Statistical Tables

Table of Contents

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THE t DISTRIBUTION

 

PROPORTION IN ONE TAIL
 

0.25

0.10

0.05

0.025

0.01

0.005
 

PROPORTION IN TWO TAILS

df

0.50

0.20

0.10

0.05

0.02

0.01

1

1.000

3.078

6.314

12.706

31.821

63.657

2

0.816

1.886

2.920

4.303

6.965

9.925

3

0.765

1.638

2.353

3.182

4.541

5.841

4

0.741

1.533

2.132

2.776

3.747

4.604

5

0.727

1.476

2.015

2.571

3.365

4.032

6

0.718

1.440

1.943

2.447

3.143

3.707

7

0.711

1.415

1.895

2.365

2.998

3.499

8

0.706

1.397

1.860

2.306

2.896

3.355

9

0.703

1.383

1.833

2.262

2.821

3.250

10

0.700

1.372

1.812

2.228

2.764

3.169

11

0.697

1.363

1.796

2.201

2.718

3.106

12

0.695

1.356

1.782

2.179

2.681

3.055

13

0.694

1.350

1.771

2.160

2.650

3.012

14

0.692

1.345

1.761

2.145

2.624

2.977

15

0.691

1.341

1.753

2.131

2.602

2.947

16

0.690

1.337

1.746

2.120

2.583

2.921

17

0.689

1.333

1.740

2.110

2.567

2.898

18

0.688

1.330

1.734

2.101

2.552

2.878

19

0.688

1.328

1.729

2.093

2.539

2.861

20

0.687

1.325

1.725

2.086

2.528

2.845

21

0.686

1.323

1.721

2.080

2.518

2.831

22

0.686

1.321

1.717

2.074

2.508

2.819

23

0.685

1.319

1.714

2.069

2.500

2.807

24

0.685

1.318

1.711

2.064

2.492

2.797

25

0.684

1.316

1.708

2.060

2.485

2.787

26

0.684

1.315

1.706

2.056

2.479

2.779

27

0.684

1.314

1.703

2.052

2.473

2.771

28

0.683

1.313

1.701

2.048

2.467

2.763

29

0.683

1.311

1.699

2.045

2.462

2.756

30

0.683

1.310

1.697

2.042

2.457

2.750

40

0.681

1.303

1.684

2.021

2.423

2.704

60

0.679

1.296

1.671

2.000

2.390

2.660

120

0.677

1.289

1.658

1.980

2.358

2.617

°

0.674

1.282

1.645

1.960

2.326

2.576

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The Unit Normal table

 

Second decimal place of z
z

.00

.01

.02

.03

.04

.05

.06

.07

.08

.09

0.0

.5000

.4960

.4920

.4880

.4840

.4801

.4761

.4721

.4681

.4641

0.1

.4602

.4562

.4522

.4483

.4443

.4404

.4364

.4325

.4286

.4247

0.2

.4207

.4168

.4129

.4090

.4052

.4013

.3974

.3936

.3897

.3859

0.3

.3821

.3783

.3745

.3707

.3669

.3632

.3594

.3557

.3520

.3483

0.4

.3446

.3409

.3372

.3336

.3300

.3264

.3228

.3192

.3156

.3121

0.5

.3085

.3050

.3015

.2981

.2946

.2912

.2877

.2843

.2810

.2776

0.6

.2743

.2709

.2676

.2643

.2611

.2578

.2546

.2514

.2483

.2451

0.7

.2420

.2389

.2358

.2327

.2297

.2266

.2236

.2206

.2177

.2148

0.8

.2119

.2090

.2061

.2033

.2005

.1977

.1949

.1922

.1894

.1867

0.9

.1841

.1814

.1788

.1762

.1736

.1711

.1685

.1660

.1635

.1611

1.0

.1587

.1562

.1539

.1515

.1492

.1469

.1446

.1423

.1401

.1379

1.1

.1357

.1335

.1314

.1292

.1271

.1251

.1230

.1210

.1190

.1170

1.2

.1151

.1131

.1112

.1093

.1075

.1056

.1038

.1020

.1003

.0985

1.3

.0968

.0951

.0934

.0918

.0901

.0885

.0869

.0853

.0838

.0823

1.4

.0808

.0793

.0778

.0764

.0749

.0735

.0721

.0708

.0694

.0681

1.5

.0668

.0655

.0643

.0630

.0618

.0606

.0594

.0582

.0571

.0559

1.6

.0548

.0537

.0526

.0516

.0505

.0495

.0485

.0475

.0465

.0455

1.7

.0446

.0436

.0427

.0418

.0409

.0401

.0392

.0384

.0375

.0367

1.8

.0359

.0351

.0344

.0336

.0329

.0322

.0314

.0307

.0301

.0294

1.9

.0287

.0281

.0274

.0268

.0262

.0256

.0250

.0244

.0239

.0233

2.0

.0228

.0222

.0217

.0212

.0207

.0202

.0197

.0192

.0188

.0183

2.1

.0179

.0174

.0170

.0166

.0162

.0158

.0154

.0150

.0146

.0143

2.2

.0139

.0136

.0132

.0129

.0125

.0122

.0119

.0116

.0113

.0110

2.3

.0107

.0104

.0102

.0099

.0096

.0094

.0091

.0089

.0087

.0084

2.4

.0082

.0080

.0078

.0075

.0073

.0071

.0069

.0068

.0066

.0064

2.5

.0062

.0060

.0059

.0057

.0055

.0054

.0052

.0051

.0049

.0048

2.6

.0047

.0045

.0044

.0043

.0041

.0040

.0039

.0038

.0037

.0036

2.7

.0035

.0034

.0033

.0032

.0031

.0030

.0029

.0028

.0027

.0026

2.8

.0026

.0025

.0024

.0023

.0023

.0022

.0021

.0021

.0020

.0019

2.9

.0019

.0018

.0018

.0017

.0016

.0016

.0015

.0015

.0014

.0014

3.0

0013

.0013

.0013

.0012

.0012

.0011

.0011

.0011

.0010

.0010

 

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The F-distributions

p = 0.05 values

Degrees of freedom for denominator

v2

Degrees of freedom for the numerator, v1

1

2

3

4

5

6

7

8

9

10

12

15

20

30

40

60

120

inf

1

161.4

199.5

215.7

224.6

230.2

234.0

236.8

238.9

240.5

241.9

243.9

245.9

248.0

250.1

251.1

252.2

253.3

254.3

2

18.51

19.00

19.16

9.25

9.30

9.33

9.35

9.37

9.38

9.40

9.41

9.43

9.45

9.46

9.47

19.48

19.49

19.50

3

10.3

9.55

9.28

912

9.01

8.94

8.89

8.85

8.81

8.79

8.74

8.70

8.66

8.62

8.59

8.57

8.55

8.53

4

7.71

6.94

6.59

6.39

6.26

6.16

6.09

6.04

6.00

5.96

5.91

5.86

5.80

5.75

5.72

5.69

5.66

5.63

5

6.61

5.79

5.41

5.19

5.05

4.95

4.88

4.82

4.77

4.74

4.68

4.62

4.56

4.50

4.46

4.43

4.40

4.36

6

5.99

5.14

4.76

4.53

4.39

4.28

4.21

4.15

4.10

4.06

4.00

3.94

3.87

3.81

3.77

3.72

370

3.67

7

5.59

4.74

4.35

4.12

3.97

3.87

3.79

3.73

3.68

3.64

3.57

3.5

3.44

3.38

3.34

3.30

3.27

3.23

8

5.32

4.46

4.07

3.84

3.69

3.58

3.50

3.44

3.39

3.35

3.28

3.22

3.15

3.08

3.04

3.01

2.97

2.93

9

5.12

4.26

3.86

3.63

3.48

3.37

3.29

3.23

3.18

3.14

3.07

3.01

2.94

2.86

2.83

2.79

2.75

2.71

10

4.96

4.10

3.71

3.48

3.33

3.22

3.14

3.07

3.02

2.98

2.91

2.85

2.77

2.70

2.66

2.62

2.58

2.54

11

4.84

3.98

3.59

3.36

3.20

3.09

3.01

2.95

2.90

2.85

2.79

2.72

2.65

2.57

2.53

2.49

2.45

2.40

12

4.75

3.89

3.49

3.26

3.11

3.00

2.91

2.85

2.80

2.75

2.69

2.62

2.54

2.47

243

2.38

2.34

2.30

13

4.67

3.81

3.41

3.18

3.03

2.92

2.83

2.77

2.71

2.67

2.60

2.53

2.46

2.38

2.34

2.30

2.25

2.21

14

4.60

3.74

3.34

3.11

29.6

2.85

2.76

2.70

2.65

2.80

2.53

24.6

2.39

2.31

2.27

2.22

2.18

2.13

15

4.54

3.68

3.29

3.06

2.90

2.79

2.71

2.64

2.59

2.54

2.48

2.40

2.33

2.25

2.20

2.16

2.11

2.07

16

4.49

3.63

3.24

3.01

2.85

2.74

2.66

2.59

2.54

2.49

2.42

2.35

2.28

2.19

2.15

2.11

2.06

2.01

17

4.45

3.59

3.20

2.96

2.81

2.70

2.61

2.55

2.49

2.45

2.38

2.31

2.23

2.15

2.10

2.06

2.01

1.96

18

4.41

3.55

3.16

2.93

2.77

2.66

2.58

2.51

2.46

2.41

2.34

2.27

2.19

2.11

2.06

2.02

1.97

1.92

19

4.38

3.52

3.13

2.90

2.74

2.63

2.54

2.48

2.42

2.38

2.31

2.23

2.16

2.07

2.03

1.98

1.93

1.88

20

4.35

3.49

3.10

2.87

2.71

2.60

2.51

2.45

2.39

2.35

2.28

2.20

2.12

2.04

1.99

1.95

1.90

1.84

21

4.32

3.47

3.07

2.84

2.68

2.57

2.49

2.42

237

2.32

2.25

2.18

2.10

2.01

1.96

1.92

1.87

1.81

22

4.30

3.44

3.0S

2.82

2.66

2.55

2.46

2.40

2.34

2.30

2.23

2.15

2.07

1.98

1.92

1.89

1.84

1.78

23

4.28

3.42

3.03

2.80

2.64

2.53

2.44

2.37

.232

2.27

2.20

2.3

2.05

1.96

1.91

1.86

1.81

1.76

24

4.26

3.40

3.01

2.78

2.62

2.51

2.42

2.36

2.30

2.25

2.18

2.11

2.03

1.94

1.89

1.84

1.79

1.73

30

4.17

3.32

2.92

2.69

2.53

2.42

2.33

2.27

2.21

2.16

2.09

2.10

1.93

1.84

1.79

1.74

1.68

1.62

40

4.08

3.23

2.84

2.61

2.45

2.34

2.25

2.18

2.12

2.08

2.00

1.92

1.84

1.74

1.69

1.64

1.58

1.51

60

4.00

3.15

2.76

2.53

2.37

2.25

2.17

2.10

2.04

1.99

1.92

1.84

1.75

1.65

1.59

1.53

1.47

1.39

120

3.92

3.07

2.68

2.45

2.29

2.7

2.09

2.02

1.96

1.91

1.83

1.75

1.66

1.55

S0

1.43

1.35

1.25

inf

3.84

3.00

2.60

2.37

2.21

2.0

2.10

1.94

1.88

1.83

1.75

1.67

1.57

1.46

1.39

1.32

1.22

1.00

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p = 0.01 values

Not yet available.

Critical Values of the Chi Square Distribution

 

 

Level of Significance

df

.05

.025

.01

1

3.84

5.02

6.64

2

5.99

7.38

9.21

3

7.81

9.35

11.34

4

9.49

11.14

13.28

5

11.07

12.83

15.09

6

12.59

14.45

16.81

7

14.07

16.01

18.48

8

15.51

17.53

20.09

9

16.92

19.02

21.67

10

18.31

20.48

23.21

11

19.68

21.92

24.72

12

21.03

23.34

26.22

13

22.36

24.74

27.69

14

23.68

26.11

29.14

15

25.00

27.49

30.58

16

26.30

28.85

32.00

17

27.59

30.19

33.41

18

28.87

31.53

34.80

19

30.14

32.85

36.19

20

31.41

34.17

37.57

21

32.67

35.48

38.93

22

33.92

36.78

40.29

23

35.17

38.08

41.64

24

36.42

39.36

42.98