﻿ Resources > Distribution tables

# Distribution tables

This section contains distribution tables for some of the more widely used probability distributions. The include the cumulative Normal distribution, the Student's t-distribution, the chi-square distribution and the F distribution. Note that distribution tables such as these can be produced directly using Excel or similar software via their various built-in functions. For example, the F distribution tables provided in this topic were generated using the Excel function FINV(0.05,df1,df2).

Normal distribution

The following table provides the cumulative distribution function of the Normal distribution, from 0 to x. To obtain a one-sided value simply add 0.5 to the table entry, or for a two-sided value (the most commonly used case) double the value in the table. The highlighted cells identify the two-sided values for 90% (+/-5%) and 95% (+/2.5%) values.

x

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

—

—

0.00399

0.00798

0.01197

0.01595

0.01994

0.02392

0.02790

0.03188

0.03586

0.10

0.03983

0.04380

0.04776

0.05172

0.05567

0.05962

0.06356

0.06749

0.07142

0.07535

0.20

0.07926

0.08317

0.08706

0.09095

0.09483

0.09871

0.10257

0.10642

0.11026

0.11409

0.30

0.11791

0.12172

0.12552

0.12930

0.13307

0.13683

0.14058

0.14431

0.14803

0.15173

0.40

0.15542

0.15910

0.16276

0.16640

0.17003

0.17364

0.17724

0.18082

0.18439

0.18793

0.50

0.19146

0.19497

0.19847

0.20194

0.20540

0.20884

0.21226

0.21566

0.21904

0.22240

0.60

0.22575

0.22907

0.23237

0.23565

0.23891

0.24215

0.24537

0.24857

0.25175

0.25490

0.70

0.25804

0.26115

0.26424

0.26730

0.27035

0.27337

0.27637

0.27935

0.28230

0.28524

0.80

0.28814

0.29103

0.29389

0.29673

0.29955

0.30234

0.30511

0.30785

0.31057

0.31327

0.90

0.31594

0.31859

0.32121

0.32381

0.32639

0.32894

0.33147

0.33398

0.33646

0.33891

1.00

0.34134

0.34375

0.34614

0.34849

0.35083

0.35314

0.35543

0.35769

0.35993

0.36214

1.10

0.36433

0.36650

0.36864

0.37076

0.37286

0.37493

0.37698

0.37900

0.38100

0.38298

1.20

0.38493

0.38686

0.38877

0.39065

0.39251

0.39435

0.39617

0.39796

0.39973

0.40147

1.30

0.40320

0.40490

0.40658

0.40824

0.40988

0.41149

0.41308

0.41466

0.41621

0.41774

1.40

0.41924

0.42073

0.42220

0.42364

0.42507

0.42647

0.42785

0.42922

0.43056

0.43189

1.50

0.43319

0.43448

0.43574

0.43699

0.43822

0.43943

0.44062

0.44179

0.44295

0.44408

1.60

0.44520

0.44630

0.44738

0.44845

0.44950

0.45053

0.45154

0.45254

0.45352

0.45449

1.70

0.45543

0.45637

0.45728

0.45818

0.45907

0.45994

0.46080

0.46164

0.46246

0.46327

1.80

0.46407

0.46485

0.46562

0.46638

0.46712

0.46784

0.46856

0.46926

0.46995

0.47062

1.90

0.47128

0.47193

0.47257

0.47320

0.47381

0.47441

0.47500

0.47558

0.47615

0.47670

2.00

0.47725

0.47778

0.47831

0.47882

0.47932

0.47982

0.48030

0.48077

0.48124

0.48169

2.10

0.48214

0.48257

0.48300

0.48341

0.48382

0.48422

0.48461

0.48500

0.48537

0.48574

2.20

0.48610

0.48645

0.48679

0.48713

0.48745

0.48778

0.48809

0.48840

0.48870

0.48899

2.30

0.48928

0.48956

0.48983

0.49010

0.49036

0.49061

0.49086

0.49111

0.49134

0.49158

2.40

0.49180

0.49202

0.49224

0.49245

0.49266

0.49286

0.49305

0.49324

0.49343

0.49361

2.50

0.49379

0.49396

0.49413

0.49430

0.49446

0.49461

0.49477

0.49492

0.49506

0.49520

2.60

0.49534

0.49547

0.49560

0.49573

0.49585

0.49598

0.49609

0.49621

0.49632

0.49643

2.70

0.49653

0.49664

0.49674

0.49683

0.49693

0.49702

0.49711

0.49720

0.49728

0.49736

2.80

0.49744

0.49752

0.49760

0.49767

0.49774

0.49781

0.49788

0.49795

0.49801

0.49807

2.90

0.49813

0.49819

0.49825

0.49831

0.49836

0.49841

0.49846

0.49851

0.49856

0.49861

3.00

0.49865

0.49869

0.49874

0.49878

0.49882

0.49886

0.49889

0.49893

0.49896

0.49900

3.10

0.49903

0.49906

0.49910

0.49913

0.49916

0.49918

0.49921

0.49924

0.49926

0.49929

3.20

0.49931

0.49934

0.49936

0.49938

0.49940

0.49942

0.49944

0.49946

0.49948

0.49950

3.30

0.49952

0.49953

0.49955

0.49957

0.49958

0.49960

0.49961

0.49962

0.49964

0.49965

3.40

0.49966

0.49968

0.49969

0.49970

0.49971

0.49972

0.49973

0.49974

0.49975

0.49976

3.50

0.49977

0.49978

0.49978

0.49979

0.49980

0.49981

0.49981

0.49982

0.49983

0.49983

3.60

0.49984

0.49985

0.49985

0.49986

0.49986

0.49987

0.49987

0.49988

0.49988

0.49989

3.70

0.49989

0.49990

0.49990

0.49990

0.49991

0.49991

0.49992

0.49992

0.49992

0.49992

3.80

0.49993

0.49993

0.49993

0.49994

0.49994

0.49994

0.49994

0.49995

0.49995

0.49995

3.90

0.49995

0.49995

0.49996

0.49996

0.49996

0.49996

0.49996

0.49996

0.49997

0.49997

4.00

0.49997

0.49997

0.49997

0.49997

0.49997

0.49997

0.49998

0.49998

0.49998

0.49998

Note that specific critical values may be computed using standard inverse functions, such as NORMINV() in Excel. For the unit Normal the table below provides the x values associated with the critical probability levels indicated (upper tail).

 p x p x 0.9999 3.7190165 0.950 1.6438848 0.999 3.0902323 0.945 1.5972948 0.995 2.5689744 0.940 1.5539347 0.990 2.3226121 0.935 1.5133137 0.985 2.1674573 0.930 1.4750467 0.980 2.0516879 0.925 1.4388254 0.975 1.9582558 0.920 1.4043992 0.970 1.879326 0.915 1.3715615 0.965 1.810618 0.910 1.3401395 0.960 1.7495268 0.905 1.3099877 0.955 1.6943437 0.900 1.280982

Student's t distribution

Upper tail critical values for the Student's t-distribution, showing the degrees of freedom (df) and probability levels from 0.1 (10%) to 0.1%. Note that for df>30 the figures are close to those for the Normal distribution, and for the infinity line they match those for the Normal distribution. Only the upper critical values are required as the distribution is symmetric, as per the Normal.

df

0.1

0.05

0.025

0.01

0.005

0.001

1

3.078

6.314

12.706

31.821

63.657

318.313

2

1.886

2.920

4.303

6.965

9.925

22.327

3

1.638

2.353

3.182

4.541

5.841

10.215

4

1.533

2.132

2.776

3.747

4.604

7.173

5

1.476

2.015

2.571

3.365

4.032

5.893

6

1.440

1.943

2.447

3.143

3.707

5.208

7

1.415

1.895

2.365

2.998

3.499

4.782

8

1.397

1.860

2.306

2.896

3.355

4.499

9

1.383

1.833

2.262

2.821

3.250

4.296

10

1.372

1.812

2.228

2.764

3.169

4.143

11

1.363

1.796

2.201

2.718

3.106

4.024

12

1.356

1.782

2.179

2.681

3.055

3.929

13

1.350

1.771

2.160

2.650

3.012

3.852

14

1.345

1.761

2.145

2.624

2.977

3.787

15

1.341

1.753

2.131

2.602

2.947

3.733

16

1.337

1.746

2.120

2.583

2.921

3.686

17

1.333

1.740

2.110

2.567

2.898

3.646

18

1.330

1.734

2.101

2.552

2.878

3.610

19

1.328

1.729

2.093

2.539

2.861

3.579

20

1.325

1.725

2.086

2.528

2.845

3.552

21

1.323

1.721

2.080

2.518

2.831

3.527

22

1.321

1.717

2.074

2.508

2.819

3.505

23

1.319

1.714

2.069

2.500

2.807

3.485

24

1.318

1.711

2.064

2.492

2.797

3.467

25

1.316

1.708

2.060

2.485

2.787

3.450

26

1.315

1.706

2.056

2.479

2.779

3.435

27

1.314

1.703

2.052

2.473

2.771

3.421

28

1.313

1.701

2.048

2.467

2.763

3.408

29

1.311

1.699

2.045

2.462

2.756

3.396

30

1.310

1.697

2.042

2.457

2.750

3.385

31

1.309

1.696

2.040

2.453

2.744

3.375

32

1.309

1.694

2.037

2.449

2.738

3.365

33

1.308

1.692

2.035

2.445

2.733

3.356

34

1.307

1.691

2.032

2.441

2.728

3.348

35

1.306

1.690

2.030

2.438

2.724

3.340

36

1.306

1.688

2.028

2.434

2.719

3.333

37

1.305

1.687

2.026

2.431

2.715

3.326

38

1.304

1.686

2.024

2.429

2.712

3.319

39

1.304

1.685

2.023

2.426

2.708

3.313

40

1.303

1.684

2.021

2.423

2.704

3.307

41

1.303

1.683

2.020

2.421

2.701

3.301

42

1.302

1.682

2.018

2.418

2.698

3.296

43

1.302

1.681

2.017

2.416

2.695

3.291

44

1.301

1.680

2.015

2.414

2.692

3.286

45

1.301

1.679

2.014

2.412

2.690

3.281

46

1.300

1.679

2.013

2.410

2.687

3.277

47

1.300

1.678

2.012

2.408

2.685

3.273

48

1.299

1.677

2.011

2.407

2.682

3.269

49

1.299

1.677

2.010

2.405

2.680

3.265

50

1.299

1.676

2.009

2.403

2.678

3.261

51

1.298

1.675

2.008

2.402

2.676

3.258

52

1.298

1.675

2.007

2.400

2.674

3.255

53

1.298

1.674

2.006

2.399

2.672

3.251

54

1.297

1.674

2.005

2.397

2.670

3.248

55

1.297

1.673

2.004

2.396

2.668

3.245

56

1.297

1.673

2.003

2.395

2.667

3.242

57

1.297

1.672

2.002

2.394

2.665

3.239

58

1.296

1.672

2.002

2.392

2.663

3.237

59

1.296

1.671

2.001

2.391

2.662

3.234

60

1.296

1.671

2.000

2.390

2.660

3.232

61

1.296

1.670

2.000

2.389

2.659

3.229

62

1.295

1.670

1.999

2.388

2.657

3.227

63

1.295

1.669

1.998

2.387

2.656

3.225

64

1.295

1.669

1.998

2.386

2.655

3.223

65

1.295

1.669

1.997

2.385

2.654

3.220

66

1.295

1.668

1.997

2.384

2.652

3.218

67

1.294

1.668

1.996

2.383

2.651

3.216

68

1.294

1.668

1.995

2.382

2.650

3.214

69

1.294

1.667

1.995

2.382

2.649

3.213

70

1.294

1.667

1.994

2.381

2.648

3.211

71

1.294

1.667

1.994

2.380

2.647

3.209

72

1.293

1.666

1.993

2.379

2.646

3.207

73

1.293

1.666

1.993

2.379

2.645

3.206

74

1.293

1.666

1.993

2.378

2.644

3.204

75

1.293

1.665

1.992

2.377

2.643

3.202

76

1.293

1.665

1.992

2.376

2.642

3.201

77

1.293

1.665

1.991

2.376

2.641

3.199

78

1.292

1.665

1.991

2.375

2.640

3.198

79

1.292

1.664

1.990

2.374

2.640

3.197

80

1.292

1.664

1.990

2.374

2.639

3.195

81

1.292

1.664

1.990

2.373

2.638

3.194

82

1.292

1.664

1.989

2.373

2.637

3.193

83

1.292

1.663

1.989

2.372

2.636

3.191

84

1.292

1.663

1.989

2.372

2.636

3.190

85

1.292

1.663

1.988

2.371

2.635

3.189

86

1.291

1.663

1.988

2.370

2.634

3.188

87

1.291

1.663

1.988

2.370

2.634

3.187

88

1.291

1.662

1.987

2.369

2.633

3.185

89

1.291

1.662

1.987

2.369

2.632

3.184

90

1.291

1.662

1.987

2.368

2.632

3.183

91

1.291

1.662

1.986

2.368

2.631

3.182

92

1.291

1.662

1.986

2.368

2.630

3.181

93

1.291

1.661

1.986

2.367

2.630

3.180

94

1.291

1.661

1.986

2.367

2.629

3.179

95

1.291

1.661

1.985

2.366

2.629

3.178

96

1.290

1.661

1.985

2.366

2.628

3.177

97

1.290

1.661

1.985

2.365

2.627

3.176

98

1.290

1.661

1.984

2.365

2.627

3.175

99

1.290

1.660

1.984

2.365

2.626

3.175

100

1.290

1.660

1.984

2.364

2.626

3.174

infinity

1.282

1.645

1.960

2.326

2.576

3.090

Chi-square distribution

The following tables provide the upper and lower percentage points of the chi-square distribution with df degrees of freedom. Both are required as the distribution is asymmetric.

df

0.100

0.050

0.025

0.010

0.001

1

2.706

3.841

5.024

6.635

10.828

2

4.605

5.991

7.378

9.210

13.816

3

6.251

7.815

9.348

11.345

16.266

4

7.779

9.488

11.143

13.277

18.467

5

9.236

11.070

12.833

15.086

20.515

6

10.645

12.592

14.449

16.812

22.458

7

12.017

14.067

16.013

18.475

24.322

8

13.362

15.507

17.535

20.090

26.125

9

14.684

16.919

19.023

21.666

27.877

10

15.987

18.307

20.483

23.209

29.588

11

17.275

19.675

21.920

24.725

31.264

12

18.549

21.026

23.337

26.217

32.910

13

19.812

22.362

24.736

27.688

34.528

14

21.064

23.685

26.119

29.141

36.123

15

22.307

24.996

27.488

30.578

37.697

16

23.542

26.296

28.845

32.000

39.252

17

24.769

27.587

30.191

33.409

40.790

18

25.989

28.869

31.526

34.805

42.312

19

27.204

30.144

32.852

36.191

43.820

20

28.412

31.410

34.170

37.566

45.315

21

29.615

32.671

35.479

38.932

46.797

22

30.813

33.924

36.781

40.289

48.268

23

32.007

35.172

38.076

41.638

49.728

24

33.196

36.415

39.364

42.980

51.179

25

34.382

37.652

40.646

44.314

52.620

26

35.563

38.885

41.923

45.642

54.052

27

36.741

40.113

43.195

46.963

55.476

28

37.916

41.337

44.461

48.278

56.892

29

39.087

42.557

45.722

49.588

58.301

30

40.256

43.773

46.979

50.892

59.703

31

41.422

44.985

48.232

52.191

61.098

32

42.585

46.194

49.480

53.486

62.487

33

43.745

47.400

50.725

54.776

63.870

34

44.903

48.602

51.966

56.061

65.247

35

46.059

49.802

53.203

57.342

66.619

36

47.212

50.998

54.437

58.619

67.985

37

48.363

52.192

55.668

59.893

69.347

38

49.513

53.384

56.896

61.162

70.703

39

50.660

54.572

58.120

62.428

72.055

40

51.805

55.758

59.342

63.691

73.402

41

52.949

56.942

60.561

64.950

74.745

42

54.090

58.124

61.777

66.206

76.084

43

55.230

59.304

62.990

67.459

77.419

44

56.369

60.481

64.201

68.710

78.750

45

57.505

61.656

65.410

69.957

80.077

46

58.641

62.830

66.617

71.201

81.400

47

59.774

64.001

67.821

72.443

82.720

48

60.907

65.171

69.023

73.683

84.037

49

62.038

66.339

70.222

74.919

85.351

50

63.167

67.505

71.420

76.154

86.661

51

64.295

68.669

72.616

77.386

87.968

52

65.422

69.832

73.810

78.616

89.272

53

66.548

70.993

75.002

79.843

90.573

54

67.673

72.153

76.192

81.069

91.872

55

68.796

73.311

77.380

82.292

93.168

56

69.919

74.468

78.567

83.513

94.461

57

71.040

75.624

79.752

84.733

95.751

58

72.160

76.778

80.936

85.950

97.039

59

73.279

77.931

82.117

87.166

98.324

60

74.397

79.082

83.298

88.379

99.607

61

75.514

80.232

84.476

89.591

100.888

62

76.630

81.381

85.654

90.802

102.166

63

77.745

82.529

86.830

92.010

103.442

64

78.860

83.675

88.004

93.217

104.716

65

79.973

84.821

89.177

94.422

105.988

66

81.085

85.965

90.349

95.626

107.258

67

82.197

87.108

91.519

96.828

108.526

68

83.308

88.250

92.689

98.028

109.791

69

84.418

89.391

93.856

99.228

111.055

70

85.527

90.531

95.023

100.425

112.317

71

86.635

91.670

96.189

101.621

113.577

72

87.743

92.808

97.353

102.816

114.835

73

88.850

93.945

98.516

104.010

116.092

74

89.956

95.081

99.678

105.202

117.346

75

91.061

96.217

100.839

106.393

118.599

76

92.166

97.351

101.999

107.583

119.850

77

93.270

98.484

103.158

108.771

121.100

78

94.374

99.617

104.316

109.958

122.348

79

95.476

100.749

105.473

111.144

123.594

80

96.578

101.879

106.629

112.329

124.839

81

97.680

103.010

107.783

113.512

126.083

82

98.780

104.139

108.937

114.695

127.324

83

99.880

105.267

110.090

115.876

128.565

84

100.980

106.395

111.242

117.057

129.804

85

102.079

107.522

112.393

118.236

131.041

86

103.177

108.648

113.544

119.414

132.277

87

104.275

109.773

114.693

120.591

133.512

88

105.372

110.898

115.841

121.767

134.746

89

106.469

112.022

116.989

122.942

135.978

90

107.565

113.145

118.136

124.116

137.208

91

108.661

114.268

119.282

125.289

138.438

92

109.756

115.390

120.427

126.462

139.666

93

110.850

116.511

121.571

127.633

140.893

94

111.944

117.632

122.715

128.803

142.119

95

113.038

118.752

123.858

129.973

143.344

96

114.131

119.871

125.000

131.141

144.567

97

115.223

120.990

126.141

132.309

145.789

98

116.315

122.108

127.282

133.476

147.010

99

117.407

123.225

128.422

134.642

148.230

100

118.498

124.342

129.561

135.807

149.449

df

0.9

0.95

0.975

0.99

0.999

1

0.016

0.004

0.001

—

—

2

0.211

0.103

0.051

0.020

0.002

3

0.584

0.352

0.216

0.115

0.024

4

1.064

0.711

0.484

0.297

0.091

5

1.610

1.145

0.831

0.554

0.210

6

2.204

1.635

1.237

0.872

0.381

7

2.833

2.167

1.690

1.239

0.598

8

3.490

2.733

2.180

1.646

0.857

9

4.168

3.325

2.700

2.088

1.152

10

4.865

3.940

3.247

2.558

1.479

11

5.578

4.575

3.816

3.053

1.834

12

6.304

5.226

4.404

3.571

2.214

13

7.042

5.892

5.009

4.107

2.617

14

7.790

6.571

5.629

4.660

3.041

15

8.547

7.261

6.262

5.229

3.483

16

9.312

7.962

6.908

5.812

3.942

17

10.085

8.672

7.564

6.408

4.416

18

10.865

9.390

8.231

7.015

4.905

19

11.651

10.117

8.907

7.633

5.407

20

12.443

10.851

9.591

8.260

5.921

21

13.240

11.591

10.283

8.897

6.447

22

14.041

12.338

10.982

9.542

6.983

23

14.848

13.091

11.689

10.196

7.529

24

15.659

13.848

12.401

10.856

8.085

25

16.473

14.611

13.120

11.524

8.649

26

17.292

15.379

13.844

12.198

9.222

27

18.114

16.151

14.573

12.879

9.803

28

18.939

16.928

15.308

13.565

10.391

29

19.768

17.708

16.047

14.256

10.986

30

20.599

18.493

16.791

14.953

11.588

31

21.434

19.281

17.539

15.655

12.196

32

22.271

20.072

18.291

16.362

12.811

33

23.110

20.867

19.047

17.074

13.431

34

23.952

21.664

19.806

17.789

14.057

35

24.797

22.465

20.569

18.509

14.688

36

25.643

23.269

21.336

19.233

15.324

37

26.492

24.075

22.106

19.960

15.965

38

27.343

24.884

22.878

20.691

16.611

39

28.196

25.695

23.654

21.426

17.262

40

29.051

26.509

24.433

22.164

17.916

41

29.907

27.326

25.215

22.906

18.575

42

30.765

28.144

25.999

23.650

19.239

43

31.625

28.965

26.785

24.398

19.906

44

32.487

29.787

27.575

25.148

20.576

45

33.350

30.612

28.366

25.901

21.251

46

34.215

31.439

29.160

26.657

21.929

47

35.081

32.268

29.956

27.416

22.610

48

35.949

33.098

30.755

28.177

23.295

49

36.818

33.930

31.555

28.941

23.983

50

37.689

34.764

32.357

29.707

24.674

51

38.560

35.600

33.162

30.475

25.368

52

39.433

36.437

33.968

31.246

26.065

53

40.308

37.276

34.776

32.018

26.765

54

41.183

38.116

35.586

32.793

27.468

55

42.060

38.958

36.398

33.570

28.173

56

42.937

39.801

37.212

34.350

28.881

57

43.816

40.646

38.027

35.131

29.592

58

44.696

41.492

38.844

35.913

30.305

59

45.577

42.339

39.662

36.698

31.020

60

46.459

43.188

40.482

37.485

31.738

61

47.342

44.038

41.303

38.273

32.459

62

48.226

44.889

42.126

39.063

33.181

63

49.111

45.741

42.950

39.855

33.906

64

49.996

46.595

43.776

40.649

34.633

65

50.883

47.450

44.603

41.444

35.362

66

51.770

48.305

45.431

42.240

36.093

67

52.659

49.162

46.261

43.038

36.826

68

53.548

50.020

47.092

43.838

37.561

69

54.438

50.879

47.924

44.639

38.298

70

55.329

51.739

48.758

45.442

39.036

71

56.221

52.600

49.592

46.246

39.777

72

57.113

53.462

50.428

47.051

40.519

73

58.006

54.325

51.265

47.858

41.264

74

58.900

55.189

52.103

48.666

42.010

75

59.795

56.054

52.942

49.475

42.757

76

60.690

56.920

53.782

50.286

43.507

77

61.586

57.786

54.623

51.097

44.258

78

62.483

58.654

55.466

51.910

45.010

79

63.380

59.522

56.309

52.725

45.764

80

64.278

60.391

57.153

53.540

46.520

81

65.176

61.261

57.998

54.357

47.277

82

66.076

62.132

58.845

55.174

48.036

83

66.976

63.004

59.692

55.993

48.796

84

67.876

63.876

60.540

56.813

49.557

85

68.777

64.749

61.389

57.634

50.320

86

69.679

65.623

62.239

58.456

51.085

87

70.581

66.498

63.089

59.279

51.850

88

71.484

67.373

63.941

60.103

52.617

89

72.387

68.249

64.793

60.928

53.386

90

73.291

69.126

65.647

61.754

54.155

91

74.196

70.003

66.501

62.581

54.926

92

75.100

70.882

67.356

63.409

55.698

93

76.006

71.760

68.211

64.238

56.472

94

76.912

72.640

69.068

65.068

57.246

95

77.818

73.520

69.925

65.898

58.022

96

78.725

74.401

70.783

66.730

58.799

97

79.633

75.282

71.642

67.562

59.577

98

80.541

76.164

72.501

68.396

60.356

99

81.449

77.046

73.361

69.230

61.137

100

82.358

77.929

74.222

70.065

61.918

F distribution

Upper critical values of the F distribution, 5% level. In the following table df1 (the row entries) provides the degrees of freedom for the numerator and df2 (the column entries) provides the degrees of freedom for the denominator in the F ratio.

df1, df2

1

2

3

4

5

6

7

8

9

10

1

161.448

199.500

215.707

224.583

230.162

233.986

236.768

238.883

240.543

241.882

2

18.513

19.000

19.164

19.247

19.296

19.330

19.353

19.371

19.385

19.396

3

10.128

9.552

9.277

9.117

9.013

8.941

8.887

8.845

8.812

8.786

4

7.709

6.944

6.591

6.388

6.256

6.163

6.094

6.041

5.999

5.964

5

6.608

5.786

5.409

5.192

5.050

4.950

4.876

4.818

4.772

4.735

6

5.987

5.143

4.757

4.534

4.387

4.284

4.207

4.147

4.099

4.060

7

5.591

4.737

4.347

4.120

3.972

3.866

3.787

3.726

3.677

3.637

8

5.318

4.459

4.066

3.838

3.687

3.581

3.500

3.438

3.388

3.347

9

5.117

4.256

3.863

3.633

3.482

3.374

3.293

3.230

3.179

3.137

10

4.965

4.103

3.708

3.478

3.326

3.217

3.135

3.072

3.020

2.978

11

4.844

3.982

3.587

3.357

3.204

3.095

3.012

2.948

2.896

2.854

12

4.747

3.885

3.490

3.259

3.106

2.996

2.913

2.849

2.796

2.753

13

4.667

3.806

3.411

3.179

3.025

2.915

2.832

2.767

2.714

2.671

14

4.600

3.739

3.344

3.112

2.958

2.848

2.764

2.699

2.646

2.602

15

4.543

3.682

3.287

3.056

2.901

2.790

2.707

2.641

2.588

2.544

16

4.494

3.634

3.239

3.007

2.852

2.741

2.657

2.591

2.538

2.494

17

4.451

3.592

3.197

2.965

2.810

2.699

2.614

2.548

2.494

2.450

18

4.414

3.555

3.160

2.928

2.773

2.661

2.577

2.510

2.456

2.412

19

4.381

3.522

3.127

2.895

2.740

2.628

2.544

2.477

2.423

2.378

20

4.351

3.493

3.098

2.866

2.711

2.599

2.514

2.447

2.393

2.348

21

4.325

3.467

3.072

2.840

2.685

2.573

2.488

2.420

2.366

2.321

22

4.301

3.443

3.049

2.817

2.661

2.549

2.464

2.397

2.342

2.297

23

4.279

3.422

3.028

2.796

2.640

2.528

2.442

2.375

2.320

2.275

24

4.260

3.403

3.009

2.776

2.621

2.508

2.423

2.355

2.300

2.255

25

4.242

3.385

2.991

2.759

2.603

2.490

2.405

2.337

2.282

2.236

26

4.225

3.369

2.975

2.743

2.587

2.474

2.388

2.321

2.265

2.220

27

4.210

3.354

2.960

2.728

2.572

2.459

2.373

2.305

2.250

2.204

28

4.196

3.340

2.947

2.714

2.558

2.445

2.359

2.291

2.236

2.190

29

4.183

3.328

2.934

2.701

2.545

2.432

2.346

2.278

2.223

2.177

30

4.171

3.316

2.922

2.690

2.534

2.421

2.334

2.266

2.211

2.165

31

4.160

3.305

2.911

2.679

2.523

2.409

2.323

2.255

2.199

2.153

32

4.149

3.295

2.901

2.668

2.512

2.399

2.313

2.244

2.189

2.142

33

4.139

3.285

2.892

2.659

2.503

2.389

2.303

2.235

2.179

2.133

34

4.130

3.276

2.883

2.650

2.494

2.380

2.294

2.225

2.170

2.123

35

4.121

3.267

2.874

2.641

2.485

2.372

2.285

2.217

2.161

2.114

36

4.113

3.259

2.866

2.634

2.477

2.364

2.277

2.209

2.153

2.106

37

4.105

3.252

2.859

2.626

2.470

2.356

2.270

2.201

2.145

2.098

38

4.098

3.245

2.852

2.619

2.463

2.349

2.262

2.194

2.138

2.091

39

4.091

3.238

2.845

2.612

2.456

2.342

2.255

2.187

2.131

2.084

40

4.085

3.232

2.839

2.606

2.449

2.336

2.249

2.180

2.124

2.077

41

4.079

3.226

2.833

2.600

2.443

2.330

2.243

2.174

2.118

2.071

42

4.073

3.220

2.827

2.594

2.438

2.324

2.237

2.168

2.112

2.065

43

4.067

3.214

2.822

2.589

2.432

2.318

2.232

2.163

2.106

2.059

44

4.062

3.209

2.816

2.584

2.427

2.313

2.226

2.157

2.101

2.054

45

4.057

3.204

2.812

2.579

2.422

2.308

2.221

2.152

2.096

2.049

46

4.052

3.200

2.807

2.574

2.417

2.304

2.216

2.147

2.091

2.044

47

4.047

3.195

2.802

2.570

2.413

2.299

2.212

2.143

2.086

2.039

48

4.043

3.191

2.798

2.565

2.409

2.295

2.207

2.138

2.082

2.035

49

4.038

3.187

2.794

2.561

2.404

2.290

2.203

2.134

2.077

2.030

50

4.034

3.183

2.790

2.557

2.400

2.286

2.199

2.130

2.073

2.026

df1, df2

11

12

13

14

15

16

17

18

19

20

1

242.983

243.906

244.690

245.364

245.950

246.464

246.918

247.323

247.686

248.013

2

19.405

19.413

19.419

19.424

19.429

19.433

19.437

19.440

19.443

19.446

3

8.763

8.745

8.729

8.715

8.703

8.692

8.683

8.675

8.667

8.660

4

5.936

5.912

5.891

5.873

5.858

5.844

5.832

5.821

5.811

5.803

5

4.704

4.678

4.655

4.636

4.619

4.604

4.590

4.579

4.568

4.558

6

4.027

4.000

3.976

3.956

3.938

3.922

3.908

3.896

3.884

3.874

7

3.603

3.575

3.550

3.529

3.511

3.494

3.480

3.467

3.455

3.445

8

3.313

3.284

3.259

3.237

3.218

3.202

3.187

3.173

3.161

3.150

9

3.102

3.073

3.048

3.025

3.006

2.989

2.974

2.960

2.948

2.936

10

2.943

2.913

2.887

2.865

2.845

2.828

2.812

2.798

2.785

2.774

11

2.818

2.788

2.761

2.739

2.719

2.701

2.685

2.671

2.658

2.646

12

2.717

2.687

2.660

2.637

2.617

2.599

2.583

2.568

2.555

2.544

13

2.635

2.604

2.577

2.554

2.533

2.515

2.499

2.484

2.471

2.459

14

2.565

2.534

2.507

2.484

2.463

2.445

2.428

2.413

2.400

2.388

15

2.507

2.475

2.448

2.424

2.403

2.385

2.368

2.353

2.340

2.328

16

2.456

2.425

2.397

2.373

2.352

2.333

2.317

2.302

2.288

2.276

17

2.413

2.381

2.353

2.329

2.308

2.289

2.272

2.257

2.243

2.230

18

2.374

2.342

2.314

2.290

2.269

2.250

2.233

2.217

2.203

2.191

19

2.340

2.308

2.280

2.256

2.234

2.215

2.198

2.182

2.168

2.155

20

2.310

2.278

2.250

2.225

2.203

2.184

2.167

2.151

2.137

2.124

21

2.283

2.250

2.222

2.197

2.176

2.156

2.139

2.123

2.109

2.096

22

2.259

2.226

2.198

2.173

2.151

2.131

2.114

2.098

2.084

2.071

23

2.236

2.204

2.175

2.150

2.128

2.109

2.091

2.075

2.061

2.048

24

2.216

2.183

2.155

2.130

2.108

2.088

2.070

2.054

2.040

2.027

25

2.198

2.165

2.136

2.111

2.089

2.069

2.051

2.035

2.021

2.007

26

2.181

2.148

2.119

2.094

2.072

2.052

2.034

2.018

2.003

1.990

27

2.166

2.132

2.103

2.078

2.056

2.036

2.018

2.002

1.987

1.974

28

2.151

2.118

2.089

2.064

2.041

2.021

2.003

1.987

1.972

1.959

29