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Table 1 Simulation study results

From: Sample size calculations based on a difference in medians for positively skewed outcomes in health care studies

Significance level = 0.05, Power = 0.8

    
     

Estimated power from simulation study

m 1

m 2

ϕ 1

ϕ 2

n

log t-test

M-W test

t-test

1

1.5

0.5

0.5

14

0.781

0.755

0.690

1

1.25

0.5

0.5

51

0.797

0.776

0.664

1

1.1

0.5

0.5

303

0.801

0.781

0.639

1

0.5

0.4

0.4

9

0.788

0.724

0.687

1

0.7

0.4

0.4

23

0.794

0.772

0.662

1

0.9

0.4

0.4

204

0.800

0.781

0.669

1

0.6

0.3

0.3

9

0.791

0.728

0.728

1

0.7

0.3

0.3

15

0.800

0.762

0.723

1

0.8

0.3

0.3

32

0.797

0.773

0.713

1

0.75

0.25

0.25

15

0.784

0.747

0.729

1

0.88

0.25

0.25

63

0.797

0.776

0.737

1

0.94

0.25

0.25

250

0.800

0.781

0.741

Significance level = 0.05, Power = 0.9

    
     

Estimated power from simulation study

m 1

m 2

ϕ 1

ϕ 2

n

log t-test

M-W test

t-test

1

1.5

0.5

0.7

23

0.888

0.873

0.847

1

1.25

0.5

0.7

87

0.898

0.883

0.910

1

1.1

0.5

0.7

530

0.900

0.886

0.992

1

0.5

0.6

0.4

14

0.890

0.872

0.800

1

0.7

0.6

0.4

40

0.897

0.882

0.875

1

0.9

0.6

0.4

383

0.900

0.886

0.993

1

0.6

0.5

0.3

16

0.896

0.874

0.867

1

0.7

0.5

0.3

28

0.894

0.877

0.897

1

0.8

0.5

0.3

65

0.896

0.880

0.946

1

0.75

0.4

0.25

29

0.892

0.875

0.906

1

0.88

0.4

0.25

131

0.898

0.882

0.970

1

0.94

0.4

0.25

537

0.900

0.883

0.998

  1. Here, m 1,m 2 are pre-specified untransformed median values for groups 1 and 2, with ϕ 1,ϕ 2 corresponding untransformed standard deviations. The column ‘n’ denotes the analytically derived sample size calculated using Eq. (4). Estimated powers are shown for a two-sample t-test of log-transformed outcomes (‘log t-test’), a Mann-Whitney U test of untransformed outcomes (‘M-W test’) and a two-sample t-test of untransformed outcomes (‘t-test’)