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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

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