//////////////////////////////////////////////////////////////// // // http://www.planetquantum.com/Tables/ChiSquare-A.txt // //////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////// // // Lower 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 .1 .05 .025 .01 .005 .0025 .001 .0005 .00025 .0001 1 .01579077 .00393214 .00098207 .00015709 3.9270e-5 9.8175e-6 1.5708e-6 3.9270e-7 9.8175e-8 1.5708e-8 2 .21072103 .10258659 .05063562 .02010067 .01002508 .00500626 .00200100 .00100025 .00050006 .00020001 3 .58437437 .35184632 .21579528 .11483180 .07172177 .04494134 .02429759 .01527897 .00961426 .00521483 4 1.0636232 .71072302 .48441856 .29710948 .20698909 .14486687 .09080404 .06392204 .04505815 .02841848 5 1.6103080 1.1454762 .83121161 .55429808 .41174190 .30748182 .21021260 .15813752 .11918370 .08217738 6 2.2041307 1.6353829 1.2373442 .87209033 .67572678 .52656896 .38106676 .29940770 .23576987 .17235211 7 2.8331069 2.1673499 1.6898692 1.2390423 .98925568 .79446801 .59849375 .48487499 .39379093 .29996687 8 3.4895391 2.7326368 2.1797307 1.6464974 1.3444131 1.1042555 .85710483 .71037932 .59030458 .46359379 9 4.1681590 3.3251128 2.7003895 2.0879007 1.7349329 1.4501445 1.1519495 .97169945 .82185955 .66080916 10 4.8651821 3.9402991 3.2469728 2.5582122 2.1558565 1.8273969 1.4787435 1.2649821 1.0850839 .88892036 11 5.5777848 4.5748131 3.8157483 3.0534841 2.6032219 2.2321386 1.8338527 1.5868477 1.3768987 1.1452951 12 6.3037961 5.2260295 4.4037885 3.5705690 3.0738236 2.6611823 2.2142093 1.9343767 1.6945720 1.4274951 13 7.0415046 5.8918643 5.0087505 4.1069155 3.5650346 3.1118830 2.6172181 2.3050577 2.0357085 1.7333180 14 7.7895336 6.5706314 5.6287261 4.6604251 4.0746750 3.5820244 3.0406725 2.6967280 2.3982156 2.0607979 15 8.5467562 7.2609439 6.2621378 5.2293489 4.6009156 4.0697322 3.4826845 3.1075186 2.7802653 2.4081880 16 9.3122364 7.9616456 6.9076644 5.8122125 5.1422054 4.5734073 3.9416278 3.5358070 3.1802561 2.7739385 17 10.085186 8.6717602 7.5641864 6.4077598 5.6972171 5.0916737 4.4160927 3.9801771 3.5967807 3.1566728 18 10.864936 9.3904551 8.2307462 7.0149109 6.2648047 5.6233385 4.9048488 4.4393867 4.0285968 3.5551653 19 11.650910 10.117013 8.9065165 7.6327296 6.8439714 6.1673602 5.4068160 4.9123401 4.4746036 3.9683219 20 12.442609 10.850811 9.5907774 8.2603983 7.4338443 6.7228234 5.9210407 5.3980662 4.9338210 4.3951627 21 13.239598 11.591305 10.282898 8.8971979 8.0336534 7.2889190 6.4466766 5.8957001 5.4053733 4.8348075 22 14.041493 12.338015 10.982321 9.5424923 8.6427164 7.8649277 6.9829684 6.4044682 5.8884743 5.2864624 23 14.847956 13.090514 11.688552 10.195716 9.2604248 8.4502072 7.5292398 6.9236751 6.3824157 5.7494097 24 15.658684 13.848425 12.401150 10.856361 9.8862335 9.0441806 8.0848816 7.4526939 6.8865574 6.2229979 25 16.473408 14.611408 13.119720 11.523975 10.519652 9.6463282 8.6493436 7.9909568 7.4003181 6.7066341 26 17.291885 15.379157 13.843905 12.198147 11.160237 10.256179 9.2221268 8.5379479 7.9231689 7.1997771 27 18.113896 16.151396 14.573383 12.878504 11.807587 10.873307 9.8027769 9.0931969 8.4546266 7.7019313 28 18.939242 16.927875 15.307861 13.564710 12.461336 11.497322 10.390879 9.6562738 8.9942489 8.2126421 29 19.767744 17.708366 16.047072 14.256455 13.121149 12.127867 10.986053 10.226784 9.5416293 8.7314908 30 20.599235 18.492661 16.790772 14.953457 13.786720 12.764616 11.587951 10.804365 10.096394 9.2580912 31 21.433565 19.280569 17.538739 15.655456 14.457767 13.407269 12.196250 11.388681 10.658196 9.7920862 32 22.270594 20.071913 18.290765 16.362216 15.134032 14.055548 12.810655 11.979425 11.226718 10.333145 33 23.110197 20.866534 19.046662 17.073514 15.815274 14.709197 13.430889 12.576309 11.801662 10.880960 34 23.952253 21.664281 19.806253 17.789147 16.501272 15.367978 14.056699 13.179068 12.382752 11.435246 35 24.796655 22.465015 20.569377 18.508926 17.191820 16.031672 14.687847 13.787453 12.969733 11.995736 36 25.643300 23.268609 21.335882 19.232676 17.886727 16.700073 15.324113 14.401235 13.562365 12.562181 37 26.492094 24.074943 22.105627 19.960232 18.585812 17.372989 15.965290 15.020198 14.160423 13.134347 38 27.342950 24.883904 22.878482 20.691442 19.288912 18.050242 16.611187 15.644139 14.763700 13.712017 39 28.195785 25.695390 23.654325 21.426163 19.995868 18.731664 17.261622 16.272871 15.371998 14.294986 40 29.050523 26.509303 24.433039 22.164261 20.706535 19.417099 17.916427 16.906216 15.985132 14.883061 41 29.907091 27.325551 25.214519 22.905611 21.420777 20.106398 18.575441 17.544008 16.602930 15.476060 42 30.765423 28.144049 25.998662 23.650095 22.138463 20.799424 19.238517 18.186088 17.225227 16.073813 43 31.625454 28.964717 26.785374 24.397601 22.859474 21.496047 19.905512 18.832309 17.851870 16.676158 44 32.487126 29.787477 27.574566 25.148025 23.583693 22.196142 20.576294 19.482532 18.482713 17.282944 45 33.350381 30.612259 28.366152 25.901269 24.311014 22.899593 21.250736 20.136625 19.117618 17.894024 46 34.215167 31.438995 29.160054 26.657239 25.041334 23.606292 21.928720 20.794461 19.756454 18.509264 47 35.081432 32.267622 29.956196 27.415847 25.774557 24.316133 22.610133 21.455924 20.399098 19.128532 48 35.949131 33.098077 30.754506 28.177009 26.510591 25.029019 23.294869 22.120900 21.045434 19.751706 49 36.818217 33.930306 31.554916 28.940646 27.249349 25.744855 23.982825 22.789283 21.695348 20.378669 50 37.688648 34.764252 32.357364 29.706683 27.990749 26.463552 24.673905 23.460971 22.348736 21.009310 51 38.560384 35.599864 33.161786 30.475048 28.734712 27.185027 25.368018 24.135868 23.005496 21.643523 52 39.433385 36.437093 33.968126 31.245673 29.481164 27.909198 26.065077 24.813882 23.665533 22.281206 53 40.307615 37.275893 34.776329 32.018493 30.230033 28.635989 26.764998 25.494926 24.328754 22.922263 54 41.183039 38.116218 35.586340 32.793447 30.981253 29.365327 27.467701 26.178915 24.995073 23.566602 55 42.059623 38.958027 36.398111 33.570475 31.734757 30.097142 28.173112 26.865770 25.664405 24.214136 56 42.937337 39.801278 37.211593 34.349522 32.490486 30.831367 28.881157 27.555415 26.336671 24.864779 57 43.816148 40.645933 38.026741 35.130533 33.248378 31.567940 29.591767 28.247776 27.011795 25.518452 58 44.696029 41.491954 38.843510 35.913458 34.008379 32.306798 30.304877 28.942784 27.689702 26.175078 59 45.576951 42.339308 39.661859 36.698246 34.770434 33.047883 31.020422 29.640372 28.370324 26.834582 60 46.458888 43.187958 40.481748 37.484852 35.534491 33.791140 31.738342 30.340475 29.053593 27.496894 61 47.341815 44.037874 41.303138 38.273228 36.300501 34.536514 32.458578 31.043033 29.739444 28.161946 62 48.225706 44.889024 42.125992 39.063333 37.068415 35.283955 33.181074 31.747985 30.427815 28.829672 63 49.110539 45.741377 42.950275 39.855125 37.838189 36.033413 33.905777 32.455275 31.118648 29.500009 64 49.996290 46.594905 43.775953 40.648563 38.609778 36.784840 34.632635 33.164849 31.811884 30.172898 65 50.882939 47.449581 44.602993 41.443609 39.383141 37.538191 35.361598 33.876655 32.507469 30.848280 66 51.770464 48.305378 45.431363 42.240227 40.158236 38.293422 36.092619 34.590640 33.205350 31.526099 67 52.658846 49.162270 46.261034 43.038380 40.935024 39.050491 36.825650 35.306758 33.905475 32.206301 68 53.548064 50.020233 47.091977 43.838035 41.713468 39.809356 37.560649 36.024960 34.607796 32.888835 69 54.438102 50.879243 47.924163 44.639158 42.493531 40.569979 38.297572 36.745203 35.312265 33.573650 70 55.328940 51.739278 48.757565 45.441717 43.275180 41.332322 39.036377 37.467442 36.018837 34.260698 71 56.220561 52.600315 49.592157 46.245683 44.058378 42.096348 39.777026 38.191635 36.727467 34.949932 72 57.112949 53.462333 50.427915 47.051025 44.843096 42.862023 40.519480 38.917742 37.438113 35.641308 73 58.006088 54.325312 51.264813 47.857715 45.629300 43.629311 41.263701 39.645723 38.150733 36.334781 74 58.899962 55.189231 52.102829 48.665725 46.416960 44.398181 42.009654 40.375541 38.865288 37.030310 75 59.794557 56.054072 52.941940 49.475029 47.206048 45.168600 42.757304 41.107159 39.581739 37.727854 76 60.689857 56.919817 53.782123 50.285600 47.996534 45.940538 43.506618 41.840542 40.300050 38.427374 77 61.585850 57.786447 54.623359 51.097415 48.788392 46.713965 44.257563 42.575655 41.020184 39.128831 78 62.482520 58.653945 55.465625 51.910448 49.581594 47.488852 45.010107 43.312465 41.742105 39.832189 79 63.379856 59.522294 56.308903 52.724676 50.376116 48.265172 45.764222 44.050940 42.465782 40.537411 80 64.277844 60.391478 57.153173 53.540077 51.171932 49.042897 46.519876 44.791048 43.191180 41.244464 81 65.176473 61.261482 57.998417 54.356629 51.969018 49.822002 47.277042 45.532761 43.918268 41.953314 82 66.075730 62.132291 58.844616 55.174311 52.767350 50.602460 48.035691 46.276047 44.647015 42.663928 83 66.975604 63.003888 59.691753 55.993101 53.566907 51.384248 48.795798 47.020880 45.377392 43.376274 84 67.876083 63.876261 60.539811 56.812981 54.367665 52.167342 49.557335 47.767231 46.109370 44.090322 85 68.777157 64.749396 61.388775 57.633930 55.169604 52.951718 50.320278 48.515074 46.842919 44.806042 86 69.678815 65.623278 62.238626 58.455930 55.972703 53.737354 51.084602 49.264382 47.578014 45.523405 87 70.581048 66.497895 63.089351 59.278962 56.776942 54.524229 51.850284 50.015131 48.314627 46.242384 88 71.483844 67.373234 63.940935 60.103009 57.582301 55.312320 52.617299 50.767296 49.052733 46.962950 89 72.387195 68.249284 64.793361 60.928054 58.388761 56.101608 53.385627 51.520852 49.792307 47.685077 90 73.291090 69.126030 65.646618 61.754079 59.196304 56.892072 54.155244 52.275778 50.533325 48.408739 91 74.195522 70.003463 66.500689 62.581069 60.004912 57.683693 54.926129 53.032050 51.275761 49.133912 92 75.100481 70.881571 67.355563 63.409007 60.814567 58.476452 55.698262 53.789647 52.019595 49.860571 93 76.005958 71.760343 68.211225 64.237879 61.625252 59.270330 56.471623 54.548547 52.764803 50.588691 94 76.911945 72.639768 69.067664 65.067668 62.436952 60.065310 57.246192 55.308730 53.511363 51.318250 95 77.818434 73.519835 69.924867 65.898361 63.249649 60.861375 58.021950 56.070174 54.259254 52.049226 96 78.725417 74.400535 70.782822 66.729944 64.063327 61.658506 58.798878 56.832861 55.008455 52.781596 97 79.632886 75.281858 71.641516 67.562402 64.877973 62.456688 59.576959 57.596772 55.758947 53.515339 98 80.540834 76.163793 72.500939 68.395722 65.693570 63.255905 60.356174 58.361887 56.510709 54.250434 99 81.449253 77.046332 73.361080 69.229890 66.510105 64.056140 61.136506 59.128188 57.263722 54.986860 100 82.358136 77.929465 74.221927 70.064895 67.327563 64.857379 61.917939 59.895658 58.017968 55.724598