Table 1 Correlation matrix, R, used in the simulations. The representative correlations were randomly selected to be between 0.35 and 0.55. These correlations in this range are commonly observed in our studies.

0.3722

1

0.3527

0.4034

0.5445

0.4073

0.522

0.5225

0.5097

0.5239

0.3733

0.5298

0.5443

0.3895

0.4547

0.5036

0.3541

0.5071

0.429

0.4089

0.412

0.3527

1

0.5456

0.359

0.5349

0.398

0.4338

0.3809

0.4903

0.409

0.3718

0.3743

0.5229

0.3965

0.5091

0.5334

0.413

0.3691

0.428

0.3719

0.4034

0.5456

1

0.5345

0.514

0.409

0.4894

0.5176

0.4007

0.3824

0.4371

0.3679

0.4261

0.4772

0.3796

0.3906

0.4217

0.4393

0.4452

0.5174

0.5445

0.359

0.5345

1

0.4061

0.418

0.4092

0.5346

0.5224

0.4241

0.3802

0.3807

0.5035

0.4824

0.4953

0.4104

0.3501

0.5438

0.5125

0.3699

0.4073

0.5349

0.514

0.4061

1

0.351

0.5327

0.434

0.4566

0.4948

0.4281

0.4867

0.4563

0.4714

0.5291

0.4009

0.354

0.503

0.4166

0.4776

0.5225

0.3979

0.4092

0.4176

0.3505

1

0.4777

0.4354

0.4761

0.4109

0.3624

0.5064

0.4444

0.4038

0.3903

0.4479

0.407

0.5217

0.5469

0.4798

0.5225

0.4338

0.4894

0.4092

0.5327

0.478

1

0.3583

0.444

0.4546

0.4606

0.4706

0.4674

0.4813

0.4581

0.5171

0.4625

0.4332

0.3834

0.4496

0.5097

0.3809

0.5176

0.5346

0.434

0.435

0.3583

1

0.5184

0.548

0.4173

0.5257

0.4726

0.3544

0.4549

0.4734

0.5458

0.4346

0.5143

0.5085

0.5239

0.4903

0.4007

0.5224

0.4566

0.476

0.444

0.5184

1

0.5253

0.5161

0.4758

0.3904

0.4799

0.4291

0.5031

0.473

0.3508

0.4288

0.5058

0.3733

0.409

0.3824

0.4241

0.4948

0.411

0.4546

0.548

0.5253

1

0.4822

0.4519

0.4779

0.4359

0.3542

0.4875

0.4398

0.3992

0.4385

0.3705

0.5298

0.3718

0.4371

0.3802

0.4281

0.362

0.4606

0.4173

0.5161

0.4822

1

0.5422

0.4317

0.4011

0.5234

0.4553

0.4305

0.432

0.391

0.3524

0.5443

0.3743

0.3679

0.3807

0.4867

0.506

0.4706

0.5257

0.4758

0.4519

0.5422

1

0.3732

0.352

0.4682

0.4535

0.3799

0.3696

0.5219

0.4731

0.3895

0.5229

0.4261

0.5035

0.4563

0.444

0.4674

0.4726

0.3904

0.4779

0.4317

0.3732

1

0.4225

0.3962

0.478

0.4375

0.5188

0.4279

0.4538

0.4547

0.3965

0.4772

0.4824

0.4714

0.404

0.4813

0.3544

0.4799

0.4359

0.4011

0.352

0.4225

1

0.4796

0.3642

0.5126

0.364

0.3575

0.4057

0.5036

0.5091

0.3796

0.4953

0.5291

0.39

0.4581

0.4549

0.4291

0.3542

0.5234

0.4682

0.3962

0.4796

1

0.41

0.5454

0.4097

0.3597

0.4246

0.3541

0.5334

0.3906

0.4104

0.4009

0.448

0.5171

0.4734

0.5031

0.4875

0.4553

0.4535

0.478

0.3642

0.41

1

0.3866

0.4484

0.5465

0.443

0.5071

0.413

0.4217

0.3501

0.354

0.407

0.4625

0.5458

0.473

0.4398

0.4305

0.3799

0.4375

0.5126

0.5454

0.3866

1

0.4062

0.3617

0.3885

0.429

0.3691

0.4393

0.5438

0.503

0.522

0.4332

0.4346

0.3508

0.3992

0.432

0.3696

0.5188

0.364

0.4097

0.4484

0.4062

1

0.3759

0.4519

0.4089

0.428

0.4452

0.5125

0.4166

0.547

0.3834

0.5143

0.4288

0.4385

0.391

0.5219

0.4279

0.3575

0.3597

0.5465

0.3617

0.3759

1