Skip to main content

Advertisement

Table 2 Left: Estimated Type I error probability of the two-sample  t  test at  α = .05 for samples that passed testing for normality of the residuals (Strategy II with  α  pre = .100, .050, .010, .005), and without pretest.—Right: Estimated Type I error for the  U  test for samples that failed testing for normality

From: To test or not to test: Preliminary assessment of normality when comparing two independent samples

   t test U test
  α pre n = 10 n = 20 n = 30 n = 40 n = 50 n = 10 n = 20 n = 30 n = 40 n = 50
Exponential distribution           
  .100 .122 .398 .709 N/A N/A .037 .049 .047 .047 .050
  .050 .096 .317 .611 .839 N/A .034 .046 .048 .050 .050
  .010 .072 .196 .421 .669 .859 .034 .046 .045 .051 .050
  .005 .064 .162 .347 .583 .792 .036 .040 .047 .044 .048
  Without pretest .044 .048 .047 .049 .051 .041 .054 .046 .044 .050
Uniform distribution           
  .100 .065 .108 .196 .333 .529 .027 .024 .029 .041 .045
  .050 .052 .081 .133 .233 .377 .025 .018 .022 .035 .044
  .010 .051 .057 .076 .116 .184 .036 .011 .013 .022 .031
  .005 .047 .050 .066 .090 .138 .046 .012 .012 .016 .029
  Without pretest .051 .048 .049 .050 .050 .043 .053 .047 .048 .050
Normal distribution           
  .100 .049 .053 .048 .053 .048 .071 .074 .063 .062 .061
  .050 .051 .052 .051 .052 .053 .085 .079 .071 .064 .067
  .010 .049 .046 .048 .051 .049 .120 .107 .087 .073 .073
  .005 .045 .051 .050 .049 .051 .153 .107 .090 .083 .079
  Without pretest .052 .051 .046 .051 .048 .044 .045 .051 .044 .050
  1. Note: N/A, not available because nearly all samples were detected to deviate significantly from the normal distribution.