Table 5 Power of six global tests of correlated P-values (The correlation coefficient for Beta random variables is ρ . Uniform distributions have random correlation matrices)

20

0.176

0.359

0.259

0.332

0.191

0.294

50

0.27

0.576

0.418

0.505

0.303

0.464

100

0.407

0.824

0.599

0.652

0.456

0.672

200

0.645

0.967

0.827

0.791

0.657

0.877

300

0.808

0.995

0.92

0.861

0.785

0.941

400

0.896

0.997

0.966

0.896

0.861

0.979

500

0.949

0.999

0.984

0.933

0.926

0.993

Correlated 0.6 Uniform (0,1) ± 0.4Beta (0.4,6), $\rho =0.2$

n

KS

Inverse chi

Inverse norm

Tippett

Wilcoxon

Logit

20

0.797

0.957

0.896

0.784

0.815

0.918

50

0.987

1

0.997

0.939

0.983

1

100

1

1

1

0.972

1

1

200

1

1

1

0.998

1

1

300

1

1

1

1

1

1

400

1

1

1

0.999

1

1

500

1

1

1

0.999

1

1

Correlated 0.9 Uniform (0,1) ± 0.1Beta (0.5,4.5), $\rho =0.2$

n

KS

Inverse chi

Inverse norm

Tippett

Wilcoxon

Logit

20

0.151

0.266

0.207

0.225

0.183

0.221

50

0.227

0.466

0.336

0.326

0.264

0.369

100

0.343

0.664

0.493

0.437

0.397

0.534

200

0.545

0.863

0.709

0.537

0.595

0.757

300

0.706

0.944

0.832

0.587

0.719

0.863

400

0.811

0.982

0.913

0.632

0.81

0.933

500

0.89

0.992

0.951

0.695

0.887

0.966

Correlated 0.6 Uniform (0,1) ± 0.4Beta (0.5,4.5), $\rho =0.2$

n

KS

Inverse chi

Inverse norm

Tippett

Wilcoxon

Logit

20

0.161

0.291

0.212

0.225

0.173

0.237

50

0.251

0.475

0.362

0.302

0.292

0.385

100

0.322

0.64

0.504

0.397

0.39

0.528

200

0.517

0.882

0.701

0.527

0.58

0.743

300

0.726

0.952

0.845

0.568

0.731

0.873

400

0.806

0.976

0.894

0.607

0.805

0.917

500

0.895

0.998

0.95

0.676

0.883

0.965

Correlated 0.9 Uniform (0,1) ± 0.1Beta (1,5), $\rho =0.2$

n

KS

Inverse chi

Inverse norm

Tippett

Wilcoxon

Logit

20

0.127

0.118

0.139

0.056

0.144

0.136

50

0.203

0.199

0.211

0.063

0.235

0.206

100

0.248

0.272

0.28

0.064

0.271

0.269

200

0.406

0.448

0.453

0.06

0.446

0.438

300

0.535

0.559

0.541

0.073

0.542

0.535

400

0.619

0.657

0.649

0.07

0.657

0.631

500

0.725

0.743

0.729

0.071

0.731

0.715

Correlated 0.6 Uniform (0,1) ± 0.4Beta (1,5), $\rho =0.2$

n

KS

Inverse chi

Inverse norm

Tippett

Wilcoxon

Logit

20

0.572

0.56

0.599

0.117

0.611

0.587

50

0.893

0.864

0.904

0.104

0.917

0.891

100

0.991

0.981

0.986

0.114

0.991

0.981

200

1

1

0.999

0.091

1

0.999

300

1

1

1

0.109

1

1

400

1

1

1

0.111

1

1

500

1

1

1

0.085

1

1