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Statistics LibreTexts

15.5: Appendix E- The F-Tables

  • Page ID
    50195

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    The tables show the critical values for a simple independent-groups ANOVA.

    When using repeated-measures ANOVA, use \(d f_e\) in place of \(d f_w\).

    When using ANOVA as part of a regression, use \(d f_M\) in place of \(d f_b\) and \(d f_e\) in place of \(d f_w\).

    When using \(\alpha\) = 0.05, use standard values.

    When using \(\alpha\) = 0.01, use bolded values.

    Degrees of Freedom Between (\(d f_b\))

    Degrees of Freedom Within (\(d f_w\))

    1

    2

    3

    4

    5

    6

    7

    8

    1

    161.448

    199.500

    215.707

    224.583

    230.162

    233.986

    236.768

    238.883

    4052.181

    4999.500

    5403.352

    5624.583

    5763.650

    5858.986

    5928.356

    5981.070

    2

    18.513

    19.000

    19.164

    19.247

    19.296

    19.330

    19.353

    19.371

    98.503

    99.000

    99.166

    99.249

    99.299

    99.333

    99.356

    99.374

    3

    10.128

    9.552

    9.277

    9.117

    9.013

    8.941

    8.887

    8.845

    34.116

    30.817

    29.457

    28.710

    28.237

    27.911

    27.672

    27.489

    4

    7.709

    6.944

    6.591

    6.388

    6.256

    6.163

    6.094

    6.041

    21.198

    18.000

    16.694

    15.977

    15.522

    15.207

    14.976

    14.799

    5

    6.608

    5.786

    5.409

    5.192

    5.050

    4.950

    4.876

    4.818

    16.258

    13.274

    12.060

    11.392

    10.967

    10.672

    10.456

    10.289

    6

    5.987

    5.143

    4.757

    4.534

    4.387

    4.284

    4.207

    4.147

    13.745

    10.925

    9.780

    9.148

    8.746

    8.466

    8.260

    8.102

    7

    5.591

    4.737

    4.347

    4.120

    3.972

    3.866

    3.787

    3.726

    12.246

    9.547

    8.451

    7.847

    7.460

    7.191

    6.993

    6.840

    8

    5.318

    4.459

    4.066

    3.838

    3.687

    3.581

    3.500

    3.438

    11.259

    8.649

    7.591

    7.006

    6.632

    6.371

    6.178

    6.029

    9

    5.117

    4.256

    3.863

    3.633

    3.482

    3.374

    3.293

    3.230

    10.561

    8.022

    6.992

    6.422

    6.057

    5.802

    5.613

    5.467

    10

    4.965

    4.103

    3.708

    3.478

    3.326

    3.217

    3.135

    3.072

    10.044

    7.559

    6.552

    5.994

    5.636

    5.386

    5.200

    5.057

    11

    4.844

    3.982

    3.587

    3.357

    3.204

    3.095

    3.012

    2.948

    9.646

    7.206

    6.217

    5.668

    5.316

    5.069

    4.886

    4.744

    12

    4.747

    3.885

    3.490

    3.259

    3.106

    2.996

    2.913

    2.849

    9.330

    6.927

    5.953

    5.412

    5.064

    4.821

    4.640

    4.499

    13

    4.667

    3.806

    3.411

    3.179

    3.025

    2.915

    2.832

    2.767

    9.074

    6.701

    5.739

    5.205

    4.862

    4.620

    4.441

    4.302

    14

    4.600

    3.739

    3.344

    3.112

    2.958

    2.848

    2.764

    2.699

    8.862

    6.515

    5.564

    5.035

    4.695

    4.456

    4.278

    4.140

    15

    4.543

    3.682

    3.287

    3.056

    2.901

    2.790

    2.707

    2.641

    8.683

    6.359

    5.417

    4.893

    4.556

    4.318

    4.142

    4.004

    16

    4.494

    3.634

    3.239

    3.007

    2.852

    2.741

    2.657

    2.591

    8.531

    6.226

    5.292

    4.773

    4.437

    4.202

    4.026

    3.890

    17

    4.451

    3.592

    3.197

    2.965

    2.810

    2.699

    2.614

    2.548

    8.400

    6.112

    5.185

    4.669

    4.336

    4.102

    3.927

    3.791

    18

    4.414

    3.555

    3.160

    2.928

    2.773

    2.661

    2.577

    2.510

    8.285

    6.013

    5.092

    4.579

    4.248

    4.015

    3.841

    3.705

    19

    4.381

    3.522

    3.127

    2.895

    2.740

    2.628

    2.544

    2.477

    8.185

    5.926

    5.010

    4.500

    4.171

    3.939

    3.765

    3.631

    20

    4.351

    3.493

    3.098

    2.866

    2.711

    2.599

    2.514

    2.447

    8.096

    5.849

    4.938

    4.431

    4.103

    3.871

    3.699

    3.564

    21

    4.325

    3.467

    3.072

    2.840

    2.685

    2.573

    2.488

    2.420

    8.017

    5.780

    4.874

    4.369

    4.042

    3.812

    3.640

    3.506

    22

    4.301

    3.443

    3.049

    2.817

    2.661

    2.549

    2.464

    2.397

    7.945

    5.719

    4.817

    4.313

    3.988

    3.758

    3.587

    3.453

    23

    4.279

    3.422

    3.028

    2.796

    2.640

    2.528

    2.442

    2.375

    7.881

    5.664

    4.765

    4.264

    3.939

    3.710

    3.539

    3.406

    24

    4.260

    3.403

    3.009

    2.776

    2.621

    2.508

    2.423

    2.355

    7.823

    5.614

    4.718

    4.218

    3.895

    3.667

    3.496

    3.363

    25

    4.242

    3.385

    2.991

    2.759

    2.603

    2.490

    2.405

    2.337

    7.770

    5.568

    4.675

    4.177

    3.855

    3.627

    3.457

    3.324

    26

    4.225

    3.369

    2.975

    2.743

    2.587

    2.474

    2.388

    2.321

    7.721

    5.526

    4.637

    4.140

    3.818

    3.591

    3.421

    3.288

    27

    4.210

    3.354

    2.960

    2.728

    2.572

    2.459

    2.373

    2.305

    7.677

    5.488

    4.601

    4.106

    3.785

    3.558

    3.388

    3.256

    28

    4.196

    3.340

    2.947

    2.714

    2.558

    2.445

    2.359

    2.291

    7.636

    5.453

    4.568

    4.074

    3.754

    3.528

    3.358

    3.226

    29

    4.183

    3.328

    2.934

    2.701

    2.545

    2.432

    2.346

    2.278

    7.598

    5.420

    4.538

    4.045

    3.725

    3.499

    3.330

    3.198

    30

    4.171

    3.316

    2.922

    2.690

    2.534

    2.421

    2.334

    2.266

    7.562

    5.390

    4.510

    4.018

    3.699

    3.473

    3.304

    3.173

    31

    4.160

    3.305

    2.911

    2.679

    2.523

    2.409

    2.323

    2.255

    7.530

    5.362

    4.484

    3.993

    3.675

    3.449

    3.281

    3.149

    32

    4.149

    3.295

    2.901

    2.668

    2.512

    2.399

    2.313

    2.244

    7.499

    5.336

    4.459

    3.969

    3.652

    3.427

    3.258

    3.127

    33

    4.139

    3.285

    2.892

    2.659

    2.503

    2.389

    2.303

    2.235

    7.471

    5.312

    4.437

    3.948

    3.630

    3.406

    3.238

    3.106

    34

    4.130

    3.276

    2.883

    2.650

    2.494

    2.380

    2.294

    2.225

    7.444

    5.289

    4.416

    3.927

    3.611

    3.386

    3.218

    3.087

    35

    4.121

    3.267

    2.874

    2.641

    2.485

    2.372

    2.285

    2.217

    7.419

    5.268

    4.396

    3.908

    3.592

    3.368

    3.200

    3.069

    36

    4.113

    3.259

    2.866

    2.634

    2.477

    2.364

    2.277

    2.209

    7.396

    5.248

    4.377

    3.890

    3.574

    3.351

    3.183

    3.052

    37

    4.105

    3.252

    2.859

    2.626

    2.470

    2.356

    2.270

    2.201

    7.373

    5.229

    4.360

    3.873

    3.558

    3.334

    3.167

    3.036

    38

    4.098

    3.245

    2.852

    2.619

    2.463

    2.349

    2.262

    2.194

    7.353

    5.211

    4.343

    3.858

    3.542

    3.319

    3.152

    3.021

    39

    4.091

    3.238

    2.845

    2.612

    2.456

    2.342

    2.255

    2.187

    7.333

    5.194

    4.327

    3.843

    3.528

    3.305

    3.137

    3.006

    40

    4.085

    3.232

    2.839

    2.606

    2.449

    2.336

    2.249

    2.180

    7.314

    5.179

    4.313

    3.828

    3.514

    3.291

    3.124

    2.993

    41

    4.079

    3.226

    2.833

    2.600

    2.443

    2.330

    2.243

    2.174

    7.296

    5.163

    4.299

    3.815

    3.501

    3.278

    3.111

    2.980

    42

    4.073

    3.220

    2.827

    2.594

    2.438

    2.324

    2.237

    2.168

    7.280

    5.149

    4.285

    3.802

    3.488

    3.266

    3.099

    2.968

    43

    4.067

    3.214

    2.822

    2.589

    2.432

    2.318

    2.232

    2.163

    7.264

    5.136

    4.273

    3.790

    3.476

    3.254

    3.087

    2.957

    44

    4.062

    3.209

    2.816

    2.584

    2.427

    2.313

    2.226

    2.157

    7.248

    5.123

    4.261

    3.778

    3.465

    3.243

    3.076

    2.946

    45

    4.057

    3.204

    2.812

    2.579

    2.422

    2.308

    2.221

    2.152

    7.234

    5.110

    4.249

    3.767

    3.454

    3.232

    3.066

    2.935

    46

    4.052

    3.200

    2.807

    2.574

    2.417

    2.304

    2.216

    2.147

    7.220

    5.099

    4.238

    3.757

    3.444

    3.222

    3.056

    2.925

    47

    4.047

    3.195

    2.802

    2.570

    2.413

    2.299

    2.212

    2.143

    7.207

    5.087

    4.228

    3.747

    3.434

    3.213

    3.046

    2.916

    48

    4.043

    3.191

    2.798

    2.565

    2.409

    2.295

    2.207

    2.138

    7.194

    5.077

    4.218

    3.737

    3.425

    3.204

    3.037

    2.907

    49

    4.038

    3.187

    2.794

    2.561

    2.404

    2.290

    2.203

    2.134

    7.182

    5.066

    4.208

    3.728

    3.416

    3.195

    3.028

    2.898

    50

    4.034

    3.183

    2.790

    2.557

    2.400

    2.286

    2.199

    2.130

    7.171

    5.057

    4.199

    3.720

    3.408

    3.186

    3.020

    2.890

    51

    4.030

    3.179

    2.786

    2.553

    2.397

    2.283

    2.195

    2.126

    7.159

    5.047

    4.191

    3.711

    3.400

    3.178

    3.012

    2.882

    52

    4.027

    3.175

    2.783

    2.550

    2.393

    2.279

    2.192

    2.122

    7.149

    5.038

    4.182

    3.703

    3.392

    3.171

    3.005

    2.874

    53

    4.023

    3.172

    2.779

    2.546

    2.389

    2.275

    2.188

    2.119

    7.139

    5.030

    4.174

    3.695

    3.384

    3.163

    2.997

    2.867

    54

    4.020

    3.168

    2.776

    2.543

    2.386

    2.272

    2.185

    2.115

    7.129

    5.021

    4.167

    3.688

    3.377

    3.156

    2.990

    2.860

    55

    4.016

    3.165

    2.773

    2.540

    2.383

    2.269

    2.181

    2.112

    7.119

    5.013

    4.159

    3.681

    3.370

    3.149

    2.983

    2.853

    56

    4.013

    3.162

    2.769

    2.537

    2.380

    2.266

    2.178

    2.109

    7.110

    5.006

    4.152

    3.674

    3.363

    3.143

    2.977

    2.847

    57

    4.010

    3.159

    2.766

    2.534

    2.377

    2.263

    2.175

    2.106

    7.102

    4.998

    4.145

    3.667

    3.357

    3.136

    2.971

    2.841

    58

    4.007

    3.156

    2.764

    2.531

    2.374

    2.260

    2.172

    2.103

    7.093

    4.991

    4.138

    3.661

    3.351

    3.130

    2.965

    2.835

    59

    4.004

    3.153

    2.761

    2.528

    2.371

    2.257

    2.169

    2.100

    7.085

    4.984

    4.132

    3.655

    3.345

    3.124

    2.959

    2.829

    60

    4.001

    3.150

    2.758

    2.525

    2.368

    2.254

    2.167

    2.097

    7.077

    4.977

    4.126

    3.649

    3.339

    3.119

    2.953

    2.823

    61

    3.998

    3.148

    2.755

    2.523

    2.366

    2.251

    2.164

    2.094

    7.070

    4.971

    4.120

    3.643

    3.333

    3.113

    2.948

    2.818

    62

    3.996

    3.145

    2.753

    2.520

    2.363

    2.249

    2.161

    2.092

    7.062

    4.965

    4.114

    3.638

    3.328

    3.108

    2.942

    2.813

    63

    3.993

    3.143

    2.751

    2.518

    2.361

    2.246

    2.159

    2.089

    7.055

    4.959

    4.109

    3.632

    3.323

    3.103

    2.937

    2.808

    64

    3.991

    3.140

    2.748

    2.515

    2.358

    2.244

    2.156

    2.087

    7.048

    4.953

    4.103

    3.627

    3.318

    3.098

    2.932

    2.803

    65

    3.989

    3.138

    2.746

    2.513

    2.356

    2.242

    2.154

    2.084

    7.042

    4.947

    4.098

    3.622

    3.313

    3.093

    2.928

    2.798

    66

    3.986

    3.136

    2.744

    2.511

    2.354

    2.239

    2.152

    2.082

    7.035

    4.942

    4.093

    3.618

    3.308

    3.088

    2.923

    2.793

    67

    3.984

    3.134

    2.742

    2.509

    2.352

    2.237

    2.150

    2.080

    7.029

    4.937

    4.088

    3.613

    3.304

    3.084

    2.919

    2.789

    68

    3.982

    3.132

    2.740

    2.507

    2.350

    2.235

    2.148

    2.078

    7.023

    4.932

    4.083

    3.608

    3.299

    3.080

    2.914

    2.785

    69

    3.980

    3.130

    2.737

    2.505

    2.348

    2.233

    2.145

    2.076

    7.017

    4.927

    4.079

    3.604

    3.295

    3.075

    2.910

    2.781

    70

    3.978

    3.128

    2.736

    2.503

    2.346

    2.231

    2.143

    2.074

    7.011

    4.922

    4.074

    3.600

    3.291

    3.071

    2.906

    2.777

    71

    3.976

    3.126

    2.734

    2.501

    2.344

    2.229

    2.142

    2.072

    7.006

    4.917

    4.070

    3.596

    3.287

    3.067

    2.902

    2.773

    72

    3.974

    3.124

    2.732

    2.499

    2.342

    2.227

    2.140

    2.070

    7.001

    4.913

    4.066

    3.591

    3.283

    3.063

    2.898

    2.769

    73

    3.972

    3.122

    2.730

    2.497

    2.340

    2.226

    2.138

    2.068

    6.995

    4.908

    4.062

    3.588

    3.279

    3.060

    2.895

    2.765

    74

    3.970

    3.120

    2.728

    2.495

    2.338

    2.224

    2.136

    2.066

    6.990

    4.904

    4.058

    3.584

    3.275

    3.056

    2.891

    2.762

    75

    3.968

    3.119

    2.727

    2.494

    2.337

    2.222

    2.134

    2.064

    6.985

    4.900

    4.054

    3.580

    3.272

    3.052

    2.887

    2.758

    76

    3.967

    3.117

    2.725

    2.492

    2.335

    2.220

    2.133

    2.063

    6.981

    4.896

    4.050

    3.577

    3.268

    3.049

    2.884

    2.755

    77

    3.965

    3.115

    2.723

    2.490

    2.333

    2.219

    2.131

    2.061

    6.976

    4.892

    4.047

    3.573

    3.265

    3.046

    2.881

    2.751

    78

    3.963

    3.114

    2.722

    2.489

    2.332

    2.217

    2.129

    2.059

    6.971

    4.888

    4.043

    3.570

    3.261

    3.042

    2.877

    2.748

    79

    3.962

    3.112

    2.720

    2.487

    2.330

    2.216

    2.128

    2.058

    6.967

    4.884

    4.040

    3.566

    3.258

    3.039

    2.874

    2.745

    80

    3.960

    3.111

    2.719

    2.486

    2.329

    2.214

    2.126

    2.056

    6.963

    4.881

    4.036

    3.563

    3.255

    3.036

    2.871

    2.742


    This page titled 15.5: Appendix E- The F-Tables is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by .

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