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Table 3 Results from the simulation study where outcome data have Exponential distributions, with analytic sample sizes (n) calculated using the formula given in Eq. 5

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 \(\frac {0.1}{\log (2)}\) \(\frac {0.3}{\log (2)}\) 29 0.890 0.933 0.975
2 1 1.5 \(\frac {1}{\log (2)}\) \(\frac {1.5}{\log (2)}\) 211 0.900 0.948 0.985
3 10 7 \(\frac {10}{\log (2)}\) \(\frac {7}{\log (2)}\) 272 0.898 0.947 0.985
4 20 15 \(\frac {20}{\log (2)}\) \(\frac {15}{\log (2)}\) 418 0.900 0.950 0.986
5 60 48 \(\frac {60}{\log (2)}\) \(\frac {48}{\log (2)}\) 695 0.899 0.949 0.985
6 80 70 \(\frac {80}{\log (2)}\) \(\frac {70}{\log (2)}\) 1939 0.898 0.949 0.985
  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’)