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Table 1 Shape parameters for the distributions produced by the simulations compared to those from the original empirical data. Parameters for the moderate negative skew are as for the moderate positive skew, except that the sign for skew is reversed.

From: Parametric versus non-parametric statistics in the analysis of randomized trials with non-normally distributed data

Distribution Post-treatment scores
  Standard deviation Skewness Kurtosis
  Empirical Simulation Empirical Simulation Empirical Simulation
Moderate positive skew 17.01 17.02 1.62 1.63 5.71 6.00
Uniform 13.49 13.49 -0.11 -0.11 2.08 2.01
Extreme asymmetry 8.96 9.78 3.03 2.90 13.77 13.97
Extreme negative skew 22.17 21.88 -1.74 -1.79 5.88 5.85
  Change scores
  Standard deviation Skewness Kurtosis
  Empirical Simulation Empirical Simulation Empirical Simulation
Moderate positive skew 10.40 18.80 0.35 0.01 4.49 5.15
Uniform 12.31 14.56 0.00 0.43 3.05 2.98
Extreme asymmetry 10.62 10.97 0.88 1.08 5.38 6.37
Extreme negative skew 15.51 15.02 0.00 0.75 6.31 8.52