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Table 1 Left: Estimated Type I error probability of the two-sample  t  test at  α = .05 after both samples had passed the Shapiro-Wilk test for normality (Strategy I with  α  pre = .100, .050, .010, .005), and without pretest.—Right: Estimated Type I error of 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 .091 .150 .170 .190 .210 .050 .048 .051 .050 .051
  .050 .079 .127 .153 .168 .188 .052 .052 .050 .045 .053
  .010 .061 .099 .112 .140 .154 .055 .051 .049 .049 .047
  .005 .060 .085 .108 .127 .144 .060 .047 .052 .049 .048
  Without pretest .045 .047 .047 .048 .047 .053 .050 .048 .050 .051
Uniform distribution           
  .100 .043 .044 .039 .039 .036 .075 .055 .052 .051 .049
  .050 .043 .037 .040 .040 .037 .093 .059 .058 .051 .051
  .010 .049 .050 .046 .045 .041 .168 .111 .074 .060 .057
  .005 .052 .050 .048 .044 .043 .233 .133 .087 .069 .059
  Without pretest .058 .047 .052 .047 .050 .050 .050 .052 .048 .049
Normal distribution           
  .100 .049 .053 .050 .049 .050 .069 .058 .055 .061 .056
  .050 .049 .050 .050 .053 .046 .069 .063 .062 .064 .059
  .010 .050 .050 .047 .048 .051 .090 .081 .073 .072 .074
  .005 .047 .047 .050 .054 .050 .093 .085 .084 .081 .073
  Without pretest .051 .053 .049 .053 .050 .054 .047 .047 .049 .049