Apéndice A 769

Proba b¡ l¡dades binomiales

n x | .01 .05 .10 .2O .30 .40 .50 .60 .7O .80 .90 .95 .99 I x

01

2

.980 .902

.020 .0950+ .002

.970 .857

.029 .1350+ .0070+ 0+.961 .81 5.039 .171.001 .0140+ 0+0+ 0+.951 .774.048 .204.001 .0210+ .0010+ 0+0+ 0+.941 .735.057 .232.001 .0310+ .0020+ 0+0+ 0+0+ 0+.932 .698.066 .257.002 .0410+ .0040+ 0+0+ 0+0+ 0+0+ 0+.923 .663.07 5 .279.003 .0510+ .0050+ 0+0+ 0+0+ 0+0+ 0+0+ 0+

.810 .640 .490

.180 .320 .420

.01 0 .040 .090

.729 .512 .343

.243 .384 .441

.027 .096 .189

.001 .008 .027

.656 .410 .240

.292 .410 .412

.049 .1 54 .265

.004 .026 .07 60+ .002 .008

.590 .328 .168

.328 .410 .360

.073 .205 .309

.008 .051 .1320 + .006 .028

0+ 0+ .002

.531 .262 .118

.354.393.303

.098 .246 .324

.015 .082 .195

.001 .015 .060

0+ .oo2 .0100+ 0+ .001

.478 .210 .092

.372 .367 .247

.124 .275 .318

.023 .1 15 .227

.003 .029 .097

0+ .004 .0250+ 0+ .0040+ 0+ 0+

.430 .168 .059

.383 .336 .1 98

.149 .294 .296

.03 3 .147 .254

.005 .046 .136

0+ .009 .0470+ .001 .01 00+ 0+ .0010+ 0+ 0+

.360 .250

.480 .500

.1 60 .250

.216 .125

.432 .37 5

.288 .37 5

.064 .125

.1 30 .062

.346 .250

.346 .37 5

.1 54 .250

.026 .062

.078 .031

.259 .1 56

.346 .312

.230 .312

.077 .156

.010 .031

.047 .016

.187 .094

.311 .234

.276 .312

.1 38 .234

.037 .094

.004 .016

.028 .008

.1 31 .055

.261 .164

.290 .273

.194 .273

.077 .1 64

.017 .055

.002 .008

.017 .004

.090 .031

.209 .109

.279 .219

.232 .273

.124 .219

.041 .1 09

.008 .031

.001 .004

.160 .090 .040

.480 .420 .320

.360 .490 .640

.064 .027 .008

.288 .189 .096

.432 .441 .384

.216 .343 .512

.026 .008 .002

.1 54 .07 6 .026

.346 .265 .1 54

.346 .412 .410

.1 30 .240 .410

.01 0 .002 0+

.077 .028 .006

.230 .132 .051

.346 .309 .205

.259 .360 .410

.078 .168 .328

.004 .001 0+

.037 .01 0 .oo2

.138 .060 .01 5

.276 .185 .082

.31 1 .324 .246

.187 .303 .393

.047 .118 .262

.002 0+ 0+

.017 .004 0 +

.077 .025 .004

.194 .097 .029

.290 .227 .1 15

.261 .31 8 .27 5

.1 31 .247 .367

.028 .082 .210

.001 0+ 0+

.008 .001 0 +

.041 .01 0 .001

.124 .047 .009

.232 .136 .046

.279 .254 .147

.209 .296 .294

.090 .1 98 .336

.o17 .058 .168

.010 .002

.180 .095

.810 .902

.001 0+

.027 .007

.243 .135

.729 .857

0+ 0+.004 0+.049 .014.292 .171.656 .815

0+ 0+0+ 0+.008 .001.073 .021.328 .204

.590 .774

0+ 0+0+ 0+.001 0+.01 5 .002.098 .031

.354 .232

.5 31 .735

0+ 0+0+ 0+0+ 0+.003 0+.023 .004

.124 .041

.372 .257

.478 .698

0+ 0+0+ 0+0+ 0+0+ 0+.005 0+.03 3 .005.149 .051.383 .279.430 .663

0+.020.980

0+0+.029.970

0+0+

.001

.039

.961

0+0+0+

.001

.048

.951

0+0+0+0+

.001

.057

.941

0+0+0+0+0+.002.066.932

0+0+0+0+0+0+.003.07 5.923

01

23

01

234

01

234

5

01

234

56

01

234

567

01

234

5678

NOIA: 0* representa una probabilidad positiva menor que 0.0005. (continúo)

Probab¡l¡dades binomiales (continuoción)

n x I .01 .05 .10 .20 .30 .40 .50 .60 .70 .80 .90 .95 .99 I x

901

234

56789

56789

56789

56789

.914 .630

.083 .2gg

.003 .0630+ .0080+ .001

0+ 0+0+ 0+0+ 0+0+ 0+0+ 0+.904 .599.091 .315.004 .07 50+ .0100+ .001

0+ 0+0+ 0+0+ 0+0+ 0+0+ 0+0+ 0+.895 .569.099 .329.005 .0870 + .0140+ .001

0+ 0+0+ 0+0+ 0+0+ 0+0+ 0+0+ 0+0+ 0+.886 .540.107 .341.006 .0990 + .0170+ .002

0+ 0+0+ 0+0+ 0+0+ 0+0+ 0+0+ 0+0+ 0+0+ 0+

.387 J34

.387 .302

.172 .302

.045 .176

.007 .066

.001 .0170 + .0030+ 0+0+ 0+0+ 0+.349 .107.387 .268.194 .302.057 .201.01 1 .088

.001 .0260+ .0060+ .0010+ 0+0+ 0+0+ 0+.314 .086.384 .236.213 .295.071 .221.01 6 .1 1 1

.002 .0390+ .01 00+ .0020+ 0+0+ 0+0+ 0+0+ 0+.282 .069.377 .206.230 .283.08s .236.021 .1 3 3

.004 .0s 30+ .0160+ .0030+ .0010+ 0+

0+ 0+0+ 0+0+ 0+

.040 .010

.1 56 .060

.267 .1 61

.267 .251

.17 2 .251

.074 .167

.021 .074

.004 .0210+ .0040+ 0+.028 .006.121 .040.233 .121.267 .21 5.200 .251

.103 .201

.037 .1 1 1

.009 .042

.001 .01 1

0+ .0020+ 0+.020 .004.093 .027.200 .089.257 .177.220 .236

.132 .221

.057 .147

.017 .070

.004 .023

.001 .005

0+ .0010+ 0+.014 .002.071 .017.168 .064.240 .142.231 .213

.1 58 .227

.079 .177

.029 .101

.008 .042

.001 .012

0+ .0020+ 0+0+ 0+

.002 0+

.01 8 .004

.070 .021

.164 .074

.246 .1 67

.246 .251

.1 64 .251

.070 .161

.018 .060

.002 .01 0

.001 0+

.010 .002

.044 .01 1

.117 .042

.205 .1 1 1

.246 .201

.205 .251

.117 .21 5

.044 .121

.01 0 .040

.001 .006

0+ 0+.005 .001.027 .005.081 .023.161 .070

.226 .147

.226 .221

.1 61 .236

.081 .177

.027 .089

.005 .0270 + .004

0+ 0+.003 0+.016 .002.054 .012.121 .042.193 .1 01.226 .177.193 .227.121 .213.054 .142

.01 6 .064

.003 .0170+ .oo2

0+ 0+ 0+0+ 0+ 0+.004 0+ 0+.021 .003 0 +.07 4 .017 .001

.172 .066 .007

.267 .17 6 .045

.267 .302 .172

.156 .302 .387

.040 .134 .387

0+ 0+ 0+0+ 0+ 0+.001 0+ 0+.009 .001 0+.037 .006 0+.103 .026 .001.200 .088 .01 1

.267 .201 .057

.233 .302 .194

.121 .269 .397

.028 .107 .349

0+ 0+ 0+0+ 0+ 0+.001 0+ 0+.004 0+ 0+.017 .002 0+.057 .01 0 0+.132 .039 .002.220 .1 1 1 .01 6.257 .221 .071.200 .295 .213

.093 .236 .384

.020 .086 .314

0+ 0+ 0+0+ 0+ 0+0+ 0+ 0+.001 0+ 0+.008 .001 0+.029 .003 0+.079 .01 6 0+.158 .053 .004.231 .133 .021.240 .236 .08s

.1 68 .283 .230

.071 .206 .377

.014 .069 .282

0+ 0+0+ 0+0+ 0+0+ 0+0+ 0+.001 0+.008 0+.063 .003.299 .083.630 .914

0+ 0+0+ 0+0+ 0+0+ 0+0+ 0+0+ 0+.001 0+.01 0 0+.07 s .004.31 5 .091

.599 .904

0+ 0+0+ 0+0+ 0+0+ 0+0+ 0+0+ 0+0+ 0+.001 0+.014 0+.087 .005

.329 .0gg

.569 .895

0+ 0+0+ 0+0+ 0+0+ 0+0+ 0+0+ 0+0+ 0+0+ 0+.002 0+.017 0 +

.099 .006

.341 .107

.s40 .886

56789

56789

10

56789

NOTA:0+ representa una probabilidad positiva menor que 0.0005. (continúo)

P roba b¡ I ¡dades binomiales (continuoción)

n x .01 .05 .10 .2O .30 .4O .50 .60 .70 .80 .90 .95 .99 I x

13

14

01

234

56789

10111213

01

234

56789

1011121314

01

234

56789

1011121314

15

.878 .513l.r rs .3s1.007 .1 1 1

0+ .0210 + .003

0+ 0+0+ 0+0+ 0+0+ 0+0+ 0+0+ 0+0+ 0+0+ 0+0+ 0+.869 .488.123 .359.008 .1230+ .0260+ .004

0+ 0+0+ 0+0+ 0+0+ 0+0+ 0+0+ 0+0+ 0+0+ 0+0+ 0+0+ 0+.860 .463.1 30 .366.009 .1 350 + .0310+ .005

0+ .0010+ 0+0+ 0+0+ 0+0+ 0+0+ 0+0+ 0+0+ 0+0+ 0+0+ 0+0+ 0+

.254 .055

.367 .179

.245 .268

.100 .246

.028 .1 54

.006 .069

.001 .0230+ .0060+ .0010+ 0+0+ 0+0+ 0+0+ 0+0+ 0+.229 .044.356 .1 54.257 .250.114 .250.035 .172

.008 .086

.001 .0320+ .0090+ .0020+ 0+0+ 0+0+ 0+0+ 0+0+ 0+0+ 0+.206 .035.343 .132.267 .231.129 .250.043 .188

.01 0 .103

.002 .o430+ .0140+ .0030+ .001

0+ 0+0+ 0+0+ 0+0+ 0+0+ 0+0+ 0+

.01 0 .001

.054 .01 1

.139 .045

.218 .111

.234 .184

.180 .221

.103 .197

.044 .131

.014 .066

.003 .024

.001 .0060+ .0010+ 0+0+ 0+.007 .001.041 .007.1 1 3 .032.194 .085.229 .155

.'196 .207

.126 .207

.062 .1 57

.023 .092

.007 .041

.001 .0140+ .0030+ .0010+ 0+0+ 0+.005 0+.031 .005.092 .022.170 .063.219 .127.206 .1 86.147 .207.081 .177.035 .118.012 .061

.003 .024

.001 .0070+ .0020+ 0+0+ 0+0+ 0+

0+ 0+.002 0+.01 0 .001.035 .006.087 .024.1 57 .066.209 .1 31.209 .197.1 57 .221.087 .184.035 .1 1 1

.01 0 .045

.002 .01 1

0+ .001

0+ 0+.001 0+.006 .001.022 .003.061 .014J22 .041.183 .092.209 .1 57.1 83 .207.122 .207

.061 .155

.022 .085

.006 .032

.001 .0070+ .001

0+ 0+0+ 0+.003 0+.014 .002.042 .007.092 .024.153 .061.196 .1 1 8.196 .177.1 5 3 .207

.092 .1 86

.042 .127

.014 .063

.003 .0220+ .0050+ 0+

0+ 0+0+ 0+0+ 0+.001 0+.003 0+.014 .001.044 .006.103 .023.1 80 .069.234 ."1 54

.218 .246

.139 .268

.054 .179

.01 0 .055

0+ 0+0+ 0+0+ 0+0+ 0+.001 0+.007 0+.023 .002.062 .009.126 .032.196 .086

.229 .172

.194 .250

.1 1 3 .250

.041 .1 54

.007 .0440+ 0+0+ 0+0+ 0+0+ 0+.001 0+.003 0 +.012 .001.035 .003.081 .014.147 .043.206 .103.219 .1 88.170 .250.092 .231.031 .132.005 .035

0+ 0+ 0+0+ 0+ 0+0+ 0+ 0+0+ 0+ 0+0+ 0+ 0+0+ 0+ 0+0+ 0+ 0+.001 0+ 0+.006 0+ 0+.028 .003 0+.100 .021 0+.245 .11 1 .007.367 .351 .115.254 .513 .8780+ 0+ 0+0+ 0+ 0+0+ 0+ 0+0+ 0+ 0+0+ 0+ 0+0+ 0+ 0+0+ 0+ 0+0+ 0+ 0+.001 0+ 0+.008 0+ 0+.035 .004 0 +.1'.4 4 .026 0+.257 .123 .008.356 .359 .'.123.229 .4gg .g69

0+ 0+ 0+0+ 0+ 0+0+ 0+ 0+0+ 0+ 0+0+ 0+ 0+0+ 0+ 0+0+ 0+ 0+0+ 0+ 0+0+ 0+ 0+.002 0+ 0+.010 .001 0+.043 .005 0+.129 .031 0+.267 .135 .009.343 .366 .130.206 .463 .860

15

01

234

56789

01

234

56789

1011121314

01

234

56789

1011121314

15

NOIA:0* representa una probabilidad positiva menor que 0.0005.

De Frederick C. Mosteller, Robert E. K. Rourke y George B. Thomas, lr., Probability with Stotistical Aplicotions, 2a. ed., @ 1970 Addison-Wesley Publishing Co., Reading, MA. Reproducido con permiso.

lcs A

Puntu ac¡ones zNEGATIVAS

Distribución normal estándar (): Área acumulativa desde la IZQUIERDA

.00 .01 .02 .03 .04 .05 .06 .07 .08 .09

.0001

.0003

.000s

.0007

.001 0

.001 3

.001 9

.0026

.0035

.0047

.0062

.0082

.0107

.01 39

.0179

.0228

.0287

.0359

.0446

.0548

.0668

.0808

.0968

.1 151

.1357

.1 587

.1841

.2119

.2420

.2743

.3085

.3446

.3821

.4207

.4602

.5000

.0003

.0005

.0007

.0009

.001 3

.001 8

.0025

.0034

.0045

.0060

.0080

.01 04

.01 36

.017 4

.0222

.0281

.0351

.0436

.0537

.0655

.0793

.0951

.1131

.1335

.1 562

.1814

.2090

.2389

.2709

.3050

.3409

.3783

.41 68

.4562

.4960

.0003

.0005

.0006

.0009

.001 3

.001 8

.0024

.003 3

.0044

.0059

.0078

.01 02

.0132

.0170

.0217

.0274

.0344

.0427

.0526

.0643

.0778

.0934

.1112

.1314

.1539

.1788

.2061

.23s8

.267 6

.301 5

.3372

.3745

.4129

.4522

.4920

.0003

.0004

.0006

.0009

.0012

.0017

.0023

.0032

.0043

.005 7

.00 z5

.0099

.0129

.0166

.0212

.0268

.03 36

.0418

.051 6

.0630

.07 64

.0918

.1093

.1292

.1515

.17 62

.2033

.2327

.2643

.2981

.3336

.3707

.4090

.4483

.4880

.0003

.0004

.0006

.0008

.001 2

.001 6

.002 3

.0031

.0041

.0055

.0073

.0096

.0125

.01 62

.0207

.0262

.0329

.0409

.0505

.061 8

.07 49

.0901

.107 5

.1271

.1 492

.1736

.2005

.2296

.2611

.2946

.3 300

.3669

.4052

.4443

.4840

.0003

.0004

.0006

.0008

.001 1

.001 6

.0022

.0030

.0040

.0054

.0071

.0094

.0122

.01 58

.0202

.0256

.0322

.0401

.0495

.0606

.0735

.0885

.1 056

.1251

.1469

.1711

.197 7

.2266

.2578

.2912

.3264

.3632

.401 3

.4404

.4801

.0003

.0004

.0006

.0008

.001 1

.001 5

.0021

.0029

.0039

.0052

.0069

.0091

.01 19

.01 54

.0197

.0250

.0314

.0392

.0485

.0594

.0721

.0869

.1 038

.1230

.1446

.1 685

.1949

.2236

.2546

.2877

.3228

.3594

.3974

.4364

.47 61

.0003

.0004

.000s

.0008

.001 1

.001 5

.0021

.0028

.0038

.0051

.0068

.0089

.01 16

.01 50

.0192

.0244

.0307

.0384

.047 5

.0582

.0708

.08s3

.1 020

.1210

.1423

.1 660

.1922

.2206

.2514

.2843

.3192

.3557

.3936

.4325

.4721

.0003 .0002

.0004 .0003

.000s .000s

.0007 .0007

.001 0 .001 0

.0014 .001 4

.0020 .001 9

.0027 .0026

.0037 .0036r .0049 .0048.0066 .0064.0087 .0084.01 13 .01 10.0146 .01 43.0188 .0183.0239 .0233.0301 .0294.037 5 .0367.0465 .0455.0571 .0559.0694 .0681.0838 .0823.1003 .0985.1 190 .1170.1 401 .1379.1 635 .1 61 1

.1894 .1867

.2177 .2148

.2483 .2451

.281 0 .2776

.31 56 .3121

.3520 .3483

.3897 .38s9

.4286 .4247

.4681 .4641

- 3.50v

menores-3.4- 3.3-3.2- 3.1

- 3.0-2.9-2.8-2.7-2.6-2.5-2.4-2.3-2.2-2.1-2.0-1 .9-1.8-1 .7-1 .6-1.5-1 .4-1.3-1 .2-1.1-1.0- 0.9- 0.8-0.7- 0.6- 0.5-0.4- 0.3-0.2- 0.1

- 0.0

NOTA: Para valores de z por debajo de -3.49, utilice 0.0001para el área.

*Utilice estos valores comunes que resultan por interpolación:

Puntuación .z Area

-1.645 0.0500

-2.57 s 0.00s0

Apéndice A 773

Puntu ac¡ones zPOSITIVAS

(continuociófl Area acumulativa desde la IZQUIERDA

z .O0 .01 .02 .03 .04 .05 .06 .07 .08 .09

0.00.10.20.30.40.s0.60.70.80.91.0'l .11.21.31.41.51.61.71.91.92.02.12.22.32.42.52.62.72,82.93.03.13.23.33.43.50v

mayores

.5000.5 398.5793.6179.6554.691 5.7257.7580.7881.8159.8413.8643.8849.9032.9192.9332.9452.9554.9641.9713.9772.9821.9861.9893.99'.18.9938.9953.9965.997 4.9981.9987.9990.9993.9995.9997.9999

.5040

.5438

.5832

.6217

.6591

.6950

.7291

.7 6'.41

.7910

.8186

.8438

.8665

.8869

.9049

.9207

.9345

.9463

.9564

.9649

.9719

.9778

.9826

.9864

.9896

.9920

.9940

.9955

.9966

.997 5

.9982

.9987

.9991

.9993

.9995

.9997

.5080.5478.5871.6255.6628.6985.7324.7642.7939.8212.8461.8686.8889.9066.9222.9357.9474.9573.9656.9726.9783.9830.9868.9898.9922.9941.9956.9967.997 6.9982.9987.9991.9994.9995.9997

.sl20.5517.5910.6293.6664.7019.7357.7 673.7967.8238.8485.8708.8907.9082.9236.9370.9484.9582.9664.9732.9788.9834.9871.9901.9925.9943.9957.9968.9977.9983.9988.9991.9994.9996.9997

.5160

.5557

.5948

.63 31

.6700

.7054

.7389

.7704

.7995

.8264

.8s08

.8729

.8925

.9099

.9251

.9382

.9495

.9591

.9671

.9738

.9793

.9838

.987 5

.9904

.9927

.9945

.99s9

.9969

.9977

.9984

.9988

.9992

.9994

.9996

.9997

.5199.5596.5987.6368.6736.7088.7422.7734.8023.8289.85 31.8749.8944.911 5.9265.9394.9505.9599.9678.9744.9798.9842.9878.9906.9929.9946.9960.9970.9978.9984.9989.9992.9994.9996.9997

.5239 .5279

.5636 .567 5

.6026 .6064

.6406 .6443

.6772 .6808

.7123 .7157

.7454 .7486

.7764 .7794

.8051 .8078

.8315 .8340

.8554 .8577

.8770 .8790

.8962 .8980

.9',131 .9147

.9279 .9292

.9406 9418

.9515 .9525

.9608 .9616

.9686 .9693

.97 50 .97 56

.9803 .9808

.9846 .9850

.988'l .9884

.9909 .9911

.9931 .9932

.9948 .9949

.9961 .9962

.9971 .9972

.9979 .9979

.9985 .9985

.9989 .9989

.9992 .9992

.9994 .9995

.9996 .9996

.9997 .9997

.5319 .5359

.5714 .57 53

.61 03 .6141

.6480 .6517

.6844 .6879

.7190 .7224

.7 517 .7 549

.7823 .7852

.81 06 .81 3 3

.8365 .8389

.8599 .8621

.881 0 .8830

.8997 .9015

.9162 .9177

.9306 .9319

.9429 .9441

.95 35 .9545

.9625 .9633

.9699 .9706

.976'l .9767

.9812 .9817

.9854 .9857

.9887 .9890

.9913 .991 6

.9934 .9936

.9951 .9952

.9963 .9964

.9973 .9974

.9980 .9981

.9986 .9986

.9990 .9990

.9993 .9993

.9995 .9995

.9996 .9997

.9997 .9998

NOTA: Para valores de z por encima de 3.49, utilice 0.9999para el área.

*Ut¡l¡ce estos valores comunes que resultan por interpolación:Pu ntuación

z

1 .645

2.57 5

Area

Valores críticoscomunes

Nivel de Valorconfianza crítico

0.9s00

0.9950

0.900.9s0.99

1 .6451.96

2.57 5

@ Distribución t: Valores críticos t

Area en una cola0.005 0.01 0 .025 0.05 0.1 0

Grados delibertad

Area en dos colas0.01 0.02 0.05 0.10 0.20

1

23456789

101112131415161718192021222324252627282930313234363840455055606570758090

J00200300400s00750

1 0002000Grande

63.6579.9255.8414.6044.0323.7073.4993.3553.2503.1693.1 063.0553.0'.422.9772.9472.9¿l2.8982.8792.96"12.8452.8312.8'.192.8072.7972.7872.7792.77'.,2.7632.7562.7502.7442.7382.7282.7'.192.7'.|22.7042.6902.6782.6682.6602.6542.6482.6432.6392.6322.6262.6012.5922.5992.5962.5822.5812.5782.576

31 .8216.9654.5413.7473.36s3.1432.9982.8962.8212.7 642.7182.6812.6502.6242.6022.5832.5672.5522.5392.5282.5182.5092.5002.4922.4952,4792.4732.4672.4622.4572.4532.4492.4412.4342.4292.4232.4122.4032.3962.3902.3952.3812.3772.3742.3682.3642.3452.3392.3362.3342.3312.3302.3282.326

12.7064.3033.'.1822.7762.57'|2.4472.3652.3062.2622.2282.2012.',|792.'1602.'1452.'.|3'.12.r1202,'1102.10'l2.O932.0962.0802.O742.0692.0642.0602.O562.O522.Og2.0452.O422.0402.0372.0322.O292.O242.O2'.12.0'|42.OOg2.OO42.000',.997'l .gg4'l .9921.ggo',.987'|.984'l .972'4.968'l .966'l .9651.963',.9621.961'1 .960

6.3142.9202.3532.1322.01 51.9431 .8951 .8601.8331 .8121 .796'l .7821.7711.7611.7531.7461.7401.7341.7291.7251.7211 .7171 .7141 .7111 .7081.7061.7031 .7011 .6991.6971 .6961.6941 .6911 .6881 .6861.6841 .6791.6761 .6731 .6711 .6691.6671 .6651.6641.6621.660,1.6531 .6501 .6491.6481 .647'l .6461.6461.645

3.0781 .8861 .6381.5331.4761 .4401.41 51.3971 .3831.3721 .3631 .3561.3501 .3451 .3411.3371.3331.3301.3281.3251.3231.3211 .3191.3181.3161.3151 .3141.31 31.31 1

1.3101 .3091 .3091 .3071 .3061 .3041 .3031 .3011.2991 .2971.2961 .2951.2941 .2931.2921 .2911.2901.2861.2841.2841.2931.2831.2821.2821.292

Cola izquierda

Cola derecha

lI

Valor críf tco fQosittvo)

lI

Valor críf tco thegativo)

Dos colas

qlz al7

Distribución chi cuadrada (x2)

Area a la derecha del valor crítico

Cradosde

libertad .995 0.99 0.975 0.9s 0.90 0.10 0.0s 0.025 0.01 0.00s

1

2345

6789

10

1112131415

1617181920

2122232425

2627282930

40s060708090

100

0.01 0 0.0200.072 0.1150.207 0.2970.412 0.554

0.67 6 0.8720.989 1.2391.344 1 .6461.735 2.0882.'.1 56 2.558

2.603 3.05 33.074 3.5713.565 4.1074.07 5 4.6604.601 5.229

5.142 5.8125.697 6.4086.265 7.0'.1 56.844 7.6337.434 8.260

8.034 8.8978.643 9.5429.260 10.1969.886 1 0.856

1 0.520 11 .524

11.160 12.1981 1 .808 12.87912.461 13.56513.121 14.2571 3 .787 1 4.9 54

20.707 22.1 6427 .991 29.70735.534 37 .48543.27 5 45.44251 .172 5 3.54059.196 6"1 .7 5467.328 70.O6s

0.001 0.004 0.01 6 2.7060.051 0.103 0.211 4.6050.21 6 0.352 0.594 6.2510.484 0.711 1 .064 7.7790.831 1.145 1.610 9.236

1.237 1 .635 2.204 10.6451 .690 2.1 67 2.833 12.0172.180 2.733 3.490 13.3622.700 3.325 4.1 68 14.6843.247 3.940 4.965 15.997

3.81 6 4.57 5 5.579 17 .27 54.404 5.226 6.304 19.5495.009 5.992 7 .042 1g .9125.629 6.571 7.790 21 .0646.262 7.261 g .547 22.307

6.908 7 .962 g .312 23.5427.564 8.672 10.085 24.7698.231 9.390 10.965 25.ggg8.907 10.117 11.651 27.2049.591 1 0.951 1 2.443 29.412

10.283 11.591 13.240 29.61 5"10.982 12.339 14.042 30.91 311 .689 1 3.091 1 4.949 32.007"l 2.401 1 3.949 1 5 .659 33 .19613.120 1 4.611 1 6.473 34.392

13.844 15.379 17.292 35.5631 4.573 1 6.1 51 1 9.1 I 4 36.7 411 5.308 16.929 1g.g3g 37 .91616.047 17 .709 19.769 39.09716.791 19.493 20.599 40.256

24.433 26.509 29.051 51 .90532.357 34.764 37 .6g9 63.16740.482 43.1 gg 46.459 74.39748.7 58 51 .739 55.329 95.52757.1 53 60.391 64.279 96.57965.647 69.126 73.291 1 07 .56574.222 77.929 92.359 11g.4gg

3.841 5 .0245.991 7 .3787 .81 5 9.3489.488 11 .143

11 .071 12.833

12.592 14.44914.067 1 6.01 31 5.507 17 .53516.919 19.02318.307 20.483

19.67 5 21 .92021 .026 23.33722.362 24.73623.685 26.11924.996 27.488

26.296 28.84527.587 30.19128.869 31 .52630.144 32.85231 .410 34.170

32.671 35.47933.924 36.78135.172 38.07 636.41 5 39.36437.652 40.646

38.885 41 .92340.1 1 3 43j9441 .337 44.46142.557 45.72243.773 46.979

55.258 59 .34267.505 7'.1 .42079.082 83.29890.5 31 95.023

101 .879 106.629113.145 118.136124.342 129 .561

6.635 7.8799.210 10.597

11 .345 1 2.83913.277 14.8601 5.086 16.7 50

1 6.812 1 8.54818.47 5 20.27820.090 21 .95521 .666 23.59923.209 25.199

24.725 26.7 5726.217 2g.2gg27 .688 29.81929.141 31 .31930.5 78 32.801

32.000 34.26733.409 35.71834.805 37.1 5636.191 38.58237 .566 39.997

38.932 41 .40140.289 42.79641 .638 44.1 8142.980 45.55944.314 46.929

45.642 49.29046.963 49.64548.278 50.99349.588 52.33650.892 53.672

63.691 66.7 6676.1 54 79.49088.379 91 .952

100.425 104.21 5112.329 116.321124.116 12g.2gg135.807 140.169

Apéndice A

De Donald B. Owen, Hondbook of Stotisticol Tobles, @ 1962 Addison-Wesley Publishing Co., Reading, MA. Reproducido con permiso deleditor.Grados de libertad

para intervalos de confianza o pruebas de hipótesis con desviación estándar o varianzapara experimentos multinomiales o bondad de ajuste con k categoríasparc tablas de contingencia con r renglones y c columnaspara la prueba de Kruskal-Wallis con k muestras

775

\

I

I.:

.|

n-1k-1(r - lXc - 1)k-1

-=

-

.lrF

Distribución F (o - 0.025 en la cola derecha)

Crados de libertad del numerador (glr)

sO)t-oE(gc.Eoc(uEoE!(5+)t-OtgoEtt,oE(ot-u

1011121314

1516171819

2021222324

2526272829

304060

120m

6.93676.72416.55386.41436.2979

6.19956.11516.04205.97815.9216

5.871s5.82665.78635.74985.7166

s.68645.65865 .63 315.6096s.5828

5.567 55.4239s.28s65.1 s235.0239

1 I 647.792 I 38.5063 I 1 7.4434 I 1 2.218

s I 10.0076 I 8.81 317 I 8.07278 I 7.57099 I 7.2093

799.5039.00016.04410.649

8.43367.25996.541 56.05955.7147

5.45645.25595.09594.96s34.8567

4.7 6504.68674.61 894.55974.507 5

4.46134.41994.38284.34924.3187

4.29094.26554.24214.22054.2006

4.18214.051 03.92s33.80463.6889

864.1 639.16515.4399.9792

7 .7 6366.s988s.88985.41 605.0781

4.82564.63004.47424.34724.2417

4.1 5284.07684.01123.95393.9034

3.8s8 73.81883.78293.7 5053.7211

3.69433.66973.64723.62643.6072

3.58943.46333.34253.22693.1 1 61

899.5839.2481 5.1 019.6045

7.38796.22725.52265.05264.71 81

4.46834.27 514.12123.99s93.8919

3.804 33.72943.66483.60833.5587

3.51473.47 543.44013.408 33.3794

3.35 303.32893.30673.28633.2674

3.24993.12613.00772.89432.7858

921 .8539.29814.8859.364s

7 .1464s.9876s.28s24.81734.4844

4.23614.04403.891 1

3.7 6673.6634

3.57 643.50213.43793.38203.3327

3.28913.25013.21 513.183s3.1548

3.12873.1 0483.08283.06263.04 38

3.026s2.90372.79632.67402.5665

937 .1139.3 3 1

1 4.7359.1973

6.97775.81 985.11864.65174.3197

4.07 213.88023.72833.60433.5014

3.41473.34063.27 673.22093 .171 8

3.12833.08953.05463.02322.9946

2.96852.94472.92282.90272.8840

2.86672.74442.62742.51 542.4082

948.2239.3 3514.6249.0741

6.85 315.69554.99494.52864.1970

3.94983.7 5863.60653.48273.3799

3.29343.21943.1 5563.09993.0509

3.00742.96862.93382.90232.8738

2.84782.82402.80212.78202.7 633

2.74602.62382.50682.39482.287 5

956.6639.37314.5408.9796

6.7 572,5.59964.89934.43 3 34.1020

3.85493.66383.51183.38803.285 3

3.19873.12483.06103.005 32.9563

2.91282.87402.83922.80772.7791

2.7 5312.72932.70742.68722.6686

2.65132.52892.41172.29942.1918

963.2839.38714.4738.9047

6.68115.52344.82324.35724.0260

3.77903.58793.4 3s83.31203.2093

3.12273.04882.98492.92912.8801

2.83652.79772.76282.7 31 32.7027

2.67 662.65282.63092.61 062.5919

2.57462.45192.33442.22172.1136

\l\lo)

E14.zgoH

Distribución F (o - 0.025 en la cola derecha) (continuoción)

Grados de libertad del numerador (gh)

1 1968.63 97 6.7139.41514.337

8.7 512

6.524s5.36624.66584.',lgg73.8682

3.62093.42963.27733.1 5323.0502

2.96332.ggg02.82492.76892.7196

2.67 582.63682.60'.172.56992.54'.1',|

2.51492.49092.46882.44842.4295

2.4'.1202.28822.',16922.0548'l .9447

984.8739.43114.2538.6565

6.42775.26874.56784.'.10'123.7694

3.52173.32993.17723.05272.9493

2.86212.787 52.72302.66672.6171

2.573'l2.s3382.49842.466s2.4374

2.41102.38672.36442.34392.3248

2.30722.18192.06131.94501.8326

993.1039.44814.1678.5599

6.32865.'.|6844.46673.99953.6669

3.41853.22613.07282.94772.8437

2.7 5592.69092.61 582.55902.s089

2.46452.42472.38902.35672.3273

2.30052.27 592.2s332.23242.2131

2.19522.06771.94451.8249'1 .7095

997.2539.45614.1248.s109

6.27805.1'1724.41 503.94723.6142

3.36543.17 253.0'1872.89322.7ggg

2.70062.62522.55982.50272.4523

2.40762.367 52.33',152.29892.2693

2.24222.2'.1742.19462.",7352.1 540

2.13592.00691.881 71 .7 597'1 .6402

1001 .439.46s14.0818.4613

6.22695.06524.36243.89403.5604

3.31 1 03.117 62.96332.83722.7324

2.64372.56792.50202.44452.3937

2.34862.30822.27192.23892.2090

2.19162.',|5652.13342.1"12'.12.0923

2.07391.94291 .&'.{-521.6899"l .5660

100s.639.473'l4.037

8.41 1 1

6.17 50s.012s4.30893.g3gg3.50ss

3.25543.061 32.90632.77972.6742

2.58502.50952.44222.38422.3329

2.28732.24652.20972.17 632.'.1460

2.11832.09282.06932.04772.0276

2.00891 .87 52'1 .74401 .61411 .4935

1009.839.48113.9928.3604

6.12254.95994.25443.78443.4493

3.19843.003s2.84782.72042.6'.442

2.52422.447'.\2.38012.32'.142.2696

2.22342.18192.14462.11072.0799

2.05162.02572.001 8'l .97971.9591

1.94001.8028'1 .66681.52991.3993

1 014.039.49013.9478.3092

6.06934.90444.19893.72793.3918

3.13992.94412.78742.6s902.5519

2.46112.393'.12.31 532.2s582.2032

2.'.15622.1'.,412.07602.041 52.0099

1.981 1

1.95451.9299'1 .90721.8861

1.86641.72421 .581 01.4327'1 .2684

1 01 8.339.49913.9029.2573

6.01534.949'l4.14233.67023.3329

3.07982.88282.72492.59552.4872

2.39s32.3"1632.24742.'.lg692.1333

2.085 32.04222.00321 .96771.9353

1 .90551.87811.8527"l .82911.8072

'l .79671 .6371'l .48211 .31 041.0000

21 39.3983 I 14.41941 8.8439

s | 6.619261 5.46'.137l 4.76118l 4.2951,91 3.9639

JO)l-oE(\5

.EEocoEEEErg+,t-(usoEttlo!(5l-rJ

1 0 | 3.7168111 3.s2s7'l21 3.373613 I 3.24971 4 | 3.'.1469

1s I 3.0602'l61 2.9862171 2.922218 I 2.8664191 2.8172

20I 2.773721 I 2.7348221 2.6999231 2.6682241 2.6396

251 2.6135261 2.599627 I 2.s676281 2.547329 I 2.5286

30 I 2.51'.|240I 2.388260 I 2.2702

1201 2.1 570@ I 2.0483

10 '12 15 20 24 30 40 60 12O @

rJ@rt{P9.oo

De Maxine Merrington y Catherine M. Thompson, "Tables of Percentage Points of the lnverted Beta (D Distribution", Biometika 33('1943):80-84. Reproducido con permiso de Biometrika Trustees. (contínúa)

\l\l\l

\l\l@

FdFl.zgo14

I

I

Distribución F (o - 0.05 en la cola derecha)

Crados de libertad del numerador (gh)

1 I 161 .45 199.5019.0009.55216.9443

5.78615.1 4334.737 44.45904.2565

4.10283.98233.885 33.80s63.7389

3.68233.63373.59153.55463.5219

3.49283.46683.44343.42213.4028

3.38s23.36903.35413.34043.3277

3.31583.23173.15043.07182.9957

21 5.7119.'.|64

9 .27 666.5914

5.40954.7 5714.34684.06623.8625

3.70833.s8743.49033.410s3.3439

3.28743.23893.19683.1 s993.1274

3.09843.07253.04913.02803.0088

2.99122.97 522.96042.94672.9340

2.92232.83872.7 5812.68022.6049

224.5819.2479.11726.3882

s.19224.53374.12033.83793.6331

3.47803.35673.25923.179'.13.1122

3.05563.00692.96472.92772.89sl

2.86612.84012.81672.79552.7763

2.7 5872.74262.72782.71412.7014

2.68962.60602.52522.44722.3719

230.1619.296

9.01 356.2561

s.05034.38743.97153.687 s3.4817

3.32583.20393.10593.02542.9s82

2.90132.85242.81 002.77292.7401

2.71 092.68482.66132.64002.6207

2.60302.58682.57192.55812.5454

2.53362.44952.36832.28992.2141

233.9919.3308.94066.1631

4.95034.29393.86603.s8063.3738

3.21723.09462.99612.91 532.8477

2.79052.7 4132.69872.66132.6283

2.s9902.57272.54912-.52772.5082

2.49042.47412.45912.44532.4324

2.42052.33s92.25412.17 502.0986

236.7719.3538.88676.0942

4.87 594.20673.78703.s00s3.2927

3.13553.01232.91342.83212.7642

2.70662.65722.61432.57672.5435

2.51402.487 62.46392.44222.4226

2.40472.39932.37322.35932.3463

2.33432.24902.16652.0g6g2.0096

2 38.8819.3718.84526.0410

4.81 834.14683.72573.43813.2296

3.O7172.94802.84862.7 6692.6987

2.64082.59112.54802.51022.47 68

2.44712.42052.39652.37482.35s'.,

2.33712.32052.30532.29132.2783

2.26622.18022.09702.01641.9384

240.5419.3858.81236.9988

4.77254.09903.67 673.38813.1789

3.02042.89622.79642.71442.6458

2.58762.53772.49432.45632.4227

2.39282.36602.34192.32012.3002

2.28212.26552.25012.23602.2229

2.21072.12402.04011 .95881.8799

2 I 18.51 33 I 10.1284 I 7.7086

s I 6.60796 I 5.98747 I s .s9148 I 5 .31779 I 5.1174

NO)t-oEñ.gEoco!EEEr5t-(u€(uEVIoE(5¡-u

10 I 4.96461 1 I 4.844312 I 4.74721 3 I 4.667214 I 4.6001

1 5 I 4.543116 I 4.494017 I q.451318 I 4.4'.13919 I 4.3807

20 I 4.351221 I +.324822 I 4.300923 I 4.279324 I 4.2597

25 I 4.241726 I 4.22s227 I 4.210028 I 4.196029 I 4.1830

30 I 4.170940 I 4.084760 I 4.0012

120 I 3 .9201@ I 3.8415

123456789

( continúo)

Distribución F (a - 0.05 en la cola derecha) (continuoción)

Crados de libertad del numerador (glr )

s(r)¡-o!ñ.cEocoEq,,E-o(gt-(u€(uE.tto!(g¡-u

1 I 241 .882 I 19.3963 I 8.78ss4 I 5.9644

s l 4.73s16 | 4.06007 I 3.636s8 I 3.34729l 3.1373

10 I 2.978211 I 2.8s36121 2.753413 I 2.671014 I 2.6022

15 I 2.543716 I 2.493517 I 2.449918 I 2.411719 I 2.3779

20 I 2.347921 { 2.321022 V 2.296723 I 2.274724 I 2.2547

2s I 2.236s26 I 2.219727 I 2.204328 I 2.190029 I 2.1768

30 I 2.164640 I 2.077260 I 1.9926

120 I 1 .910soo I 1 .8307

243.9119 .4138.74465.9117

4.67773.99993.57 473.28393.0729

2.91302.787 62.68662.60372.5342

2.47 532.42472.38072.34212.3080

2.277 62.25042.22582.20362.1834

2.16492.14792.13232.11792.1045

2.09212.0035'l .91741.83371 .7 522

245.9519.4298.70295.85 78

4.61883.93813.51073.2'.1943.0061

2.84s02.71862.61692.53312.4630

2.40342.3s222.30772.26862.2341

2.20332.17 572.1s082.12822.1077

2.08892.07162.05582.041'.12.027 5

2.01481.92451.83641 .7 50s1.6664

248.0119.4468.66025.8025

4.55813.87423.44453.1s032.936s

2.77402.64642.54362.45892.3879

2.327 52.27 562.23042.19062.1 555

2.12422.09602.07072.04762.0267

2.007 51.98981.97361.95861.9446

1 .93171.83891.74801.65871 .5705

249.05'19.4548.638s5.77 44

4.52723.84153.41053.11 522.9005

2.73722.60902.50s52.42022.3487

2.28782.23542.18982.'.,4972.1141

2.0825i 2.0540' 2.0283

2.00s01 .9838

1.96431.94641.92991 .91471.900s

'l .88741.79291 .70011.60841.5173

2s0.1 019.4628.61665.7459

4.49573.80823. 3 7583.07942.8637

2.69962.57052.46632.38032.3082

2.24682.19382.14772.10712.0712

2.03912.01021.98421 .9605'1 .9390

1.91921 .901 01.8842.1.86871 .8543

1.84091.74441.64911 .55431.459'.1

251 .1419.4718.59445.7',170

4.46383.77433.34043.04282.8259

2.66092.53092.42592.33922.2664

2.20432.'.15072.10402.06292.0264

1.99381.96451.93801 .9'.1391.8920

1.87181.85331 .83611.82031 .80s5

1 .79181.6928'1 .59431.49521.3940

252.2019.4798.57205.6877

4.43143.73983.30433.00s32.7872

2.62'.112.49012.38422.29662.2229

2.160',2.10s82.05842.0'l661.9795

1.94641 .91651.88941.8648'4.8424

1 .82171.80271.7851'l .76g91 .7 537

1.73961.63731.53431.42901 .3180

253.2519.4878.54945.6581

4.39853.70473.26742.96692.747 5

2.58012.44802.34102.25242.1778

2.11412.05892.01071.96811.9302

1.8963',.86571 .83801 .8128"l .7896

'l .7 684'1 .74881.73061.71381.6981

1.683s1 .57 661.46731.35191 .2214

254.3119.4968.52645.6281

4.36503.66893.22982.92762.7067

2.53792.40452.29622.20642.1307

2.06582.00961.96041 .91681 .8780

'l .84321.8117'l .783'.,'l .7 5701.7330

1 .7110'1 .69061.67171.654'.11 .637 6

1.62231.50891.38931.25391.0000

10 12 15 20 24 30 40 60 120 ú

U(!.I{Pp.H.oo

De Maxine Merrington y Catherine M. Thompson, "Tables of Percentage Points of the lnverted Beta (F) Distribution", Biometriko 33(1943):80-84. Reproducido con permiso de Biometrika Trustees. \l\l(o

780 ApÉnorcn A

Valores crít¡cos delcoeficiente de corre-lación de Pearson r

n I a-.05 I a-.01

89

10t1

12131415

16'1718'19

20253035

40455060

708090

100

.950

.878

.81 1

.7 54

.707

.666

.632

.602

.57 6

.553

.532

.s',|.4

.497

.482

.468

.456

.444

.396

.36'l

.335

.312

.294

.279

.254

.236

.220

.207

.196

.999

.959

.917

.875

.834

.798

.765

.735

.709

.684

.661

.64'.i-

.623

.606

.590

.57 5

.561

.505

.463

.430

.402

.378

.361

.330

.305

.286

.269

.256

NOIA; Para probar Ho: p - 0 contra H¡p * 0, rechace He si el valor absoluto de res mayor que el valor crítico en la tabla.

Apéndice A 787

Valores crít¡cos para la prueba del signo

1

23456789

1011'1213',415,r,6

171819202122

.232425

*******

00001

1

1

22233344455

******00001

1

1

222334445556

*

0001

1

1

22233444555667

****0001

1

1

223334455566777

NOIAS;

1 . * indica que no es posible obtener un valor en la región crítica.2. Rechace la hipótesis nula si el número del signo menos frecuente (x) es menor que

o igual al valor en la tabla.3. Para valores de n mayores que 25, se utiliza ción normal con

(x

tfn2

782 ApÉmprcn A

Valores críticos de T para la prueba de rangoscon signo de Wilcoxon

56789

1011"42

131415'161718192021222324252627282930

***

02357

10131619232832374349556168768492

100109

**

02357

10131620242833384349566269778593

102111120

;2468

1114172125303s404652596673819098

107117127137

1

2468

1114'17212630364147546068758392

101110120130141152

NOTAS:

1. * indica que no es posible obtener un valor en la región crítica.

2. Rechace la hipótesis nula si el estadístico de prueba f es menor que o igual al valor críticoencontrado en esta tabla. No rechace la hipótesis nula si el estadístico de prueba fesmayor que el valor crítico encontrado en la tabla.

De Some Rapid Approximote Statistical Procedures, Copyright @ 1949,1964 LederleLaboratories Division of American Cyanamid Company. Reimpreso con permiso de laAmerican Cyanamid Company.

Apéndice A

NOIAS:

1. Para n > 30, utilice + : tzlll=1 donde z corresponde al nivel de significancia. Porejemplo, si a : 0.05, then z : 1.96.

2. Si el valor absoluto del estadístico de prueba r, excede al valor crítico positivo, entoncesrechace Hoi p, = 0 y concluya que existe una correlación.

Basado en datos de " Biostatisticol Analysis, 4th edition", @ '1999, de Jerrold Zar, Prentice Hall,lnc., Upper Saddle River, Nueva lersey, y "Distribution of Sums of Squares of Rank Differencesto Small Numbers with lndividuals" , The Annols of Mathematicol Statistics, vol. 9, núm. 2, conpermiso del lnst¡tute of Mathematical Stat¡stics.

783

Valores crít¡cos del coeficiente de correlación de rangosde Spearman rs

n I a:0.10 I a:0.05 I a:O.O2 I a:0.0156789

10

11'12131415

1617181920

2122232425

2627282930

.900

.829

.714

.643

.600

.564

.536

.503

.484

.464

.446

.429

.414

.40'l

.391

.380

.370

.36'.,

.35 3

.344

.337

.331

.324

.3'.17

.312

.306

.886

.786

.738

.700

.648

.61 8

.587

.560

.538

.521

.503

.485

.472

.460

.447

.435

.425

.41 5

.406

.398

.390

.382

.37 5

.368

.362

.943

.893

.933

.783

.745

.709

.678

.648

.626

.604

.582

.566

.550

.5 35

.520

.508

.496

.486

.476

.466

.457

.448

.440

.433

.425

.929

.881

.83 3

.794

.7 55

.727

.703

.679

.654

.635

.61 5

.600

.584

.570

.556

.544

.532

.521

.51 1

.501

.491

.483

.47 5

.467

784 ApÉnorcn A

Valores críticos para el número de rachas C

{ 10O

:11o(5

12

13

14

Valor de n,

7 8 9 10 11 12

111112666666222222888888233333

10 10 10 10 10 10333344

11 11 12 12 12 12334444

12 12 13 13 13 13344555

13 13 14 14 14 14445556

13 14 14 15 15 16455566

14 14 15 16 16 16555667

14 15 16 16 17 17556677

14 15 16 17 17 18566777

14 16 16 17 18 19566778

15 16 17 18 19 19567788

15 16 17 18 19 20667788

15 16 18 18 19 20667889

16 17 18 19 20 21677899

16 17 18 19 20 21678899

16 17 18 19 20 216 7 8 8 9 10

16 17 18 20 21 226 7 8 9 9 10

16 17 18 20 21 22

1

61

61

61

61

61

61

61

61

61

6262626262626262626

11116 6 6611128 8 8811 228 9 9912 2 38 9 10 1022338 9 10 1122338 10 11 1223338 10 11 1223348 10 12 1323348 10 12 132 3 448 10 12 132 3 448 10 12 132 3 4 58 10 12 142 3 4 58 10 12 143 3 4 58 10 12 143 4 4 58 10 12 143 4 4 58 10 12 '443 4 558 10 12 1434568 10 12 1434568 10 12 14

22226666223388883334

10 10 10 104444

12 12 12 125555

14 14 14 145566

15 15 15 '.16

666616 16 16 176777

17 17 18 187778

18 18 18 197888

19 19 19 208889

19 20 20 218999

20 20 21 219 9 9 10

20 21 22 229 9 10 10

21 22 22 239 10 10 11

21 22 23 2310 10 11 1122 23 23 2410 10 11 1122 23 24 2510 11 _1 1 '1223 23 24 2510 11 12 1223 24 25 25

22226666333388884444

10 10 10 104555

12 12 12 125566

14 14 14 146666

16 16 16 167777

17 17 17 177888

18 18 18 188889

19 19 20 209999

20 20 21 219 9 10 10

21 21 22 2210 10 10 1022 22 23 2310 10 11 1123 23 23 2411 11 11 '.42

23 24 24 2511 11 12 1224 25 25 2511 12 12 1325 25 26 2612 12 13 1325 26 26 2712 13 13 1326 26 27 2713 13 13 1426 27 27 28

15

16

17

18

19

20

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

NOIAS;

1. Los valores en esta tabla son los valores críticos C, suponiendo una prueba de

2. La hipótesis nula de aleatoriedad se rechaza si el número total de rachas C es

o igual al valor más alto.

De "Tables for Testing Randomness of Croupings in a Sequence of Alternatives",núm. 1. Reproducido con permiso del lnstitute of Mathematical Statistics.

dos colas con un nivel de significancia de a: 0.05.

menor que o igual al valor más bajo, o si es mayor que

The Annols of Mothemotical Statistics, vol . 14,