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Table 3: Estimated Type I error probability of the two-stage procedure (Student’s t  test or Mann-Whitney’s  U  test depending on preliminary Shapiro-Wilk test for normality) for different sample sizes and  α  pre

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

   Strategy I Strategy II
  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 .050 .050 .048 .049 .048 .053 .050 .048 .049 .048
  .050 .053 .050 .048 .049 .050 .055 .052 .048 .049 .050
  .010 .054 .054 .048 .049 .050 .054 .054 .048 .049 .050
  .005 .050 .056 .050 .048 .049 .050 .055 .049 .048 .049
Uniform distribution           
  .100 .049 .050 .047 .049 .049 .052 .051 .048 .049 .049
  .050 .051 .050 .050 .049 .048 .053 .051 .051 .050 .048
  .010 .051 .050 .051 .050 .051 .051 .051 .052 .051 .051
  .005 .052 .049 .049 .051 .050 .052 .050 .050 .052 .050
Normal distribution           
  .100 .050 .052 .052 .051 .052 .051 .052 .053 .051 .051
  .050 .051 .051 .051 .051 .051 .051 .051 .051 .051 .050
  .010 .049 .051 .051 .051 .051 .050 .051 .051 .051 .051
  .005 .051 .050 .049 .050 .050 .051 .050 .049 .050 .050
  1. Note: Type I error of the unconditional application of Student’s t test and Mann-Whitney’s U test is shown in Table 1 and Table 2.