This document contains a table with percentiles for the chi-squared distribution across various degrees of freedom (g.l.) and significance levels. It shows the critical value needed to reject the null hypothesis for different sample sizes and confidence levels in chi-squared tests of independence and goodness of fit.

1. g.l. 0,001 0,005 0,01 0,02 0,025 0,05 0,1 0,2 0,3 0,4
1 10,82757 7,879439 6,634897 5,411895 5,023886 3,841459 2,705544 1,642375 1,074195 0,708326
2 13,81551 10,59663 9,21034 7,824046 7,377759 5,991465 4,60517 3,218876 2,407946 1,832581
3 16,26624 12,83816 11,34487 9,837409 9,348404 7,814728 6,251388 4,641628 3,66487 2,946166
4 18,46683 14,86026 13,2767 11,66784 11,14329 9,487729 7,77944 5,988617 4,878433 4,044626
5 20,51501 16,7496 15,08627 13,38822 12,8325 11,0705 9,236357 7,289276 6,06443 5,131867
6 22,45774 18,54758 16,81189 15,03321 14,44938 12,59159 10,64464 8,55806 7,231135 6,210757
7 24,32189 20,27774 18,47531 16,62242 16,01276 14,06714 12,01704 9,80325 8,383431 7,283208
8 26,12448 21,95495 20,09024 18,16823 17,53455 15,50731 13,36157 11,03009 9,524458 8,350525
9 27,87716 23,58935 21,66599 19,67902 19,02277 16,91898 14,68366 12,24215 10,65637 9,41364
10 29,5883 25,18818 23,20925 21,16077 20,48318 18,30704 15,98718 13,44196 11,78072 10,47324
11 31,26413 26,75685 24,72497 22,61794 21,92005 19,67514 17,27501 14,63142 12,89867 11,52983
12 32,90949 28,29952 26,21697 24,05396 23,33666 21,02607 18,54935 15,81199 14,0111 12,58384
13 34,52818 29,81947 27,68825 25,47151 24,7356 22,36203 19,81193 16,9848 15,11872 13,63557
14 36,12327 31,31935 29,14124 26,87276 26,11895 23,68479 21,06414 18,15077 16,2221 14,68529
15 37,6973 32,80132 30,57791 28,2595 27,48839 24,99579 22,30713 19,31066 17,32169 15,73322
16 39,25235 34,26719 31,99993 29,63318 28,84535 26,29623 23,54183 20,46508 18,41789 16,77954
17 40,79022 35,71847 33,40866 30,99505 30,19101 27,58711 24,76904 21,61456 19,51102 17,82439
18 42,3124 37,15645 34,80531 32,34616 31,52638 28,8693 25,98942 22,75955 20,60135 18,8679
19 43,8202 38,58226 36,19087 33,68743 32,85233 30,14353 27,20357 23,90042 21,68913 19,9102
20 45,31475 39,99685 37,56623 35,01963 34,16961 31,41043 28,41198 25,03751 22,77455 20,95137
21 46,79704 41,40106 38,93217 36,34345 35,47888 32,67057 29,61509 26,1711 23,85779 21,9915
22 48,26794 42,79565 40,28936 37,6595 36,78071 33,92444 30,81328 27,30145 24,93902 23,03066
23 49,72823 44,18128 41,6384 38,96831 38,07563 35,17246 32,0069 28,42879 26,01837 24,06892
24 51,1786 45,55851 42,97982 40,27036 39,36408 36,41503 33,19624 29,55332 27,09596 25,10635
25 52,61966 46,92789 44,3141 41,56607 40,64647 37,65248 34,38159 30,6752 28,17192 26,14298
26 54,05196 48,28988 45,64168 42,85583 41,92317 38,88514 35,56317 31,79461 29,24633 27,17888
27 55,47602 49,64492 46,96294 44,13999 43,19451 40,11327 36,74122 32,91169 30,31929 28,21408
28 56,89229 50,99338 48,27824 45,41885 44,46079 41,33714 37,91592 34,02657 31,39088 29,24862
29 58,30117 52,33562 49,58788 46,6927 45,72229 42,55697 39,08747 35,13936 32,46117 30,28254
30 59,70306 53,67196 50,89218 47,9618 46,97924 43,77297 40,25602 36,25019 33,53023 31,31586
35 66,61883 60,27477 57,34207 54,24383 53,20335 49,80185 46,05879 41,77796 38,85914 36,47461
40 73,40196 66,76596 63,69074 60,43613 59,34171 55,75848 51,80506 47,26854 44,16487 41,62219
45 80,07673 73,16606 69,95683 66,55527 65,41016 61,65623 57,5053 52,72881 49,45171 46,76069
50 86,66082 79,48998 76,15389 72,61325 71,4202 67,50481 63,16712 58,1638 54,72279 51,89158
55 93,16753 85,74895 82,29212 78,61914 77,38047 73,31149 68,79621 63,57724 59,98045 57,01601
60 99,60723 91,9517 88,37942 84,57995 83,29768 79,08194 74,39701 68,97207 65,22651 62,13484
65 105,9881 98,10514 94,42208 90,50124 89,17715 84,82065 79,973 74,35058 70,46239 67,24877
70 112,3169 104,2149 100,4252 96,38754 95,02318 90,53123 85,52704 79,71465 75,68928 72,35835
75 118,5991 110,2856 106,3929 102,2425 100,8393 96,21667 91,06146 85,06581 80,90812 77,46405
80 124,8392 116,3211 112,3288 108,0693 106,6286 101,8795 96,5782 90,40535 86,11971 82,56625
85 131,0412 122,3246 118,2357 113,8706 112,3934 107,5217 102,0789 95,73434 91,32473 87,66528
90 137,2084 128,2989 124,1163 119,6485 118,1359 113,1453 107,565 101,0537 96,52376 92,76142
95 143,3435 134,2465 129,9727 125,4049 123,858 118,7516 113,0377 106,3643 101,7173 97,85491
100 149,4493 140,1695 135,8067 131,1417 129,5612 124,3421 118,498 111,6667 106,9058 102,9459
120 173,6174 163,6482 158,9502 153,9182 152,2114 146,5674 140,2326 132,8063 127,6159 123,289
140 197,4508 186,8468 181,8403 176,4709 174,6478 168,613 161,827 153,8537 148,2686 143,6043
160 221,019 209,8239 204,5301 198,8464 196,9151 190,5165 183,3106 174,8283 168,8759 163,8977
180 244,3705 232,6198 227,0561 221,0772 219,0443 212,3039 204,7037 195,7434 189,4462 184,1732
200 267,5405 255,2642 249,4451 243,1869 241,0579 233,9943 226,021 216,6088 209,9854 204,4337
220 290,5558 277,7792 271,7172 265,1934 262,9729 255,6018 247,2739 237,4317 230,4982 224,6814
240 313,4369 300,1822 293,8881 287,1103 284,8025 277,1376 268,4707 258,2179 250,9881 244,9181
260 336,2003 322,487 315,9702 308,9489 306,5572 298,6106 289,6186 278,9718 271,4579 265,1451
280 358,8595 344,7047 337,9735 330,7179 328,2455 320,0278 310,723 299,6972 291,9099 285,3634
300 381,4252 366,8444 359,9064 352,4247 349,8745 341,3951 331,7885 320,3971 312,346 305,5741
320 403,9069 388,914 381,7759 374,0754 371,4499 362,7175 352,819 341,074 332,7678 325,7779
340 426,3121 410,9197 403,5877 395,6752 392,9768 383,9991 373,8177 361,7299 353,1765 345,9753
360 448,6477 432,8673 425,347 417,2286 414,4593 405,2435 394,7874 382,3668 373,5734 366,1671
380 470,9192 454,7615 447,058 438,7393 435,9011 426,4537 415,7305 402,9862 393,9593 386,3535
400 493,1318 476,6064 468,7245 460,2108 457,3055 447,6325 436,649 423,5895 414,3353 406,5352
PERCENTILES DISTRIBUCION JI-CUADRADO

2. g.l. 0,5 0,6 0,7 0,8 0,900 0,950 0,975 0,980 0,990 0,995 0,999
1 0,454936 0,274996 0,148472 0,064185 0,015791 0,003932 0,000982 0,000628 0,000157 3,92704E-05 1,57E-06
2 1,386294 1,021651 0,71335 0,446287 0,210721 0,102587 0,050636 0,040405 0,020101 0,010025084 0,002001
3 2,365974 1,869168 1,423652 1,005174 0,584374 0,351846 0,215795 0,184832 0,114832 0,071721775 0,024298
4 3,356694 2,752843 2,194698 1,648777 1,063623 0,710723 0,484419 0,429398 0,297109 0,206989093 0,090804
5 4,35146 3,6555 2,999908 2,342534 1,610308 1,145476 0,831212 0,751889 0,554298 0,411741904 0,210213
6 5,348121 4,570154 3,827552 3,070088 2,204131 1,635383 1,237344 1,134419 0,87209 0,675726778 0,381067
7 6,345811 5,493235 4,671331 3,822322 2,833107 2,16735 1,689869 1,564293 1,239042 0,989255685 0,598494
8 7,344122 6,422646 5,527422 4,593574 3,489539 2,732637 2,179731 2,032477 1,646497 1,344413088 0,857105
9 8,342833 7,357035 6,393306 5,380053 4,168159 3,325113 2,70039 2,532379 2,087901 1,734932909 1,15195
10 9,341818 8,295472 7,267218 6,179079 4,865182 3,940299 3,246973 3,059051 2,558212 2,155856482 1,478743
11 10,341 9,237286 8,147868 6,988674 5,577785 4,574813 3,815748 3,608687 3,053484 2,603221895 1,833853
12 11,34032 10,18197 9,034277 7,807328 6,303796 5,226029 4,403789 4,178287 3,570569 3,073823653 2,214209
13 12,33976 11,12914 9,925683 8,633861 7,041505 5,891864 5,008751 4,765445 4,106915 3,565034584 2,617218
14 13,33927 12,07848 10,82148 9,467328 7,789534 6,570631 5,628726 5,368197 4,660425 4,074674969 3,040673
15 14,33886 13,02975 11,72117 10,30696 8,546756 7,260944 6,262138 5,984916 5,229349 4,600915599 3,482684
16 15,3385 13,98274 12,62435 11,15212 9,312236 7,961646 6,907664 6,614237 5,812213 5,142205451 3,941628
17 16,33818 14,93727 13,53068 12,00227 10,08519 8,67176 7,564186 7,255003 6,40776 5,697217119 4,416093
18 17,3379 15,89321 14,43986 12,85695 10,86494 9,390455 8,230746 7,906221 7,014911 6,264804719 4,904849
19 18,33765 16,85043 15,35166 13,71579 11,65091 10,11701 8,906517 8,567035 7,63273 6,843971456 5,406816
20 19,33743 17,80883 16,26586 14,57844 12,44261 10,85081 9,590778 9,236699 8,260398 7,433844283 5,921041
21 20,33723 18,76831 17,18227 15,44461 13,2396 11,59131 10,2829 9,914556 8,897198 8,033653456 6,446677
22 21,33705 19,72879 18,10072 16,31404 14,04149 12,33801 10,98232 10,60003 9,542492 8,642716463 6,982968
23 22,33688 20,6902 19,02109 17,18651 14,84796 13,09051 11,68855 11,2926 10,19572 9,260424795 7,52924
24 23,33673 21,65249 19,94323 18,0618 15,65868 13,84843 12,40115 11,99182 10,85636 9,886233535 8,084882
25 24,33659 22,61558 20,86703 18,93975 16,47341 14,61141 13,11972 12,69727 11,52398 10,51965217 8,649344
26 25,33646 23,57943 21,7924 19,82019 17,29189 15,37916 13,84391 13,40858 12,19815 11,16023749 9,222127
27 26,33634 24,54401 22,71924 20,70298 18,1139 16,1514 14,57338 14,12542 12,8785 11,80758738 9,802777
28 27,33623 25,50925 23,64746 21,58797 18,93924 16,92788 15,30786 14,84748 13,56471 12,46133599 10,39088
29 28,33613 26,47514 24,57699 22,47505 19,76774 17,70837 16,04707 15,57448 14,25645 13,12114895 10,98605
30 29,33603 27,44162 25,50776 23,36412 20,59923 18,49266 16,79077 16,30617 14,95346 13,78671996 11,58795
35 34,33564 32,28212 30,17817 27,83587 24,79666 22,46502 20,56938 20,02743 18,50893 17,19182048 14,68785
40 39,33535 37,13396 34,87194 32,34495 29,05052 26,5093 24,43304 23,83757 22,16426 20,70653548 17,91643
45 44,33512 41,99503 39,5847 36,88441 33,35038 30,61226 28,36615 27,72034 25,90127 24,31101434 21,25074
50 49,33494 46,86378 44,31331 41,44921 37,68865 34,76425 32,35736 31,66386 29,70668 27,99074904 24,67391
55 54,33479 51,73906 49,05539 46,03559 42,05962 38,95803 36,39811 35,65921 33,57048 31,73475764 28,17311
60 59,33467 56,62 53,80913 50,64062 46,45889 43,18796 40,48175 39,69942 37,48485 35,53449152 31,73834
65 64,33456 61,50587 58,57306 55,26198 50,88294 47,44958 44,60299 43,779 41,44361 39,3831412 35,3616
70 69,33448 66,39612 63,34603 59,89781 55,32894 51,73928 48,75757 47,89345 45,44172 43,27517986 39,03638
75 74,3344 71,29027 68,12705 64,54656 59,79456 56,05407 52,94194 52,03909 49,47503 47,20604798 42,7573
80 79,33433 76,18793 72,91534 69,20694 64,27785 60,39148 57,15317 56,21285 53,54008 51,17193241 46,51988
85 84,33427 81,08879 77,71022 73,87787 68,77716 64,7494 61,38878 60,41211 57,63393 55,16960469 50,32028
90 89,33422 85,99255 82,5111 78,55843 73,29109 69,12603 65,64662 64,63466 61,75408 59,19630494 54,15524
95 94,33417 90,89897 87,31749 83,24782 77,81844 73,51984 69,92487 68,87857 65,89836 63,2496491 58,02195
100 99,33414 95,80785 92,12895 87,94534 82,35814 77,92947 74,22193 73,14218 70,0649 67,32756375 61,91794
120 119,334 115,4645 111,4186 106,8056 100,6236 95,70464 91,57264 90,36674 86,92328 83,85157283 77,75514
140 139,3339 135,1491 130,7657 125,7581 119,0293 113,6593 109,1369 107,8149 104,0344 100,6548424 93,92565
160 159,3338 154,8555 150,1583 144,7834 137,5457 131,7561 126,8701 125,44 121,3456 117,6792626 110,3603
180 179,3338 174,5799 169,5879 163,8682 156,1526 149,9688 144,7413 143,2096 138,8204 134,8844509 127,0111
200 199,3337 194,3193 189,0486 183,0028 174,8353 168,2786 162,728 161,1003 156,432 152,2409932 143,8428
220 219,3337 214,0715 208,5358 202,1798 193,5825 186,6711 180,8132 179,0941 174,1604 169,7266818 160,829
240 239,3337 233,8348 228,0458 221,3936 212,3856 205,1354 198,9839 197,1774 191,9899 187,324257 177,9491
260 259,3337 253,6078 247,576 240,6396 231,2378 223,6625 217,2293 215,3391 209,9082 205,0199951 195,1867
280 279,3336 273,3894 267,1239 259,9142 250,1334 242,2454 235,5411 233,5703 227,9051 222,802765 212,5285
300 299,3336 293,1787 286,6878 279,2143 269,0679 260,8781 253,9123 251,8637 245,9725 240,6633915 229,9634
320 319,3336 312,9749 306,266 298,5375 288,0374 279,5558 272,337 270,2131 264,1033 258,5942104 247,4825
340 339,3336 332,7774 325,8572 317,8815 307,0387 298,2742 290,8102 288,6134 282,2916 276,5887344 265,0778
360 359,3336 352,5856 345,4603 337,2446 326,069 317,0299 309,3278 307,0601 300,5325 294,6414191 282,7428
380 379,3336 372,3991 365,0744 356,6251 345,1259 335,8197 327,886 325,5494 318,8217 312,7474803 300,4717
400 399,3336 392,2175 384,6984 376,0218 364,2074 354,641 346,4818 344,0781 337,1553 330,9027538 318,2596
PERCENTILES DISTRIBUCION JI-CUADRADO