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Table 7 Relative efficiency of ANCOVA and Mann-Whitney for the extreme asymmetry distribution. Values less than 1 indicate greater power of ANCOVA; greater than 1 indicates superiority of Mann-Whitney. In blank cells, the power of one or both tests was 100%.

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

Sample size

Post-treatment score

Change score

 

ANCOVA v. Mann-Whitney

log ANCOVA v. Mann-Whitney

ANCOVA v. Mann-Whitney

log ANCOVA v. Mann-Whitney

 

Shift

Ratio

Shift

Ratio

Shift

Ratio

Shift

Ratio

10

3.0404

4.1864

0.8862

1.1179

1.2586

1.9736

0.5567

0.539

20

1.2037

2.6045

0.8073

1.2589

0.5480

0.7372

0.3473

0.2983

30

1.1503

1.7717

0.9409

1.2707

0.3084

0.3860

0.2472

0.2701

40

1.1730

1.4786

1.0233

1.4105

0.2643

0.2772

0.2446

0.2421

60

1.1853

1.2015

1.1118

1.4062

0.2115

0.2121

0.1898

0.2586

100

1.2682

1.0648

1.1842

1.4789

0.2224

0.1753

0.2065

0.2545

200

1.2880

0.9257

1.2570

1.5437

0.2078

0.1496

0.1985

0.2544

400

1.3576

0.9089

1.3112

1.5308

0.1961

0.1358

0.1816

0.2418

800

1.4222

-

1.4116

-

0.2038

-

0.1783

0.2444