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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