Lower Tail Critical Values of Chi Square Distribution
One sided test Prob(χ2≤c) = p
Reference: NIST/SEMATECH e-Handbook of Statistical Methods |
| ν\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 |
|---|
|
| TXT Version: ChiSquare-A.txt |
|
