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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’)