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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
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
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)
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
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