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Appendix 05: Critical Values for the F-Test

  • Page ID
    6641
  • The following tables provide values for F(0.05, νnum, νdenom) for one-tailed and for two-tailed F-tests. To use these tables, decide whether the situation calls for a one-tailed or a two-tailed analysis and calculate Fexp

    \[F_\ce{exp} = \dfrac{s_\ce{A}^2}{s_\ce{B}^2}\]

    where sA2 is greater than sB2. Compare Fexp to F(0.05, νnum, νdenom) and reject the null hypothesis if Fexp > F(0.05, νnum, νdenom). You may replace s with σ if you know the population’s standard deviation.

    F(0.05,νnum, νdenom) for a One-Tailed F-Test

    νnum

    νdenom

    1

    2

    3

    4

    5

    6

    7

    8

    9

    10

    15

    20

    1

    161.4

    199.5

    215.7

    224.6

    230.2

    234.0

    236.8

    238.9

    240.5

    241.9

    245.9

    248.0

    254.3

    2

    18.51

    19.00

    19.16

    19.25

    19.30

    19.33

    19.35

    19.37

    19.38

    19.40

    19.43

    19.45

    19.50

    3

    10.13

    9.552

    9.277

    9.117

    9.013

    8.941

    8.887

    8.845

    8.812

    8.786

    8.703

    8.660

    8.526

    4

    7.709

    6.994

    6.591

    6.388

    6.256

    6.163

    6.094

    6.041

    5.999

    5.964

    5.858

    5.803

    5.628

    5

    6.608

    5.786

    5.409

    5.192

    5.050

    4.950

    4.876

    4.818

    4.722

    4.753

    4.619

    4.558

    4.365

    6

    5.591

    5.143

    4.757

    4.534

    4.387

    4.284

    4.207

    4.147

    4.099

    4.060

    3.938

    3.874

    3.669

    7

    5.591

    4.737

    4.347

    4.120

    3.972

    3.866

    3.787

    3.726

    3.677

    3.637

    3.511

    3.445

    3.230

    8

    5.318

    4.459

    4.066

    3.838

    3.687

    3.581

    3.500

    3.438

    3.388

    3.347

    3.218

    3.150

    2.928

    9

    5.117

    4.256

    3.863

    3.633

    3.482

    3.374

    3.293

    3.230

    3.179

    3.137

    3.006

    2.936

    2.707

    10

    4.965

    4.103

    3.708

    3.478

    3.326

    3.217

    3.135

    3.072

    3.020

    2.978

    2.845

    2.774

    2.538

    11

    4.844

    3.982

    3.587

    3.257

    3.204

    3.095

    3.012

    2.948

    2.896

    2.854

    2.719

    2.646

    2.404

    12

    4.747

    3.885

    3.490

    3.259

    3.106

    2.996

    2.913

    2.849

    2.796

    2.753

    2.617

    2.544

    2.296

    13

    4.667

    3.806

    3.411

    3.179

    3.025

    2.915

    2.832

    2.767

    2.714

    2.671

    2.533

    2.459

    2.206

    14

    4.600

    3.739

    3.344

    3.112

    2.958

    2.848

    2.764

    2.699

    2.646

    2.602

    2.463

    2.388

    2.131

    15

    4.534

    3.682

    3.287

    3.056

    2.901

    2.790

    2.707

    2.641

    2.588

    2.544

    2.403

    2.328

    2.066

    16

    4.494

    3.634

    3.239

    3.007

    2.852

    2.741

    2.657

    2.591

    2.538

    2.494

    2.352

    2.276

    2.010

    17

    4.451

    3.592

    3.197

    2.965

    2.810

    2.699

    2.614

    2.548

    2.494

    2.450

    2.308

    2.230

    1.960

    18

    4.414

    3.555

    3.160

    2.928

    2.773

    2.661

    2.577

    2.510

    2.456

    2.412

    2.269

    2.191

    1.917

    19

    4.381

    3.552

    3.127

    2.895

    2.740

    2.628

    2.544

    2.477

    2.423

    2.378

    2.234

    2.155

    1.878

    20

    4,351

    3.493

    3.098

    2.866

    2.711

    2.599

    2.514

    2.447

    2.393

    2.348

    2.203

    2.124

    1.843

    3.842

    2.996

    2.605

    2.372

    2.214

    2.099

    2.010

    1.938

    1.880

    1.831

    1.666

    1.570

    1.000

     

    F(0.05,νnum, νdenom) for a Two-Tailed F-Test

    νnum

    νdenom

    1

    2

    3

    4

    5

    6

    7

    8

    9

    10

    15

    20

    1

    647.8

    799.5

    864.2

    899.6

    921.8

    937.1

    948.2

    956.7

    963.3

    968.6

    984.9

    993.1

    1018

    2

    38.51

    39.00

    39.17

    39.25

    39.30

    39.33

    39.36

    39.37

    39.39

    39.40

    39.43

    39.45

    39.50

    3

    17.44

    16.04

    15.44

    15.10

    14.88

    14.73

    14.62

    14.54

    14.47

    14.42

    14.25

    14.17

    13.90

    4

    12.22

    10.65

    9.979

    9.605

    9.364

    9.197

    9.074

    8.980

    8.905

    8.444

    8.657

    8.560

    8.257

    5

    10.01

    8.434

    7.764

    7.388

    7.146

    6.978

    6.853

    6.757

    6.681

    6.619

    6.428

    6.329

    6.015

    6

    8.813

    7.260

    6.599

    6.227

    5.988

    5.820

    5.695

    5.600

    5.523

    5.461

    5.269

    5.168

    4.894

    7

    8.073

    6.542

    5.890

    5.523

    5.285

    5.119

    4.995

    4.899

    4.823

    4.761

    4.568

    4.467

    4.142

    8

    7.571

    6.059

    5.416

    5.053

    4.817

    4.652

    4.529

    4.433

    4.357

    4.259

    4.101

    3.999

    3.670

    9

    7.209

    5.715

    5.078

    4.718

    4.484

    4.320

    4.197

    4.102

    4.026

    3.964

    3.769

    3.667

    3.333

    10

    6.937

    5.456

    4.826

    4.468

    4.236

    4.072

    3.950

    3.855

    3.779

    3.717

    3.522

    3.419

    3.080

    11

    6.724

    5.256

    4.630

    4.275

    4.044

    3.881

    3.759

    3.644

    3.588

    3.526

    3.330

    3.226

    2.883

    12

    6.544

    5.096

    4.474

    4.121

    3.891

    3.728

    3.607

    3.512

    3.436

    3.374

    3.177

    3.073

    2.725

    13

    6.414

    4.965

    4.347

    3.996

    3.767

    3.604

    3.483

    3.388

    3.312

    3.250

    3.053

    2.948

    2.596

    14

    6.298

    4.857

    4.242

    3.892

    3.663

    3.501

    3.380

    3.285

    3.209

    3.147

    2.949

    2.844

    2.487

    15

    6.200

    4.765

    4.153

    3.804

    3.576

    3.415

    3.293

    3.199

    3.123

    3.060

    2.862

    2.756

    2.395

    16

    6.115

    4.687

    4.077

    3.729

    3.502

    3.341

    3.219

    3.125

    3.049

    2.986

    2.788

    2.681

    2.316

    17

    6.042

    4.619

    4.011

    3.665

    3.438

    3.277

    3.156

    3.061

    2.985

    2.922

    2.723

    2.616

    2.247

    18

    5.978

    4.560

    3.954

    3.608

    3.382

    3.221

    3.100

    3.005

    2.929

    2.866

    2.667

    2.559

    2.187

    19

    5.922

    4.508

    3.903

    3.559

    3.333

    3.172

    3.051

    2.956

    2.880

    2.817

    2.617

    2.509

    2.133

    20

    5.871

    4.461

    3.859

    3.515

    3.289

    3.128

    3.007

    2.913

    2.837

    2.774

    2.573

    2.464

    2.085

    5.024

    3.689

    3.116

    2.786

    2.567

    2.408

    2.288

    2.192

    2.114

    2.048

    1.833

    1.708

    1.000