Tabled are critical values for the ratio of the largest of independent estimates of a variance, each based on observations, to the sum of the estimates of the variances. Normality of the observations is assumed. The null hypothesis is that all variances are the same; the test for equality of variances is Cochran's test. The column headings are the values of .
 df df Upper 0.01 significance level critical values 2 3 4 5 6 7 8 9 10 11 17 37 145 2 .9999 .9950 .9794 .9586 .9373 .9172 .8988 .8823 .8674 .8539 .7949 .7067 .6062 .5000 3 .9933 .9423 .8831 .8335 .7933 .7606 .7335 .7107 .6912 .6743 .6059 .5153 .4230 .3333 4 .9676 .8643 .7814 .7212 .6761 .6410 .6129 .5897 .5702 .5536 .4884 .4057 .3251 .2500 5 .9279 .7885 .6957 .6329 .5875 .5531 .5259 .5037 .4854 .4697 .4094 .3351 .2644 .2000 6 .8828 .7218 .6258 .5635 .5195 .4866 .4608 .4401 .4229 .4084 .3529 .2858 .2229 .1667 7 .8376 .6644 .5685 .5080 .4659 .4347 .4105 .3911 .3751 .3616 .3105 .2494 .1929 .1429 8 .7945 .6152 .5209 .4627 .4226 .3932 .3704 .3522 .3373 .3248 .2779 .2214 .1700 .1250 9 .7544 .5727 .4810 .4251 .3870 .3592 .3378 .3207 .3067 .2950 .2514 .1992 .1521 .1111 10 .7175 .5358 .4469 .3934 .3572 .3308 .3106 .2945 .2813 .2704 .2297 .1811 .1376 .1000 12 .6528 .4751 .3919 .3428 .3099 .2861 .2680 .2535 .2419 .2320 .1961 .1535 .1157 .0833 15 .5747 .4069 .3317 .2882 .2593 .2386 .2228 .2104 .2002 .1918 .1612 .1251 .0934 .0667 20 .4799 .3297 .2654 .2288 .2048 .1877 .1748 .1646 .1567 .1501 .1248 .0960 .0709 .0500 24 .4247 .2871 .2295 .1970 .1759 .1608 .1495 .1406 .1338 .1283 .1060 .0810 .0595 .0417 30 .3632 .2412 .1913 .1635 .1454 .1327 .1232 .1157 .1100 .1054 .0867 .0658 .0480 .0333 40 .2940 .1915 .1508 .1281 .1135 .1033 .0957 .0898 .0853 .0816 .0668 .0503 .0363 .0250 60 .2151 .1371 .1069 .0902 .0796 .0722 .0668 .0625 .0594 .0567 .0461 .0344 .0245 .0167 120 .1225 .0759 .0585 .0489 .0429 .0387 .0357 .0334 .0316 .0302 .0242 .0178 .0125 .0083 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 Upper 0.05 significance level critical values 2 3 4 5 6 7 8 9 10 11 17 37 145 2 .9985 .9750 .9392 .9057 .8772 .8534 .8332 .8159 .8010 .7880 .7341 .6602 .5813 .5000 3 .9669 .8709 .7977 .7457 .7071 .6771 .6530 .6333 .6167 .6025 .5466 .4748 .4031 .3333 4 .9065 .7679 .6841 .6287 .5895 .5598 .5365 .5175 .5017 .4884 .4366 .3720 .3093 .2500 5 .8412 .6838 .5981 .5441 .5065 .4783 .4564 .4387 .4241 .4118 .3645 .3066 .2513 .2000 6 .7808 .6161 .5321 .4803 .4447 .4184 .3980 .3817 .3682 .3568 .3135 .2612 .2119 .1667 7 .7271 .5612 .4800 .4307 .3974 .3726 .3535 .3384 .3259 .3154 .2756 .2278 .1833 .1429 8 .6798 .5157 .4377 .3910 .3595 .3362 .3185 .3043 .2926 .2862 .2462 .2022 .1616 .1250 9 .6385 .4775 .4027 .3584 .3286 .3067 .2901 .2768 .2659 .2568 .2226 .1820 .1446 .1111 10 .6020 .4450 .3733 .3311 .3029 .2823 .2666 .2541 .2439 .2353 .2032 .1655 .1308 .1000 12 .5410 .3924 .3264 .2880 .2624 .2439 .2299 .2187 .2098 .2020 .1737 .1403 .1100 .0833 15 .4709 .3346 .2758 .2419 .2195 .2034 .1911 .1815 .1736 .1671 .1429 .1144 .0889 .0667 20 .3894 .2705 .2205 .1921 .1735 .1602 .1501 .1422 .1357 .1303 .1108 .0879 .0675 .0500 24 .3434 .2354 .1907 .1656 .1493 .1374 .1286 .1216 .1160 .1113 .0942 .0743 .0567 .0417 30 .2929 .1980 .1593 .1377 .1237 .1137 .1061 .1002 .0958 .0921 .0771 .0604 .0457 .0333 40 .2370 .1576 .1259 .1082 .0968 .0887 .0827 .0780 .0745 .0713 .0595 .0462 .0347 .0250 60 .1737 .1131 .0895 .0765 .0682 .0623 .0583 .0552 .0520 .0497 .0411 .0316 .0234 .0167 120 .0998 .0632 .0495 .0419 .0371 .0337 .0312 .0292 .0279 .0266 .0218 .0165 .0120 .0083 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000