In our simulation study, equally sized samples for two
groups were drawn from three different distributions,
covering a variety of shapes of data encountered in clinical
research. Two selection strategies were examined for
the main test to be applied. In Strategy I, the twosample
t test was conducted if both samples had passed
the preliminary Shapiro-Wilk test for normality; otherwise,
we applied Mann-Whitney’s U test. In Strategy II, the
t test was conducted if the residuals ð Þ xi mX ;ð Þ yi mY
from both samples had passed the pretest; otherwise, we
used the U test. The difference between the two strategies
is that, in Strategy I, the Shapiro-Wilk test for normality is
separately conducted on raw data from each sample,
whereas in Strategy II, the preliminary test is applied only
once, i.e. to the collapsed set of residuals from both
samples.