Tabla distribución chi-cuadrado, inversa
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k \ P | 0,01 | 0,05 | 0,10 | 0,20 | 0,25 | 0,30 | 0,40 | 0,50 | 0,60 | 0,70 | 0,75 | 0,80 | 0,90 | 0,95 | 0,99 |
1 | 0,000 | 0,004 | 0,016 | 0,064 | 0,102 | 0,148 | 0,275 | 0,455 | 0,708 | 1,074 | 1,323 | 1,642 | 2,706 | 3,841 | 6,635 |
2 | 0,020 | 0,103 | 0,211 | 0,446 | 0,575 | 0,713 | 1,022 | 1,386 | 1,833 | 2,408 | 2,773 | 3,219 | 4,605 | 5,991 | 9,210 |
3 | 0,115 | 0,352 | 0,584 | 1,005 | 1,213 | 1,424 | 1,869 | 2,366 | 2,946 | 3,665 | 4,108 | 4,642 | 6,251 | 7,815 | 11,34 |
4 | 0,297 | 0,711 | 1,064 | 1,649 | 1,923 | 2,195 | 2,753 | 3,357 | 4,045 | 4,878 | 5,385 | 5,989 | 7,779 | 9,488 | 13,28 |
5 | 0,554 | 1,145 | 1,610 | 2,343 | 2,675 | 3,000 | 3,656 | 4,351 | 5,132 | 6,064 | 6,626 | 7,289 | 9,236 | 11,07 | 15,09 |
6 | 0,872 | 1,635 | 2,204 | 3,070 | 3,455 | 3,828 | 4,570 | 5,348 | 6,211 | 7,231 | 7,841 | 8,558 | 10,64 | 12,59 | 16,81 |
7 | 1,239 | 2,167 | 2,833 | 3,822 | 4,255 | 4,671 | 5,493 | 6,346 | 7,283 | 8,383 | 9,037 | 9,803 | 12,02 | 14,07 | 18,48 |
8 | 1,647 | 2,733 | 3,490 | 4,594 | 5,071 | 5,527 | 6,423 | 7,344 | 8,351 | 9,524 | 10,22 | 11,03 | 13,36 | 15,51 | 20,09 |
9 | 2,088 | 3,325 | 4,168 | 5,380 | 5,899 | 6,393 | 7,357 | 8,343 | 9,414 | 10,66 | 11,39 | 12,24 | 14,68 | 16,92 | 21,67 |
10 | 2,558 | 3,940 | 4,865 | 6,179 | 6,737 | 7,267 | 8,295 | 9,342 | 10,47 | 11,78 | 12,55 | 13,44 | 15,99 | 18,31 | 23,21 |
11 | 3,053 | 4,575 | 5,578 | 6,989 | 7,584 | 8,148 | 9,237 | 10,34 | 11,53 | 12,90 | 13,70 | 14,63 | 17,28 | 19,68 | 24,73 |
12 | 3,571 | 5,226 | 6,304 | 7,807 | 8,438 | 9,034 | 10,18 | 11,34 | 12,58 | 14,01 | 14,85 | 15,81 | 18,55 | 21,03 | 26,22 |
13 | 4,107 | 5,892 | 7,041 | 8,634 | 9,299 | 9,926 | 11,13 | 12,34 | 13,64 | 15,12 | 15,98 | 16,98 | 19,81 | 22,36 | 27,69 |
14 | 4,660 | 6,571 | 7,790 | 9,467 | 10,17 | 10,82 | 12,08 | 13,34 | 14,69 | 16,22 | 17,12 | 18,15 | 21,06 | 23,68 | 29,14 |
15 | 5,229 | 7,261 | 8,547 | 10,31 | 11,04 | 11,72 | 13,03 | 14,34 | 15,73 | 17,32 | 18,25 | 19,31 | 22,31 | 25,00 | 30,58 |
16 | 5,812 | 7,962 | 9,312 | 11,15 | 11,91 | 12,62 | 13,98 | 15,34 | 16,78 | 18,42 | 19,37 | 20,47 | 23,54 | 26,30 | 32,00 |
17 | 6,408 | 8,672 | 10,09 | 12,00 | 12,79 | 13,53 | 14,94 | 16,34 | 17,82 | 19,51 | 20,49 | 21,61 | 24,77 | 27,59 | 33,41 |
18 | 7,015 | 9,390 | 10,86 | 12,86 | 13,68 | 14,44 | 15,89 | 17,34 | 18,87 | 20,60 | 21,60 | 22,76 | 25,99 | 28,87 | 34,81 |
19 | 7,633 | 10,12 | 11,65 | 13,72 | 14,56 | 15,35 | 16,85 | 18,34 | 19,91 | 21,69 | 22,72 | 23,90 | 27,20 | 30,14 | 36,19 |
20 | 8,260 | 10,85 | 12,44 | 14,58 | 15,45 | 16,27 | 17,81 | 19,34 | 20,95 | 22,77 | 23,83 | 25,04 | 28,41 | 31,41 | 37,57 |
21 | 8,897 | 11,59 | 13,24 | 15,44 | 16,34 | 17,18 | 18,77 | 20,34 | 21,99 | 23,86 | 24,93 | 26,17 | 29,62 | 32,67 | 38,93 |
22 | 9,542 | 12,34 | 14,04 | 16,31 | 17,24 | 18,10 | 19,73 | 21,34 | 23,03 | 24,94 | 26,04 | 27,30 | 30,81 | 33,92 | 40,29 |
23 | 10,20 | 13,09 | 14,85 | 17,19 | 18,14 | 19,02 | 20,69 | 22,34 | 24,07 | 26,02 | 27,14 | 28,43 | 32,01 | 35,17 | 41,64 |
24 | 10,86 | 13,85 | 15,66 | 18,06 | 19,04 | 19,94 | 21,65 | 23,34 | 25,11 | 27,10 | 28,24 | 29,55 | 33,20 | 36,42 | 42,98 |
25 | 11,52 | 14,61 | 16,47 | 18,94 | 19,94 | 20,87 | 22,62 | 24,34 | 26,14 | 28,17 | 29,34 | 30,68 | 34,38 | 37,65 | 44,31 |
26 | 12,20 | 15,38 | 17,29 | 19,82 | 20,84 | 21,79 | 23,58 | 25,34 | 27,18 | 29,25 | 30,43 | 31,79 | 35,56 | 38,89 | 45,64 |
27 | 12,88 | 16,15 | 18,11 | 20,70 | 21,75 | 22,72 | 24,54 | 26,34 | 28,21 | 30,32 | 31,53 | 32,91 | 36,74 | 40,11 | 46,96 |
28 | 13,56 | 16,93 | 18,94 | 21,59 | 22,66 | 23,65 | 25,51 | 27,34 | 29,25 | 31,39 | 32,62 | 34,03 | 37,92 | 41,34 | 48,28 |
29 | 14,26 | 17,71 | 19,77 | 22,48 | 23,57 | 24,58 | 26,48 | 28,34 | 30,28 | 32,46 | 33,71 | 35,14 | 39,09 | 42,56 | 49,59 |
30 | 14,95 | 18,49 | 20,60 | 23,36 | 24,48 | 25,51 | 27,44 | 29,34 | 31,32 | 33,53 | 34,80 | 36,25 | 40,26 | 43,77 | 50,89 |
31 | 15,66 | 19,28 | 21,43 | 24,26 | 25,39 | 26,44 | 28,41 | 30,34 | 32,35 | 34,60 | 35,89 | 37,36 | 41,42 | 44,99 | 52,19 |
32 | 16,36 | 20,07 | 22,27 | 25,15 | 26,30 | 27,37 | 29,38 | 31,34 | 33,38 | 35,66 | 36,97 | 38,47 | 42,58 | 46,19 | 53,49 |
33 | 17,07 | 20,87 | 23,11 | 26,04 | 27,22 | 28,31 | 30,34 | 32,34 | 34,41 | 36,73 | 38,06 | 39,57 | 43,75 | 47,40 | 54,78 |
34 | 17,79 | 21,66 | 23,95 | 26,94 | 28,14 | 29,24 | 31,31 | 33,34 | 35,44 | 37,80 | 39,14 | 40,68 | 44,90 | 48,60 | 56,06 |
35 | 18,51 | 22,47 | 24,80 | 27,84 | 29,05 | 30,18 | 32,28 | 34,34 | 36,47 | 38,86 | 40,22 | 41,78 | 46,06 | 49,80 | 57,34 |
36 | 19,23 | 23,27 | 25,64 | 28,73 | 29,97 | 31,12 | 33,25 | 35,34 | 37,50 | 39,92 | 41,30 | 42,88 | 47,21 | 51,00 | 58,62 |
37 | 19,96 | 24,07 | 26,49 | 29,64 | 30,89 | 32,05 | 34,22 | 36,34 | 38,53 | 40,98 | 42,38 | 43,98 | 48,36 | 52,19 | 59,89 |
38 | 20,69 | 24,88 | 27,34 | 30,54 | 31,81 | 32,99 | 35,19 | 37,34 | 39,56 | 42,05 | 43,46 | 45,08 | 49,51 | 53,38 | 61,16 |
39 | 21,43 | 25,70 | 28,20 | 31,44 | 32,74 | 33,93 | 36,16 | 38,34 | 40,59 | 43,11 | 44,54 | 46,17 | 50,66 | 54,57 | 62,43 |
40 | 22,16 | 26,51 | 29,05 | 32,34 | 33,66 | 34,87 | 37,13 | 39,34 | 41,62 | 44,16 | 45,62 | 47,27 | 51,81 | 55,76 | 63,69 |
41 | 22,91 | 27,33 | 29,91 | 33,25 | 34,58 | 35,81 | 38,11 | 40,34 | 42,65 | 45,22 | 46,69 | 48,36 | 52,95 | 56,94 | 64,95 |
42 | 23,65 | 28,14 | 30,77 | 34,16 | 35,51 | 36,75 | 39,08 | 41,34 | 43,68 | 46,28 | 47,77 | 49,46 | 54,09 | 58,12 | 66,21 |
43 | 24,40 | 28,96 | 31,63 | 35,07 | 36,44 | 37,70 | 40,05 | 42,34 | 44,71 | 47,34 | 48,84 | 50,55 | 55,23 | 59,30 | 67,46 |
44 | 25,15 | 29,79 | 32,49 | 35,97 | 37,36 | 38,64 | 41,02 | 43,34 | 45,73 | 48,40 | 49,91 | 51,64 | 56,37 | 60,48 | 68,71 |
45 | 25,90 | 30,61 | 33,35 | 36,88 | 38,29 | 39,58 | 42,00 | 44,34 | 46,76 | 49,45 | 50,98 | 52,73 | 57,51 | 61,66 | 69,96 |
46 | 26,66 | 31,44 | 34,22 | 37,80 | 39,22 | 40,53 | 42,97 | 45,34 | 47,79 | 50,51 | 52,06 | 53,82 | 58,64 | 62,83 | 71,20 |
47 | 27,42 | 32,27 | 35,08 | 38,71 | 40,15 | 41,47 | 43,94 | 46,34 | 48,81 | 51,56 | 53,13 | 54,91 | 59,77 | 64,00 | 72,44 |
48 | 28,18 | 33,10 | 35,95 | 39,62 | 41,08 | 42,42 | 44,92 | 47,34 | 49,84 | 52,62 | 54,20 | 55,99 | 60,91 | 65,17 | 73,68 |
49 | 28,94 | 33,93 | 36,82 | 40,53 | 42,01 | 43,37 | 45,89 | 48,33 | 50,87 | 53,67 | 55,27 | 57,08 | 62,04 | 66,34 | 74,92 |
50 | 29,71 | 34,76 | 37,69 | 41,45 | 42,94 | 44,31 | 46,86 | 49,33 | 51,89 | 54,72 | 56,33 | 58,16 | 63,17 | 67,50 | 76,15 |
51 | 30,48 | 35,60 | 38,56 | 42,36 | 43,87 | 45,26 | 47,84 | 50,33 | 52,92 | 55,78 | 57,40 | 59,25 | 64,30 | 68,67 | 77,39 |
52 | 31,25 | 36,44 | 39,43 | 43,28 | 44,81 | 46,21 | 48,81 | 51,33 | 53,94 | 56,83 | 58,47 | 60,33 | 65,42 | 69,83 | 78,62 |
53 | 32,02 | 37,28 | 40,31 | 44,20 | 45,74 | 47,16 | 49,79 | 52,33 | 54,97 | 57,88 | 59,53 | 61,41 | 66,55 | 70,99 | 79,84 |
54 | 32,79 | 38,12 | 41,18 | 45,12 | 46,68 | 48,11 | 50,76 | 53,33 | 55,99 | 58,93 | 60,60 | 62,50 | 67,67 | 72,15 | 81,07 |
55 | 33,57 | 38,96 | 42,06 | 46,04 | 47,61 | 49,06 | 51,74 | 54,33 | 57,02 | 59,98 | 61,67 | 63,58 | 68,80 | 73,31 | 82,29 |
56 | 34,35 | 39,80 | 42,94 | 46,96 | 48,55 | 50,01 | 52,71 | 55,33 | 58,04 | 61,03 | 62,73 | 64,66 | 69,92 | 74,47 | 83,51 |
57 | 35,13 | 40,65 | 43,82 | 47,88 | 49,48 | 50,96 | 53,69 | 56,33 | 59,06 | 62,08 | 63,79 | 65,74 | 71,04 | 75,62 | 84,73 |
58 | 35,91 | 41,49 | 44,70 | 48,80 | 50,42 | 51,91 | 54,67 | 57,33 | 60,09 | 63,13 | 64,86 | 66,82 | 72,16 | 76,78 | 85,95 |
59 | 36,70 | 42,34 | 45,58 | 49,72 | 51,36 | 52,86 | 55,64 | 58,33 | 61,11 | 64,18 | 65,92 | 67,89 | 73,28 | 77,93 | 87,17 |
60 | 37,48 | 43,19 | 46,46 | 50,64 | 52,29 | 53,81 | 56,62 | 59,33 | 62,13 | 65,23 | 66,98 | 68,97 | 74,40 | 79,08 | 88,38 |
70 | 45,44 | 51,74 | 55,33 | 59,90 | 61,70 | 63,35 | 66,40 | 69,33 | 72,36 | 75,69 | 77,58 | 79,71 | 85,53 | 90,53 | 100,4 |
80 | 53,54 | 60,39 | 64,28 | 69,21 | 71,14 | 72,92 | 76,19 | 79,33 | 82,57 | 86,12 | 88,13 | 90,41 | 96,58 | 101,9 | 112,3 |
90 | 61,75 | 69,13 | 73,29 | 78,56 | 80,62 | 82,51 | 85,99 | 89,33 | 92,76 | 96,52 | 98,65 | 101,1 | 107,6 | 113,1 | 124,1 |
100 | 70,06 | 77,93 | 82,36 | 87,95 | 90,13 | 92,13 | 95,81 | 99,33 | 102,9 | 106,9 | 109,1 | 111,7 | 118,5 | 124,3 | 135,8 |
110 | 78,46 | 86,79 | 91,47 | 97,36 | 99,67 | 101,8 | 105,6 | 109,3 | 113,1 | 117,3 | 119,6 | 122,2 | 129,4 | 135,5 | 147,4 |
120 | 86,92 | 95,70 | 100,6 | 106,8 | 109,2 | 111,4 | 115,5 | 119,3 | 123,3 | 127,6 | 130,1 | 132,8 | 140,2 | 146,6 | 159,0 |
130 | 95,45 | 104,7 | 109,8 | 116,3 | 118,8 | 121,1 | 125,3 | 129,3 | 133,4 | 137,9 | 140,5 | 143,3 | 151,0 | 157,6 | 170,4 |
140 | 104,0 | 113,7 | 119,0 | 125,8 | 128,4 | 130,8 | 135,1 | 139,3 | 143,6 | 148,3 | 150,9 | 153,9 | 161,8 | 168,6 | 181,8 |
150 | 112,7 | 122,7 | 128,3 | 135,3 | 138,0 | 140,5 | 145,0 | 149,3 | 153,8 | 158,6 | 161,3 | 164,3 | 172,6 | 179,6 | 193,2 |
160 | 121,3 | 131,8 | 137,5 | 144,8 | 147,6 | 150,2 | 154,9 | 159,3 | 163,9 | 168,9 | 171,7 | 174,8 | 183,3 | 190,5 | 204,5 |
170 | 130,1 | 140,8 | 146,8 | 154,3 | 157,2 | 159,9 | 164,7 | 169,3 | 174,0 | 179,2 | 182,0 | 185,3 | 194,0 | 201,4 | 215,8 |
180 | 138,8 | 150,0 | 156,2 | 163,9 | 166,9 | 169,6 | 174,6 | 179,3 | 184,2 | 189,4 | 192,4 | 195,7 | 204,7 | 212,3 | 227,1 |
190 | 147,6 | 159,1 | 165,5 | 173,4 | 176,5 | 179,3 | 184,4 | 189,3 | 194,3 | 199,7 | 202,8 | 206,2 | 215,4 | 223,2 | 238,3 |
200 | 156,4 | 168,3 | 174,8 | 183,0 | 186,2 | 189,0 | 194,3 | 199,3 | 204,4 | 210,0 | 213,1 | 216,6 | 226,0 | 234,0 | 249,4 |