Планирование эксперимента и математическая обработка данных. Учебное пособие

v2\v1

10

12

15

20

24

30

40

60

120

∞

1

968,63

976,71

984,87

993,10

997,25

1001,4

1005,6

1009,8

1014,0

1018,3

2

39,398

39,415

39,431

39,448

39,456

39,465

39,473

39,481

39,490

39,498

3

14,419

14,337

14,253

14,167

14,124

14,081

14,037

13,992

13,943

13,902

4

8,8439

8,7512

8,6565

8,5599

8,5109

8,4613

8,4111

8,3604

8,3091

8,2573

5

6,6192

6,5246

6,4227

6,3285

6,2780

6,2269

6,1751

6,1225

6,0693

6,0153

6

5,4613

5,3662

5,2687

5,1684

5,1172

5,0652

5,0125

4,9589

4,9045

4,8491

7

4,7611

4,6658

4,5678

4,4667

4,4150

4,3624

4,3089

4,2544

4,1989

4,1423

8

4,2951

4,1997

4,1012

3,9995

3,9472

3,8940

3,8398

3,7844

3,7279

3,6702

9

3,9639

3,8682

3,7694

3,6669

3,6142

3,5604

3,5055

3,4493

3,3918

3,3329

10

3,7168

3,6209

3,5217

3,4186

3,3654

3,3110

3,2554

3,1984

3,1399

3,0798

11

3,5257

3,4296

3,3299

3,2261

3,1725

3,1176

3,0613

3,0035

2,9441

2,8828

12

3,3736

3,2773

3,1772

3,0728

3,0187

2,9633

2,9063

2,8478

2,7874

2,7249

13

3,2497

3,1532

3,0527

2,9477

2,8932

2,8373

2,7797

2,7204

2,6590

2,5955

14

3,1469

3,0501

2,9493

2,8437

2,7888

2,7324

2,6742

2,6142

2,5519

2,4872

15

3,0602

2,9633

2,8621

2,7559

2,7006

2,6437

2,5850

2,5242

2,4611

2,3953

16

2,9862

2,8890

2,7875

2,6808

2,6252

2,5678

2,5085

2,4471

2,3831

2,3163

17

2,9222

2,8249

2,7230

2,6158

2,5598

2,5021

2,4422

2,3801

2,3153

2,2474

18

2,8664

2,7689

2,6667

2,5590

2,5027

2,4445

2,3842

2,3214

2,2558

2,1869

19

2,8173

2,7196

2,6171

2,5089

2,4523

2,3937

2,3329

2,2695

2,2032

2,1333

20

2,7737

2,6758

2,5731

2,4645

2,4076

2,3486

2,2873

2,2234

2,1562

2,0853

21

2,7348

2,6368

2,5338

2,4247

2,3675

2,3082

2,2465

2,1819

2,1141

2,0422

22

2,6998

2,6017

2,4984

2,3890

2,3315

2,2718

2,2097

2,1446

2,0760

2,0032

23

2,6682

2,5699

2,4665

2,3567

2,2989

2,2389

2,1763

2,1107

2,0415

1,9677

24

2,6396

2,5412

2,4374

2,3273

2,2693

2,2090

2,1460

2,0799

2,0099

1,9353

25

2,6135

2,5149

2,4110

2,3005

2,2422

2,1816

2,1183

2,0517

1,9811

1,9055

26

2,5895

2,4909

2,3867

2,2759

2,2174

2,1565

2,0928

2,0257

1,9545

1,8781

27

2,5676

2,4688

2,3644

2,2533

2,1946

2,1334

2,0693

2,0018

1,9299

1,8527

28

2,5473

2,4484

2,3438

2,2324

2,1735

2,1121

2,0477

1,9796

1,9072

1,8291

29

2,5286

2,4295

2,3248

2,2131

2,1540

2,0923

2,0276

1,9591

1,8861

1,8072

30

2,5112

2,4120

2,3072

2,1952

2,1359

2,0739

2,0089

1,9400

1,8664

1,7867

40

2,3882

2,2882

2,1819

2,0677

2,0069

1,9429

1,8752

1,8028

1,7242

1,6371

60

2,2702

2,1692

2,0613

1,9445

1,8817

1,8152

1,7440

1,6668

1,5810

1,4822

120

2,1570

2,0548

1,9450

1,8249

1,7597

1,6899

1,6141

1,5299

1,4327

1,3104

2,0843

1,9447

1,8326

1,7085

1,6402

1,5660

1,4835

1,3883

1,2684

1,0000

v2\v1

1

2

3

4

5

6

7

8

9

1

4052,2

4999,5

5403,3

5624,6

5763,7

5859,0

5928,3

5981,1

6022,5

2

98,503

99,000

99,166

99,249

99,299

99,332

99,356

99,374

99,388

3

34,116

30,817

29,457

28,457

28,237

27,911

27,672

27,489

27,345

4

21,198

18,000

16,694

15,977

15,522

15,207

14,976

14,799

14,659

5

16,258

13,274

12,060

11,392

10,967

10,672

10,456

10,289

10,158

6

13,745

10,925

9,7795

9,1483

8,7459

8,4661

8,2600

8,1016

7,9761

7

12,246

9,5466

8,4513

7,8467

7,4604

7,1914

6,9928

6,8401

6,7188

8

11,259

8,6491

7,5910

7,0060

6,6318

6,3707

6,1776

6,0289

5,9106

9

10,561

8,0215

6,9919

6,4221

6,0569

5,8018

5,6129

5,4671

5,3511

10

10,044

7,5594

6,5523

5,9943

5,6363

5,3858

5,2001

5,0567

4,9424

11

9,6460

7,2057

6,2167

5,6683

5,3160

5,0692

4,8861

4,7445

4,6315

12

9,3302

6,9266

5,9526

5,4119

5,0643

4,8206

4,6395

4,4994

4,3875

13

9,0738

6,7010

5,7394

5,2053

4,8616

4,6204

4,4410

4,3021

4,1911

14

8,8616

6,5149

5,5639

5,0354

4,6950

4,4558

4,2779

4,1399

4,0297

15

8,6831

6,3589

5,4170

4,8932

4,5556

4,3183

4,1415

4,0045

3,8948

16

8,5310

6,2262

5,2922

4,7726

4,4374

4,2016

4,0259

3,8896

3,7804

17

8,3997

6,1121

5,1850

4,6690

4,3359

4,1015

3,9267

3,7910

3,6822

18

8,2854

6,0129

5,0919

4,5790

4,2479

4,0146

3,8406

3,7054

3,5971

19

8,1850

5,9259

5,0103

4,5003

4,1708

3,9386

3,7653

3,6305

3,5225

20

8,0960

5,8489

4,9382

4,4307

4,1027

3,8714

3,6987

3,5644

3,4567

21

8,0166

5,7804

4,8740

4,3688

4,0421

3,8117

3,6396

3,5056

3,3981

22

7,9454

5,7190

4,8166

4,3134

3,9880

3,7583

3,5867

3,4530

3,3458

23

7,8811

5,6637

4,7649

4,2635

3,9392

3,7102

3,5390

3,4057

3,2986

24

7,8229

5,6136

4,7181

4,2184

3,8951

3,6667

3,4959

3,3629

3,2560

25

7,7698

5,5680

4,6755

4,1774

3,8550

3,6272

3,4568

3,3239

3,2172

26

7,7213

5,5263

4,6366

4,1400

3,8183

3,5911

3,4210

3,2884

3,1818

27

7,6767

5,4881

4,6009

4,1056

3,7848

3,5580

3,3882

3,2558

3,1494

28

7,6356

5,4529

4,5681

4,0740

3,7539

3,5276

3,3581

3,2259

3,1195

29

7,5976

5,4205

4,5378

4,0449

3,7254

3,4995

3,3302

3,1982

3,0920

30

7,5625

5,3903

4,5097

4,0179

3,6990

3,4735

3,3045

3,1726

3,0665

40

7,3141

5,1785

4,3126

3,8283

3,5138

3,2910

3,1238

2,9930

2,8876

60

7,0771

4,9774

4,1259

3,6491

3,3389

3,1187

2,9530

2,8233

2,7185

120

5,8510

4,7865

3,9491

3,4796

3,1735

2,9559

2,7918

2,6629

2,5586

3,6349

4,6052

3,7816

3,3192

3,0173

2,8020

2,6393

2,5113

2,4073

v2\v1

10

12

15

20

24

30

40

60

120

1

6055,8

6106,3

6157,3

6208,7

6234,6

6260,7

6286,8

6313,0

6339,4

6366,0

2

99,399

99,416

99,432

99,449

99,458

99,466

99,474

99,483

99,491

99,499

3

27,229

27,052

26,872

26,690

26,598

26,505

26,411

26,316

26,221

26,125

4

14,546

14,374

14,198

14,020

13,929

13,838

13,745

13,652

13,558

13,463

5

10,051

9,8883

9,7222

9,5527

9,4665

9,3793

9,2912

9,2020

9,1118

9,0204

6

7,8741

7,7183

7,5590

7,3958

7,3127

7,2285

7,1432

7,0568

6,9690

6,8801

7

6,6201

6,4691

6,3143

6,1554

6,0743

5,9921

5,9084

5,8236

5,7372

5,6495

8

5,8143

5,6668

5,5151

5,3591

5,2793

5,1981

5,1156

5,0316

4,9460

4,8588

9

5,2565

5,1114

4,9621

4,8080

4,7290

4,6486

4,5667

4,4831

4,3978

4,3105

10

4,8492

4,7059

4,5582

4,4054

4,3269

4,2469

4,1653

4,0819

3,9965

3,9090

11

4,5393

4,3974

4,2509

4,0990

4,0209

3,9411

3,8596

3,7761

3,6904

3,6025

12

4,2961

4,1553

4,0096

3,8584

3,7805

3,7008

3,6192

3,5355

3,4494

3,3608

13

4,1003

3,9603

3,8154

3,6646

3,5868

3,5070

3,4253

3,3413

3,2548

3,1654

14

3,9394

3,8001

3,6557

3,5052

3,4274

3,3476

3,2656

3,1813

3,0942

3,0040

15

3,8049

3,6662

3,5222

3,3719

3,2940

3,2141

3,1319

3,0471

2,9595

2,8684

16

3,6909

3,5527

3,4089

3,2588

3,1808

3,1007

3,0182

2,9330

2,8447

2,7528

17

3,5931

3,4552

3,3117

3,1615

3,0835

3,0032

2,9205

2,8348

2,7459

2,6530

18

3,5082

3,3706

3,3373

3,0771

2,9990

2,9185

2,8354

2,7493

2,6597

2,5660

19

3,4338

3,2965

3,1533

3,0031

2,9249

2,8442

2,7608

2,6742

2,5839

2,4893

20

3,3682

3,2311

3,0880

2,9377

2,8594

2,7785

2,6947

2,6077

2,5168

2,4212

21

3,3098

3,1729

3,0299

2,8796

2,8011

2,7200

2,6359

2,5484

2,4568

2,3603

22

3,2576

3,1209

2,9780

2,8444

2,7488

2,6675

2,5831

2,4951

2,4029

2,3055

23

3,2106

3,0740

2,9311

2,7805

2,7017

2,6206

2,5355

2,4471

2,3542

2,2559

24

3,1681

3,0316

2,8887

2,7380

2,6591

2,5773

2,4923

2,4035

2,3099

2,2107

25

3,1294

2,9931

2,8502

2,6993

2,6203

2,5383

2,4530

2,3637

2,2695

2,1694

26

3,0941

2,9579

2,8150

2,6640

2,5848

2,5026

2,4170

2,3273

2,2325

2,1315

27

3,0618

2,9256

2,7827

2,6316

2,5522

2,4699

2,3840

2,2938

2,1984

2,0965

28

3,0320

2,8959

2,7530

2,6017

2,5223

2,4397

2,3535

2,2629

2,1670

2,0642

29

3,0045

2,8685

2,7256

2,5742

2,4946

2,4118

2,3253

2,2344

2,1378

2,0342

30

2,9791

2,8431

2,7002

2,5487

2,4689

2,3860

2,2992

2,2079

2,1107

2,0062

40

2,8005

2,6648

2,5216

2,3689

2,2880

2,2034

2,1142

2,0194

1,9172

1,8047

60

2,6318

2,4961

2,3523

2,1978

2,1150

2,0285

1,9360

1,8363

1,7263

1,6006

120

2,4721

2,3363

2,1915

2,0346

1,9500

1,8600

1,7628

1,6557

1,5330

1,3805

2,3209

2,1848

2,0385

1,8783

1,7908

1,6964

1,5923

1,4730

1,3246

1,0000

Число

Число степеней свободы V

изме-

1

2

3

4

5

6

8

10

16

36

∞

рений

k

2

9985

9750

9392

9057

8772

8534

8159

7880

7341

6602

5000

3

9669

8709

0797

7454

7071

6771

6333

6025

5466

4748

3333

4

9065

7679

6841

6287

5895

5598

5175

4884

4366

3720

2500

5

8412

6838

5981

5441

5065

4783

4387

4118

3645

3066

2000

6

7808

6161

5321

4803

4447

4184

3817

3568

3135

2612

1667

7

7271

5612

4800

4307

3974

3726

3384

3154

2756

2278

1429

8

6798

5157

4377

3910

3595

3362

3043

2829

2462

2022

1250

9

6385

4775

4027

3584

7276

3067

2768

2568

2226

1820

1111

10

6020

4450

3733

3311

3029

2823

2541

2353

2032

1655

1000

12

5410

3924

3264

2880

2624

2439

2187

2020

1737

1403

0833

15

4709

3346

2758

2419

2195

2034

1815

1671

1429

1144

0667

20

3894

2705

2205

1921

1735

1602

1422

1303

1108

0879

0500

24

3434

2354

1907

1656

1493

1374

1216

1113

0942

0743

0417

30

2929

1980

1593

1377

1237

1137

1001

0921

0771

0604

0333

40

2370

1576

1259

1082

0968

0887

5950

0713

0595

0462

0250

60

1737

1131

0895

0765

0682

0623

0552

0497

0411

0316

0167

120

0998

0632

0495

0419

0371

0337

0292

0266

0218

0165

0083

∞

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

Число

Доверительная вероятность р, %

степеней

80

90

95

98

99

99,5

99,8

99,9

свободы V

1

3,0777

6,3138

12,7062

31,8205

63,6567

127,3213

318,3088

636,6192

2

1,8856

2,9200

4,3027

6,9646

9,9248

14,0890

22,3271

31,5991

3

1,6377

2,3534

3,1824

4,5407

5,8409

7,4533

10,2145

12,9240

4

1,5332

2,1318

2,7764

3,7469

4,6041

5,5976

7,1732

8,6103

5

1,4759

2,0150

2,5706

3,3649

4,0321

4,7733

5,8934

6,8688

6

1,4398

1,9432

2,4469

3,1427

3,7074

4,3168

5,2076

5,9588

7

1,4149

1,8946

2,3646

2,9980

3,4995

4,0293

4,7853

5,4079

8

1,3968

1,8595

2,3060

2,8965

3,3554

3,8325

4,5008

5,0413

9

1,3830

1,8331

2,2622

2,8214

3,2498

3,6897

4,2968

4,7809

10

1,3722

1,8125

2,2281

2,7638

3,1693

3,5814

4,1437

4,5869

11

1,3634

1,7959

2,2010

2,7181

3,1058

3,4966

4,0247

4,4370

Число

Доверительная вероятность р, %

степеней

80

90

95

98

99

99,5

99,8

99,9

свободы V

12

1,3562

1,7823

2,1788

2,6810

3,0545

3,4284

3,9296

4,3178

13

1,3502

1,7709

2,1604

2,6503

3,0123

3,3725

3,8520

4,2208

14

1,3450

1,7613

2,1448

2,6245

2,9768

3,3257

3,7874

4,1405

15

1,3406

1,7531

2,1314

2,6025

2,9467

3,2860

3,7328

4,0728

16

1,3368

1,7459

2,1199

2,5835

2,9208

3,2520

3,6862

4,0150

17

1,3334

1,7396

2,1098

2,5669

2,8982

3,2224

3,6458

3,9651

18

1,3304

1,7341

2,1009

2,5524

2,8784

3,1966

3,6105

3,9216

19

1,3277

1,7291

2,0930

2,5395

2,8609

3,1737

3,5794

3,8834

20

1,3253

1,7247

2,0860

2,5280

2,8453

3,1534

3,5518

3,8495

21

1,3232

1,7207

2,0796

2,5176

2,8314

3,1352

3,5272

3,8193

22

1,3212

1,7171

2,0739

2,5083

2,8188

3,1188

3,5050

3,7921

23

1,3195

1,7139

2,0687

2,4999

2,8073

3,1040

3,4850

3,7676

24

1,3178

1,7109

2,0639

2,4922

2,7969

3,0905

3,4668

3,7454

25

1,3163

1,7081

2,0595

2,4851

2,7874

3,0782

3,4502

3,7251

26

1,3150

1,7056

2,0555

2,4786

2,7787

3,0669

3,4350

3,7066

27

1,3137

1,7033

2,0518

2,4727

2,7707

3,0565

3,4210

3,6896

28

1,3125

1,7011

2,0484

2,4671

2,7633

3,0469

3,4082

3,6739

29

1,3114

1,6991

2,0452

2,4620

2,7564

3,0380

3,3962

3,6594

30

1,3104

1,6973

2,0423

2,4573

2,7500

3,0298

3,3852

3,6460

32

1,3086

1,6939

2,0369

2,4487

2,7385

3,0149

3,3653

3,6218

34

1,3070

1,6909

2,0322

2,4411

2,7284

3,0020

3,3479

3,6007

36

1,3055

1,6883

2,0281

2,4345

2,7195

2,9905

3,3326

3,5821

38

1,3042

1,6860

2,0244

2,4286

2,7116

2,9803

3,3190

3,5657

40

1,3031

1,6839

2,0211

2,4233

2,7045

2,9712

3,3069

3,5510

42

1,3020

1,6820

2,0181

2,4185

2,6981

2,9630

3,2960

3,5377

44

1,3011

1,6802

2,0154

2,4141

2,6923

2,9555

3,2861

3,5258

46

1,3002

1,6787

2,0129

2,4102

2,6870

2,9488

3,2771

3,5150

48

1,2994

1,6772

2,0106

2,4066

2,6822

2,9426

3,2689

3,5051

50

1,2987

1,6759

2,0086

2,4033

2,6778

2,9370

3,2614

3,4960

55

1,2971

1,6730

2,0040

2,3961

2,6682

2,9247

3,2451

3,4764

60

1,2958

1,6706

2,0003

2,3901

2,6603

2,9146

3,2317

3,4602

65

1,2947

1,6686

1,9971

2,3851

2,6536

2,9060

3,2204

3,4466

70

1,2938

1,6669

1,9944

2,3808

2,6479

2,8987

3,2108

3,4350

80

1,2922

1,6641

1,9901

2,3739

2,6387

2,8870

3,1953

3,4163

90

1,2910

1,6620

1,9867

2,3685

2,6316

2,8779

3,1833

3,4019

100

1,2901

1,6602

1,9840

2,3642

2,6259

2,8707

3,1737

3,3905

110

1,2893

1,6588

1,9818

2,3607

2,6213

2,8648

3,1660

3,3812

120

1,2886

1,6577

1,9799

2,3578

2,6174

2,8599

3,1595

3,3735

130

1,2881

1,6567

1,9784

2,3554

2,6142

2,8557

3,1541

3,3669

140

1,2876

1,6558

1,9771

2,3533

2,6114

2,8522

3,1495

3,3614

150

1,2872

1,6551

1,9759

2,3515

2,6090

2,8492

3,1455

3,3566

160

1,2869

1,6544

1,9749

2,3499

2,6069

2,8465

3,1419

3,3524

170

1,2866

1,6539

1,9740

2,3485

2,6051

2,8441

3,1389

3,3487

180

1,2863

1,6534

1,9732

2,3472

2,6034

2,8421

3,1361

3,3454

Число

Доверительная вероятность р, %

степеней

80

90

95

98

99

99,5

99,8

99,9

свободы V

190

1,2860

1,6529

1,9725

2,3461

2,6020

2,8402

3,1337

3,3425

200

1,2858

1,6525

1,9719

2,3451

2,6006

2,8385

3,1315

3,3398

250

1,2849

1,6510

1,9695

2,3414

2,5956

2,8322

3,1232

3,3299

300

1,2844

1,6499

1,9679

2,3388

2,5923

2,8279

3,1176

3,3233

350

1,2840

1,6492

1,9668

2,3370

2,5899

2,8249

3,1137

3,3185

400

1,2837

1,6487

1,9659

2,3357

2,5882

2,8227

3,1107

3,3150

450

1,2834

1,6482

1,9652

2,3347

2,5868

2,8209

3,1084

3,3123

500

1,2832

1,6479

1,9647

2,3338

2,5857

2,8195

3,1066

3,3101

550

1,2831

1,6476

1,9643

2,3331

2,5848

2,8184

3,1051

3,3083

600

1,2830

1,6474

1,9639

2,3326

2,5840

2,8175

3,1039

3,3068