Table 1 Percentage of significant Bayesian indices of significance and effect size for varying sample sizes for small, medium, large and no existing effects using a wide C(0,1) prior on the effect size δ

No effect

p-value

0.0483

0.0500

0.0552

0.0508

0.0507

0.0500

0.0491

0.0499

0.0520

0.0529

BF₁₀

0.0221

0.0175

0.0192

0.0124

0.0137

0.0120

0.0104

0.0100

0.0100

0.0094

95% ROPE

0.0145

0.0159

0.0172

0.0127

0.0130

0.0107

0.0088

0.0083

0.0085

0.0069

Full ROPE

0.0002

0.0001

0.0000

0.0001

0.0000

0.0002

0.0000

0.0000

0.0000

0.0000

PD

0.0003

0.0003

0.0000

0.0004

0.0004

0.0006

0.0003

0.0003

0.0004

0.0002

MAP-p-value

0.0060

0.0075

0.0118

0.0096

0.0120

0.0111

0.0107

0.0107

0.0121

0.0117

\(\overline {\text {ev}}\)

0.0225

0.0273

0.0311

0.0342

0.0362

0.0383

0.0404

0.0386

0.0393

0.0391

\(\overline {\text {ev}}\) with C(0,1)

0.0490

0.0470

0.0477

0.0459

0.0480

0.0471

0.0487

0.0458

0.0481

0.0474

Small effect

p-value

0.1081

0.1990

0.2807

0.3457

0.4224

0.4890

0.5534

0.6149

0.6655

0.7092

BF₁₀

0.0559

0.1045

0.1490

0.1835

0.2319

0.2682

0.3221

0.3648

0.4150

0.4562

95% ROPE

0.0433

0.0945

0.1423

0.1752

0.2238

0.2526

0.3014

0.3374

0.3831

0.4165

Full ROPE

0.0005

0.0012

0.0024

0.0047

0.0061

0.0107

0.0139

0.0186

0.0235

0.0289

PD

0.0010

0.0034

0.0090

0.0144

0.0265

0.0333

0.0538

0.0747

0.0953

0.1175

MAP-p-value

0.0222

0.0590

0.1082

0.1539

0.2137

0.2593

0.3219

0.3746

0.4369

0.4878

\(\overline {\text {ev}}\)

0.0671

0.1417

0.2252

0.2976

0.3720

0.4415

0.5171

0.5659

0.6175

0.6755

\(\overline {\text {ev}}\) with C(0,1)

0.1164

0.1972

0.2763

0.3436

0.4180

0.4835

0.5527

0.5976

0.6459

0.7018

Medium Effect

p-value

0.2762

0.5149

0.6930

0.8193

0.8899

0.9417

0.9717

0.9831

0.9907

0.9951

BF₁₀

0.1709

0.3443

0.5013

0.6519

0.7439

0.8342

0.8928

0.9269

0.9561

0.9741

95% ROPE

0.1392

0.3247

0.4850

0.6389

0.7303

0.8197

0.8779

0.9165

0.9464

0.9685

Full ROPE

0.0017

0.0170

0.0382

0.0752

0.1282

0.1944

0.2769

0.3504

0.4386

0.5050

PD

0.0044

0.0320

0.0801

0.1635

0.2620

0.3830

0.4986

0.6010

0.6878

0.7606

MAP-p-value

0.0694

0.2431

0.4249

0.6039

0.7196

0.8256

0.8930

0.9317

0.9605

0.9779

\(\overline {\text {ev}}\)

0.1779

0.4373

0.6244

0.7698

0.8714

0.9256

0.9584

0.9752

0.9882

0.9951

\(\overline {\text {ev}}\) with C(0,1)

0.2773

0.5227

0.6880

0.8083

0.8953

0.9376

0.9663

0.9807

0.9908

0.9960

Large Effect

p-value

0.5824

0.8814

0.9746

0.9955

0.9987

1.0000

0.9999

1.0000

1.0000

1.0000

BF₁₀

0.4438

0.7776

0.9254

0.9801

0.9937

0.9986

0.9999

0.9999

1.0000

1.0000

95% ROPE

0.3844

0.7584

0.9185

0.9787

0.9928

0.9984

0.9997

0.9999

1.0000

1.0000

Full ROPE

0.0182

0.1252

0.3133

0.5407

0.7192

0.8535

0.9259

0.9664

0.9851

0.9929

PD

0.0268

0.2052

0.4704

0.7217

0.8597

0.9450

0.9795

0.9933

0.9969

0.9997

MAP-p-value

0.0694

0.2431

0.4249

0.6039

0.7196

0.8256

0.8930

0.9317

0.9605

0.9779

\(\overline {\text {ev}}\)

0.4486

0.8367

0.9597

0.9927

0.9990

0.9996

1.0000

1.0000

1.0000

1.0000

\(\overline {\text {ev}}\) with C(0,1)

0.5800

0.8862

0.9743

0.9945

0.9992

0.9998

1.0000

1.0000

1.0000

1.0000