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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.
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BMC Medical Research Methodology

ISSN: 1471-2288

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