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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’)