Distribución
2
con
n
grados de libertad
F
(
x
) =
Z
x
0
1
2
n
2
n
2
t
n
2
1
exp
t
2
dt
Para grados de libertad superiores a 100 se puede utilizar la aproximación
P
fp
2
X
p
2
n
1
2
A
g
P
f
Z
2
A
g
;
8
A
R
siendo
Z
N
(0
;
1)
.
Probabilidades
n
0.0005 0.001 0.0025 0.005 0.01 0.025 0.05 0.075 0.1 0.2 0.3 0.4
1 3.92
10
7
1.57
10
6
9.81
10
6
3.92
10
5
1.57
10
5
9.82
10
4
3.93
10
3
8.86
10
3
0.01579 0.06418 0.14847 0.27499
2 0.00100 0.00200 0.00500 0.01002 0.02010 0.05063 0.10258 0.15592 0.21072 0.44628 0.71335 1.02165
3 0.01527 0.02429 0.04494 0.07172 0.11483 0.21579 0.35184 0.47199 0.58437 1.00517 1.42365 1.86917
4 0.06392 0.09080 0.14486 0.20698 0.29710 0.48442 0.71072 0.89693 1.06362 1.64878 2.19470 2.75284
5 0.15813 0.21021 0.30748 0.41174 0.55429 0.83121 1.14548 1.39371 1.61031 2.34253 2.99991 3.65550
6 0.29940 0.38106 0.52656 0.67572 0.87209 1.23734 1.63538 1.94149 2.20413 3.07009 3.82755 4.57015
7 0.48487 0.59849 0.79446 0.98925 1.23904 1.68987 2.16735 2.52766 2.83311 3.82232 4.67133 5.49323
8 0.71037 0.85710 1.10426 1.34441 1.64650 2.17973 2.73264 3.14397 3.48954 4.59357 5.52742 6.42265
9 0.97169 1.15195 1.45014 1.73493 2.08790 2.70039 3.32511 3.78475 4.16816 5.38005 6.39331 7.35703
10 1.26498 1.47874 1.82740 2.15586 2.55821 3.24697 3.94030 4.44587 4.86518 6.17908 7.26722 8.29547
11 1.58685 1.83385 2.23214 2.60322 3.05348 3.81575 4.57481 5.12425 5.57778 6.98867 8.14787 9.23729
12 1.93438 2.21421 2.66118 3.07382 3.57057 4.40379 5.22603 5.81751 6.30380 7.80733 9.03428 10.1820
13 2.30506 2.61722 3.11188 3.56503 4.10692 5.00875 5.89186 6.52377 7.04150 8.63386 9.92568 11.1291
14 2.69673 3.04067 3.58202 4.07467 4.66043 5.62873 6.57063 7.24151 7.78953 9.46733 10.8215 12.0785
15 3.10752 3.48268 4.06973 4.60092 5.22935 6.26214 7.26094 7.96949 8.54676 10.3070 11.7212 13.0297
16 3.53581 3.94163 4.57341 5.14221 5.81221 6.90766 7.96165 8.70667 9.31224 11.1521 12.6243 13.9827
17 3.98018 4.41609 5.09167 5.69722 6.40776 7.56419 8.67176 9.45217 10.0852 12.0023 13.5307 14.9373
18 4.43939 4.90485 5.62334 6.26480 7.01491 8.23075 9.39046 10.2053 10.8649 12.8570 14.4399 15.8932
19 4.91234 5.40682 6.16736 6.84397 7.63273 8.90652 10.1170 10.9653 11.6509 13.7158 15.3517 16.8504
20 5.39807 5.92104 6.72282 7.43384 8.26040 9.59078 10.8508 11.7317 12.4426 14.5784 16.2659 17.8088
21 5.89570 6.44668 7.28892 8.03365 8.89720 10.2829 11.5913 12.5041 13.2396 15.4446 17.1823 18.7683
22 6.40447 6.98297 7.86493 8.64272 9.54249 10.9823 12.3380 13.2819 14.0415 16.3140 18.1007 19.7288
23 6.92368 7.52924 8.45021 9.26042 10.1957 11.6886 13.0905 14.0648 14.8480 17.1865 19.0211 20.6902
24 7.45269 8.08488 9.04418 9.88623 10.8564 12.4012 13.8484 14.8525 15.6587 18.0618 19.9432 21.6525
25 7.99096 8.64934 9.64633 10.5197 11.5240 13.1197 14.6114 15.6447 16.4734 18.9398 20.8670 22.6156
26 8.53795 9.22213 10.2562 11.1602 12.1981 13.8439 15.3792 16.4410 17.2919 19.8202 21.7924 23.5794
27 9.09320 9.80278 10.8733 11.8076 12.8785 14.5734 16.1514 17.2414 18.1139 20.7030 22.7192 24.5440
28 9.65627 10.3909 11.4973 12.4613 13.5647 15.3079 16.9279 18.0454 18.9392 21.5880 23.6475 25.5093
29 10.2268 10.9861 12.1279 13.1211 14.2565 16.0471 17.7084 18.8530 19.7677 22.4751 24.5770 26.4751
30 10.8044 11.5880 12.7646 13.7867 14.9535 16.7908 18.4927 19.6639 20.5992 23.3641 25.5078 27.4416
40 16.9062 17.9164 19.4171 20.7065 22.1643 24.4330 26.5093 27.9258 29.0505 32.3450 34.8719 37.1340
50 23.4610 24.6739 26.4636 27.9907 29.7067 32.3574 34.7643 36.3971 37.6886 41.4492 44.3133 46.8638
60 30.3405 31.7383 33.7911 35.5345 37.4849 40.4817 43.1880 45.0165 46.4589 50.6406 53.8091 56.6200
70 37.4674 39.0364 41.3323 43.2752 45.4417 48.7576 51.7393 53.7478 55.3289 59.8978 63.3460 66.3961
80 44.7910 46.5199 49.0429 51.1719 53.5401 57.1532 60.3915 62.5676 64.2778 69.2069 72.9153 76.1879
90 52.2758 54.1552 56.8921 59.1963 61.7541 65.6466 69.1260 71.4596 73.2911 78.5584 82.5111 85.9925
100 59.8957 61.9179 64.8574 67.3276 70.0649 74.2219 77.9295 80.4119 82.3581 87.9453 92.1289 95.8078
1
