Transact-SQL Cookbook

   

Appendix A. The T-Distribution Table

The t-distribution is a probability distribution with a symmetrical, bell-shaped curve (similar to the standard normal curve), the shape of which is affected by a parameter known as the "degrees of freedom." We used t-distributions in Chapter 8 of this book to compute confidence intervals. In that usage, the degrees of freedom controlled how far out you had to go (in terms of standard deviations) on the t-distribution curve from the mean to encompass a given percentage of values. The higher the degrees of freedom, the larger the interval on the curve.

Table A-1 gives t-distribution values for various probabilities, with each row representing 1 additional degree of freedom. Those values in the column for 0.05 (95%) were used in Chapter 8.

Table A-1. The t-distribution table referenced in Chapter 8

DF

Probabilities

 

0.2

0.1

0.05

0.02

0.01

0.002

0.001

1

3.078

6.314

12.706

31.82

63.66

318.3

637

2

1.886

2.92

4.303

6.965

9.925

22.33

31.6

3

1.638

2.353

3.182

4.541

5.841

10.21

12.92

4

1.533

2.132

2.776

3.747

4.604

7.173

8.61

5

1.476

2.015

2.571

3.365

4.032

5.893

6.869

6

1.44

1.943

2.447

3.143

3.707

5.208

5.959

7

1.415

1.895

2.365

2.998

3.499

4.785

5.408

8

1.397

1.86

2.306

2.896

3.355

4.501

5.041

9

1.383

1.833

2.262

2.821

3.25

4.297

4.781

10

1.372

1.812

2.228

2.764

3.169

4.144

4.587

11

1.363

1.796

2.201

2.718

3.106

4.025

4.437

12

1.356

1.782

2.179

2.681

3.055

3.93

4.318

13

1.35

1.771

2.16

2.65

3.012

3.852

4.221

14

1.345

1.761

2.145

2.624

2.977

3.787

4.14

15

1.341

1.753

2.131

2.602

2.947

3.733

4.073

16

1.337

1.746

2.12

2.583

2.921

3.686

4.015

17

1.333

1.74

2.11

2.567

2.898

3.646

3.965

18

1.33

1.734

2.101

2.552

2.878

3.61

3.922

19

1.328

1.729

2.093

2.539

2.861

3.579

3.883

20

1.325

1.725

2.086

2.528

2.845

3.552

3.85

21

1.323

1.721

2.08

2.518

2.831

3.527

3.819

22

1.321

1.717

2.074

2.508

2.819

3.505

3.792

23

1.319

1.714

2.069

2.5

2.807

3.485

3.768

24

1.318

1.711

2.064

2.492

2.797

3.467

3.745

25

1.316

1.708

2.06

2.485

2.787

3.45

3.725

26

1.315

1.706

2.056

2.479

2.779

3.435

3.707

27

1.314

1.703

2.052

2.473

2.771

3.421

3.69

28

1.313

1.701

2.048

2.467

2.763

3.408

3.674

29

1.311

1.699

2.045

2.462

2.756

3.396

3.659

30

1.31

1.697

2.042

2.457

2.75

3.385

3.646

32

1.309

1.694

2.037

2.449

2.738

3.365

3.622

34

1.307

1.691

2.032

2.441

2.728

3.348

3.601

36

1.306

1.688

2.028

2.434

2.719

3.333

3.582

38

1.304

1.686

2.024

2.429

2.712

3.319

3.566

40

1.303

1.684

2.021

2.423

2.704

3.307

3.551

42

1.302

1.682

2.018

2.418

2.698

3.296

3.538

44

1.301

1.68

2.015

2.414

2.692

3.286

3.526

46

1.3

1.679

2.013

2.41

2.687

3.277

3.515

48

1.299

1.677

2.011

2.407

2.682

3.269

3.505

50

1.299

1.676

2.009

2.403

2.678

3.261

3.496

55

1.297

1.673

2.004

2.396

2.668

3.245

3.476

60

1.296

1.671

2

2.39

2.66

3.232

3.46

65

1.295

1.669

1.997

2.385

2.654

3.22

3.447

70

1.294

1.667

1.994

2.381

2.648

3.211

3.435

80

1.292

1.664

1.99

2.374

2.639

3.195

3.416

100

1.29

1.66

1.984

2.364

2.626

3.174

3.39

150

1.287

1.655

1.976

2.351

2.609

3.145

3.357

200

1.286

1.653

1.972

2.345

2.601

3.131

3.34

   
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