Student’s two-sample t test is generally used for comparing the means of two independent samples,
for example, two treatment arms. Under the null hypothesis, the t test assumes that the two samples arise from the
same normally distributed population with unknown variance. Adequate control of the Type I error requires that
the normality assumption holds, which is often examined by means of a preliminary Shapiro-Wilk test. The
following two-stage procedure is widely accepted: If the preliminary test for normality is not significant, the t test is
used; if the preliminary test rejects the null hypothesis of normality, a nonparametric test is applied in the
main analysis.