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Table 6 Relative efficiency of ANCOVA and Mann-Whitney combining all sample sizes. Mann-Whitney is always analyzed using the post-treatment score. 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 postive skew: shift

0.9397

0.9184

0.8831

0.8433

0.8012

0.7384

0.6701

0.5627

0.4214

Moderate postive skew: ratio

1.1430

1.1415

1.1036

1.0849

1.0541

0.9759

0.9090

0.7662

0.5947

Moderate negative skew: shift

0.9293

0.9281

0.8844

0.8326

0.7973

0.7256

0.6631

0.5556

0.4077

Moderate negative skew: ratio

1.1724

1.1871

1.1453

1.1103

1.0568

0.9867

0.9004

0.7665

0.5783

Uniform: shift

0.9324

0.9136

0.8926

0.8609

0.7741

0.7341

0.6483

0.5632

0.4147

Uniform: ratio

0.9475

0.9385

0.8957

0.8497

0.8191

0.7507

0.6659

0.5723

0.4297

Extreme negative skew: shift

1.4043

1.3724

1.3504

1.2859

1.2534

1.1947

1.0992

0.9472

0.7523

Extreme negative skew: ratio

1.6803

1.6120

1.6265

1.5843

1.4941

1.4206

1.2697

1.0932

0.858

Extreme negative skew: shift. ANCOVA log transformed

0.9709

0.9600

0.9638

0.9043

0.8940

0.8633

0.8109

0.7443

0.6680

Extreme negative skew: ratio. ANCOVA log transformed

0.9502

0.9298

0.9317

0.9077

0.8662

0.8282

0.7834

0.7161

0.6408

Normal: shift

0.9712

0.9258

0.9081

0.8618

0.7841

0.7272

0.6423

0.5349

0.3896

Normal: ratio

0.9550

0.9557

0.9183

0.8692

0.8139

0.7652

0.6527

0.5427

0.4131