GB 4086.3-1983 统计分布数值表 t分布

中华人民共和国国家标准

UDC311.13(083.5)

统计分布数值表

t分布

Tablesforstatisticaldistributions

t-distribution

GB4086.3一83

本标准包括统计学中常用的t分布的两种数值表，它们的名称、表距和精度如下:

t分布函数表v二1(1)20(2)30(5)50,606位小数

t二0(0.1)4(0.2)5(0.5)7

t分布分位数表p=0.5(0.05)0.95,0.975,0.98,0.99,0.995,5位小数

0.9975,0_998,0.999,0.9995,0.9998,0.9999

v=1(1)30(2)40(5)70(10)120,150,180,240,+

表中的分位数对应于下侧概率。

虽然表I扫给出5-6位小数，但是在使用中需要取几位，要由实{如门题决定。

在应用中不能满足要求时，可参考附录的处理方法。

国家标准局1983一12一21发布

1984一10--01实施

GB4086.3一83

1t分布函数表

尸(‘;?，=丁

tZ训一仁”+1’

B(1/2,v/2)

(it

0.500000

0.531726

0.562833

0.592774

0.621119

0.500000

0.536674

0.572865

0.608118

0.642032

0.500000

0.537422

0.574381

0.610439

0.645201

0.500000

0.537885

0.575320

0.611875

0.647163

0.500000

0.538199

0.575957

0.612850

0.648496

0.500000

0.538426

0.576417

0.613555

0.649459

0.500000

0.538598

0.576765

0.614088

0.650188

0.500000

0.5弓8732

0.577037

0.614505

0.650758

0.500000﹃05700140605757﹃

M01喊侧州

0.647584

0.672021

0.694400

0.714777

0.733262

0.666667

0.695283

0.721803

0.746183

0.768447

0.674276

0.704599

0.732837

0.758901

0.782774

0.678335

0.709579

0.738750

0.765736

0.790497

0.680851

0.712670

0.742426

0.769993

0.795314

0.682560

0.714772

0.744928

0.772895

0.798602

0.683796

0.716293

0.746741

0.774999

0.800988

0.684732

0.717445

0.748114

0.7了乙595

0.802798

0.5M0.708州

0.750000

0.765146

0.778858

0.791286

0.802568

0.788675

0.806980

0.823498

0.838376

0.851763

0.804499

0.824158

0.841869

0.857766

0.871996

0.813050

0.833458

0.851824

0.868274

0.882950

0.818391

0.839275

0.858054

0.874850

0.889798

0.822041

0.843252

0.862316

0.879347

0.894479

0.826703

0.848336

0.867766

0.885098

0.900460

0.685464

0.718347

0.749190

0.777844

0.804217

0.828282

0.850059

0.869613

0.887047

0.902486

0.812833

0.822192

0.830747

0.838586

0.845786

0.863803

0.874634

0.884383

0.893167

0.901090

0.884708

0.896048

0.906155

0.915160

0.923184

0.896000

0.907575

0.917823

0.926881

0.934881

0.903048

0.914752

0.925062

0.934121

0.942068

0.907860

0.919642

0.929980

0.939024

0.946915

0.824692

0.846142

0865414

0.882616

0.897879

0.911351

0.923184

0.933536

0.942558

0.950397

0.913998

0.925867

0.936224

0.945223

0.953016

0.916075

0.9279f1

0.93832乙

0.947305

0.955056

0.852416

0.858537

0.864200

0.869452

0.874334

0.908248

0.914725

0.920596

0.925926

0.930775

0.930337

0.936717

0.942414

0.947506

0.952063

0.949030

0.955123

0.960453

0.965114

0.969190

0.953787

0.959761

0.964949

0.969450

0.973353

0.957190

0.963064

0.968134

0.972504

0.976267

0.959742

0.965531

0.970503

0.974765

0.978412

0.961724

0.967有41

0.972330

0.976500

0.980051

0.68乙053

0.719072

0.750056

0.778850

0.805360

0.82S55乙

0.851447

0.8711CZ

0.-名吕617

0.>Oa117

0.-1'746

0.659

0.v.

0.94897'

0.956689

0.965三0

0.968961

0.973779

0.977873

0.98134:

2.0川胡劫州

0.878881

0.88引25

0.887094

0.890812

0.894302

0.935194

0.939229

0.942921

0.946304

0.949410

0.956147

0.959812

0.96引07

0.966074

0.968749

0.941942

0.948173

0.953674

0.958530

0.962822

0.966617

0.969976

0.972953

0.975594

0.977941

0.972755

0.975875

0.978608

0.981003

0.983105

0.976736

0.979669

0.982212

0.984418

0.986333

0.979504

0.982287

0.984680

0.986738

0.988507

0.990029

0.991339

0.992467

0.993440

0.994279

0.981529

0.984191

0.986463

0.988401

0.990054

0.983069

0.985631

0.987803

0宁吕9644

0.991707

0.984277

0.986754

0.988843

0.990603

0.997083

2.52.62.72.82.9

0.897584

0.900674

0.903589

0.906342

0.908947

0.971166

0.973352

0.975334

0.977133

0.978769

0.980029

0.981889

0.983550

0.985033

0.986361

0.984950

0.986573

0.988002

0.989262

0.990374

0.987996

0.989442

0.990700

0.991796

0.992752

0.991464

0.992667

0.993694

0.994571

0.995320

0.992522

0.9宁363宁

0.994584

0.995385

0.996063

0.993328

0.994375

0.995254

0.995993

0.996(114

到3.1狱粥州

0.911414

0.913755

0.915978

0.918091

0.920103

0.922021

0.925597

0.928865

0.931862

0.934621

0.937167

0.942751

0.947432

0.951410

0.954833

0.963586

0.965379

0.967047

0.968600

0.970050

0.980259

0.981619

0.982861

0.983998

0.985040

0.987552

0.988621

0.989582

0.990448

0.991229

0.991358

0.992228

0.993000

0.993686

0.994295

0.995003

0.995630

0.996173

0.996643

0.997051

0.995960

0.996509

0.996979

0.997382

0.997728

0.996638

0.997126

0.997540

0.997891

0.998190

0.997137

0.997576

0.991946

0.998257

0.998519

M刘扮3.8挤

0.971405

0.973858

0.976017

0.977924

0.979616

0.985996

0.987684

0.989118

0.990344

0.991396

991935

.993.994152154

.994985

.995676

0.994838

0.995755

0.996489

0.997080

0.997558

0.998025

0.998502

0.998857

0.999122

0.999322

0.998445

0.998847

0.999140

0.999355

0.999513

0.?98741

0.999086

0.999332

0.999510

0.999638

钊们州4.64.8

0.981125

0.984248

0.986664

0.988570

0.990098

0.992304

0.994085

0.995364

0.996303

0.997007

0.996255

0.997336

0.998059

0.998555

0.998904

0.997948

0.998642

0.999077

0.999357

0.999542

0.993587

0.994引7

0.994956

0.995516

0.996008

0.996441

0.997157

0.997716

0.998154

0.998500

0.998774

0.999243

0.999518

0.999684

0.999788

0.999217

0.999547

0.999729

0.999833

0.999894

0.999474

0.999713

0.999838

0，，9906

0勺999今夺

0.宁Q，6引

0，9?甲810

0.9宁9899

0.9?99乌今

0.999968

0.宁99了引

0.，甲宁869

0.宁qQg弓石

0.9，，966

0‘99?981

5.0幼划幼翻

本表对{一自山度，和t给出1分布函数尸‘1;们的数值

任1}:又寸十、二8和t=3.9，P{t;飞，)一0.997728

GB4086.3一83

It分布函数表

尸夭‘;，，，=J

(1+t2v)

币厂B(12,万而丁dt

﹃︸价介﹃

oc氏几民

0.500000

0.538928

0.5了7435

勺.615115

0.651593

0.500000

0.539002

0.577585

06飞5345

0.651907

0.500000

0.539065

0.577712

0.615540

0.652174

0.500000

0.539119

0.5778)2

0.615707

0.652403

洲湘书刃81

0.686537

0.719668

0.750768

0.779677

0.806300

0.686941

0.720167

0.751363

0.780369

0.807087

0.687284

0.720590

0.751868

0.780957

0.807755

0.500000

0.539166

0.577917

0.615853

0.652603

0.687835

0.7'1269

0.752679

0.781901

0.808829

0.500000

0.539243

0.578073

0.616093

0.652931

0.;曰C门0门

0多二9;三0

0.5了3于三，)

Ot6{乙石乙5

C.亡匕三三C尸

M州叼叼0.4

0.688257

0.721790

0.753302

0.78'626

0.809654

0.1-

0.马50之了.〕

0.5了8三。

0.616193

0.653068

0.乙88434

0.了2200了

0.753562

0.了82929

0.809998

0.85乙了}已

0.85了082

0.87715)

0.吕9,"9夕

0.910711

只只试

扰〕:一:

一{〔

吕飞，拜〔

0凡07已_升}二权脚

肠喊0.7M0.9

0.8306000.8引4750.8322190.8328590.83弘150.8339030.834334

0.8525890.8535450.8543580.8550560.8556640.8561960.856667

0.8723270.8733530..8742240.8749740.8756250.8761970.876702

0.8899090.8909910.8919110.8927010.8933880.8939910.894524

0.9054600.9065830.9075380.90833590.9090720.9096980.910251

{{)

矛，ZG

狱)任

们洲怕撇

{今一一;{;

伙氏认叭认

0.919121

0.9引048

0.941402

0.950342

0.958025

0.920271

0.932210

0.942560

0.951484

0.959138

0.9'1248

0.93引95

0.943542

0.952451

0.960079

0.922087

0.934042

0.944385

0.953280

0.960886

0.，2402}

0.935992

0946324

0.955184

0.962734

0.9<425

0.93E-98

0.9460之7

0.955679

0.963713

口.。乙几子只三

0，了2三之飞

必.甘舀万〔苏介

臼Q弓奋少1抢

0.。，曰1产

翻4777训洲阴

0.92瀚协姗096

曰1.1叹1.3以防曰曰18川

0.964598

0.970200

0.974957

0.978984

0.982384

0.965672

0.971228

0.975932

0.979901

0.983241

0.966580

0.9'2094

0.976751

0.980671

0.983957

967356

0.968027

0.973472

0.978052

0.981888

0.985088

0.96宁131

0.974520

0.979038

0.982806

0.9859.37

0.969`;吕。

0.974955

0.979八46

0.983186

0.987,287

勿沂几下门

0刃几全宇

0.。热0’之厂

0.)众三巧乙之

0.，阶仍下、

一口︸﹄

0.985247

0.987653

0.989672

0.991363

0.992777

0.986042

0.988387

0.990345

0.991978

0.993337

0.986706

0.988997

0.990903

0.992485

0.993796

0.987747

0.989950

0.991771

0.993270

0.994503

0.988163

0.990330

0.992丁{4

0.993579

0.994779

0.988526

0.990660

0.992412

0.993847

0.995019

葱获爸

;{脚1

协仲﹄介﹄

已以已C氏

份0989511价~0994179

劫机洲拙翻

0.993960

0.994948

0.995773

0.996461

0.997035

0.994881

0.995777

0.996516

0.997126

0.997629

0.995224

0.99608'4

0.996790

0.997369

0.997844

0.995514

0996341

0.997018

0.997571

0.998021

0.995760

0，9965乙0

0.997211

0.997740

0.998170

摘洲邵洲协

娜娜娜洲洲

0.995975﹃﹃介0.998296

呵协996184996830997365

氏0.已C以

0.997515

0.997915

0.998249

0.998528

0.998762

0.997809

0.998177

0.998482

0.998735

0.998945

0.998232

0.998551

0.998811

0.999025

0.999199

0.998518

0.998800

0.999029

0.999214

0.999363

0.998628

0.998896

0.999111

0.999285

0.999424

0.998722

0.998976

0.999181

0.999344

0.999475

998388998687998930吟999289

氏0.0.氏氏

99804399858499866599889e999087

0.0，0.认0.

幼漏封M3.9

淡姗洲洲哪

碎0990.99哪娜

0.998957

0.999257

0.999468

0.999618

0.999723

0.999119

0.999384

0.999567

0.999695

0.999783

0.999244

0.999480

0.999641

0.999751

0.999827

0.999420

0.999614

0.999742

0.999827

0.999883

0.999484

0.999661

0.999776

0.999852

0.99?902

0.999536

0.999699

0.999804

0.999872

0.999917

0.999580

0.999731

0.999827

0.999889

0.999928

钊州俐4.6棍

0NM99994500.9999760.9999800一一

0.999845

0.999932

0.999969

0.999985

0.999993

0.999879

0.999949

0.999978

0.999990

0.999995

0.999903

0.999961

0.999984

0.999993

0.999997

0.999921

0.999969

0.999988

0.999995

0.999998

.999954

.999984

9，9994

999998

.999999

0。尹八0了6

0.宁多乙?;己

0.。吞7户下3

0.1之0

0.46}:,

0.。乙日日印宁

MIS'

0.91

0.985'...

0.986'

0.989'.

0.宁。120了

0."v口写

0，宁‘户自己吕8

O.v9S}',I

0.，0;引。

0.

0.6a

0.1。吕'17

0，宁8X98

0.9988C-

0.999046

0..`.,iC

0.9甲9595

0.999519

0?99乙{了

0.999了，了

0.9996

0.99990

0.499938

0.9999乙0

0.999987

0.999996

0.999998

0.99今，，9

0.,-

0.',qI

L宁，Q万宁1

几广，今9场介弓公

0，甲号甲三5全

0.9甲9乙4Z

0.宁甲。7已口

0.甲。03毛亡

0.9。?9苏

0.999口今5

0.9999-.

0ono-,8宁

0.9?',,..

0.9991

{OOOC..

肖︺尸﹃护‘CJL盆划户叼

八自﹄仁少了八匕

，.OQ.﹃丫Q

Q了OJQJ八丫八，

0月n丫n丫门了门丫

自丫OJn丫0.OJ

0.氏已氏乐

知幼曰幼7.0

乍表对)一[l山度t，和l给出t分布函数F'(t:v)的数4`{

冈:对厂】，一l4和1二。.7,尸(t;v)。752302

GB4086.3一83

1t分布函数表

““;v，一工

(1+t2%v)

抓vB(1/2,v/2)

dt

v!2224262830354045

506O

0.500000

0.539543

0.578681

0.617024

0.654206

0.500000

0.539578

0.578753

0.611135

0.654358

0.689509

0.723334

0.755149

0.784777

0.812102

0.689638

0.723494

0.755340

0.785000

0.812356

0.689898

0.723814

0.755723

0.785446

0.812864

0.690093

0.724055

0.756011

0.785782

0.813247

0.500000

0.539606

0.578809

0.617221

0.654475

0.690244

0.724242

0.756235

0.786043

0.813544

0.500000

0.539628

M7885478854

0.617290

0.654570

Moo000

053561

0.57'"..'

M1,弓.3

0.6547i1

0.00.10.20.3州

0.6yv548

0.724617

0.了56684

0.786567

0.814141

0.50.60.70.80，9

n冲凸州nC曰n叼

0.837346

0.859960

0.880235

0.898250

0.914115

0.837913

0.860580

0.880900

0.898951

0.914842

0.838339

0.861046

0.881401

0.899479

0.915389

.838671

.861409

.881790

.899890

.915815

0.926085

0.938069

0.948386

0.957205

0.964690

0.927170

06939159

0.949467

0.958262

0.965711

0.971976

0.977209

0.981553

0.985136

0.988075

0.9292670.929701

0.94126600941702

0.9515520.951963

0.9602970.960717

0.9676710.968074

0.690366

0.724392

0.756414

0.786252

0.813783

0.838937

0.861700

0.882103

0.900219

0.916156

0.930049

0.942050

0.952328

0.961052

0.968396

0.971530

0.976789

0.981162

0.984775

0.987745

0.973346

0.978497

0.982750

0.986236

0.989075

0.973839

0.978959

0.983177

0.986628

0.989430

0.974221

0.979引7

0.983508

0.986930

0.989703

2.02.1次2.32.4

0.989816

0.991827

0.993461

0.994782

0.995847

0.991934

0.993717

0.995132

0.996249

0.997124

0.974526

0.979602

0.983772

0.987170

0.989920

0.992128

0.993888

0.995282

0.996378

0.997234

劫翻2.72.8酬

0.996703

0.997387

0.997934

0.998369

0.998714

0.997057

0.997695

0.998199

0.998596

0.998908

0.997191

0.997810

0.998297

0.998680

0.998979

0.997305

0.997908

0.998381

0.998750

0.999038

0.997685

0.998232

0.998655

0.998981

0.999230

0.997805

0.998333

0.998740

0.999052

0.999289

0.997899

09，841之

0.998806

0.999106

0.999114

3.0州狱扣州

0.998988

0.999204

0.999375

0.999509

0.999615

0.999262

0.999434

0.999568

0.999670

0.999749

0.999356

0.999512

0.999632

0.999723

0.999792

0.999421

0.999566

0.999676

0.999758

0.999821

0.999469

0.999605

0.999708

0.999784

0.999841

0.999506

0.999635

0.999731

0.999803

0.999856

粥刘扮3.83.9

0.999698

0.999815

0.999886

0.999930

0.999957

0.999766

0.999861

0.999918

0.999952

0.999972

0.999790

0.999877

0.999929

0.999959

0.999976

0.999809

0.999890

0.999937

0.999964

0.999980

0.999844

0.999913

0.999952

0.999973

0.999985

0.999883

0999938

0.999967

0.999983

0.999991

0.999895

0.999945

0.9999

0.999985

0.999993

4.04.24.4钊挑

0.999974

0.9宁夕992

0.999998

0.999999

1.000000

0.996897

0.997556

0.998080

0.998494

0.998821

0.999079

0.999281

0.999440

0.999564

0.999661

0.999737

0.999841

0.999904

0.999943

0.999965

0.999979

0.999994

0.999998

0.999999

1.000000

0.999983

0.999995

0.999999

1.000000

1.000000

0.999986

0.999996

0.999999

1.000000

1.000000

0.999988

0.999997

0.999999

1.000000

1.000000

0.999，92

0.999998

1.000000

1.000000

1.000000

0.999867

0.999928

0.999961

0.999979

0.999989

0.999994

0.999999

1.000000

1.000000

1.000000

0.999995

0.999999

1.000000

1.000000

、000000

0.999996

0.999999

1.000000

1.000000

1.000000

0.839337

0.862137

0.882572

0.900713

09飞乙6乙8

0.930，了)

0.942574

0.952845

C.961556

0.968879

0.974983

0.980029

0.984165

0.98了529

0.990242

0.992415

0.994140

0.99550乙

0.996507

0.997396

0.998036

0.998527

0.998901

0.999185

0.999398

0.999559

0.999677

0.999了65

0.999830

0.999877

0.999912

0.>

0.宁9OQ了了

0..,..8a

0.9，9，95

09OgQ，2

】000eOO

1,

}tO00000

1.已臼0000

刘幼6.06.57.0

ti表对于自由度v和t给出t分布函数尸(t;v)的数值

列对Fv=45和t=3,尸(八训二0.997805

GB4086.3一83

Zt分布分位数表

丁

In,n)

(1十12;们‘”寸

v下刀(土2v2

dt一0

atou}>

50000.55000.60000.65000.7000

0.75000.80000.85000.90000.9500

0.00000

0.00000

0.00000

0.00000

0.00000

0.32492

0.28868

0.27667

0.27072

0.26718

0001

6501

土卜仁卜1.

仲06066978479409691954

氏0.氏

489070

1.96261

1.38621

1.24978

1.18957

1.15577

6.引i75

2.91999

2.3:336

2.13185

2.01505

洲洲姗姗训

134

.119

.108

朋.09

53

72669

71756

.71114

.70639

.70272

.69981

69745

。69548

.69383

.69242

.69120

.69013

68920

.68836

.68762

.乙a乙95

0.90570

0.89603

0.88889

0.88340

0.87906306

1.43976

1.41492

1.39682

1.38303

1.37218

飞.94318

1.89458

1.85955

1.83引1

1.81246

暇洲脚054洲

0.26483

0.26引7

0.26192

0.26096

0.26018

0.25956

0.25903

0.25859

0.25821

0.25789

0.50953

0.444了5

0.42420

0.41416

0.40823

0.40431

0.40154

0.39947

0.39787

0.39659

3108泌洲犯2889

0.53994

0.53862

0.53750

05365，

0.53573

0.87553

0.87261

0.87015

0.86805

0.86624

1.08767

1.08321

1.07947

1.07628

1.07353

1.79588

1.78229

1.77093

1.761引

1.75305

姗瑕洲27962781

何0.000000.00000呵0.00000﹃0.000000.00000呵呵

0.00000

0.00000

0.00000

0.00000

0.00000

2767

2755

乙745

2735

2727

0.25760

0.25735

0.25712

0.25692

0.25674

0.53501

0.53438

053382

0.53331

0.53286

1.07114

1.06903

1.06717

7.06551

1.06402

1.36343

1.35622

1.35017

1.34503

1.34061

135676

133338

1.33039

1.32773

1.32534

1.74588

1.73961

1.73406

172913

7_77472

朴和沙和39091

氏氏氏D.氏

.72074

.71714

.71387

71088

70814

了0562

70329

.70113

69913

69726

认以0.认已

565!

564

5631

0.39064

0.39039

0.39017

0.38997

0.38978

0.53246

0.53208

0.53175

0.53144

0.53115

0.86467

0.86328

0.86205

0.86095

0.85996

0.85907

0.85827

0.85753

0.85686

0.85624

1.06267

1.06145

1.060弘

1.05932

1.05838

323

:吕55会10二

0.00000

0.00000

0.00000

0.00000

0.00000

删58945如朴38903

0.00000

0.00000

0.00000

0.00000

0.00000

2689

2685

2681

2677

2673

0.25595

0.25586

0.25577

0.25568

0.25561

0.53089

0.53065

0.53042

0.53021

0.53002

0.85567

0.85514

0.85465

0.85419

0.85377

26乙乙

26乙0

265，

2650

2646.25504

0.38880

0.38859

0.38841

0.38825

0.38810

0.52967

0.52935

0.52908

0.52883

0.52861

0.68404

0.68368

0.68335

0.68304

0.68276

0.68223

0.68177

0.68137

0.68100

0.68067

0.85300

0.85232

0.85172

0.85118

0.85070

.05752

05673

05599

.05530

.05466

.05350

05248

.05158

05077

.05005

.04852

.04729

.04630

.0454了

04477

1.308571

1.306951

1.305511.

1.304231.

1.303081.

00000000000000000000

氏0.以仇0.

1.67943

1.6了59了

1.67303

1.67065

1.66864

妙2?871朴沙朴

0.38779

0.38754

0.38734

0.38717

0.38703

0.52814

0.52776

0.52745

0.52720

0.52698

0.67998

0.67943

0.67898

0.67860

0.67828

0.849681

0.848871

0.848211

0.84765，

0.847191

眼峨0.20.20.2

0.00000

0.00000

0.00000

0.00000

0.00000

2637

2630

2624

2619

2615

0.38691

0.38671

0.38655

0.38643

0.3吕633

0。52680

0.52650

0.52626

0.52608

0.52592

0.52580

0.52552

0.52533

0.52510

0.52440

0.67801

0.67757

0.67723

0.67695

0.67673

0.84679

0.84614

0.84563

0.84523

0.84490

干04417

1.0'4320

1.04244

1.04184

1.04134

‘'9376

.292之2

.29103

.29007

.28930

.28865

.28722

.28627

28509

28155

1.66691

166412

1乙乙{9乙

1.66023

1.65882

侧奴0.2眼眼

0.00000

0.00000

0.00000

0.00000

0.00000

枯1718仰加川加舀洲巧况盯邓朋孔驻弘弘邓如朽知巧胡的70别知0010

0.00000

0.00000

0.00000

0.00000

0.00000

2593

2587

2584

2579

256乙

0.25391

0.25380

0.25372

0.25363

0.25335

0.38624

0.38606

0.58594

0.38578

0.38532

0,67654

0.67613

0.67586

0.67551

0.67449

0.844631.040931

0.844021.040031

0.843621.039431

0.84引21.038681

0.841621.036431

1.乙，2t;5

1.65508

I6533乙

1.65123

1.64485

010101州州0.10.1010.10.1州0.10.10.10.1州0.1州0.10101010.1州0.10.10.10.10.10.1010101州0.101010.1州0.101州州州0.10.10.1州0.10.1

120150180川

本表对于自由度v和卜侧概率户给出t分布的分位数了

例:对{一r=100和p一0.90