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Table 5 Relative efficiency of ANCOVA and Mann-Whitney combining all sample sizes. Values less than 1 indicate greater power of ANCOVA; greater than 1 indicates superiority of Mann-Whitney.

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

Distribution

Correlation between baseline and post-treatment score

 

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Moderate positive skew: shift

0.9342

0.9257

0.8707

0.8532

0.8569

0.9030

0.9447

0.9538

0.9963

Moderate positive skew: ratio

1.1560

1.1300

1.1074

1.0800

0.8170

0.8656

0.9065

0.9231

0.9720

Moderate negative skew: shift

0.9392

0.9058

0.8837

0.8444

0.8799

0.9114

0.9421

0.9593

0.9885

Moderate negative skew: ratio

1.1766

1.1946

1.1467

1.0980

0.8851

0.9319

0.9671

1.0241

1.0390

Uniform: shift

0.9492

0.9170

0.8869

0.8480

0.8586

0.8977

0.9281

0.9723

1.0021

Uniform: ratio

0.9575

0.9384

0.8862

0.8499

0.8604

0.8849

0.9213

0.9467

0.9895

Extreme negative skew: shift

1.4019

1.3718

1.3339

1.3045

0.8987

0.9425

0.9475

0.9405

0.9345

Extreme negative skew: ratio

1.6914

1.6185

1.6101

1.5835

1.0153

1.0367

1.0247

1.0344

1.0062

Normal: shift

0.9700

0.9393

0.9142

0.8445

0.8372

0.8840

0.9065

0.9485

0.9734

Normal: ratio

0.9551

0.9506

0.9126

0.8791

0.8536

0.8859

0.9072

0.9293

0.9654