//////////////////////////////////////////////////////////////// // // http://www.planetquantum.com/Tables/ChiSquare-B.txt // //////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////// // // Upper Tail Critical Values of Chi Square Distribution // One sided test Prob(chi^2<=c) == p // // Reference: NIST/SEMATECH e-Handbook of Statistical Methods // http://www.itl.nist.gov/div898/handbook/eda/section3/eda3674.htm //////////////////////////////////////////////////////////////// nu\p .9 .95 .975 .99 .995 .9975 .999 .9995 .99975 .9999 1 2.7055435 3.8414588 5.0238862 6.6348966 7.8794386 9.1405935 10.827566 12.115665 13.412148 15.136705 2 4.6051702 5.9914645 7.3777589 9.2103404 10.596635 11.982929 13.815511 15.201805 16.588099 18.420681 3 6.2513886 7.8147279 9.3484036 11.344867 12.838156 14.320347 16.266236 17.729996 19.187885 21.107513 4 7.7794403 9.4877290 11.143287 13.276704 14.860259 16.423936 18.466827 19.997355 21.517275 23.512742 5 9.2363569 11.070498 12.832502 15.086272 16.749602 18.385613 20.515006 22.105327 23.680983 25.744832 6 10.644641 12.591587 14.449375 16.811894 18.547584 20.249402 22.457744 24.102799 25.729594 27.856341 7 12.017037 14.067140 16.012764 18.475307 20.277740 22.040391 24.321886 26.017768 27.692135 29.877504 8 13.361566 15.507313 17.534546 20.090235 21.954955 23.774474 26.124482 27.868046 29.587105 31.827628 9 14.683657 16.918978 19.022768 21.665994 23.589351 25.462479 27.877165 29.665808 31.427163 33.719948 10 15.987179 18.307038 20.483177 23.209251 25.188180 27.112171 29.588298 31.419813 33.221430 35.564014 11 17.275009 19.675138 21.920049 24.724970 26.756849 28.729350 31.264134 33.136615 34.976737 37.366986 12 18.549348 21.026070 23.336664 26.216967 28.299519 30.318479 32.909490 34.821275 36.698362 39.134404 13 19.811929 22.362032 24.735605 27.688250 29.819471 31.883085 34.528179 36.477794 38.390482 40.870655 14 21.064144 23.684791 26.118948 29.141238 31.319350 33.426011 36.123274 38.109404 40.056473 42.579289 15 22.307130 24.995790 27.488393 30.577914 32.801321 34.949585 37.697298 39.718760 41.699110 44.263225 16 23.541829 26.296228 28.845351 31.999927 34.267187 36.455749 39.252355 41.308074 43.320706 45.924899 17 24.769035 27.587112 30.191009 33.408664 35.718466 37.946139 40.790217 42.879213 44.923215 47.566370 18 25.989423 28.869299 31.526378 34.805306 37.156451 39.422147 42.312396 44.433771 46.508306 49.189394 19 27.203571 30.143527 32.852327 36.190869 38.582257 40.884974 43.820196 45.973120 48.077414 50.795490 20 28.411981 31.410433 34.169607 37.566235 39.996846 42.335660 45.314747 47.498452 49.631790 52.385973 21 29.615089 32.670573 35.478876 38.932173 41.401065 43.775117 46.797038 49.010812 51.172528 53.962000 22 30.813282 33.924438 36.780712 40.289360 42.795655 45.204146 48.267942 50.511119 52.700591 55.524589 23 32.006900 35.172462 38.075627 41.638398 44.181275 46.623458 49.728232 52.000189 54.216836 57.074643 24 33.196244 36.415029 39.364077 42.979820 45.558512 48.033687 51.178598 53.478751 55.722025 58.612970 25 34.381587 37.652484 40.646469 44.314105 46.927890 49.435400 52.619656 54.947455 57.216843 60.140292 26 35.563171 38.885139 41.923170 45.641683 48.289882 50.829106 54.051962 56.406890 58.701907 61.657261 27 36.741217 40.113272 43.194511 46.962942 49.644915 52.215269 55.476020 57.857586 60.177772 63.164467 28 37.915923 41.337138 44.460792 48.278236 50.993376 53.594306 56.892285 59.300025 61.644946 64.662446 29 39.087470 42.556968 45.722286 49.587884 52.335618 54.966599 58.301173 60.734647 63.103890 66.151685 30 40.256024 43.772972 46.979242 50.892181 53.671962 56.332496 59.703064 62.161853 64.555025 67.632630 31 41.421736 44.985343 48.231890 52.191395 55.002704 57.692316 61.098306 63.582011 65.998738 69.105692 32 42.584745 46.194260 49.480438 53.485772 56.328115 59.046352 62.487219 64.995459 67.435386 70.571248 33 43.745180 47.399884 50.725080 54.775540 57.648445 60.394877 63.870099 66.402511 68.865295 72.029644 34 44.903158 48.602367 51.965995 56.060909 58.963926 61.738139 65.247217 67.803455 70.288770 73.481203 35 46.058788 49.801850 53.203349 57.342073 60.274771 63.076371 66.618829 69.198559 71.706093 74.926222 36 47.212174 50.998460 54.437294 58.619215 61.581179 64.409788 67.985168 70.588070 73.117523 76.364979 37 48.363408 52.192320 55.667973 59.892500 62.883335 65.738589 69.346452 71.972221 74.523306 77.797732 38 49.512580 53.383541 56.895521 61.162087 64.181412 67.062963 70.702887 73.351228 75.923667 79.224721 39 50.659770 54.572228 58.120060 62.428121 65.475571 68.383082 72.054663 74.725292 77.318819 80.646171 40 51.805057 55.758479 59.341707 63.690740 66.765962 69.699112 73.401958 76.094602 78.708961 82.062294 41 52.948512 56.942387 60.560572 64.950071 68.052726 71.011203 74.744938 77.459336 80.094279 83.473286 42 54.090202 58.124038 61.776756 66.206236 69.335997 72.319502 76.083763 78.819659 81.474948 84.879334 43 55.230192 59.303512 62.990356 67.459348 70.615900 73.624142 77.418578 80.175728 82.851132 86.280612 44 56.368541 60.480887 64.201461 68.709513 71.892550 74.925251 78.749524 81.527691 84.222987 87.677284 45 57.505305 61.656233 65.410159 69.956832 73.166061 76.222950 80.076732 82.875687 85.590660 89.069507 46 58.640537 62.829620 66.616529 71.201400 74.436535 77.517351 81.400326 84.219847 86.954288 90.457427 47 59.774289 64.001112 67.820647 72.443307 75.704073 78.808562 82.720423 85.560295 88.314003 91.841183 48 60.906607 65.170769 69.022586 73.682639 76.968768 80.096684 84.037134 86.897150 89.669928 93.220906 49 62.037537 66.338649 70.222414 74.919474 78.230708 81.381815 85.350565 88.230522 91.022181 94.596722 50 63.167121 67.504807 71.420195 76.153891 79.489978 82.664045 86.660815 89.560519 92.370873 95.968748 51 64.295400 68.669294 72.615992 77.385962 80.746659 83.943461 87.967980 90.887240 93.716111 97.337098 52 65.422413 69.832160 73.809863 78.615756 82.000826 85.220146 89.272151 92.210781 95.057996 98.701879 53 66.548197 70.993453 75.001864 79.843338 83.252551 86.494179 90.573412 93.531234 96.396622 100.06319 54 67.672786 72.153216 76.192048 81.068772 84.501905 87.765634 91.871847 94.848686 97.732083 101.42113 55 68.796214 73.311493 77.380466 82.292117 85.748952 89.034583 93.167533 96.163219 99.064465 102.77580 56 69.918513 74.468324 78.567165 83.513430 86.993755 90.301093 94.460545 97.474912 100.39385 104.12728 57 71.039713 75.623748 79.752192 84.732766 88.236375 91.565231 95.750954 98.783842 101.72032 105.47565 58 72.159844 76.777803 80.935592 85.950176 89.476870 92.827059 97.038829 100.09008 103.04395 106.82100 59 73.278932 77.930524 82.117406 87.165711 90.715293 94.086636 98.324234 101.39370 104.36482 108.16340 60 74.397006 79.081944 83.297675 88.379419 91.951698 95.344019 99.607233 102.69476 105.68299 109.50293 61 75.514089 80.232098 84.476437 89.591344 93.186135 96.599263 100.88789 103.99332 106.99853 110.83966 62 76.630208 81.381015 85.653731 90.801532 94.418653 97.852420 102.16625 105.28946 108.31150 112.17366 63 77.745385 82.528727 86.829591 92.010024 95.649297 99.103542 103.44238 106.58322 109.62197 113.50499 64 78.859642 83.675261 88.004051 93.216860 96.878113 100.35268 104.71633 107.87467 110.92999 114.83372 65 79.973003 84.820645 89.177145 94.422079 98.105144 101.59987 105.98814 109.16385 112.23563 116.15991 66 81.085486 85.964907 90.348904 95.625719 99.330430 102.84516 107.25788 110.45083 113.53893 117.48361 67 82.197113 87.108072 91.519359 96.827816 100.55401 104.08861 108.52558 111.73564 114.83996 118.80488 68 83.307902 88.250164 92.688539 98.028403 101.77592 105.33024 109.79130 113.01834 116.13875 120.12378 69 84.417873 89.391208 93.856471 99.227515 102.99621 106.57010 111.05507 114.29897 117.43536 121.44035 70 85.527043 90.531225 95.023184 100.42518 104.21490 107.80822 112.31693 115.57758 118.72984 122.75465 71 86.635429 91.670239 96.188704 101.62144 105.43203 109.04465 113.57694 116.85422 120.02224 124.06673 72 87.743048 92.808270 97.353055 102.81631 106.64763 110.27942 114.83512 118.12891 121.31258 125.37663 73 88.849916 93.945340 98.516262 104.00983 107.86174 111.51256 116.09151 119.40171 122.60093 126.68440 74 89.956048 95.081467 99.678349 105.20203 109.07438 112.74411 117.34616 120.67266 123.88731 127.99007 75 91.061460 96.216671 100.83934 106.39292 110.28558 113.97409 118.59909 121.94178 125.17178 129.29370 76 92.166166 97.350970 101.99925 107.58254 111.49538 115.20255 119.85035 123.20912 126.45436 130.59533 77 93.270180 98.484383 103.15811 108.77092 112.70380 116.42951 121.09996 124.47471 127.73509 131.89498 78 94.373516 99.616927 104.31594 109.95807 113.91087 117.65500 122.34795 125.73858 129.01401 133.19271 79 95.476186 100.74862 105.47275 111.14402 115.11661 118.87905 123.59437 127.00077 130.29116 134.48854 80 96.578204 101.87947 106.62857 112.32879 116.32106 120.10168 124.83922 128.26131 131.56656 135.78252 81 97.679581 103.00951 107.78341 113.51241 117.52422 121.32292 126.08256 129.52023 132.84026 137.07468 82 98.780329 104.13874 108.93729 114.69489 118.72613 122.54280 127.32440 130.77756 134.11228 138.36504 83 99.880461 105.26718 110.09024 115.87627 119.92682 123.76134 128.56477 132.03333 135.38264 139.65365 84 100.97999 106.39484 111.24226 117.05654 121.12629 124.97857 129.80369 133.28757 136.65139 140.94054 85 102.07892 107.52174 112.39337 118.23575 122.32458 126.19451 131.04120 134.54030 137.91855 142.22573 86 103.17726 108.64789 113.54360 119.41390 123.52170 127.40919 132.27732 135.79156 139.18415 143.50926 87 104.27504 109.77331 114.69295 120.59101 124.71768 128.62261 133.51207 137.04136 140.44822 144.79115 88 105.37225 110.89800 115.84144 121.76711 125.91254 129.83482 134.74548 138.28973 141.71077 146.07143 89 106.46890 112.02199 116.98908 122.94221 127.10628 131.04582 135.97757 139.53669 142.97185 147.35014 90 107.56501 113.14527 118.13589 124.11632 128.29894 132.25563 137.20835 140.78228 144.23146 148.62729 91 108.66058 114.26787 119.28189 125.28946 129.49053 133.46429 138.43786 142.02651 145.48964 149.90291 92 109.75563 115.38979 120.42708 126.46166 130.68107 134.67180 139.66612 143.26940 146.74642 151.17703 93 110.85015 116.51105 121.57148 127.63291 131.87058 135.87818 140.89313 144.51098 148.00180 152.44967 94 111.94417 117.63165 122.71511 128.80325 133.05906 137.08346 142.11894 145.75127 149.25582 153.72085 95 113.03769 118.75161 123.85797 129.97268 134.24655 138.28765 143.34354 146.99028 150.50850 154.99061 96 114.13071 119.87094 125.00007 131.14122 135.43305 139.49076 144.56697 148.22804 151.75985 156.25895 97 115.22324 120.98964 126.14144 132.30888 136.61858 140.69282 145.78923 149.46457 153.00990 157.52590 98 116.31530 122.10773 127.28207 133.47567 137.80315 141.89384 147.01036 150.69989 154.25867 158.79149 99 117.40688 123.22522 128.42199 134.64162 138.98678 143.09384 148.23036 151.93401 155.50618 160.05574 100 118.49800 124.34211 129.56120 135.80672 140.16949 144.29283 149.44925 153.16696 156.75245 161.31866