In a preliminary test, a specific assumption is checked;
the outcome of the pretest then determines which
method should be used for assessing the main hypothesis
[25-28]. For the paired t test, Freidlin et al. ([29],
p. 887) referred to as “a natural adaptive procedure (...)
to first apply the Shapiro-Wilk test to the differences: if
normality is accepted, the t test is used; otherwise the
Wilcoxon signed ranked test is used.” Similar two-stage
procedures including a preliminary test for normality are
common for two-sample t tests [30,31]. Therefore, conventional
statistical practice for comparing continuous
outcomes from two independent samples is to use a pretest for normality (H0: “The true distribution is normal”
against H1: “The true distribution is non-normal”)
at significance level αpre before testing the main hypothesis.
If the pretest is not significant, the statistic T is used
to test the main hypothesis of equal population means at
significance level α. If the pretest is significant, MannWhitney’s
U test may be applied to compare the two
groups. Such a two-stage procedure (Additional file 1)
appears logical, and goodness-of-fit tests for normality
are frequently reported in articles [32-35].