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Table 2 Results from the simulation study where outcome data have Exponential distributions

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

Significance level = 0.05, Power = 0.9      
       Estimated power from simulation study
Scenario m 1 m 2 ϕ 1 ϕ 2 n log t-test M-W test t-test
1 0.1 0.3 \(\frac {0.1}{\log (2)}\) \(\frac {0.3}{\log (2)}\) 13 0.576 0.600 0.661
2 1 1.5 \(\frac {1}{\log (2)}\) \(\frac {1.5}{\log (2)}\) 91 0.567 0.650 0.769
3 10 7 \(\frac {10}{\log (2)}\) \(\frac {7}{\log (2)}\) 117 0.564 0.649 0.768
4 20 15 \(\frac {20}{\log (2)}\) \(\frac {15}{\log (2)}\) 180 0.565 0.654 0.772
5 60 48 \(\frac {60}{\log (2)}\) \(\frac {48}{\log (2)}\) 299 0.564 0.653 0.775
6 80 70 \(\frac {80}{\log (2)}\) \(\frac {70}{\log (2)}\) 833 0.565 0.654 0.778
  1. Here, m j and ϕ j denote the median and standard deviation of the outcome data for group j. 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’)