Table 10: Chi-Square Quantiles (cont'd)
The p-th quantiles (i.e., 100p-th percentiles) of the Chi-Square distribution are tabulated for degrees of freedom m = 1, 2, ...,100. Selected lower-tail quantiles are tabulated here for p = 0.0005, 0.001, 0.005, 0.01, 0.025, 0.05, 0.10. The first part of this table contains selected upper-tail quantiles for p = 0.90, 0.95, 0.975, 0.99, 0.995, 0.999, 0.9995.
| 100p | |||||||
| m | 0.05 | 0.10 | 0.50 | 1.0 | 2.5 | 5.0 | 10.0 |
| 1 | 0.00000 | 0.00000 | 0.00004 | 0.00016 | 0.00098 | 0.00393 | 0.01579 |
| 2 | 0.00100 | 0.00200 | 0.01003 | 0.02010 | 0.05064 | 0.10259 | 0.21072 |
| 3 | 0.01528 | 0.02430 | 0.07172 | 0.11483 | 0.21580 | 0.35185 | 0.58437 |
| 4 | 0.06392 | 0.09080 | 0.20699 | 0.29711 | 0.48442 | 0.71072 | 1.06362 |
| 5 | 0.15814 | 0.21021 | 0.41174 | 0.55430 | 0.83121 | 1.14548 | 1.61031 |
| 6 | 0.29941 | 0.38107 | 0.67573 | 0.87209 | 1.23734 | 1.63538 | 2.20413 |
| 7 | 0.48487 | 0.59849 | 0.98926 | 1.23904 | 1.68987 | 2.16735 | 2.83311 |
| 8 | 0.71038 | 0.85710 | 1.34441 | 1.64650 | 2.17973 | 2.73264 | 3.48954 |
| 9 | 0.97170 | 1.15195 | 1.73493 | 2.08790 | 2.70039 | 3.32511 | 4.16816 |
| 10 | 1.26498 | 1.47874 | 2.15586 | 2.55821 | 3.24697 | 3.94030 | 4.86518 |
| 11 | 1.58685 | 1.83385 | 2.60322 | 3.05348 | 3.81575 | 4.57481 | 5.57778 |
| 12 | 1.93438 | 2.21421 | 3.07382 | 3.57057 | 4.40379 | 5.22603 | 6.30380 |
| 13 | 2.30506 | 2.61722 | 3.56503 | 4.10692 | 5.00875 | 5.89186 | 7.04150 |
| 14 | 2.69673 | 3.04067 | 4.07467 | 4.66043 | 5.62873 | 6.57063 | 7.78953 |
| 15 | 3.10752 | 3.48268 | 4.60092 | 5.22935 | 6.26214 | 7.26094 | 8.54676 |
| 16 | 3.53581 | 3.94163 | 5.14221 | 5.81221 | 6.90766 | 7.96165 | 9.31224 |
| 17 | 3.98018 | 4.41609 | 5.69722 | 6.40776 | 7.56419 | 8.67176 | 10.08519 |
| 18 | 4.43939 | 4.90485 | 6.26480 | 7.01491 | 8.23075 | 9.39046 | 10.86494 |
| 19 | 4.91234 | 5.40682 | 6.84397 | 7.63273 | 8.90652 | 10.11701 | 11.65091 |
| 20 | 5.39807 | 5.92104 | 7.43384 | 8.26040 | 9.59078 | 10.85081 | 12.44261 |
| 21 | 5.89570 | 6.44668 | 8.03365 | 8.89720 | 10.28290 | 11.59131 | 13.23960 |
| 22 | 6.40447 | 6.98297 | 8.64272 | 9.54249 | 10.98232 | 12.33801 | 14.04149 |
| 23 | 6.92368 | 7.52924 | 9.26042 | 10.19572 | 11.68855 | 13.09051 | 14.84796 |
| 24 | 7.45269 | 8.08488 | 9.88623 | 10.85636 | 12.40115 | 13.84843 | 15.65868 |
| 25 | 7.99096 | 8.64934 | 10.51965 | 11.52398 | 13.11972 | 14.61141 | 16.47341 |
| 26 | 8.53795 | 9.22213 | 11.16024 | 12.19815 | 13.84390 | 15.37916 | 17.29188 |
| 27 | 9.09320 | 9.80278 | 11.80759 | 12.87850 | 14.57338 | 16.15140 | 18.11390 |
| 28 | 9.65627 | 10.39088 | 12.46134 | 13.56471 | 15.30786 | 16.92788 | 18.93924 |
| 29 | 10.22678 | 10.98605 | 13.12115 | 14.25645 | 16.04707 | 17.70837 | 19.76774 |
| 30 | 10.80436 | 11.58795 | 13.78672 | 14.95346 | 16.79077 | 18.49266 | 20.59923 |
| 31 | 11.38868 | 12.19625 | 14.45777 | 15.65546 | 17.53874 | 19.28057 | 21.43356 |
| 32 | 11.97943 | 12.81065 | 15.13403 | 16.36222 | 18.29076 | 20.07191 | 22.27059 |
| 33 | 12.57631 | 13.43089 | 15.81527 | 17.07351 | 19.04666 | 20.86653 | 23.11020 |
| 34 | 13.17907 | 14.05670 | 16.50127 | 17.78915 | 19.80625 | 21.66428 | 23.95225 |
| 35 | 13.78745 | 14.68785 | 17.19182 | 18.50893 | 20.56938 | 22.46502 | 24.79665 |
| 36 | 14.40124 | 15.32411 | 17.88673 | 19.23268 | 21.33588 | 23.26861 | 25.64330 |
| 37 | 15.02020 | 15.96529 | 18.58581 | 19.96023 | 22.10563 | 24.07494 | 26.49209 |
| 38 | 15.64414 | 16.61119 | 19.28891 | 20.69144 | 22.87848 | 24.88390 | 27.34295 |
| 39 | 16.27287 | 17.26162 | 19.99587 | 21.42616 | 23.65432 | 25.69539 | 28.19579 |
| 40 | 16.90622 | 17.91643 | 20.70654 | 22.16426 | 24.43304 | 26.50930 | 29.05052 |
| 41 | 17.54401 | 18.57544 | 21.42078 | 22.90561 | 25.21452 | 27.32555 | 29.90709 |
| 42 | 18.18609 | 19.23852 | 22.13846 | 23.65009 | 25.99866 | 28.14405 | 30.76542 |
| 43 | 18.83231 | 19.90551 | 22.85947 | 24.39760 | 26.78537 | 28.96472 | 31.62545 |
| 44 | 19.48253 | 20.57629 | 23.58369 | 25.14803 | 27.57457 | 29.78748 | 32.48713 |
| 45 | 20.13662 | 21.25074 | 24.31101 | 25.90127 | 28.36615 | 30.61226 | 33.35038 |
| 46 | 20.79446 | 21.92872 | 25.04133 | 26.65724 | 29.16005 | 31.43900 | 34.21517 |
| 47 | 21.45592 | 22.61013 | 25.77456 | 27.41585 | 29.95620 | 32.26762 | 35.08143 |
| 48 | 22.12090 | 23.29487 | 26.51059 | 28.17701 | 30.75451 | 33.09808 | 35.94913 |
| 49 | 22.78928 | 23.98282 | 27.24935 | 28.94065 | 31.55492 | 33.93031 | 36.81822 |
| 50 | 23.46097 | 24.67391 | 27.99075 | 29.70668 | 32.35736 | 34.76425 | 37.68865 |
| 51 | 24.13587 | 25.36802 | 28.73471 | 30.47505 | 33.16179 | 35.59986 | 38.56038 |
| 52 | 24.81388 | 26.06508 | 29.48116 | 31.24567 | 33.96813 | 36.43709 | 39.43338 |
| 53 | 25.49493 | 26.76500 | 30.23003 | 32.01849 | 34.77633 | 37.27589 | 40.30761 |
| 54 | 26.17892 | 27.46770 | 30.98125 | 32.79345 | 35.58634 | 38.11622 | 41.18304 |
| 55 | 26.86577 | 28.17311 | 31.73476 | 33.57048 | 36.39811 | 38.95803 | 42.05962 |
| 56 | 27.55542 | 28.88116 | 32.49049 | 34.34952 | 37.21159 | 39.80128 | 42.93734 |
| 57 | 28.24778 | 29.59177 | 33.24838 | 35.13053 | 38.02674 | 40.64593 | 43.81615 |
| 58 | 28.94278 | 30.30488 | 34.00838 | 35.91346 | 38.84351 | 41.49195 | 44.69603 |
| 59 | 29.64037 | 31.02042 | 34.77043 | 36.69825 | 39.66186 | 42.33931 | 45.57695 |
| 60 | 30.34048 | 31.73834 | 35.53449 | 37.48485 | 40.48175 | 43.18796 | 46.45889 |
| 61 | 31.04303 | 32.45858 | 36.30050 | 38.27323 | 41.30314 | 44.03787 | 47.34181 |
| 62 | 31.74799 | 33.18107 | 37.06842 | 39.06333 | 42.12599 | 44.88902 | 48.22571 |
| 63 | 32.45528 | 33.90578 | 37.83819 | 39.85512 | 42.95027 | 45.74138 | 49.11054 |
| 64 | 33.16485 | 34.63264 | 38.60978 | 40.64856 | 43.77595 | 46.59491 | 49.99629 |
| 65 | 33.87665 | 35.36160 | 39.38314 | 41.44361 | 44.60299 | 47.44958 | 50.88294 |
| 66 | 34.59064 | 36.09262 | 40.15824 | 42.24023 | 45.43136 | 48.30538 | 51.77046 |
| 67 | 35.30676 | 36.82565 | 40.93502 | 43.03838 | 46.26103 | 49.16227 | 52.65885 |
| 68 | 36.02496 | 37.56065 | 41.71347 | 43.83803 | 47.09198 | 50.02023 | 53.54806 |
| 69 | 36.74520 | 38.29757 | 42.49353 | 44.63916 | 47.92416 | 50.87924 | 54.43810 |
| 70 | 37.46744 | 39.03638 | 43.27518 | 45.44172 | 48.75756 | 51.73928 | 55.32894 |
| 71 | 38.19164 | 39.77703 | 44.05838 | 46.24568 | 49.59216 | 52.60031 | 56.22056 |
| 72 | 38.91774 | 40.51948 | 44.84310 | 47.05103 | 50.42791 | 53.46233 | 57.11295 |
| 73 | 39.64572 | 41.26370 | 45.62930 | 47.85772 | 51.26481 | 54.32531 | 58.00609 |
| 74 | 40.37554 | 42.00965 | 46.41696 | 48.66573 | 52.10283 | 55.18923 | 58.89996 |
| 75 | 41.10716 | 42.75730 | 47.20605 | 49.47503 | 52.94194 | 56.05407 | 59.79456 |
| 76 | 41.84054 | 43.50662 | 47.99653 | 50.28560 | 53.78212 | 56.91982 | 60.68986 |
| 77 | 42.57565 | 44.25756 | 48.78839 | 51.09741 | 54.62336 | 57.78645 | 61.58585 |
| 78 | 43.31246 | 45.01011 | 49.58159 | 51.91045 | 55.46562 | 58.65394 | 62.48252 |
| 79 | 44.05094 | 45.76422 | 50.37612 | 52.72468 | 56.30890 | 59.52229 | 63.37986 |
| 80 | 44.79105 | 46.51988 | 51.17193 | 53.54008 | 57.15317 | 60.39148 | 64.27784 |
| 81 | 45.53276 | 47.27704 | 51.96902 | 54.35663 | 57.99842 | 61.26148 | 65.17647 |
| 82 | 46.27605 | 48.03569 | 52.76735 | 55.17431 | 58.84462 | 62.13229 | 66.07573 |
| 83 | 47.02088 | 48.79580 | 53.56691 | 55.99310 | 59.69175 | 63.00389 | 66.97560 |
| 84 | 47.76723 | 49.55733 | 54.36767 | 56.81298 | 60.53981 | 63.87626 | 67.87608 |
| 85 | 48.51507 | 50.32028 | 55.16960 | 57.63393 | 61.38877 | 64.74940 | 68.77716 |
| 86 | 49.26438 | 51.08460 | 55.97270 | 58.45593 | 62.23863 | 65.62328 | 69.67882 |
| 87 | 50.01513 | 51.85028 | 56.77694 | 59.27896 | 63.08935 | 66.49790 | 70.58105 |
| 88 | 50.76730 | 52.61730 | 57.58230 | 60.10301 | 63.94093 | 67.37323 | 71.48384 |
| 89 | 51.52085 | 53.38563 | 58.38876 | 60.92805 | 64.79336 | 68.24928 | 72.38719 |
| 90 | 52.27578 | 54.15524 | 59.19630 | 61.75408 | 65.64662 | 69.12603 | 73.29109 |
| 91 | 53.03205 | 54.92613 | 60.00491 | 62.58107 | 66.50069 | 70.00346 | 74.19552 |
| 92 | 53.78965 | 55.69826 | 60.81457 | 63.40901 | 67.35556 | 70.88157 | 75.10048 |
| 93 | 54.54855 | 56.47162 | 61.62525 | 64.23788 | 68.21123 | 71.76034 | 76.00596 |
| 94 | 55.30873 | 57.24619 | 62.43695 | 65.06767 | 69.06766 | 72.63977 | 76.91195 |
| 95 | 56.07017 | 58.02195 | 63.24965 | 65.89836 | 69.92487 | 73.51984 | 77.81843 |
| 96 | 56.83286 | 58.79888 | 64.06333 | 66.72994 | 70.78282 | 74.40054 | 78.72542 |
| 97 | 57.59677 | 59.57696 | 64.87797 | 67.56240 | 71.64152 | 75.28186 | 79.63289 |
| 98 | 58.36189 | 60.35617 | 65.69357 | 68.39572 | 72.50094 | 76.16379 | 80.54083 |
| 99 | 59.12819 | 61.13651 | 66.51011 | 69.22989 | 73.36108 | 77.04633 | 81.44925 |
| 100 | 59.89566 | 61.91794 | 67.32756 | 70.06489 | 74.22193 | 77.92947 | 82.35814 |
Tabulated by S L C Saw
