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].