for all three distributions considered, irrespectively of the strategy chosen for the preliminary test.