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Appendix 05: Critical Values for the F-Test

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