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Chi square
- 1. df 0.995 0.99 0.975 0.95 0.9 df 0.995 0.99 0.975 0.95 0.9 df 0.995 0.99 0.975 0.95
1 0.0000 0.00016 0.000982 0.00393 0.0158 71 44.05838 46.24568 49.5922 52.60032 56.22056 141 101.5012 104.89558 110.01982 114.561
2 0.0100 0.0201 0.050636 0.10259 0.2107 72 44.8431 47.05103 50.4279 53.46233 57.11295 142 102.3481 105.75723 110.90318 115.463
3 0.0717 0.11483 0.215795 0.35185 0.5844 73 45.6293 47.85772 51.2648 54.32531 58.00609 143 103.1956 106.61938 111.78695 116.366
4 0.2070 0.29711 0.484419 0.71072 1.0636 74 46.41696 48.66573 52.1028 55.18923 58.89996 144 104.0435 107.482 112.67113 117.268
5 0.4117 0.5543 0.831212 1.14548 1.6103 75 47.20605 49.47503 52.9419 56.05407 59.79456 145 104.8920 108.3451 113.55571 118.171
6 0.6757 0.87209 1.237344 1.63538 2.2041 76 47.99653 50.2856 53.7821 56.91982 60.68986 146 105.7411 109.20867 114.44069 119.075
7 0.9893 1.23904 1.689869 2.16735 2.8331 77 48.78839 51.09742 54.6234 57.78645 61.58585 147 106.5906 110.07271 115.32607 119.979
8 1.3444 1.6465 2.179731 2.73264 3.4895 78 49.58159 51.91045 55.4656 58.65395 62.48252 148 107.4406 110.93721 116.21183 120.883
9 1.7349 2.0879 2.700389 3.32511 4.1682 79 50.37612 52.72468 56.3089 59.52229 63.37986 149 108.2912 111.80217 117.09798 121.787
10 2.1559 2.55821 3.246973 3.9403 4.8652 80 51.17193 53.54008 57.1532 60.39148 64.27785 150 109.1422 112.66758 117.98452 122.692
11 2.6032 3.05348 3.815748 4.57481 5.5778 81 51.96902 54.35663 57.9984 61.26148 65.17647 151 109.9938 113.53344 118.87143 123.597
12 3.0738 3.57057 4.403789 5.22603 6.3038 82 52.76735 55.17431 58.8446 62.13229 66.07573 152 110.8458 114.39974 119.75871 124.502
13 3.5650 4.10692 5.008751 5.89186 7.0415 83 53.56691 55.9931 59.6918 63.00389 66.9756 153 111.6984 115.26649 120.64637 125.408
14 4.0747 4.66043 5.628726 6.57063 7.7895 84 54.36767 56.81298 60.5398 63.87626 67.87608 154 112.5514 116.13366 121.53439 126.314
15 4.6009 5.22935 6.262138 7.26094 8.5468 85 55.1696 57.63393 61.3888 64.7494 68.77716 155 113.4049 117.00127 122.42278 127.22
16 5.1422 5.81221 6.907664 7.96165 9.3122 86 55.9727 58.45593 62.2386 65.62328 69.67882 156 114.2588 117.86931 123.31153 128.127
17 5.6972 6.40776 7.564186 8.67176 10.085 87 56.77694 59.27896 63.0894 66.4979 70.58105 157 115.1132 118.73776 124.20063 129.034
18 6.2648 7.01491 8.230746 9.39046 10.865 88 57.5823 60.10301 63.9409 67.37324 71.48384 158 115.9681 119.60664 125.09009 129.941
19 6.8440 7.63273 8.906516 10.117 11.651 89 58.38876 60.92805 64.7934 68.24928 72.3872 159 116.8235 120.47593 125.9799 130.848
20 7.4338 8.2604 9.590777 10.8508 12.443 90 59.1963 61.75408 65.6466 69.12603 73.29109 160 117.6793 121.34563 126.87005 131.756
21 8.0337 8.8972 10.2829 11.5913 13.24 91 60.00491 62.58107 66.5007 70.00346 74.19552 161 118.5355 122.21574 127.76055 132.664
22 8.6427 9.54249 10.98232 12.338 14.041 92 60.81457 63.40901 67.3556 70.88157 75.10048 162 119.3922 123.08625 128.65138 133.572
23 9.2604 10.1957 11.68855 13.0905 14.848 93 61.62525 64.23788 68.2112 71.76034 76.00596 163 120.2493 123.95716 129.54256 134.481
24 9.8862 10.8564 12.40115 13.8484 15.659 94 62.43695 65.06767 69.0677 72.63977 76.91195 164 121.1069 124.82846 130.43407 135.39
25 10.5197 11.524 13.11972 14.6114 16.473 95 63.24965 65.89836 69.9249 73.51984 77.81844 165 121.9649 125.70016 131.32591 136.299
26 11.1602 12.1981 13.8439 15.3792 17.292 96 64.06333 66.72994 70.7828 74.40054 78.72542 166 122.8233 126.57225 132.21807 137.209
27 11.8076 12.8785 14.57338 16.1514 18.114 97 64.87797 67.5624 71.6415 75.28186 79.63289 167 123.6822 127.44472 133.11057 138.118
28 12.4613 13.5647 15.30786 16.9279 18.939 98 65.69357 68.39572 72.5009 76.16379 80.54084 168 124.5415 128.31757 134.00338 139.028
29 13.1211 14.2565 16.04707 17.7084 19.768 99 66.51011 69.22989 73.3611 77.04633 81.44925 169 125.4012 129.1908 134.89651 139.939
30 13.7867 14.9535 16.79077 18.4927 20.599 100 67.32756 70.0649 74.2219 77.92947 82.35814 170 126.2613 130.0644 135.78996 140.849
31 14.4578 15.6555 17.53874 19.2806 21.434 101 68.14593 70.90072 75.0835 78.81319 83.26748 171 127.1218 130.93838 136.68372 141.76
32 15.1340 16.3622 18.29076 20.0719 22.271 102 68.96519 71.73736 75.9457 79.69748 84.17727 172 127.9828 131.81272 137.5778 142.671
33 15.8153 17.0735 19.04666 20.8665 23.11 103 69.78534 72.5748 76.8086 80.58234 85.0875 173 128.8441 132.68743 138.47218 143.582
34 16.5013 17.7891 19.80625 21.6643 23.952 104 70.60636 73.41303 77.6722 81.46777 85.99817 174 129.7058 133.56251 139.36687 144.494
35 17.1918 18.5089 20.56938 22.465 24.797 105 71.42823 74.25203 78.5364 82.35374 86.90928 175 130.5680 134.43794 140.26186 145.406
36 17.8867 19.2327 21.33588 23.2686 25.643 106 72.25095 75.0918 79.4013 83.24026 87.8208 176 131.4305 135.31372 141.15715 146.318
37 18.5858 19.9602 22.10563 24.0749 26.492 107 73.0745 75.93232 80.2668 84.12732 88.73275 177 132.2934 136.18986 142.05273 147.23
38 19.2889 20.6914 22.87848 24.8839 27.343 108 73.89888 76.77359 81.1329 85.0149 89.64511 178 133.1567 137.06635 142.94862 148.143
39 19.9959 21.4262 23.65432 25.6954 28.196 109 74.72406 77.61559 81.9997 85.90301 90.55787 179 134.0204 137.94318 143.84479 149.056
40 20.7065 22.1643 24.43304 26.5093 29.051 110 75.55005 78.45831 82.8671 86.79163 91.47104 180 134.8844 138.82036 144.74126 149.969
41 21.4208 22.9056 25.21452 27.3256 29.907 111 76.37682 79.30175 83.735 87.68076 92.3846 181 135.7489 139.69788 145.63801 150.882
42 22.1385 23.6501 25.99866 28.144 30.765 112 77.20437 80.14589 84.6036 88.57038 93.29855 182 136.6137 140.57573 146.53505 151.796
43 22.8595 24.3976 26.78537 28.9647 31.625 113 78.03269 80.99073 85.4728 89.4605 94.21289 183 137.4789 141.45393 147.43237 152.709
44 23.5837 25.148 27.57457 29.7875 32.487 114 78.86176 81.83625 86.3425 90.35111 95.12761 184 138.3444 142.33245 148.32997 153.623
45 24.3110 25.9013 28.36615 30.6123 33.35 115 79.69158 82.68245 87.2128 91.2422 96.04271 185 139.2104 143.21131 149.22785 154.538
46 25.0413 26.6572 29.16005 31.439 34.215 116 80.52214 83.52931 88.0837 92.13376 96.95817 186 140.0766 144.09049 150.12601 155.452
47 25.7746 27.4158 29.9562 32.2676 35.081 117 81.35343 84.37684 88.9551 93.0258 97.874 187 140.9433 144.96999 151.02444 156.367
48 26.5106 28.177 30.75451 33.0981 35.949 118 82.18544 85.22501 89.8271 93.91829 98.79019 188 141.8103 145.84982 151.92314 157.282
49 27.2493 28.9406 31.55492 33.9303 36.818 119 83.01816 86.07383 90.6996 94.81124 99.70674 189 142.6776 146.72997 152.82211 158.197
50 27.9907 29.7067 32.35736 34.7643 37.689 120 83.85157 86.92328 91.5726 95.70464 100.6236 190 143.5453 147.61043 153.72135 159.113
51 28.7347 30.475 33.16179 35.5999 38.56 121 84.68568 87.77336 92.4462 96.59848 101.5409 191 144.4134 148.49121 154.62085 160.028
52 29.4812 31.2457 33.96813 36.4371 39.433 122 85.52048 88.62406 93.3203 97.49277 102.4585 192 145.2818 149.3723 155.52062 160.944
53 30.2300 32.0185 34.77633 37.2759 40.308 123 86.35594 89.47536 94.195 98.38749 103.3764 193 146.1505 150.2537 156.42064 161.86
54 30.9813 32.7934 35.58634 38.1162 41.183 124 87.19208 90.32728 95.0701 99.28263 104.2947 194 147.0196 151.13541 157.32093 162.776
55 31.7348 33.5705 36.39811 38.958 42.06 125 88.02887 91.17978 95.9457 100.1782 105.2132 195 147.8890 152.01742 158.22148 163.693
56 32.4905 34.3495 37.21159 39.8013 42.937 126 88.86632 92.03288 96.8219 101.0742 106.1322 196 148.7587 152.89973 159.12227 164.61
57 33.2484 35.1305 38.02674 40.6459 43.816 127 89.70441 92.88656 97.6985 101.9706 107.0514 197 149.6288 153.78235 160.02333 165.527
58 34.0084 35.9135 38.84351 41.492 44.696 128 90.54313 93.74081 98.5756 102.8674 107.971 198 150.4992 154.66526 160.92463 166.444
59 34.7704 36.6982 39.66186 42.3393 45.577 129 91.38248 94.59564 99.4532 103.7646 108.8908 199 151.3699 155.54847 161.82618 167.361
60 35.5345 37.4849 40.48175 43.188 46.459 130 92.22246 95.45102 100.331 104.6622 109.811 200 152.2410 156.43197 162.72798 168.279
61 36.3005 38.2732 41.30314 44.0379 47.342 131 93.06305 96.30696 101.21 105.5602 110.7315 201 153.1124 157.31576 163.63003 169.196
62 37.0684 39.0633 42.12599 44.889 48.226 132 93.90424 97.16345 102.089 106.4586 111.6523 202 153.9841 158.19984 164.53232 170.114
63 37.8382 39.8551 42.95027 45.7414 49.111 133 94.74603 98.02048 102.968 107.3574 112.5734 203 154.8561 159.0842 165.43485 171.032
64 38.6098 40.6486 43.77595 46.5949 49.996 134 95.58842 98.87805 103.848 108.2566 113.4948 204 155.7284 159.96886 166.33762 171.951
65 39.3831 41.4436 44.60299 47.4496 50.883 135 96.4314 99.73615 104.729 109.1561 114.4165 205 156.6011 160.85379 167.24063 172.869
66 40.1582 42.2402 45.43136 48.3054 51.77 136 97.27495 100.5948 105.609 110.056 115.3385 206 157.4740 161.739 168.14388 173.788
67 40.9350 43.0384 46.26103 49.1623 52.659 137 98.11908 101.4539 106.491 110.9563 116.2608 207 158.3473 162.6245 169.04736 174.707
68 41.7135 43.838 47.09198 50.0202 53.548 138 98.96377 102.3136 107.372 111.857 117.1833 208 159.2208 163.51027 169.95107 175.626
69 42.4935 44.6392 47.92416 50.8792 54.438 139 99.80903 103.1737 108.254 112.758 118.1061 209 160.0947 164.39631 170.85502 176.546
70 43.2752 45.4417 48.75756 51.7393 55.329 140 100.6548 104.0344 109.137 113.6593 119.0293 210 160.9689 165.28262 171.75919 177.465
Chi Square Table (Left tail Values)
