χ2 (chi squared) Table

df 0.005 0.010 0.025 0.050 0.100 0.500 0.900 0.950 0.975 0.990 0.995
1 0.0000 0.0002 0.0010 0.0039 0.0158 0.4549 2.7055 3.8415 5.0239 6.6349 7.8794
2 0.0100 0.0201 0.0506 0.1026 0.2107 1.3863 4.6052 5.9915 7.3778 9.2103 10.5966
3 0.0717 0.1148 0.2158 0.3518 0.5844 2.3660 6.2514 7.8147 9.3484 11.3449 12.8382
4 0.2070 0.2971 0.4844 0.7107 1.0636 3.3567 7.7794 9.4877 11.1433 13.2767 14.8603
5 0.4117 0.5543 0.8312 1.1455 1.6103 4.3515 9.2364 11.0705 12.8325 15.0863 16.7496
6 0.6757 0.8721 1.2373 1.6354 2.2041 5.3481 10.6446 12.5916 14.4494 16.8119 18.5476
7 0.9893 1.2390 1.6899 2.1673 2.8331 6.3458 12.0170 14.0671 16.0128 18.4753 20.2777
8 1.3444 1.6465 2.1797 2.7326 3.4895 7.3441 13.3616 15.5073 17.5345 20.0902 21.9550
9 1.7349 2.0879 2.7004 3.3251 4.1682 8.3428 14.6837 16.9190 19.0228 21.6660 23.5894
10 2.1559 2.5582 3.2470 3.9403 4.8652 9.3418 15.9872 18.3070 20.4832 23.2093 25.1882
11 2.6032 3.0535 3.8157 4.5748 5.5778 10.3410 17.2750 19.6751 21.9200 24.7250 26.7568
12 3.0738 3.5706 4.4038 5.2260 6.3038 11.3403 18.5493 21.0261 23.3367 26.2170 28.2995
13 3.5650 4.1069 5.0088 5.8919 7.0415 12.3398 19.8119 22.3620 24.7356 27.6882 29.8195
14 4.0747 4.6604 5.6287 6.5706 7.7895 13.3393 21.0641 23.6848 26.1189 29.1412 31.3193
15 4.6009 5.2293 6.2621 7.2609 8.5468 14.3389 22.3071 24.9958 27.4884 30.5779 32.8013
16 5.1422 5.8122 6.9077 7.9616 9.3122 15.3385 23.5418 26.2962 28.8454 31.9999 34.2672
17 5.6972 6.4078 7.5642 8.6718 10.0852 16.3382 24.7690 27.5871 30.1910 33.4087 35.7185
18 6.2648 7.0149 8.2307 9.3905 10.8649 17.3379 25.9894 28.8693 31.5264 34.8053 37.1565
19 6.8440 7.6327 8.9065 10.1170 11.6509 18.3377 27.2036 30.1435 32.8523 36.1909 38.5823
20 7.4338 8.2604 9.5908 10.8508 12.4426 19.3374 28.4120 31.4104 34.1696 37.5662 39.9968
21 8.0337 8.8972 10.2829 11.5913 13.2396 20.3372 29.6151 32.6706 35.4789 38.9322 41.4011
22 8.6427 9.5425 10.9823 12.3380 14.0415 21.3370 30.8133 33.9244 36.7807 40.2894 42.7957
23 9.2604 10.1957 11.6886 13.0905 14.8480 22.3369 32.0069 35.1725 38.0756 41.6384 44.1813
24 9.8862 10.8564 12.4012 13.8484 15.6587 23.3367 33.1962 36.4150 39.3641 42.9798 45.5585
25 10.5197 11.5240 13.1197 14.6114 16.4734 24.3366 34.3816 37.6525 40.6465 44.3141 46.9279
26 11.1602 12.1981 13.8439 15.3792 17.2919 25.3365 35.5632 38.8851 41.9232 45.6417 48.2899
27 11.8076 12.8785 14.5734 16.1514 18.1139 26.3363 36.7412 40.1133 43.1945 46.9629 49.6449
28 12.4613 13.5647 15.3079 16.9279 18.9392 27.3362 37.9159 41.3371 44.4608 48.2782 50.9934
29 13.1211 14.2565 16.0471 17.7084 19.7677 28.3361 39.0875 42.5570 45.7223 49.5879 52.3356
30 13.7867 14.9535 16.7908 18.4927 20.5992 29.3360 40.2560 43.7730 46.9792 50.8922 53.6720
31 14.4578 15.6555 17.5387 19.2806 21.4336 30.3359 41.4217 44.9853 48.2319 52.1914 55.0027
32 15.1340 16.3622 18.2908 20.0719 22.2706 31.3359 42.5847 46.1943 49.4804 53.4858 56.3281
33 15.8153 17.0735 19.0467 20.8665 23.1102 32.3358 43.7452 47.3999 50.7251 54.7755 57.6484
34 16.5013 17.7891 19.8063 21.6643 23.9523 33.3357 44.9032 48.6024 51.9660 56.0609 58.9639
35 17.1918 18.5089 20.5694 22.4650 24.7967 34.3356 46.0588 49.8018 53.2033 57.3421 60.2748
36 17.8867 19.2327 21.3359 23.2686 25.6433 35.3356 47.2122 50.9985 54.4373 58.6192 61.5812
37 18.5858 19.9602 22.1056 24.0749 26.4921 36.3355 48.3634 52.1923 55.6680 59.8925 62.8833
38 19.2889 20.6914 22.8785 24.8839 27.3430 37.3355 49.5126 53.3835 56.8955 61.1621 64.1814
39 19.9959 21.4262 23.6543 25.6954 28.1958 38.3354 50.6598 54.5722 58.1201 62.4281 65.4756
40 20.7065 22.1643 24.4330 26.5093 29.0505 39.3353 51.8051 55.7585 59.3417 63.6907 66.7660
41 21.4208 22.9056 25.2145 27.3256 29.9071 40.3353 52.9485 56.9424 60.5606 64.9501 68.0527
42 22.1385 23.6501 25.9987 28.1440 30.7654 41.3352 54.0902 58.1240 61.7768 66.2062 69.3360
43 22.8595 24.3976 26.7854 28.9647 31.6255 42.3352 55.2302 59.3035 62.9904 67.4593 70.6159
44 23.5837 25.1480 27.5746 29.7875 32.4871 43.3352 56.3685 60.4809 64.2015 68.7095 71.8926
45 24.3110 25.9013 28.3662 30.6123 33.3504 44.3351 57.5053 61.6562 65.4102 69.9568 73.1661
46 25.0413 26.6572 29.1601 31.4390 34.2152 45.3351 58.6405 62.8296 66.6165 71.2014 74.4365
47 25.7746 27.4158 29.9562 32.2676 35.0814 46.3350 59.7743 64.0011 67.8206 72.4433 75.7041
48 26.5106 28.1770 30.7545 33.0981 35.9491 47.3350 60.9066 65.1708 69.0226 73.6826 76.9688
49 27.2493 28.9406 31.5549 33.9303 36.8182 48.3350 62.0375 66.3386 70.2224 74.9195 78.2307
50 27.9907 29.7067 32.3574 34.7643 37.6886 49.3349 63.1671 67.5048 71.4202 76.1539 79.4900
51 28.7347 30.4750 33.1618 35.5999 38.5604 50.3349 64.2954 68.6693 72.6160 77.3860 80.7467
52 29.4812 31.2457 33.9681 36.4371 39.4334 51.3349 65.4224 69.8322 73.8099 78.6158 82.0008
53 30.2300 32.0185 34.7763 37.2759 40.3076 52.3348 66.5482 70.9935 75.0019 79.8433 83.2526
54 30.9813 32.7934 35.5863 38.1162 41.1830 53.3348 67.6728 72.1532 76.1920 81.0688 84.5019
55 31.7348 33.5705 36.3981 38.9580 42.0596 54.3348 68.7962 73.3115 77.3805 82.2921 85.7490
56 32.4905 34.3495 37.2116 39.8013 42.9373 55.3348 69.9185 74.4683 78.5672 83.5134 86.9938
57 33.2484 35.1305 38.0267 40.6459 43.8161 56.3347 71.0397 75.6237 79.7522 84.7328 88.2364
58 34.0084 35.9135 38.8435 41.4920 44.6960 57.3347 72.1598 76.7778 80.9356 85.9502 89.4769
59 34.7704 36.6982 39.6619 42.3393 45.5770 58.3347 73.2789 77.9305 82.1174 87.1657 90.7153
60 35.5345 37.4849 40.4817 43.1880 46.4589 59.3347 74.3970 79.0819 83.2977 88.3794 91.9517
61 36.3005 38.2732 41.3031 44.0379 47.3418 60.3346 75.5141 80.2321 84.4764 89.5913 93.1861
62 37.0684 39.0633 42.1260 44.8890 48.2257 61.3346 76.6302 81.3810 85.6537 90.8015 94.4187
63 37.8382 39.8551 42.9503 45.7414 49.1105 62.3346 77.7454 82.5287 86.8296 92.0100 95.6493
64 38.6098 40.6486 43.7760 46.5949 49.9963 63.3346 78.8596 83.6753 88.0041 93.2169 96.8781
65 39.3831 41.4436 44.6030 47.4496 50.8829 64.3346 79.9730 84.8206 89.1771 94.4221 98.1051
66 40.1582 42.2402 45.4314 48.3054 51.7705 65.3345 81.0855 85.9649 90.3489 95.6257 99.3304
67 40.9350 43.0384 46.2610 49.1623 52.6588 66.3345 82.1971 87.1081 91.5194 96.8278 100.5540
68 41.7135 43.8380 47.0920 50.0202 53.5481 67.3345 83.3079 88.2502 92.6885 98.0284 101.7759
69 42.4935 44.6392 47.9242 50.8792 54.4381 68.3345 84.4179 89.3912 93.8565 99.2275 102.9962
70 43.2752 45.4417 48.7576 51.7393 55.3289 69.3345 85.5270 90.5312 95.0232 100.4252 104.2149
71 44.0584 46.2457 49.5922 52.6003 56.2206 70.3345 86.6354 91.6702 96.1887 101.6214 105.4320
72 44.8431 47.0510 50.4279 53.4623 57.1129 71.3344 87.7430 92.8083 97.3531 102.8163 106.6476
73 45.6293 47.8577 51.2648 54.3253 58.0061 72.3344 88.8499 93.9453 98.5163 104.0098 107.8617
74 46.4170 48.6657 52.1028 55.1892 58.9000 73.3344 89.9560 95.0815 99.6783 105.2020 109.0744
75 47.2060 49.4750 52.9419 56.0541 59.7946 74.3344 91.0615 96.2167 100.8393 106.3929 110.2856
76 47.9965 50.2856 53.7821 56.9198 60.6899 75.3344 92.1662 97.3510 101.9993 107.5825 111.4954
77 48.7884 51.0974 54.6234 57.7864 61.5858 76.3344 93.2702 98.4844 103.1581 108.7709 112.7038
78 49.5816 51.9104 55.4656 58.6539 62.4825 77.3344 94.3735 99.6169 104.3159 109.9581 113.9109
79 50.3761 52.7247 56.3089 59.5223 63.3799 78.3343 95.4762 100.7486 105.4728 111.1440 115.1166
80 51.1719 53.5401 57.1532 60.3915 64.2778 79.3343 96.5782 101.8795 106.6286 112.3288 116.3211
81 51.9690 54.3566 57.9984 61.2615 65.1765 80.3343 97.6796 103.0095 107.7834 113.5124 117.5242
82 52.7674 55.1743 58.8446 62.1323 66.0757 81.3343 98.7803 104.1387 108.9373 114.6949 118.7261
83 53.5669 55.9931 59.6918 63.0039 66.9756 82.3343 99.8805 105.2672 110.0902 115.8763 119.9268
84 54.3677 56.8130 60.5398 63.8763 67.8761 83.3343 100.9800 106.3948 111.2423 117.0565 121.1263
85 55.1696 57.6339 61.3888 64.7494 68.7772 84.3343 102.0789 107.5217 112.3934 118.2357 122.3246
86 55.9727 58.4559 62.2386 65.6233 69.6788 85.3343 103.1773 108.6479 113.5436 119.4139 123.5217
87 56.7769 59.2790 63.0894 66.4979 70.5810 86.3342 104.2750 109.7733 114.6929 120.5910 124.7177
88 57.5823 60.1030 63.9409 67.3732 71.4838 87.3342 105.3722 110.8980 115.8414 121.7671 125.9125
89 58.3888 60.9281 64.7934 68.2493 72.3872 88.3342 106.4689 112.0220 116.9891 122.9422 127.1063
90 59.1963 61.7541 65.6466 69.1260 73.2911 89.3342 107.5650 113.1453 118.1359 124.1163 128.2989
91 60.0049 62.5811 66.5007 70.0035 74.1955 90.3342 108.6606 114.2679 119.2819 125.2895 129.4905
92 60.8146 63.4090 67.3556 70.8816 75.1005 91.3342 109.7556 115.3898 120.4271 126.4617 130.6811
93 61.6253 64.2379 68.2112 71.7603 76.0060 92.3342 110.8502 116.5110 121.5715 127.6329 131.8706
94 62.4370 65.0677 69.0677 72.6398 76.9119 93.3342 111.9442 117.6317 122.7151 128.8032 133.0591
95 63.2496 65.8984 69.9249 73.5198 77.8184 94.3342 113.0377 118.7516 123.8580 129.9727 134.2465
96 64.0633 66.7299 70.7828 74.4005 78.7254 95.3342 114.1307 119.8709 125.0001 131.1412 135.4330
97 64.8780 67.5624 71.6415 75.2819 79.6329 96.3342 115.2232 120.9896 126.1414 132.3089 136.6186
98 65.6936 68.3957 72.5009 76.1638 80.5408 97.3341 116.3153 122.1077 127.2821 133.4757 137.8032
99 66.5101 69.2299 73.3611 77.0463 81.4493 98.3341 117.4069 123.2252 128.4220 134.6416 138.9868
100 67.3276 70.0649 74.2219 77.9295 82.3581 99.3341 118.4980 124.3421 129.5612 135.8067 140.1695