t分布及t分布表

t分布及t分布表

http://baike.baidu.com/view/1419652.htm

下表列出了自由度为1-30以及80、100、120等t-分布的单侧和双侧区间值。例如,当样本数量n=5时,则自由度v=4,我们就可以查找表中以4开头的行。该行第5列值为2.132,对应的单侧值为95%(双侧值为90%)。这也就是说,T小于2.132的概率为95%(即单侧),记为Pr(−∞ < T < 2.132) = 0.95;同时,T值介于-2.132和2.132之间的概率为90%(即双侧),记为Pr(−2.132 < T < 2.132) = 0.9。

这是根据分布的对称性计算得到的,

Pr(T < −2.132) = 1 − Pr(T > −2.132) = 1 − 0.95 = 0.05,

因此,

Pr(−2.132 < T < 2.132) = 1 − 2(0.05) = 0.9.

注意 关于表格的最后一行的值:自由度为无限大(n=120)的t-分布和正态分布等价。

单侧

75%

80%

85%

90%

95%

97.5%

99%

99.5%

99.75%

99.9%

99.95%

双侧

50%

60%

70%

80%

90%

95%

98%

99%

99.5%

99.8%

99.9%

1

1.000

1.376

1.963

3.078

6.314

12.71

31.82

63.66

127.3

318.3

636.6

2

0.816

1.061

1.386

1.886

2.920

4.303

6.965

9.925

14.09

22.33

31.60

3

0.765

0.978

1.250

1.638

2.353

3.182

4.541

5.841

7.453

10.21

12.92

4

0.741

0.941

1.190

1.533

2.132

2.776

3.747

4.604

5.598

7.173

8.610

5

0.727

0.920

1.156

1.476

2.015

2.571

3.365

4.032

4.773

5.893

6.869

6

0.718

0.906

1.134

1.440

1.943

2.447

3.143

3.707

4.317

5.208

5.959

7

0.711

0.896

1.119

1.415

1.895

2.365

2.998

3.499

4.029

4.785

5.408

8

0.706

0.889

1.108

1.397

1.860

2.306

2.896

3.355

3.833

4.501

5.041

9

0.703

0.883

1.100

1.383

1.833

2.262

2.821

3.250

3.690

4.297

4.781

10

0.700

0.879

1.093

1.372

1.812

2.228

2.764

3.169

3.581

4.144

4.587

11

0.697

0.876

1.088

1.363

1.796

2.201

2.718

3.106

3.497

4.025

4.437

12

0.695

0.873

1.083

1.356

1.782

2.179

2.681

3.055

3.428

3.930

4.318

13

0.694

0.870

1.079

1.350

1.771

2.160

2.650

3.012

3.372

3.852

4.221

14

0.692

0.868

1.076

1.345

1.761

2.145

2.624

2.977

3.326

3.787

4.140

15

0.691

0.866

1.074

1.341

1.753

2.131

2.602

2.947

3.286

3.733

4.073

16

0.690

0.865

1.071

1.337

1.746

2.120

2.583

2.921

3.252

3.686

4.015

17

0.689

0.863

1.069

1.333

1.740

2.110

2.567

2.898

3.222

3.646

3.965

18

0.688

0.862

1.067

1.330

1.734

2.101

2.552

2.878

3.197

3.610

3.922

19

0.688

0.861

1.066

1.328

1.729

2.093

2.539

2.861

3.174

3.579

3.883

20

0.687

0.860

1.064

1.325

1.725

2.086

2.528

2.845

3.153

3.552

3.850

21

0.686

0.859

1.063

1.323

1.721

2.080

2.518

2.831

3.135

3.527

3.819

22

0.686

0.858

1.061

1.321

1.717

2.074

2.508

2.819

3.119

3.505

3.792

23

0.685

0.858

1.060

1.319

1.714

2.069

2.500

2.807

3.104

3.485

3.767

24

0.685

0.857

1.059

1.318

1.711

2.064

2.492

2.797

3.091

3.467

3.745

25

0.684

0.856

1.058

1.316

1.708

2.060

2.485

2.787

3.078

3.450

3.725

26

0.684

0.856

1.058

1.315

1.706

2.056

2.479

2.779

3.067

3.435

3.707

27

0.684

0.855

1.057

1.314

1.703

2.052

2.473

2.771

3.057

3.421

3.690

28

0.683

0.855

1.056

1.313

1.701

2.048

2.467

2.763

3.047

3.408

3.674

29

0.683

0.854

1.055

1.311

1.699

2.045

2.462

2.756

3.038

3.396

3.659

30

0.683

0.854

1.055

1.310

1.697

2.042

2.457

2.750

3.030

3.385

3.646

40

0.681

0.851

1.050

1.303

1.684

2.021

2.423

2.704

2.971

3.307

3.551

50

0.679

0.849

1.047

1.299

1.676

2.009

2.403

2.678

2.937

3.261

3.496

60

0.679

0.848

1.045

1.296

1.671

2.000

2.390

2.660

2.915

3.232

3.460

80

0.678

0.846

1.043

1.292

1.664

1.990

2.374

2.639

2.887

3.195

3.416

100

0.677

0.845

1.042

1.290

1.660

1.984

2.364

2.626

2.871

3.174

3.390

120

0.677

0.845

1.041

1.289

1.658

1.980

2.358

2.617

2.860

3.160

3.373

0.674

0.842

1.036

1.282

1.645

1.960

2.326

2.576

2.807

3.090

3.291

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