Tables Z,t,f,chi-square
This document was uploaded by user and they confirmed that they have the permission to share it. If you are author or own the copyright of this book, please report to us by using this DMCA report form. Report DMCA
Overview
Download & View Tables Z,t,f,chi-square as PDF for free.
More details
- Words: 4,450
- Pages: 7
The Z distribution table 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9
0 0.00000 0.03983 0.07926 0.11791 0.15542 0.19146 0.22575 0.25804 0.28814 0.31594 0.34134 0.36433 0.38493 0.40320 0.41924 0.43319 0.44520 0.45543 0.46407 0.47128 0.47725 0.48214 0.48610 0.48928 0.49180 0.49379 0.49534 0.49653 0.49744 0.49813 0.49865 0.49903 0.49931 0.49952 0.49966 0.49977 0.49984 0.49989 0.49993 0.49995 0.49997 0.49998 0.49999 0.49999 0.49999 0.50000 0.50000 0.50000 0.50000 0.50000
1 0.00399 0.04380 0.08317 0.12172 0.15910 0.19497 0.22907 0.26115 0.29103 0.31859 0.34375 0.36650 0.38686 0.40490 0.42073 0.43448 0.44630 0.45637 0.46485 0.47193 0.47778 0.48257 0.48645 0.48956 0.49202 0.49396 0.49547 0.49664 0.49752 0.49819 0.49869 0.49906 0.49934 0.49953 0.49968 0.49978 0.49985 0.49990 0.49993 0.49995 0.49997 0.49998 0.49999 0.49999 0.49999 0.50000 0.50000 0.50000 0.50000 0.50000
2 0.00798 0.04776 0.08706 0.12552 0.16276 0.19847 0.23237 0.26424 0.29389 0.32121 0.34614 0.36864 0.38877 0.40658 0.42220 0.43574 0.44738 0.45728 0.46562 0.47257 0.47831 0.48300 0.48679 0.48983 0.49224 0.49413 0.49560 0.49674 0.49760 0.49825 0.49874 0.49910 0.49936 0.49955 0.49969 0.49978 0.49985 0.49990 0.49993 0.49996 0.49997 0.49998 0.49999 0.49999 0.50000 0.50000 0.50000 0.50000 0.50000 0.50000
3 0.01197 0.05172 0.09095 0.12930 0.16640 0.20194 0.23565 0.26730 0.29673 0.32381 0.34849 0.37076 0.39065 0.40824 0.42364 0.43699 0.44845 0.45818 0.46638 0.47320 0.47882 0.48341 0.48713 0.49010 0.49245 0.49430 0.49573 0.49683 0.49767 0.49831 0.49878 0.49913 0.49938 0.49957 0.49970 0.49979 0.49986 0.49990 0.49994 0.49996 0.49997 0.49998 0.49999 0.49999 0.50000 0.50000 0.50000 0.50000 0.50000 0.50000
4 0.01595 0.05567 0.09483 0.13307 0.17003 0.20540 0.23891 0.27035 0.29955 0.32639 0.35083 0.37286 0.39251 0.40988 0.42507 0.43822 0.44950 0.45907 0.46712 0.47381 0.47932 0.48382 0.48745 0.49036 0.49266 0.49446 0.49585 0.49693 0.49774 0.49836 0.49882 0.49916 0.49940 0.49958 0.49971 0.49980 0.49986 0.49991 0.49994 0.49996 0.49997 0.49998 0.49999 0.49999 0.50000 0.50000 0.50000 0.50000 0.50000 0.50000
5 0.01994 0.05962 0.09871 0.13683 0.17364 0.20884 0.24215 0.27337 0.30234 0.32894 0.35314 0.37493 0.39435 0.41149 0.42647 0.43943 0.45053 0.45994 0.46784 0.47441 0.47982 0.48422 0.48778 0.49061 0.49286 0.49461 0.49598 0.49702 0.49781 0.49841 0.49886 0.49918 0.49942 0.49960 0.49972 0.49981 0.49987 0.49991 0.49994 0.49996 0.49997 0.49998 0.49999 0.49999 0.50000 0.50000 0.50000 0.50000 0.50000 0.50000
6 0.02392 0.06356 0.10257 0.14058 0.17724 0.21226 0.24537 0.27637 0.30511 0.33147 0.35543 0.37698 0.39617 0.41309 0.42785 0.44062 0.45154 0.46080 0.46856 0.47500 0.48030 0.48461 0.48809 0.49086 0.49305 0.49477 0.49609 0.49711 0.49788 0.49846 0.49889 0.49921 0.49944 0.49961 0.49973 0.49981 0.49987 0.49992 0.49994 0.49996 0.49998 0.49998 0.49999 0.49999 0.50000 0.50000 0.50000 0.50000 0.50000 0.50000
7 0.02790 0.06749 0.10642 0.14431 0.18082 0.21566 0.24857 0.27935 0.30785 0.33398 0.35769 0.37900 0.39796 0.41466 0.42922 0.44179 0.45254 0.46164 0.46926 0.47558 0.48077 0.48500 0.48840 0.49111 0.49324 0.49492 0.49621 0.49720 0.49795 0.49851 0.49893 0.49924 0.49946 0.49962 0.49974 0.49982 0.49988 0.49992 0.49995 0.49996 0.49998 0.49998 0.49999 0.49999 0.50000 0.50000 0.50000 0.50000 0.50000 0.50000
8 0.03188 0.07142 0.11026 0.14803 0.18439 0.21904 0.25175 0.28230 0.31057 0.33646 0.35993 0.38100 0.39973 0.41621 0.43056 0.44295 0.45352 0.46246 0.46995 0.47615 0.48124 0.48537 0.48870 0.49134 0.49343 0.49506 0.49632 0.49728 0.49801 0.49856 0.49896 0.49926 0.49948 0.49964 0.49975 0.49983 0.49988 0.49992 0.49995 0.49997 0.49998 0.49999 0.49999 0.49999 0.50000 0.50000 0.50000 0.50000 0.50000 0.50000
9 0.03586 0.07535 0.11409 0.15173 0.18793 0.22240 0.25490 0.28524 0.31327 0.33891 0.36214 0.38298 0.40147 0.41774 0.43189 0.44408 0.45449 0.46327 0.47062 0.47670 0.48169 0.48574 0.48899 0.49158 0.49361 0.49520 0.49643 0.49736 0.49807 0.49861 0.49900 0.49929 0.49950 0.49965 0.49976 0.49983 0.49989 0.49992 0.49995 0.49997 0.49998 0.49999 0.49999 0.49999 0.50000 0.50000 0.50000 0.50000 0.50000 0.50000
The t distribution table ν 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 infinity
0.1 3.0777 1.8856 1.6377 1.5332 1.4759 1.4398 1.4149 1.3968 1.3830 1.3722 1.3634 1.3562 1.3502 1.3450 1.3406 1.3368 1.3334 1.3304 1.3277 1.3253 1.3232 1.3212 1.3195 1.3178 1.3163 1.3150 1.3137 1.3125 1.3114 1.3104 1.3095 1.3086 1.3077 1.3070 1.3062 1.3055 1.3049 1.3042 1.3036 1.3031 1.3025 1.3020 1.3016 1.3011 1.3006 1.3002 1.2998 1.2994 1.2991 1.2816
0.075 4.1653 2.2819 1.9243 1.7782 1.6994 1.6502 1.6166 1.5922 1.5737 1.5592 1.5476 1.5380 1.5299 1.5231 1.5172 1.5121 1.5077 1.5037 1.5002 1.4970 1.4942 1.4916 1.4893 1.4871 1.4852 1.4834 1.4817 1.4801 1.4787 1.4774 1.4761 1.4749 1.4738 1.4728 1.4718 1.4709 1.4701 1.4692 1.4685 1.4677 1.4670 1.4664 1.4657 1.4651 1.4645 1.4640 1.4635 1.4629 1.4625
0.05 6.3138 2.9200 2.3534 2.1318 2.0150 1.9432 1.8946 1.8595 1.8331 1.8125 1.7959 1.7823 1.7709 1.7613 1.7531 1.7459 1.7396 1.7341 1.7291 1.7247 1.7207 1.7171 1.7139 1.7109 1.7081 1.7056 1.7033 1.7011 1.6991 1.6973 1.6955 1.6939 1.6924 1.6909 1.6896 1.6883 1.6871 1.6860 1.6849 1.6839 1.6829 1.6820 1.6811 1.6802 1.6794 1.6787 1.6779 1.6772 1.6766 1.6449
0.025 12.7062 4.3027 3.1824 2.7764 2.5706 2.4469 2.3646 2.3060 2.2622 2.2281 2.2010 2.1788 2.1604 2.1448 2.1314 2.1199 2.1098 2.1009 2.0930 2.0860 2.0796 2.0739 2.0687 2.0639 2.0595 2.0555 2.0518 2.0484 2.0452 2.0423 2.0395 2.0369 2.0345 2.0322 2.0301 2.0281 2.0262 2.0244 2.0227 2.0211 2.0195 2.0181 2.0167 2.0154 2.0141 2.0129 2.0117 2.0106 2.0096 1.9599
0.01 31.8205 6.9646 4.5407 3.7469 3.3649 3.1427 2.9980 2.8965 2.8214 2.7638 2.7181 2.6810 2.6503 2.6245 2.6025 2.5835 2.5669 2.5524 2.5395 2.5280 2.5176 2.5083 2.4999 2.4922 2.4851 2.4786 2.4727 2.4671 2.4620 2.4573 2.4528 2.4487 2.4448 2.4411 2.4377 2.4345 2.4314 2.4286 2.4258 2.4233 2.4208 2.4185 2.4163 2.4141 2.4121 2.4102 2.4083 2.4066 2.4049 2.3264
0.0075 42.4335 8.0728 5.0473 4.0880 3.6338 3.3723 3.2032 3.0851 2.9982 2.9316 2.8789 2.8363 2.8010 2.7714 2.7462 2.7245 2.7056 2.6889 2.6742 2.6611 2.6493 2.6387 2.6290 2.6203 2.6122 2.6049 2.5981 2.5918 2.5860 2.5806 2.5755 2.5708 2.5664 2.5623 2.5584 2.5547 2.5513 2.5480 2.5449 2.5420 2.5392 2.5366 2.5340 2.5316 2.5294 2.5272 2.5251 2.5231 2.5212
0.005 63.6567 9.9248 5.8409 4.6041 4.0321 3.7074 3.4995 3.3554 3.2498 3.1693 3.1058 3.0545 3.0123 2.9768 2.9467 2.9208 2.8982 2.8784 2.8609 2.8453 2.8314 2.8188 2.8073 2.7969 2.7874 2.7787 2.7707 2.7633 2.7564 2.7500 2.7440 2.7385 2.7333 2.7284 2.7238 2.7195 2.7154 2.7116 2.7079 2.7045 2.7012 2.6981 2.6951 2.6923 2.6896 2.6870 2.6846 2.6822 2.6800 2.5758
0.0025 127.3213 14.0890 7.4533 5.5976 4.7733 4.3168 4.0293 3.8325 3.6897 3.5814 3.4966 3.4284 3.3725 3.3257 3.2860 3.2520 3.2224 3.1966 3.1737 3.1534 3.1352 3.1188 3.1040 3.0905 3.0782 3.0669 3.0565 3.0469 3.0380 3.0298 3.0221 3.0149 3.0082 3.0020 2.9960 2.9905 2.9852 2.9803 2.9756 2.9712 2.9670 2.9630 2.9592 2.9555 2.9521 2.9488 2.9456 2.9426 2.9397
0.001 318.3088 22.3271 10.2145 7.1732 5.8934 5.2076 4.7853 4.5008 4.2968 4.1437 4.0247 3.9296 3.8520 3.7874 3.7328 3.6862 3.6458 3.6105 3.5794 3.5518 3.5272 3.5050 3.4850 3.4668 3.4502 3.4350 3.4210 3.4082 3.3962 3.3852 3.3749 3.3653 3.3563 3.3479 3.3400 3.3326 3.3256 3.3190 3.3128 3.3069 3.3013 3.2960 3.2909 3.2861 3.2815 3.2771 3.2729 3.2689 3.2651
0.0005 636.6192 31.5991 12.9240 8.6103 6.8688 5.9588 5.4079 5.0413 4.7809 4.5869 4.4370 4.3178 4.2208 4.1405 4.0728 4.0150 3.9651 3.9216 3.8834 3.8495 3.8193 3.7921 3.7676 3.7454 3.7251 3.7066 3.6896 3.6739 3.6594 3.6460 3.6335 3.6218 3.6109 3.6007 3.5911 3.5821 3.5737 3.5657 3.5581 3.5510 3.5442 3.5377 3.5316 3.5258 3.5203 3.5150 3.5099 3.5051 3.5004 3.2905
The F distribution table (0.05 level) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 120
1 161.45 18.51 10.13 7.71 6.61 5.99 5.59 5.32 5.12 4.96 4.84 4.75 4.67 4.60 4.54 4.49 4.45 4.41 4.38 4.35 4.32 4.30 4.28 4.26 4.24 4.23 4.21 4.20 4.18 4.17 3.92
2 199.50 19.00 9.55 6.94 5.79 5.14 4.74 4.46 4.26 4.10 3.98 3.89 3.81 3.74 3.68 3.63 3.59 3.55 3.52 3.49 3.47 3.44 3.42 3.40 3.39 3.37 3.35 3.34 3.33 3.32 3.07
3 215.71 19.16 9.28 6.59 5.41 4.76 4.35 4.07 3.86 3.71 3.59 3.49 3.41 3.34 3.29 3.24 3.20 3.16 3.13 3.10 3.07 3.05 3.03 3.01 2.99 2.98 2.96 2.95 2.93 2.92 2.68
4 224.58 19.25 9.12 6.39 5.19 4.53 4.12 3.84 3.63 3.48 3.36 3.26 3.18 3.11 3.06 3.01 2.96 2.93 2.90 2.87 2.84 2.82 2.80 2.78 2.76 2.74 2.73 2.71 2.70 2.69 2.45
5 230.16 19.30 9.01 6.26 5.05 4.39 3.97 3.69 3.48 3.33 3.20 3.11 3.03 2.96 2.90 2.85 2.81 2.77 2.74 2.71 2.68 2.66 2.64 2.62 2.60 2.59 2.57 2.56 2.55 2.53 2.29
6 233.99 19.33 8.94 6.16 4.95 4.28 3.87 3.58 3.37 3.22 3.09 3.00 2.92 2.85 2.79 2.74 2.70 2.66 2.63 2.60 2.57 2.55 2.53 2.51 2.49 2.47 2.46 2.45 2.43 2.42 2.18
7 236.77 19.35 8.89 6.09 4.88 4.21 3.79 3.50 3.29 3.14 3.01 2.91 2.83 2.76 2.71 2.66 2.61 2.58 2.54 2.51 2.49 2.46 2.44 2.42 2.40 2.39 2.37 2.36 2.35 2.33 2.09
8 238.88 19.37 8.85 6.04 4.82 4.15 3.73 3.44 3.23 3.07 2.95 2.85 2.77 2.70 2.64 2.59 2.55 2.51 2.48 2.45 2.42 2.40 2.37 2.36 2.34 2.32 2.31 2.29 2.28 2.27 2.02
9 240.54 19.38 8.81 6.00 4.77 4.10 3.68 3.39 3.18 3.02 2.90 2.80 2.71 2.65 2.59 2.54 2.49 2.46 2.42 2.39 2.37 2.34 2.32 2.30 2.28 2.27 2.25 2.24 2.22 2.21 1.96
10 241.88 19.40 8.79 5.96 4.74 4.06 3.64 3.35 3.14 2.98 2.85 2.75 2.67 2.60 2.54 2.49 2.45 2.41 2.38 2.35 2.32 2.30 2.27 2.25 2.24 2.22 2.20 2.19 2.18 2.16 1.91
11 242.98 19.40 8.76 5.94 4.70 4.03 3.60 3.31 3.10 2.94 2.82 2.72 2.63 2.57 2.51 2.46 2.41 2.37 2.34 2.31 2.28 2.26 2.24 2.22 2.20 2.18 2.17 2.15 2.14 2.13 1.87
12 243.91 19.41 8.74 5.91 4.68 4.00 3.57 3.28 3.07 2.91 2.79 2.69 2.60 2.53 2.48 2.42 2.38 2.34 2.31 2.28 2.25 2.23 2.20 2.18 2.16 2.15 2.13 2.12 2.10 2.09 1.83
13 244.69 19.42 8.73 5.89 4.66 3.98 3.55 3.26 3.05 2.89 2.76 2.66 2.58 2.51 2.45 2.40 2.35 2.31 2.28 2.25 2.22 2.20 2.18 2.15 2.14 2.12 2.10 2.09 2.08 2.06 1.80
14 245.36 19.42 8.71 5.87 4.64 3.96 3.53 3.24 3.03 2.86 2.74 2.64 2.55 2.48 2.42 2.37 2.33 2.29 2.26 2.22 2.20 2.17 2.15 2.13 2.11 2.09 2.08 2.06 2.05 2.04 1.78
15 245.95 19.43 8.70 5.86 4.62 3.94 3.51 3.22 3.01 2.85 2.72 2.62 2.53 2.46 2.40 2.35 2.31 2.27 2.23 2.20 2.18 2.15 2.13 2.11 2.09 2.07 2.06 2.04 2.03 2.01 1.75
16 246.46 19.43 8.69 5.84 4.60 3.92 3.49 3.20 2.99 2.83 2.70 2.60 2.51 2.44 2.38 2.33 2.29 2.25 2.21 2.18 2.16 2.13 2.11 2.09 2.07 2.05 2.04 2.02 2.01 1.99 1.73
s
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 120
17 246.92 19.44 8.68 5.83 4.59 3.91 3.48 3.19 2.97 2.81 2.69 2.58 2.50 2.43 2.37 2.32 2.27 2.23 2.20 2.17 2.14 2.11 2.09 2.07 2.05 2.03 2.02 2.00 1.99 1.98 1.71
18 247.32 19.44 8.67 5.82 4.58 3.90 3.47 3.17 2.96 2.80 2.67 2.57 2.48 2.41 2.35 2.30 2.26 2.22 2.18 2.15 2.12 2.10 2.08 2.05 2.04 2.02 2.00 1.99 1.97 1.96 1.69
19 247.69 19.44 8.67 5.81 4.57 3.88 3.46 3.16 2.95 2.79 2.66 2.56 2.47 2.40 2.34 2.29 2.24 2.20 2.17 2.14 2.11 2.08 2.06 2.04 2.02 2.00 1.99 1.97 1.96 1.95 1.67
20 248.01 19.45 8.66 5.80 4.56 3.87 3.44 3.15 2.94 2.77 2.65 2.54 2.46 2.39 2.33 2.28 2.23 2.19 2.16 2.12 2.10 2.07 2.05 2.03 2.01 1.99 1.97 1.96 1.94 1.93 1.66
21 248.31 19.45 8.65 5.79 4.55 3.86 3.43 3.14 2.93 2.76 2.64 2.53 2.45 2.38 2.32 2.26 2.22 2.18 2.14 2.11 2.08 2.06 2.04 2.01 2.00 1.98 1.96 1.95 1.93 1.92 1.64
22 248.58 19.45 8.65 5.79 4.54 3.86 3.43 3.13 2.92 2.75 2.63 2.52 2.44 2.37 2.31 2.25 2.21 2.17 2.13 2.10 2.07 2.05 2.02 2.00 1.98 1.97 1.95 1.93 1.92 1.91 1.63
23 248.83 19.45 8.64 5.78 4.53 3.85 3.42 3.12 2.91 2.75 2.62 2.51 2.43 2.36 2.30 2.24 2.20 2.16 2.12 2.09 2.06 2.04 2.01 1.99 1.97 1.96 1.94 1.92 1.91 1.90 1.62
24 249.05 19.45 8.64 5.77 4.53 3.84 3.41 3.12 2.90 2.74 2.61 2.51 2.42 2.35 2.29 2.24 2.19 2.15 2.11 2.08 2.05 2.03 2.01 1.98 1.96 1.95 1.93 1.91 1.90 1.89 1.61
25 249.26 19.46 8.63 5.77 4.52 3.83 3.40 3.11 2.89 2.73 2.60 2.50 2.41 2.34 2.28 2.23 2.18 2.14 2.11 2.07 2.05 2.02 2.00 1.97 1.96 1.94 1.92 1.91 1.89 1.88 1.60
26 249.45 19.46 8.63 5.76 4.52 3.83 3.40 3.10 2.89 2.72 2.59 2.49 2.41 2.33 2.27 2.22 2.17 2.13 2.10 2.07 2.04 2.01 1.99 1.97 1.95 1.93 1.91 1.90 1.88 1.87 1.59
27 249.63 19.46 8.63 5.76 4.51 3.82 3.39 3.10 2.88 2.72 2.59 2.48 2.40 2.33 2.27 2.21 2.17 2.13 2.09 2.06 2.03 2.00 1.98 1.96 1.94 1.92 1.90 1.89 1.88 1.86 1.58
28 249.80 19.46 8.62 5.75 4.50 3.82 3.39 3.09 2.87 2.71 2.58 2.48 2.39 2.32 2.26 2.21 2.16 2.12 2.08 2.05 2.02 2.00 1.97 1.95 1.93 1.91 1.90 1.88 1.87 1.85 1.57
The F distribution table (0.01 level)
29 249.95 19.46 8.62 5.75 4.50 3.81 3.38 3.08 2.87 2.70 2.58 2.47 2.39 2.31 2.25 2.20 2.15 2.11 2.08 2.05 2.02 1.99 1.97 1.95 1.93 1.91 1.89 1.88 1.86 1.85 1.56
30 250.10 19.46 8.62 5.75 4.50 3.81 3.38 3.08 2.86 2.70 2.57 2.47 2.38 2.31 2.25 2.19 2.15 2.11 2.07 2.04 2.01 1.98 1.96 1.94 1.92 1.90 1.88 1.87 1.85 1.84 1.55
60 252.20 19.48 8.57 5.69 4.43 3.74 3.30 3.01 2.79 2.62 2.49 2.38 2.30 2.22 2.16 2.11 2.06 2.02 1.98 1.95 1.92 1.89 1.86 1.84 1.82 1.80 1.79 1.77 1.75 1.74 1.43
120 253.25 19.49 8.55 5.66 4.40 3.70 3.27 2.97 2.75 2.58 2.45 2.34 2.25 2.18 2.11 2.06 2.01 1.97 1.93 1.90 1.87 1.84 1.81 1.79 1.77 1.75 1.73 1.71 1.70 1.68 1.35
1 2 1 4052.18 4999.50 17 18 98.50 6191.53 99.00 12 6181.43 3 34.12 30.82 2 99.44 99.44 21.20 26.75 18.00 34 26.79 16.26 14.08 13.27 45 14.11 13.75 10.92 56 9.64 9.61 67 7.48 7.45 12.25 9.55 78 6.24 6.21 11.26 8.65 89 5.44 5.41 10.56 8.02 910 4.89 4.86 10.04 7.56 10 4.49 4.46 11 9.65 7.21 11 4.18 4.15 12 9.33 6.93 12 3.94 3.91 13 9.07 6.70 13 3.75 3.72 14 8.86 6.51 14 3.59 3.56 15 8.68 6.36 15 3.45 3.42 16 8.53 6.23 16 3.34 3.31 17 8.40 6.11 17 3.24 3.21 18 8.29 6.01 18 3.16 3.13 19 8.18 5.93 19 3.08 3.05 20 8.10 5.85 20 3.02 2.99 21 8.02 5.78 21 2.96 2.93 22 7.95 5.72 22 2.91 2.88 23 7.88 5.66 23 2.86 2.83 24 7.82 5.61 24 2.82 2.79 25 7.77 5.57 25 2.78 2.75 26 7.72 5.53 26 2.75 2.72 27 7.68 5.49 27 2.71 2.68 28 7.64 5.45 28 2.68 2.65 29 7.60 5.42 29 2.66 2.63 30 7.56 5.39 30 2.63 2.60 60 7.08 4.98 60 2.28 2.25 120 6.85 4.79
120
2.12
2.09
3 4 5 6 7 8 9 10 11 12 5403.35 5624.58 5763.65 5858.99 5928.36 5981.07 6022.47 6055.85 6083.32 6106.32 19 20 21 22 23 24 25 26 27 28 99.17 6208.73 99.25 6216.12 99.30 6222.84 99.33 6228.99 99.36 6234.63 99.37 6239.83 99.39 6244.62 99.40 6249.07 99.41 99.42 6200.58 6253.20 29.46 28.71 28.24 27.91 27.67 27.49 27.35 27.23 27.13 27.05 99.45 99.45 99.45 99.45 99.46 99.46 99.46 99.46 99.46 99.46 16.69 15.98 15.52 15.21 14.98 14.80 14.66 14.55 14.45 14.37 26.72 26.69 26.66 26.64 26.62 26.60 26.58 26.56 26.55 26.53 12.06 11.39 10.97 10.67 10.46 10.29 10.16 10.05 9.96 9.89 14.05 14.02 13.99 13.97 13.95 13.93 13.91 13.89 13.88 13.86 9.78 9.15 8.75 8.47 8.26 8.10 7.98 7.87 7.79 7.72 9.58 9.55 9.53 9.51 9.49 9.47 9.45 9.43 9.42 9.40 7.42 7.40 7.37 7.35 7.33 7.31 7.30 7.28 7.27 7.25 8.45 7.85 7.46 7.19 6.99 6.84 6.72 6.62 6.54 6.47 6.18 6.16 6.13 6.11 6.09 6.07 6.06 6.04 6.03 6.02 7.59 7.01 6.63 6.37 6.18 6.03 5.91 5.81 5.73 5.67 5.38 5.36 5.34 5.32 5.30 5.28 5.26 5.25 5.23 5.22 6.99 6.42 6.06 5.80 5.61 5.47 5.35 5.26 5.18 5.11 4.83 4.81 4.79 4.77 4.75 4.73 4.71 4.70 4.68 4.67 6.55 5.99 5.64 5.39 5.20 5.06 4.94 4.85 4.77 4.71 4.43 4.41 4.38 4.36 4.34 4.33 4.31 4.30 4.28 4.27 6.22 5.67 5.32 5.07 4.89 4.74 4.63 4.54 4.46 4.40 4.12 4.10 4.08 4.06 4.04 4.02 4.01 3.99 3.98 3.96 5.95 5.41 5.06 4.82 4.64 4.50 4.39 4.30 4.22 4.16 3.88 3.86 3.84 3.82 3.80 3.78 3.76 3.75 3.74 3.72 5.74 5.21 4.86 4.62 4.44 4.30 4.19 4.10 4.02 3.96 3.69 3.66 3.64 3.62 3.60 3.59 3.57 3.56 3.54 3.53 5.56 5.04 4.69 4.46 4.28 4.14 4.03 3.94 3.86 3.80 3.53 3.51 3.48 3.46 3.44 3.43 3.41 3.40 3.38 3.37 5.42 4.89 4.56 4.32 4.14 4.00 3.89 3.80 3.73 3.67 3.40 3.37 3.35 3.33 3.31 3.29 3.28 3.26 3.25 3.24 5.29 4.77 4.44 4.20 4.03 3.89 3.78 3.69 3.62 3.55 3.28 3.26 3.24 3.22 3.20 3.18 3.16 3.15 3.14 3.12 5.18 4.67 4.34 4.10 3.93 3.79 3.68 3.59 3.52 3.46 3.19 3.16 3.14 3.12 3.10 3.08 3.07 3.05 3.04 3.03 5.09 4.58 4.25 4.01 3.84 3.71 3.60 3.51 3.43 3.37 3.10 3.08 3.05 3.03 3.02 3.00 2.98 2.97 2.95 2.94 5.01 4.50 4.17 3.94 3.77 3.63 3.52 3.43 3.36 3.30 3.03 3.00 2.98 2.96 2.94 2.92 2.91 2.89 2.88 2.87 4.94 4.43 4.10 3.87 3.70 3.56 3.46 3.37 3.29 3.23 2.96 2.94 2.92 2.90 2.88 2.86 2.84 2.83 2.81 2.80 4.87 4.37 4.04 3.81 3.64 3.51 3.40 3.31 3.24 3.17 2.90 2.88 2.86 2.84 2.82 2.80 2.79 2.77 2.76 2.74 4.82 4.31 3.99 3.76 3.59 3.45 3.35 3.26 3.18 3.12 2.85 2.83 2.81 2.78 2.77 2.75 2.73 2.72 2.70 2.69 4.76 4.26 3.94 3.71 3.54 3.41 3.30 3.21 3.14 3.07 2.80 2.78 2.76 2.74 2.72 2.70 2.69 2.67 2.66 2.64 4.72 4.22 3.90 3.67 3.50 3.36 3.26 3.17 3.09 3.03 2.76 2.74 2.72 2.70 2.68 2.66 2.64 2.63 2.61 2.60 4.68 4.18 3.85 3.63 3.46 3.32 3.22 3.13 3.06 2.99 2.72 2.70 2.68 2.66 2.64 2.62 2.60 2.59 2.58 2.56 4.64 4.14 3.82 3.59 3.42 3.29 3.18 3.09 3.02 2.96 2.69 2.66 2.64 2.62 2.60 2.58 2.57 2.55 2.54 2.53 4.60 4.11 3.78 3.56 3.39 3.26 3.15 3.06 2.99 2.93 2.66 2.63 2.61 2.59 2.57 2.55 2.54 2.52 2.51 2.49 4.57 4.07 3.75 3.53 3.36 3.23 3.12 3.03 2.96 2.90 2.63 2.60 2.58 2.56 2.54 2.52 2.51 2.49 2.48 2.46 4.54 4.04 3.73 3.50 3.33 3.20 3.09 3.00 2.93 2.87 2.60 2.57 2.55 2.53 2.51 2.49 2.48 2.46 2.45 2.44 4.51 4.02 3.70 3.47 3.30 3.17 3.07 2.98 2.91 2.84 2.57 2.55 2.53 2.51 2.49 2.47 2.45 2.44 2.42 2.41 4.13 3.65 3.34 3.12 2.95 2.82 2.72 2.63 2.56 2.50 2.22 2.20 2.17 2.15 2.13 2.12 2.10 2.08 2.07 2.05 3.95 3.48 3.17 2.96 2.79 2.66 2.56 2.47 2.40 2.34
2.06
2.03
2.01
1.99
1.97
1.95
1.93
1.92
1.90
1.89
13 6125.86 29 99.42 6257.05 26.98 99.46 14.31 26.52 9.82 13.85 7.66 9.39 7.24 6.41 6.00 5.61 5.21 5.05 4.66 4.65 4.26 4.34 3.95 4.10 3.71 3.91 3.52 3.75 3.36 3.61 3.23 3.50 3.11 3.40 3.01 3.32 2.93 3.24 2.86 3.18 2.79 3.12 2.73 3.07 2.68 3.02 2.63 2.98 2.59 2.94 2.55 2.90 2.51 2.87 2.48 2.84 2.45 2.81 2.42 2.79 2.40 2.44 2.04 2.28
1.87
14 6142.67 30 99.43 6260.65 26.92 99.47 14.25 26.50 9.77 13.84 7.60 9.38 7.23 6.36 5.99 5.56 5.20 5.01 4.65 4.60 4.25 4.29 3.94 4.05 3.70 3.86 3.51 3.70 3.35 3.56 3.21 3.45 3.10 3.35 3.00 3.27 2.92 3.19 2.84 3.13 2.78 3.07 2.72 3.02 2.67 2.97 2.62 2.93 2.58 2.89 2.54 2.86 2.50 2.82 2.47 2.79 2.44 2.77 2.41 2.74 2.39 2.39 2.03 2.23
1.86
15 6157.28 60 99.43 6313.03 26.87 99.48 14.20 26.32 9.72 13.65 7.56 9.20 7.06 6.31 5.82 5.52 5.03 4.96 4.48 4.56 4.08 4.25 3.78 4.01 3.54 3.82 3.34 3.66 3.18 3.52 3.05 3.41 2.93 3.31 2.83 3.23 2.75 3.15 2.67 3.09 2.61 3.03 2.55 2.98 2.50 2.93 2.45 2.89 2.40 2.85 2.36 2.81 2.33 2.78 2.29 2.75 2.26 2.73 2.23 2.70 2.21 2.35 1.84 2.19
1.66
16 6170.10 120 99.44 6339.39 26.83 99.49 14.15 26.22 9.68 13.56 7.52 9.11 6.97 6.28 5.74 5.48 4.95 4.92 4.40 4.52 4.00 4.21 3.69 3.97 3.45 3.78 3.25 3.62 3.09 3.49 2.96 3.37 2.84 3.27 2.75 3.19 2.66 3.12 2.58 3.05 2.52 2.99 2.46 2.94 2.40 2.89 2.35 2.85 2.31 2.81 2.27 2.78 2.23 2.75 2.20 2.72 2.17 2.69 2.14 2.66 2.11 2.31 1.73 2.15
1.53
The Chi-Squared () distribution table 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
0.005 0.000 0.010 0.072 0.207 0.412 0.676 0.989 1.344 1.735 2.156 2.603 3.074 3.565 4.075 4.601 5.142 5.697 6.265 6.844 7.434 8.034 8.643 9.260 9.886 10.520 11.160 11.808 12.461 13.121 13.787 14.458 15.134 15.815 16.501 17.192 17.887
0.01 0.000 0.020 0.115 0.297 0.554 0.872 1.239 1.646 2.088 2.558 3.053 3.571 4.107 4.660 5.229 5.812 6.408 7.015 7.633 8.260 8.897 9.542 10.196 10.856 11.524 12.198 12.879 13.565 14.256 14.953 15.655 16.362 17.074 17.789 18.509 19.233
0.025 0.001 0.051 0.216 0.484 0.831 1.237 1.690 2.180 2.700 3.247 3.816 4.404 5.009 5.629 6.262 6.908 7.564 8.231 8.907 9.591 10.283 10.982 11.689 12.401 13.120 13.844 14.573 15.308 16.047 16.791 17.539 18.291 19.047 19.806 20.569 21.336
0.05 0.004 0.103 0.352 0.711 1.145 1.635 2.167 2.733 3.325 3.940 4.575 5.226 5.892 6.571 7.261 7.962 8.672 9.390 10.117 10.851 11.591 12.338 13.091 13.848 14.611 15.379 16.151 16.928 17.708 18.493 19.281 20.072 20.867 21.664 22.465 23.269
0.1 0.016 0.211 0.584 1.064 1.610 2.204 2.833 3.490 4.168 4.865 5.578 6.304 7.042 7.790 8.547 9.312 10.085 10.865 11.651 12.443 13.240 14.041 14.848 15.659 16.473 17.292 18.114 18.939 19.768 20.599 21.434 22.271 23.110 23.952 24.797 25.643
0.25 0.102 0.575 1.213 1.923 2.675 3.455 4.255 5.071 5.899 6.737 7.584 8.438 9.299 10.165 11.037 11.912 12.792 13.675 14.562 15.452 16.344 17.240 18.137 19.037 19.939 20.843 21.749 22.657 23.567 24.478 25.390 26.304 27.219 28.136 29.054 29.973
0.5 0.455 1.386 2.366 3.357 4.351 5.348 6.346 7.344 8.343 9.342 10.341 11.340 12.340 13.339 14.339 15.338 16.338 17.338 18.338 19.337 20.337 21.337 22.337 23.337 24.337 25.336 26.336 27.336 28.336 29.336 30.336 31.336 32.336 33.336 34.336 35.336
0.75 1.323 2.773 4.108 5.385 6.626 7.841 9.037 10.219 11.389 12.549 13.701 14.845 15.984 17.117 18.245 19.369 20.489 21.605 22.718 23.828 24.935 26.039 27.141 28.241 29.339 30.435 31.528 32.620 33.711 34.800 35.887 36.973 38.058 39.141 40.223 41.304
0.9 2.706 4.605 6.251 7.779 9.236 10.645 12.017 13.362 14.684 15.987 17.275 18.549 19.812 21.064 22.307 23.542 24.769 25.989 27.204 28.412 29.615 30.813 32.007 33.196 34.382 35.563 36.741 37.916 39.087 40.256 41.422 42.585 43.745 44.903 46.059 47.212
0.95 3.841 5.991 7.815 9.488 11.070 12.592 14.067 15.507 16.919 18.307 19.675 21.026 22.362 23.685 24.996 26.296 27.587 28.869 30.144 31.410 32.671 33.924 35.172 36.415 37.652 38.885 40.113 41.337 42.557 43.773 44.985 46.194 47.400 48.602 49.802 50.998
0.975 5.024 7.378 9.348 11.143 12.833 14.449 16.013 17.535 19.023 20.483 21.920 23.337 24.736 26.119 27.488 28.845 30.191 31.526 32.852 34.170 35.479 36.781 38.076 39.364 40.646 41.923 43.195 44.461 45.722 46.979 48.232 49.480 50.725 51.966 53.203 54.437
0.99 6.635 9.210 11.345 13.277 15.086 16.812 18.475 20.090 21.666 23.209 24.725 26.217 27.688 29.141 30.578 32.000 33.409 34.805 36.191 37.566 38.932 40.289 41.638 42.980 44.314 45.642 46.963 48.278 49.588 50.892 52.191 53.486 54.776 56.061 57.342 58.619
0.995 7.879 10.597 12.838 14.860 16.750 18.548 20.278 21.955 23.589 25.188 26.757 28.300 29.819 31.319 32.801 34.267 35.718 37.156 38.582 39.997 41.401 42.796 44.181 45.559 46.928 48.290 49.645 50.993 52.336 53.672 55.003 56.328 57.648 58.964 60.275 61.581
0.999 10.828 13.816 16.266 18.467 20.515 22.458 24.322 26.124 27.877 29.588 31.264 32.909 34.528 36.123 37.697 39.252 40.790 42.312 43.820 45.315 46.797 48.268 49.728 51.179 52.620 54.052 55.476 56.892 58.301 59.703 61.098 62.487 63.870 65.247 66.619 67.985
37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 80 90 100
18.586 19.289 19.996 20.707 21.421 22.138 22.859 23.584 24.311 25.041 25.775 26.511 27.249 27.991 28.735 29.481 30.230 30.981 31.735 32.490 33.248 34.008 34.770 35.534 36.301 37.068 37.838 38.610 39.383 40.158 40.935 41.713 42.494 43.275 51.172 59.196 67.328
19.960 20.691 21.426 22.164 22.906 23.650 24.398 25.148 25.901 26.657 27.416 28.177 28.941 29.707 30.475 31.246 32.018 32.793 33.570 34.350 35.131 35.913 36.698 37.485 38.273 39.063 39.855 40.649 41.444 42.240 43.038 43.838 44.639 45.442 53.540 61.754 70.065
22.106 22.878 23.654 24.433 25.215 25.999 26.785 27.575 28.366 29.160 29.956 30.755 31.555 32.357 33.162 33.968 34.776 35.586 36.398 37.212 38.027 38.844 39.662 40.482 41.303 42.126 42.950 43.776 44.603 45.431 46.261 47.092 47.924 48.758 57.153 65.647 74.222
24.075 24.884 25.695 26.509 27.326 28.144 28.965 29.787 30.612 31.439 32.268 33.098 33.930 34.764 35.600 36.437 37.276 38.116 38.958 39.801 40.646 41.492 42.339 43.188 44.038 44.889 45.741 46.595 47.450 48.305 49.162 50.020 50.879 51.739 60.391 69.126 77.929
26.492 27.343 28.196 29.051 29.907 30.765 31.625 32.487 33.350 34.215 35.081 35.949 36.818 37.689 38.560 39.433 40.308 41.183 42.060 42.937 43.816 44.696 45.577 46.459 47.342 48.226 49.111 49.996 50.883 51.770 52.659 53.548 54.438 55.329 64.278 73.291 82.358
30.893 31.815 32.737 33.660 34.585 35.510 36.436 37.363 38.291 39.220 40.149 41.079 42.010 42.942 43.874 44.808 45.741 46.676 47.610 48.546 49.482 50.419 51.356 52.294 53.232 54.171 55.110 56.050 56.990 57.931 58.872 59.814 60.756 61.698 71.145 80.625 90.133
36.336 37.335 38.335 39.335 40.335 41.335 42.335 43.335 44.335 45.335 46.335 47.335 48.335 49.335 50.335 51.335 52.335 53.335 54.335 55.335 56.335 57.335 58.335 59.335 60.335 61.335 62.335 63.335 64.335 65.335 66.335 67.335 68.334 69.334 79.334 89.334 99.334
42.383 43.462 44.539 45.616 46.692 47.766 48.840 49.913 50.985 52.056 53.127 54.196 55.265 56.334 57.401 58.468 59.534 60.600 61.665 62.729 63.793 64.857 65.919 66.981 68.043 69.104 70.165 71.225 72.285 73.344 74.403 75.461 76.519 77.577 88.130 98.650 109.141
48.363 49.513 50.660 51.805 52.949 54.090 55.230 56.369 57.505 58.641 59.774 60.907 62.038 63.167 64.295 65.422 66.548 67.673 68.796 69.919 71.040 72.160 73.279 74.397 75.514 76.630 77.745 78.860 79.973 81.085 82.197 83.308 84.418 85.527 96.578 107.565 118.498
52.192 53.384 54.572 55.758 56.942 58.124 59.304 60.481 61.656 62.830 64.001 65.171 66.339 67.505 68.669 69.832 70.993 72.153 73.311 74.468 75.624 76.778 77.931 79.082 80.232 81.381 82.529 83.675 84.821 85.965 87.108 88.250 89.391 90.531 101.879 113.145 124.342
55.668 56.896 58.120 59.342 60.561 61.777 62.990 64.201 65.410 66.617 67.821 69.023 70.222 71.420 72.616 73.810 75.002 76.192 77.380 78.567 79.752 80.936 82.117 83.298 84.476 85.654 86.830 88.004 89.177 90.349 91.519 92.689 93.856 95.023 106.629 118.136 129.561
59.893 61.162 62.428 63.691 64.950 66.206 67.459 68.710 69.957 71.201 72.443 73.683 74.919 76.154 77.386 78.616 79.843 81.069 82.292 83.513 84.733 85.950 87.166 88.379 89.591 90.802 92.010 93.217 94.422 95.626 96.828 98.028 99.228 100.425 112.329 124.116 135.807
62.883 64.181 65.476 66.766 68.053 69.336 70.616 71.893 73.166 74.437 75.704 76.969 78.231 79.490 80.747 82.001 83.253 84.502 85.749 86.994 88.236 89.477 90.715 91.952 93.186 94.419 95.649 96.878 98.105 99.330 100.554 101.776 102.996 104.215 116.321 128.299 140.169
69.346 70.703 72.055 73.402 74.745 76.084 77.419 78.750 80.077 81.400 82.720 84.037 85.351 86.661 87.968 89.272 90.573 91.872 93.168 94.461 95.751 97.039 98.324 99.607 100.888 102.166 103.442 104.716 105.988 107.258 108.526 109.791 111.055 112.317 124.839 137.208 149.449
0 0.00000 0.03983 0.07926 0.11791 0.15542 0.19146 0.22575 0.25804 0.28814 0.31594 0.34134 0.36433 0.38493 0.40320 0.41924 0.43319 0.44520 0.45543 0.46407 0.47128 0.47725 0.48214 0.48610 0.48928 0.49180 0.49379 0.49534 0.49653 0.49744 0.49813 0.49865 0.49903 0.49931 0.49952 0.49966 0.49977 0.49984 0.49989 0.49993 0.49995 0.49997 0.49998 0.49999 0.49999 0.49999 0.50000 0.50000 0.50000 0.50000 0.50000
1 0.00399 0.04380 0.08317 0.12172 0.15910 0.19497 0.22907 0.26115 0.29103 0.31859 0.34375 0.36650 0.38686 0.40490 0.42073 0.43448 0.44630 0.45637 0.46485 0.47193 0.47778 0.48257 0.48645 0.48956 0.49202 0.49396 0.49547 0.49664 0.49752 0.49819 0.49869 0.49906 0.49934 0.49953 0.49968 0.49978 0.49985 0.49990 0.49993 0.49995 0.49997 0.49998 0.49999 0.49999 0.49999 0.50000 0.50000 0.50000 0.50000 0.50000
2 0.00798 0.04776 0.08706 0.12552 0.16276 0.19847 0.23237 0.26424 0.29389 0.32121 0.34614 0.36864 0.38877 0.40658 0.42220 0.43574 0.44738 0.45728 0.46562 0.47257 0.47831 0.48300 0.48679 0.48983 0.49224 0.49413 0.49560 0.49674 0.49760 0.49825 0.49874 0.49910 0.49936 0.49955 0.49969 0.49978 0.49985 0.49990 0.49993 0.49996 0.49997 0.49998 0.49999 0.49999 0.50000 0.50000 0.50000 0.50000 0.50000 0.50000
3 0.01197 0.05172 0.09095 0.12930 0.16640 0.20194 0.23565 0.26730 0.29673 0.32381 0.34849 0.37076 0.39065 0.40824 0.42364 0.43699 0.44845 0.45818 0.46638 0.47320 0.47882 0.48341 0.48713 0.49010 0.49245 0.49430 0.49573 0.49683 0.49767 0.49831 0.49878 0.49913 0.49938 0.49957 0.49970 0.49979 0.49986 0.49990 0.49994 0.49996 0.49997 0.49998 0.49999 0.49999 0.50000 0.50000 0.50000 0.50000 0.50000 0.50000
4 0.01595 0.05567 0.09483 0.13307 0.17003 0.20540 0.23891 0.27035 0.29955 0.32639 0.35083 0.37286 0.39251 0.40988 0.42507 0.43822 0.44950 0.45907 0.46712 0.47381 0.47932 0.48382 0.48745 0.49036 0.49266 0.49446 0.49585 0.49693 0.49774 0.49836 0.49882 0.49916 0.49940 0.49958 0.49971 0.49980 0.49986 0.49991 0.49994 0.49996 0.49997 0.49998 0.49999 0.49999 0.50000 0.50000 0.50000 0.50000 0.50000 0.50000
5 0.01994 0.05962 0.09871 0.13683 0.17364 0.20884 0.24215 0.27337 0.30234 0.32894 0.35314 0.37493 0.39435 0.41149 0.42647 0.43943 0.45053 0.45994 0.46784 0.47441 0.47982 0.48422 0.48778 0.49061 0.49286 0.49461 0.49598 0.49702 0.49781 0.49841 0.49886 0.49918 0.49942 0.49960 0.49972 0.49981 0.49987 0.49991 0.49994 0.49996 0.49997 0.49998 0.49999 0.49999 0.50000 0.50000 0.50000 0.50000 0.50000 0.50000
6 0.02392 0.06356 0.10257 0.14058 0.17724 0.21226 0.24537 0.27637 0.30511 0.33147 0.35543 0.37698 0.39617 0.41309 0.42785 0.44062 0.45154 0.46080 0.46856 0.47500 0.48030 0.48461 0.48809 0.49086 0.49305 0.49477 0.49609 0.49711 0.49788 0.49846 0.49889 0.49921 0.49944 0.49961 0.49973 0.49981 0.49987 0.49992 0.49994 0.49996 0.49998 0.49998 0.49999 0.49999 0.50000 0.50000 0.50000 0.50000 0.50000 0.50000
7 0.02790 0.06749 0.10642 0.14431 0.18082 0.21566 0.24857 0.27935 0.30785 0.33398 0.35769 0.37900 0.39796 0.41466 0.42922 0.44179 0.45254 0.46164 0.46926 0.47558 0.48077 0.48500 0.48840 0.49111 0.49324 0.49492 0.49621 0.49720 0.49795 0.49851 0.49893 0.49924 0.49946 0.49962 0.49974 0.49982 0.49988 0.49992 0.49995 0.49996 0.49998 0.49998 0.49999 0.49999 0.50000 0.50000 0.50000 0.50000 0.50000 0.50000
8 0.03188 0.07142 0.11026 0.14803 0.18439 0.21904 0.25175 0.28230 0.31057 0.33646 0.35993 0.38100 0.39973 0.41621 0.43056 0.44295 0.45352 0.46246 0.46995 0.47615 0.48124 0.48537 0.48870 0.49134 0.49343 0.49506 0.49632 0.49728 0.49801 0.49856 0.49896 0.49926 0.49948 0.49964 0.49975 0.49983 0.49988 0.49992 0.49995 0.49997 0.49998 0.49999 0.49999 0.49999 0.50000 0.50000 0.50000 0.50000 0.50000 0.50000
9 0.03586 0.07535 0.11409 0.15173 0.18793 0.22240 0.25490 0.28524 0.31327 0.33891 0.36214 0.38298 0.40147 0.41774 0.43189 0.44408 0.45449 0.46327 0.47062 0.47670 0.48169 0.48574 0.48899 0.49158 0.49361 0.49520 0.49643 0.49736 0.49807 0.49861 0.49900 0.49929 0.49950 0.49965 0.49976 0.49983 0.49989 0.49992 0.49995 0.49997 0.49998 0.49999 0.49999 0.49999 0.50000 0.50000 0.50000 0.50000 0.50000 0.50000
The t distribution table ν 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 infinity
0.1 3.0777 1.8856 1.6377 1.5332 1.4759 1.4398 1.4149 1.3968 1.3830 1.3722 1.3634 1.3562 1.3502 1.3450 1.3406 1.3368 1.3334 1.3304 1.3277 1.3253 1.3232 1.3212 1.3195 1.3178 1.3163 1.3150 1.3137 1.3125 1.3114 1.3104 1.3095 1.3086 1.3077 1.3070 1.3062 1.3055 1.3049 1.3042 1.3036 1.3031 1.3025 1.3020 1.3016 1.3011 1.3006 1.3002 1.2998 1.2994 1.2991 1.2816
0.075 4.1653 2.2819 1.9243 1.7782 1.6994 1.6502 1.6166 1.5922 1.5737 1.5592 1.5476 1.5380 1.5299 1.5231 1.5172 1.5121 1.5077 1.5037 1.5002 1.4970 1.4942 1.4916 1.4893 1.4871 1.4852 1.4834 1.4817 1.4801 1.4787 1.4774 1.4761 1.4749 1.4738 1.4728 1.4718 1.4709 1.4701 1.4692 1.4685 1.4677 1.4670 1.4664 1.4657 1.4651 1.4645 1.4640 1.4635 1.4629 1.4625
0.05 6.3138 2.9200 2.3534 2.1318 2.0150 1.9432 1.8946 1.8595 1.8331 1.8125 1.7959 1.7823 1.7709 1.7613 1.7531 1.7459 1.7396 1.7341 1.7291 1.7247 1.7207 1.7171 1.7139 1.7109 1.7081 1.7056 1.7033 1.7011 1.6991 1.6973 1.6955 1.6939 1.6924 1.6909 1.6896 1.6883 1.6871 1.6860 1.6849 1.6839 1.6829 1.6820 1.6811 1.6802 1.6794 1.6787 1.6779 1.6772 1.6766 1.6449
0.025 12.7062 4.3027 3.1824 2.7764 2.5706 2.4469 2.3646 2.3060 2.2622 2.2281 2.2010 2.1788 2.1604 2.1448 2.1314 2.1199 2.1098 2.1009 2.0930 2.0860 2.0796 2.0739 2.0687 2.0639 2.0595 2.0555 2.0518 2.0484 2.0452 2.0423 2.0395 2.0369 2.0345 2.0322 2.0301 2.0281 2.0262 2.0244 2.0227 2.0211 2.0195 2.0181 2.0167 2.0154 2.0141 2.0129 2.0117 2.0106 2.0096 1.9599
0.01 31.8205 6.9646 4.5407 3.7469 3.3649 3.1427 2.9980 2.8965 2.8214 2.7638 2.7181 2.6810 2.6503 2.6245 2.6025 2.5835 2.5669 2.5524 2.5395 2.5280 2.5176 2.5083 2.4999 2.4922 2.4851 2.4786 2.4727 2.4671 2.4620 2.4573 2.4528 2.4487 2.4448 2.4411 2.4377 2.4345 2.4314 2.4286 2.4258 2.4233 2.4208 2.4185 2.4163 2.4141 2.4121 2.4102 2.4083 2.4066 2.4049 2.3264
0.0075 42.4335 8.0728 5.0473 4.0880 3.6338 3.3723 3.2032 3.0851 2.9982 2.9316 2.8789 2.8363 2.8010 2.7714 2.7462 2.7245 2.7056 2.6889 2.6742 2.6611 2.6493 2.6387 2.6290 2.6203 2.6122 2.6049 2.5981 2.5918 2.5860 2.5806 2.5755 2.5708 2.5664 2.5623 2.5584 2.5547 2.5513 2.5480 2.5449 2.5420 2.5392 2.5366 2.5340 2.5316 2.5294 2.5272 2.5251 2.5231 2.5212
0.005 63.6567 9.9248 5.8409 4.6041 4.0321 3.7074 3.4995 3.3554 3.2498 3.1693 3.1058 3.0545 3.0123 2.9768 2.9467 2.9208 2.8982 2.8784 2.8609 2.8453 2.8314 2.8188 2.8073 2.7969 2.7874 2.7787 2.7707 2.7633 2.7564 2.7500 2.7440 2.7385 2.7333 2.7284 2.7238 2.7195 2.7154 2.7116 2.7079 2.7045 2.7012 2.6981 2.6951 2.6923 2.6896 2.6870 2.6846 2.6822 2.6800 2.5758
0.0025 127.3213 14.0890 7.4533 5.5976 4.7733 4.3168 4.0293 3.8325 3.6897 3.5814 3.4966 3.4284 3.3725 3.3257 3.2860 3.2520 3.2224 3.1966 3.1737 3.1534 3.1352 3.1188 3.1040 3.0905 3.0782 3.0669 3.0565 3.0469 3.0380 3.0298 3.0221 3.0149 3.0082 3.0020 2.9960 2.9905 2.9852 2.9803 2.9756 2.9712 2.9670 2.9630 2.9592 2.9555 2.9521 2.9488 2.9456 2.9426 2.9397
0.001 318.3088 22.3271 10.2145 7.1732 5.8934 5.2076 4.7853 4.5008 4.2968 4.1437 4.0247 3.9296 3.8520 3.7874 3.7328 3.6862 3.6458 3.6105 3.5794 3.5518 3.5272 3.5050 3.4850 3.4668 3.4502 3.4350 3.4210 3.4082 3.3962 3.3852 3.3749 3.3653 3.3563 3.3479 3.3400 3.3326 3.3256 3.3190 3.3128 3.3069 3.3013 3.2960 3.2909 3.2861 3.2815 3.2771 3.2729 3.2689 3.2651
0.0005 636.6192 31.5991 12.9240 8.6103 6.8688 5.9588 5.4079 5.0413 4.7809 4.5869 4.4370 4.3178 4.2208 4.1405 4.0728 4.0150 3.9651 3.9216 3.8834 3.8495 3.8193 3.7921 3.7676 3.7454 3.7251 3.7066 3.6896 3.6739 3.6594 3.6460 3.6335 3.6218 3.6109 3.6007 3.5911 3.5821 3.5737 3.5657 3.5581 3.5510 3.5442 3.5377 3.5316 3.5258 3.5203 3.5150 3.5099 3.5051 3.5004 3.2905
The F distribution table (0.05 level) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 120
1 161.45 18.51 10.13 7.71 6.61 5.99 5.59 5.32 5.12 4.96 4.84 4.75 4.67 4.60 4.54 4.49 4.45 4.41 4.38 4.35 4.32 4.30 4.28 4.26 4.24 4.23 4.21 4.20 4.18 4.17 3.92
2 199.50 19.00 9.55 6.94 5.79 5.14 4.74 4.46 4.26 4.10 3.98 3.89 3.81 3.74 3.68 3.63 3.59 3.55 3.52 3.49 3.47 3.44 3.42 3.40 3.39 3.37 3.35 3.34 3.33 3.32 3.07
3 215.71 19.16 9.28 6.59 5.41 4.76 4.35 4.07 3.86 3.71 3.59 3.49 3.41 3.34 3.29 3.24 3.20 3.16 3.13 3.10 3.07 3.05 3.03 3.01 2.99 2.98 2.96 2.95 2.93 2.92 2.68
4 224.58 19.25 9.12 6.39 5.19 4.53 4.12 3.84 3.63 3.48 3.36 3.26 3.18 3.11 3.06 3.01 2.96 2.93 2.90 2.87 2.84 2.82 2.80 2.78 2.76 2.74 2.73 2.71 2.70 2.69 2.45
5 230.16 19.30 9.01 6.26 5.05 4.39 3.97 3.69 3.48 3.33 3.20 3.11 3.03 2.96 2.90 2.85 2.81 2.77 2.74 2.71 2.68 2.66 2.64 2.62 2.60 2.59 2.57 2.56 2.55 2.53 2.29
6 233.99 19.33 8.94 6.16 4.95 4.28 3.87 3.58 3.37 3.22 3.09 3.00 2.92 2.85 2.79 2.74 2.70 2.66 2.63 2.60 2.57 2.55 2.53 2.51 2.49 2.47 2.46 2.45 2.43 2.42 2.18
7 236.77 19.35 8.89 6.09 4.88 4.21 3.79 3.50 3.29 3.14 3.01 2.91 2.83 2.76 2.71 2.66 2.61 2.58 2.54 2.51 2.49 2.46 2.44 2.42 2.40 2.39 2.37 2.36 2.35 2.33 2.09
8 238.88 19.37 8.85 6.04 4.82 4.15 3.73 3.44 3.23 3.07 2.95 2.85 2.77 2.70 2.64 2.59 2.55 2.51 2.48 2.45 2.42 2.40 2.37 2.36 2.34 2.32 2.31 2.29 2.28 2.27 2.02
9 240.54 19.38 8.81 6.00 4.77 4.10 3.68 3.39 3.18 3.02 2.90 2.80 2.71 2.65 2.59 2.54 2.49 2.46 2.42 2.39 2.37 2.34 2.32 2.30 2.28 2.27 2.25 2.24 2.22 2.21 1.96
10 241.88 19.40 8.79 5.96 4.74 4.06 3.64 3.35 3.14 2.98 2.85 2.75 2.67 2.60 2.54 2.49 2.45 2.41 2.38 2.35 2.32 2.30 2.27 2.25 2.24 2.22 2.20 2.19 2.18 2.16 1.91
11 242.98 19.40 8.76 5.94 4.70 4.03 3.60 3.31 3.10 2.94 2.82 2.72 2.63 2.57 2.51 2.46 2.41 2.37 2.34 2.31 2.28 2.26 2.24 2.22 2.20 2.18 2.17 2.15 2.14 2.13 1.87
12 243.91 19.41 8.74 5.91 4.68 4.00 3.57 3.28 3.07 2.91 2.79 2.69 2.60 2.53 2.48 2.42 2.38 2.34 2.31 2.28 2.25 2.23 2.20 2.18 2.16 2.15 2.13 2.12 2.10 2.09 1.83
13 244.69 19.42 8.73 5.89 4.66 3.98 3.55 3.26 3.05 2.89 2.76 2.66 2.58 2.51 2.45 2.40 2.35 2.31 2.28 2.25 2.22 2.20 2.18 2.15 2.14 2.12 2.10 2.09 2.08 2.06 1.80
14 245.36 19.42 8.71 5.87 4.64 3.96 3.53 3.24 3.03 2.86 2.74 2.64 2.55 2.48 2.42 2.37 2.33 2.29 2.26 2.22 2.20 2.17 2.15 2.13 2.11 2.09 2.08 2.06 2.05 2.04 1.78
15 245.95 19.43 8.70 5.86 4.62 3.94 3.51 3.22 3.01 2.85 2.72 2.62 2.53 2.46 2.40 2.35 2.31 2.27 2.23 2.20 2.18 2.15 2.13 2.11 2.09 2.07 2.06 2.04 2.03 2.01 1.75
16 246.46 19.43 8.69 5.84 4.60 3.92 3.49 3.20 2.99 2.83 2.70 2.60 2.51 2.44 2.38 2.33 2.29 2.25 2.21 2.18 2.16 2.13 2.11 2.09 2.07 2.05 2.04 2.02 2.01 1.99 1.73
s
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 120
17 246.92 19.44 8.68 5.83 4.59 3.91 3.48 3.19 2.97 2.81 2.69 2.58 2.50 2.43 2.37 2.32 2.27 2.23 2.20 2.17 2.14 2.11 2.09 2.07 2.05 2.03 2.02 2.00 1.99 1.98 1.71
18 247.32 19.44 8.67 5.82 4.58 3.90 3.47 3.17 2.96 2.80 2.67 2.57 2.48 2.41 2.35 2.30 2.26 2.22 2.18 2.15 2.12 2.10 2.08 2.05 2.04 2.02 2.00 1.99 1.97 1.96 1.69
19 247.69 19.44 8.67 5.81 4.57 3.88 3.46 3.16 2.95 2.79 2.66 2.56 2.47 2.40 2.34 2.29 2.24 2.20 2.17 2.14 2.11 2.08 2.06 2.04 2.02 2.00 1.99 1.97 1.96 1.95 1.67
20 248.01 19.45 8.66 5.80 4.56 3.87 3.44 3.15 2.94 2.77 2.65 2.54 2.46 2.39 2.33 2.28 2.23 2.19 2.16 2.12 2.10 2.07 2.05 2.03 2.01 1.99 1.97 1.96 1.94 1.93 1.66
21 248.31 19.45 8.65 5.79 4.55 3.86 3.43 3.14 2.93 2.76 2.64 2.53 2.45 2.38 2.32 2.26 2.22 2.18 2.14 2.11 2.08 2.06 2.04 2.01 2.00 1.98 1.96 1.95 1.93 1.92 1.64
22 248.58 19.45 8.65 5.79 4.54 3.86 3.43 3.13 2.92 2.75 2.63 2.52 2.44 2.37 2.31 2.25 2.21 2.17 2.13 2.10 2.07 2.05 2.02 2.00 1.98 1.97 1.95 1.93 1.92 1.91 1.63
23 248.83 19.45 8.64 5.78 4.53 3.85 3.42 3.12 2.91 2.75 2.62 2.51 2.43 2.36 2.30 2.24 2.20 2.16 2.12 2.09 2.06 2.04 2.01 1.99 1.97 1.96 1.94 1.92 1.91 1.90 1.62
24 249.05 19.45 8.64 5.77 4.53 3.84 3.41 3.12 2.90 2.74 2.61 2.51 2.42 2.35 2.29 2.24 2.19 2.15 2.11 2.08 2.05 2.03 2.01 1.98 1.96 1.95 1.93 1.91 1.90 1.89 1.61
25 249.26 19.46 8.63 5.77 4.52 3.83 3.40 3.11 2.89 2.73 2.60 2.50 2.41 2.34 2.28 2.23 2.18 2.14 2.11 2.07 2.05 2.02 2.00 1.97 1.96 1.94 1.92 1.91 1.89 1.88 1.60
26 249.45 19.46 8.63 5.76 4.52 3.83 3.40 3.10 2.89 2.72 2.59 2.49 2.41 2.33 2.27 2.22 2.17 2.13 2.10 2.07 2.04 2.01 1.99 1.97 1.95 1.93 1.91 1.90 1.88 1.87 1.59
27 249.63 19.46 8.63 5.76 4.51 3.82 3.39 3.10 2.88 2.72 2.59 2.48 2.40 2.33 2.27 2.21 2.17 2.13 2.09 2.06 2.03 2.00 1.98 1.96 1.94 1.92 1.90 1.89 1.88 1.86 1.58
28 249.80 19.46 8.62 5.75 4.50 3.82 3.39 3.09 2.87 2.71 2.58 2.48 2.39 2.32 2.26 2.21 2.16 2.12 2.08 2.05 2.02 2.00 1.97 1.95 1.93 1.91 1.90 1.88 1.87 1.85 1.57
The F distribution table (0.01 level)
29 249.95 19.46 8.62 5.75 4.50 3.81 3.38 3.08 2.87 2.70 2.58 2.47 2.39 2.31 2.25 2.20 2.15 2.11 2.08 2.05 2.02 1.99 1.97 1.95 1.93 1.91 1.89 1.88 1.86 1.85 1.56
30 250.10 19.46 8.62 5.75 4.50 3.81 3.38 3.08 2.86 2.70 2.57 2.47 2.38 2.31 2.25 2.19 2.15 2.11 2.07 2.04 2.01 1.98 1.96 1.94 1.92 1.90 1.88 1.87 1.85 1.84 1.55
60 252.20 19.48 8.57 5.69 4.43 3.74 3.30 3.01 2.79 2.62 2.49 2.38 2.30 2.22 2.16 2.11 2.06 2.02 1.98 1.95 1.92 1.89 1.86 1.84 1.82 1.80 1.79 1.77 1.75 1.74 1.43
120 253.25 19.49 8.55 5.66 4.40 3.70 3.27 2.97 2.75 2.58 2.45 2.34 2.25 2.18 2.11 2.06 2.01 1.97 1.93 1.90 1.87 1.84 1.81 1.79 1.77 1.75 1.73 1.71 1.70 1.68 1.35
1 2 1 4052.18 4999.50 17 18 98.50 6191.53 99.00 12 6181.43 3 34.12 30.82 2 99.44 99.44 21.20 26.75 18.00 34 26.79 16.26 14.08 13.27 45 14.11 13.75 10.92 56 9.64 9.61 67 7.48 7.45 12.25 9.55 78 6.24 6.21 11.26 8.65 89 5.44 5.41 10.56 8.02 910 4.89 4.86 10.04 7.56 10 4.49 4.46 11 9.65 7.21 11 4.18 4.15 12 9.33 6.93 12 3.94 3.91 13 9.07 6.70 13 3.75 3.72 14 8.86 6.51 14 3.59 3.56 15 8.68 6.36 15 3.45 3.42 16 8.53 6.23 16 3.34 3.31 17 8.40 6.11 17 3.24 3.21 18 8.29 6.01 18 3.16 3.13 19 8.18 5.93 19 3.08 3.05 20 8.10 5.85 20 3.02 2.99 21 8.02 5.78 21 2.96 2.93 22 7.95 5.72 22 2.91 2.88 23 7.88 5.66 23 2.86 2.83 24 7.82 5.61 24 2.82 2.79 25 7.77 5.57 25 2.78 2.75 26 7.72 5.53 26 2.75 2.72 27 7.68 5.49 27 2.71 2.68 28 7.64 5.45 28 2.68 2.65 29 7.60 5.42 29 2.66 2.63 30 7.56 5.39 30 2.63 2.60 60 7.08 4.98 60 2.28 2.25 120 6.85 4.79
120
2.12
2.09
3 4 5 6 7 8 9 10 11 12 5403.35 5624.58 5763.65 5858.99 5928.36 5981.07 6022.47 6055.85 6083.32 6106.32 19 20 21 22 23 24 25 26 27 28 99.17 6208.73 99.25 6216.12 99.30 6222.84 99.33 6228.99 99.36 6234.63 99.37 6239.83 99.39 6244.62 99.40 6249.07 99.41 99.42 6200.58 6253.20 29.46 28.71 28.24 27.91 27.67 27.49 27.35 27.23 27.13 27.05 99.45 99.45 99.45 99.45 99.46 99.46 99.46 99.46 99.46 99.46 16.69 15.98 15.52 15.21 14.98 14.80 14.66 14.55 14.45 14.37 26.72 26.69 26.66 26.64 26.62 26.60 26.58 26.56 26.55 26.53 12.06 11.39 10.97 10.67 10.46 10.29 10.16 10.05 9.96 9.89 14.05 14.02 13.99 13.97 13.95 13.93 13.91 13.89 13.88 13.86 9.78 9.15 8.75 8.47 8.26 8.10 7.98 7.87 7.79 7.72 9.58 9.55 9.53 9.51 9.49 9.47 9.45 9.43 9.42 9.40 7.42 7.40 7.37 7.35 7.33 7.31 7.30 7.28 7.27 7.25 8.45 7.85 7.46 7.19 6.99 6.84 6.72 6.62 6.54 6.47 6.18 6.16 6.13 6.11 6.09 6.07 6.06 6.04 6.03 6.02 7.59 7.01 6.63 6.37 6.18 6.03 5.91 5.81 5.73 5.67 5.38 5.36 5.34 5.32 5.30 5.28 5.26 5.25 5.23 5.22 6.99 6.42 6.06 5.80 5.61 5.47 5.35 5.26 5.18 5.11 4.83 4.81 4.79 4.77 4.75 4.73 4.71 4.70 4.68 4.67 6.55 5.99 5.64 5.39 5.20 5.06 4.94 4.85 4.77 4.71 4.43 4.41 4.38 4.36 4.34 4.33 4.31 4.30 4.28 4.27 6.22 5.67 5.32 5.07 4.89 4.74 4.63 4.54 4.46 4.40 4.12 4.10 4.08 4.06 4.04 4.02 4.01 3.99 3.98 3.96 5.95 5.41 5.06 4.82 4.64 4.50 4.39 4.30 4.22 4.16 3.88 3.86 3.84 3.82 3.80 3.78 3.76 3.75 3.74 3.72 5.74 5.21 4.86 4.62 4.44 4.30 4.19 4.10 4.02 3.96 3.69 3.66 3.64 3.62 3.60 3.59 3.57 3.56 3.54 3.53 5.56 5.04 4.69 4.46 4.28 4.14 4.03 3.94 3.86 3.80 3.53 3.51 3.48 3.46 3.44 3.43 3.41 3.40 3.38 3.37 5.42 4.89 4.56 4.32 4.14 4.00 3.89 3.80 3.73 3.67 3.40 3.37 3.35 3.33 3.31 3.29 3.28 3.26 3.25 3.24 5.29 4.77 4.44 4.20 4.03 3.89 3.78 3.69 3.62 3.55 3.28 3.26 3.24 3.22 3.20 3.18 3.16 3.15 3.14 3.12 5.18 4.67 4.34 4.10 3.93 3.79 3.68 3.59 3.52 3.46 3.19 3.16 3.14 3.12 3.10 3.08 3.07 3.05 3.04 3.03 5.09 4.58 4.25 4.01 3.84 3.71 3.60 3.51 3.43 3.37 3.10 3.08 3.05 3.03 3.02 3.00 2.98 2.97 2.95 2.94 5.01 4.50 4.17 3.94 3.77 3.63 3.52 3.43 3.36 3.30 3.03 3.00 2.98 2.96 2.94 2.92 2.91 2.89 2.88 2.87 4.94 4.43 4.10 3.87 3.70 3.56 3.46 3.37 3.29 3.23 2.96 2.94 2.92 2.90 2.88 2.86 2.84 2.83 2.81 2.80 4.87 4.37 4.04 3.81 3.64 3.51 3.40 3.31 3.24 3.17 2.90 2.88 2.86 2.84 2.82 2.80 2.79 2.77 2.76 2.74 4.82 4.31 3.99 3.76 3.59 3.45 3.35 3.26 3.18 3.12 2.85 2.83 2.81 2.78 2.77 2.75 2.73 2.72 2.70 2.69 4.76 4.26 3.94 3.71 3.54 3.41 3.30 3.21 3.14 3.07 2.80 2.78 2.76 2.74 2.72 2.70 2.69 2.67 2.66 2.64 4.72 4.22 3.90 3.67 3.50 3.36 3.26 3.17 3.09 3.03 2.76 2.74 2.72 2.70 2.68 2.66 2.64 2.63 2.61 2.60 4.68 4.18 3.85 3.63 3.46 3.32 3.22 3.13 3.06 2.99 2.72 2.70 2.68 2.66 2.64 2.62 2.60 2.59 2.58 2.56 4.64 4.14 3.82 3.59 3.42 3.29 3.18 3.09 3.02 2.96 2.69 2.66 2.64 2.62 2.60 2.58 2.57 2.55 2.54 2.53 4.60 4.11 3.78 3.56 3.39 3.26 3.15 3.06 2.99 2.93 2.66 2.63 2.61 2.59 2.57 2.55 2.54 2.52 2.51 2.49 4.57 4.07 3.75 3.53 3.36 3.23 3.12 3.03 2.96 2.90 2.63 2.60 2.58 2.56 2.54 2.52 2.51 2.49 2.48 2.46 4.54 4.04 3.73 3.50 3.33 3.20 3.09 3.00 2.93 2.87 2.60 2.57 2.55 2.53 2.51 2.49 2.48 2.46 2.45 2.44 4.51 4.02 3.70 3.47 3.30 3.17 3.07 2.98 2.91 2.84 2.57 2.55 2.53 2.51 2.49 2.47 2.45 2.44 2.42 2.41 4.13 3.65 3.34 3.12 2.95 2.82 2.72 2.63 2.56 2.50 2.22 2.20 2.17 2.15 2.13 2.12 2.10 2.08 2.07 2.05 3.95 3.48 3.17 2.96 2.79 2.66 2.56 2.47 2.40 2.34
2.06
2.03
2.01
1.99
1.97
1.95
1.93
1.92
1.90
1.89
13 6125.86 29 99.42 6257.05 26.98 99.46 14.31 26.52 9.82 13.85 7.66 9.39 7.24 6.41 6.00 5.61 5.21 5.05 4.66 4.65 4.26 4.34 3.95 4.10 3.71 3.91 3.52 3.75 3.36 3.61 3.23 3.50 3.11 3.40 3.01 3.32 2.93 3.24 2.86 3.18 2.79 3.12 2.73 3.07 2.68 3.02 2.63 2.98 2.59 2.94 2.55 2.90 2.51 2.87 2.48 2.84 2.45 2.81 2.42 2.79 2.40 2.44 2.04 2.28
1.87
14 6142.67 30 99.43 6260.65 26.92 99.47 14.25 26.50 9.77 13.84 7.60 9.38 7.23 6.36 5.99 5.56 5.20 5.01 4.65 4.60 4.25 4.29 3.94 4.05 3.70 3.86 3.51 3.70 3.35 3.56 3.21 3.45 3.10 3.35 3.00 3.27 2.92 3.19 2.84 3.13 2.78 3.07 2.72 3.02 2.67 2.97 2.62 2.93 2.58 2.89 2.54 2.86 2.50 2.82 2.47 2.79 2.44 2.77 2.41 2.74 2.39 2.39 2.03 2.23
1.86
15 6157.28 60 99.43 6313.03 26.87 99.48 14.20 26.32 9.72 13.65 7.56 9.20 7.06 6.31 5.82 5.52 5.03 4.96 4.48 4.56 4.08 4.25 3.78 4.01 3.54 3.82 3.34 3.66 3.18 3.52 3.05 3.41 2.93 3.31 2.83 3.23 2.75 3.15 2.67 3.09 2.61 3.03 2.55 2.98 2.50 2.93 2.45 2.89 2.40 2.85 2.36 2.81 2.33 2.78 2.29 2.75 2.26 2.73 2.23 2.70 2.21 2.35 1.84 2.19
1.66
16 6170.10 120 99.44 6339.39 26.83 99.49 14.15 26.22 9.68 13.56 7.52 9.11 6.97 6.28 5.74 5.48 4.95 4.92 4.40 4.52 4.00 4.21 3.69 3.97 3.45 3.78 3.25 3.62 3.09 3.49 2.96 3.37 2.84 3.27 2.75 3.19 2.66 3.12 2.58 3.05 2.52 2.99 2.46 2.94 2.40 2.89 2.35 2.85 2.31 2.81 2.27 2.78 2.23 2.75 2.20 2.72 2.17 2.69 2.14 2.66 2.11 2.31 1.73 2.15
1.53
The Chi-Squared () distribution table 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
0.005 0.000 0.010 0.072 0.207 0.412 0.676 0.989 1.344 1.735 2.156 2.603 3.074 3.565 4.075 4.601 5.142 5.697 6.265 6.844 7.434 8.034 8.643 9.260 9.886 10.520 11.160 11.808 12.461 13.121 13.787 14.458 15.134 15.815 16.501 17.192 17.887
0.01 0.000 0.020 0.115 0.297 0.554 0.872 1.239 1.646 2.088 2.558 3.053 3.571 4.107 4.660 5.229 5.812 6.408 7.015 7.633 8.260 8.897 9.542 10.196 10.856 11.524 12.198 12.879 13.565 14.256 14.953 15.655 16.362 17.074 17.789 18.509 19.233
0.025 0.001 0.051 0.216 0.484 0.831 1.237 1.690 2.180 2.700 3.247 3.816 4.404 5.009 5.629 6.262 6.908 7.564 8.231 8.907 9.591 10.283 10.982 11.689 12.401 13.120 13.844 14.573 15.308 16.047 16.791 17.539 18.291 19.047 19.806 20.569 21.336
0.05 0.004 0.103 0.352 0.711 1.145 1.635 2.167 2.733 3.325 3.940 4.575 5.226 5.892 6.571 7.261 7.962 8.672 9.390 10.117 10.851 11.591 12.338 13.091 13.848 14.611 15.379 16.151 16.928 17.708 18.493 19.281 20.072 20.867 21.664 22.465 23.269
0.1 0.016 0.211 0.584 1.064 1.610 2.204 2.833 3.490 4.168 4.865 5.578 6.304 7.042 7.790 8.547 9.312 10.085 10.865 11.651 12.443 13.240 14.041 14.848 15.659 16.473 17.292 18.114 18.939 19.768 20.599 21.434 22.271 23.110 23.952 24.797 25.643
0.25 0.102 0.575 1.213 1.923 2.675 3.455 4.255 5.071 5.899 6.737 7.584 8.438 9.299 10.165 11.037 11.912 12.792 13.675 14.562 15.452 16.344 17.240 18.137 19.037 19.939 20.843 21.749 22.657 23.567 24.478 25.390 26.304 27.219 28.136 29.054 29.973
0.5 0.455 1.386 2.366 3.357 4.351 5.348 6.346 7.344 8.343 9.342 10.341 11.340 12.340 13.339 14.339 15.338 16.338 17.338 18.338 19.337 20.337 21.337 22.337 23.337 24.337 25.336 26.336 27.336 28.336 29.336 30.336 31.336 32.336 33.336 34.336 35.336
0.75 1.323 2.773 4.108 5.385 6.626 7.841 9.037 10.219 11.389 12.549 13.701 14.845 15.984 17.117 18.245 19.369 20.489 21.605 22.718 23.828 24.935 26.039 27.141 28.241 29.339 30.435 31.528 32.620 33.711 34.800 35.887 36.973 38.058 39.141 40.223 41.304
0.9 2.706 4.605 6.251 7.779 9.236 10.645 12.017 13.362 14.684 15.987 17.275 18.549 19.812 21.064 22.307 23.542 24.769 25.989 27.204 28.412 29.615 30.813 32.007 33.196 34.382 35.563 36.741 37.916 39.087 40.256 41.422 42.585 43.745 44.903 46.059 47.212
0.95 3.841 5.991 7.815 9.488 11.070 12.592 14.067 15.507 16.919 18.307 19.675 21.026 22.362 23.685 24.996 26.296 27.587 28.869 30.144 31.410 32.671 33.924 35.172 36.415 37.652 38.885 40.113 41.337 42.557 43.773 44.985 46.194 47.400 48.602 49.802 50.998
0.975 5.024 7.378 9.348 11.143 12.833 14.449 16.013 17.535 19.023 20.483 21.920 23.337 24.736 26.119 27.488 28.845 30.191 31.526 32.852 34.170 35.479 36.781 38.076 39.364 40.646 41.923 43.195 44.461 45.722 46.979 48.232 49.480 50.725 51.966 53.203 54.437
0.99 6.635 9.210 11.345 13.277 15.086 16.812 18.475 20.090 21.666 23.209 24.725 26.217 27.688 29.141 30.578 32.000 33.409 34.805 36.191 37.566 38.932 40.289 41.638 42.980 44.314 45.642 46.963 48.278 49.588 50.892 52.191 53.486 54.776 56.061 57.342 58.619
0.995 7.879 10.597 12.838 14.860 16.750 18.548 20.278 21.955 23.589 25.188 26.757 28.300 29.819 31.319 32.801 34.267 35.718 37.156 38.582 39.997 41.401 42.796 44.181 45.559 46.928 48.290 49.645 50.993 52.336 53.672 55.003 56.328 57.648 58.964 60.275 61.581
0.999 10.828 13.816 16.266 18.467 20.515 22.458 24.322 26.124 27.877 29.588 31.264 32.909 34.528 36.123 37.697 39.252 40.790 42.312 43.820 45.315 46.797 48.268 49.728 51.179 52.620 54.052 55.476 56.892 58.301 59.703 61.098 62.487 63.870 65.247 66.619 67.985
37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 80 90 100
18.586 19.289 19.996 20.707 21.421 22.138 22.859 23.584 24.311 25.041 25.775 26.511 27.249 27.991 28.735 29.481 30.230 30.981 31.735 32.490 33.248 34.008 34.770 35.534 36.301 37.068 37.838 38.610 39.383 40.158 40.935 41.713 42.494 43.275 51.172 59.196 67.328
19.960 20.691 21.426 22.164 22.906 23.650 24.398 25.148 25.901 26.657 27.416 28.177 28.941 29.707 30.475 31.246 32.018 32.793 33.570 34.350 35.131 35.913 36.698 37.485 38.273 39.063 39.855 40.649 41.444 42.240 43.038 43.838 44.639 45.442 53.540 61.754 70.065
22.106 22.878 23.654 24.433 25.215 25.999 26.785 27.575 28.366 29.160 29.956 30.755 31.555 32.357 33.162 33.968 34.776 35.586 36.398 37.212 38.027 38.844 39.662 40.482 41.303 42.126 42.950 43.776 44.603 45.431 46.261 47.092 47.924 48.758 57.153 65.647 74.222
24.075 24.884 25.695 26.509 27.326 28.144 28.965 29.787 30.612 31.439 32.268 33.098 33.930 34.764 35.600 36.437 37.276 38.116 38.958 39.801 40.646 41.492 42.339 43.188 44.038 44.889 45.741 46.595 47.450 48.305 49.162 50.020 50.879 51.739 60.391 69.126 77.929
26.492 27.343 28.196 29.051 29.907 30.765 31.625 32.487 33.350 34.215 35.081 35.949 36.818 37.689 38.560 39.433 40.308 41.183 42.060 42.937 43.816 44.696 45.577 46.459 47.342 48.226 49.111 49.996 50.883 51.770 52.659 53.548 54.438 55.329 64.278 73.291 82.358
30.893 31.815 32.737 33.660 34.585 35.510 36.436 37.363 38.291 39.220 40.149 41.079 42.010 42.942 43.874 44.808 45.741 46.676 47.610 48.546 49.482 50.419 51.356 52.294 53.232 54.171 55.110 56.050 56.990 57.931 58.872 59.814 60.756 61.698 71.145 80.625 90.133
36.336 37.335 38.335 39.335 40.335 41.335 42.335 43.335 44.335 45.335 46.335 47.335 48.335 49.335 50.335 51.335 52.335 53.335 54.335 55.335 56.335 57.335 58.335 59.335 60.335 61.335 62.335 63.335 64.335 65.335 66.335 67.335 68.334 69.334 79.334 89.334 99.334
42.383 43.462 44.539 45.616 46.692 47.766 48.840 49.913 50.985 52.056 53.127 54.196 55.265 56.334 57.401 58.468 59.534 60.600 61.665 62.729 63.793 64.857 65.919 66.981 68.043 69.104 70.165 71.225 72.285 73.344 74.403 75.461 76.519 77.577 88.130 98.650 109.141
48.363 49.513 50.660 51.805 52.949 54.090 55.230 56.369 57.505 58.641 59.774 60.907 62.038 63.167 64.295 65.422 66.548 67.673 68.796 69.919 71.040 72.160 73.279 74.397 75.514 76.630 77.745 78.860 79.973 81.085 82.197 83.308 84.418 85.527 96.578 107.565 118.498
52.192 53.384 54.572 55.758 56.942 58.124 59.304 60.481 61.656 62.830 64.001 65.171 66.339 67.505 68.669 69.832 70.993 72.153 73.311 74.468 75.624 76.778 77.931 79.082 80.232 81.381 82.529 83.675 84.821 85.965 87.108 88.250 89.391 90.531 101.879 113.145 124.342
55.668 56.896 58.120 59.342 60.561 61.777 62.990 64.201 65.410 66.617 67.821 69.023 70.222 71.420 72.616 73.810 75.002 76.192 77.380 78.567 79.752 80.936 82.117 83.298 84.476 85.654 86.830 88.004 89.177 90.349 91.519 92.689 93.856 95.023 106.629 118.136 129.561
59.893 61.162 62.428 63.691 64.950 66.206 67.459 68.710 69.957 71.201 72.443 73.683 74.919 76.154 77.386 78.616 79.843 81.069 82.292 83.513 84.733 85.950 87.166 88.379 89.591 90.802 92.010 93.217 94.422 95.626 96.828 98.028 99.228 100.425 112.329 124.116 135.807
62.883 64.181 65.476 66.766 68.053 69.336 70.616 71.893 73.166 74.437 75.704 76.969 78.231 79.490 80.747 82.001 83.253 84.502 85.749 86.994 88.236 89.477 90.715 91.952 93.186 94.419 95.649 96.878 98.105 99.330 100.554 101.776 102.996 104.215 116.321 128.299 140.169
69.346 70.703 72.055 73.402 74.745 76.084 77.419 78.750 80.077 81.400 82.720 84.037 85.351 86.661 87.968 89.272 90.573 91.872 93.168 94.461 95.751 97.039 98.324 99.607 100.888 102.166 103.442 104.716 105.988 107.258 108.526 109.791 111.055 112.317 124.839 137.208 149.449
