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Tablas - Triola - 10 Edicion
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Transcript of Tablas - Triola - 10 Edicion
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,