APPENDIX 3
Tables
Table 1 Binomial Probabilities
Tabulated values are P(Y ≤ a) =a∑
y=0p(y). (Computations are rounded at third decimal place.)
(a) n = 5
p
a 0.01 0.05 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 0.95 0.99 a
0 .951 .774 .590 .328 .168 .078 .031 .010 .002 .000 .000 .000 .000 01 .999 .977 .919 .737 .528 .337 .188 .087 .031 .007 .000 .000 .000 12 1.000 .999 .991 .942 .837 .683 .500 .317 .163 .058 .009 .001 .000 23 1.000 1.000 1.000 .993 .969 .913 .812 .663 .472 .263 .081 .023 .001 34 1.000 1.000 1.000 1.000 .998 .990 .969 .922 .832 .672 .410 .226 .049 4
(b) n = 10
p
a 0.01 0.05 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 0.95 0.99 a
0 .904 .599 .349 .107 .028 .006 .001 .000 .000 .000 .000 .000 .000 01 .996 .914 .736 .376 .149 .046 .011 .002 .000 .000 .000 .000 .000 12 1.000 .988 .930 .678 .383 .167 .055 .012 .002 .000 .000 .000 .000 23 1.000 .999 .987 .879 .650 .382 .172 .055 .011 .001 .000 .000 .000 34 1.000 1.000 .998 .967 .850 .633 .377 .166 .047 .006 .000 .000 .000 45 1.000 1.000 1.000 .994 .953 .834 .623 .367 .150 .033 .002 .000 .000 56 1.000 1.000 1.000 .999 .989 .945 .828 .618 .350 .121 .013 .001 .000 67 1.000 1.000 1.000 1.000 .998 .988 .945 .833 .617 .322 .070 .012 .000 78 1.000 1.000 1.000 1.000 1.000 .998 .989 .954 .851 .624 .264 .086 .004 89 1.000 1.000 1.000 1.000 1.000 1.000 .999 .994 .972 .893 .651 .401 .096 9
839
840 Appendix 3 Tables
Table 1 (Continued )
(c) n = 15
p
a 0.01 0.05 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 0.95 0.99 a
0 .860 .463 .206 .035 .005 .000 .000 .000 .000 .000 .000 .000 .000 01 .990 .829 .549 .167 .035 .005 .000 .000 .000 .000 .000 .000 .000 12 1.000 .964 .816 .398 .127 .027 .004 .000 .000 .000 .000 .000 .000 23 1.000 .995 .944 .648 .297 .091 .018 .002 .000 .000 .000 .000 .000 34 1.000 .999 .987 .836 .515 .217 .059 .009 .001 .000 .000 .000 .000 45 1.000 1.000 .998 .939 .722 .403 .151 .034 .004 .000 .000 .000 .000 56 1.000 1.000 1.000 .982 .869 .610 .304 .095 .015 .001 .000 .000 .000 67 1.000 1.000 1.000 .996 .950 .787 .500 .213 .050 .004 .000 .000 .000 78 1.000 1.000 1.000 .999 .985 .905 .696 .390 .131 .018 .000 .000 .000 89 1.000 1.000 1.000 1.000 .996 .966 .849 .597 .278 .061 .002 .000 .000 9
10 1.000 1.000 1.000 1.000 .999 .991 .941 .783 .485 .164 .013 .001 .000 1011 1.000 1.000 1.000 1.000 1.000 .998 .982 .909 .703 .352 .056 .005 .000 1112 1.000 1.000 1.000 1.000 1.000 1.000 .996 .973 .873 .602 .184 .036 .000 1213 1.000 1.000 1.000 1.000 1.000 1.000 1.000 .995 .965 .833 .451 .171 .010 1314 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 .995 .965 .794 .537 .140 14
(d) n = 20
p
a 0.01 0.05 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 0.95 0.99 a
0 .818 .358 .122 .012 .001 .000 .000 .000 .000 .000 .000 .000 .000 01 .983 .736 .392 .069 .008 .001 .000 .000 .000 .000 .000 .000 .000 12 .999 .925 .677 .206 .035 .004 .000 .000 .000 .000 .000 .000 .000 23 1.000 .984 .867 .411 .107 .016 .001 .000 .000 .000 .000 .000 .000 34 1.000 .997 .957 .630 .238 .051 .006 .000 .000 .000 .000 .000 .000 45 1.000 1.000 .989 .804 .416 .126 .021 .002 .000 .000 .000 .000 .000 56 1.000 1.000 .998 .913 .608 .250 .058 .006 .000 .000 .000 .000 .000 67 1.000 1.000 1.000 .968 .772 .416 .132 .021 .001 .000 .000 .000 .000 78 1.000 1.000 1.000 .990 .887 .596 .252 .057 .005 .000 .000 .000 .000 89 1.000 1.000 1.000 .997 .952 .755 .412 .128 .017 .001 .000 .000 .000 9
10 1.000 1.000 1.000 .999 .983 .872 .588 .245 .048 .003 .000 .000 .000 1011 1.000 1.000 1.000 1.000 .995 .943 .748 .404 .113 .010 .000 .000 .000 1112 1.000 1.000 1.000 1.000 .999 .979 .868 .584 .228 .032 .000 .000 .000 1213 1.000 1.000 1.000 1.000 1.000 .994 .942 .750 .392 .087 .002 .000 .000 1314 1.000 1.000 1.000 1.000 1.000 .998 .979 .874 .584 .196 .011 .000 .000 1415 1.000 1.000 1.000 1.000 1.000 1.000 .994 .949 .762 .370 .043 .003 .000 1516 1.000 1.000 1.000 1.000 1.000 1.000 .999 .984 .893 .589 .133 .016 .000 1617 1.000 1.000 1.000 1.000 1.000 1.000 1.000 .996 .965 .794 .323 .075 .001 1718 1.000 1.000 1.000 1.000 1.000 1.000 1.000 .999 .992 .931 .608 .264 .017 1819 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 .999 .988 .878 .642 .182 19
Tables 841
Table 1 (Continued )
(e) n = 25
p
a 0.01 0.05 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 0.95 0.99 a
0 .778 .277 .072 .004 .000 .000 .000 .000 .000 .000 .000 .000 .000 01 .974 .642 .271 .027 .002 .000 .000 .000 .000 .000 .000 .000 .000 12 .998 .873 .537 .098 .009 .000 .000 .000 .000 .000 .000 .000 .000 23 1.000 .966 .764 .234 .033 .002 .000 .000 .000 .000 .000 .000 .000 34 1.000 .993 .902 .421 .090 .009 .000 .000 .000 .000 .000 .000 .000 45 1.000 .999 .967 .617 .193 .029 .002 .000 .000 .000 .000 .000 .000 56 1.000 1.000 .991 .780 .341 .074 .007 .000 .000 .000 .000 .000 .000 67 1.000 1.000 .998 .891 .512 .154 .022 .001 .000 .000 .000 .000 .000 78 1.000 1.000 1.000 .953 .677 .274 .054 .004 .000 .000 .000 .000 .000 89 1.000 1.000 1.000 .983 .811 .425 .115 .013 .000 .000 .000 .000 .000 9
10 1.000 1.000 1.000 .994 .902 .586 .212 .034 .002 .000 .000 .000 .000 1011 1.000 1.000 1.000 .998 .956 .732 .345 .078 .006 .000 .000 .000 .000 1112 1.000 1.000 1.000 1.000 .983 .846 .500 .154 .017 .000 .000 .000 .000 1213 1.000 1.000 1.000 1.000 .994 .922 .655 .268 .044 .002 .000 .000 .000 1314 1.000 1.000 1.000 1.000 .998 .966 .788 .414 .098 .006 .000 .000 .000 1415 1.000 1.000 1.000 1.000 1.000 .987 .885 .575 .189 .017 .000 .000 .000 1516 1.000 1.000 1.000 1.000 1.000 .996 .946 .726 .323 .047 .000 .000 .000 1617 1.000 1.000 1.000 1.000 1.000 .999 .978 .846 .488 .109 .002 .000 .000 1718 1.000 1.000 1.000 1.000 1.000 1.000 .993 .926 .659 .220 .009 .000 .000 1819 1.000 1.000 1.000 1.000 1.000 1.000 .998 .971 .807 .383 .033 .001 .000 1920 1.000 1.000 1.000 1.000 1.000 1.000 1.000 .991 .910 .579 .098 .007 .000 2021 1.000 1.000 1.000 1.000 1.000 1.000 1.000 .998 .967 .766 .236 .034 .000 2122 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 .991 .902 .463 .127 .002 2223 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 .998 .973 .729 .358 .026 2324 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 .996 .928 .723 .222 24
842 Appendix 3 Tables
Table 2 Table of e−x
x e−x x e−x x e−x x e−x
0.00 1.000000 2.60 .074274 5.10 .006097 7.60 .0005010.10 .904837 2.70 .067206 5.20 .005517 7.70 .0004530.20 .818731 2.80 .060810 5.30 .004992 7.80 .0004100.30 .740818 2.90 .055023 5.40 .004517 7.90 .0003710.40 .670320 3.00 .049787 5.50 .004087 8.00 .0003360.50 .606531 3.10 .045049 5.60 .003698 8.10 .0003040.60 .548812 3.20 .040762 5.70 .003346 8.20 .0002750.70 .496585 3.30 .036883 5.80 .003028 8.30 .0002490.80 .449329 3.40 .033373 5.90 .002739 8.40 .0002250.90 .406570 3.50 .030197 6.00 .002479 8.50 .0002041.00 .367879 3.60 .027324 6.10 .002243 8.60 .0001841.10 .332871 3.70 .024724 6.20 .002029 8.70 .0001671.20 .301194 3.80 .022371 6.30 .001836 8.80 .0001511.30 .272532 3.90 .020242 6.40 .001661 8.90 .0001361.40 .246597 4.00 .018316 6.50 .001503 9.00 .0001231.50 .223130 4.10 .016573 6.60 .001360 9.10 .0001121.60 .201897 4.20 .014996 6.70 .001231 9.20 .0001011.70 .182684 4.30 .013569 6.80 .001114 9.30 .0000911.80 .165299 4.40 .012277 6.90 .001008 9.40 .0000831.90 .149569 4.50 .011109 7.00 .000912 9.50 .0000752.00 .135335 4.60 .010052 7.10 .000825 9.60 .0000682.10 .122456 4.70 .009095 7.20 .000747 9.70 .0000612.20 .110803 4.80 .008230 7.30 .000676 9.80 .0000562.30 .100259 4.90 .007447 7.40 .000611 9.90 .0000502.40 .090718 5.00 .006738 7.50 .000553 10.00 .0000452.50 .082085
Tables 843
Table 3 Poisson Probabilities
P(Y ≤ a) =a∑
y=0
e−λ λy
y!
aλ 0 1 2 3 4 5 6 7 8 9
0.02 0.980 1.0000.04 0.961 0.999 1.0000.06 0.942 0.998 1.0000.08 0.923 0.997 1.0000.10 0.905 0.995 1.000
0.15 0.861 0.990 0.999 1.0000.20 0.819 0.982 0.999 1.0000.25 0.779 0.974 0.998 1.0000.30 0.741 0.963 0.996 1.000
0.35 0.705 0.951 0.994 1.0000.40 0.670 0.938 0.992 0.999 1.0000.45 0.638 0.925 0.989 0.999 1.0000.50 0.607 0.910 0.986 0.998 1.000
0.55 0.577 0.894 0.982 0.988 1.0000.60 0.549 0.878 0.977 0.997 1.0000.65 0.522 0.861 0.972 0.996 0.999 1.0000.70 0.497 0.844 0.966 0.994 0.999 1.0000.75 0.472 0.827 0.959 0.993 0.999 1.000
0.80 0.449 0.809 0.953 0.991 0.999 1.0000.85 0.427 0.791 0.945 0.989 0.998 1.0000.90 0.407 0.772 0.937 0.987 0.998 1.0000.95 0.387 0.754 0.929 0.981 0.997 1.0001.00 0.368 0.736 0.920 0.981 0.996 0.999 1.000
1.1 0.333 0.699 0.900 0.974 0.995 0.999 1.0001.2 0.301 0.663 0.879 0.966 0.992 0.998 1.0001.3 0.273 0.627 0.857 0.957 0.989 0.998 1.0001.4 0.247 0.592 0.833 0.946 0.986 0.997 0.999 1.0001.5 0.223 0.558 0.809 0.934 0.981 0.996 0.999 1.000
1.6 0.202 0.525 0.783 0.921 0.976 0.994 0.999 1.0001.7 0.183 0.493 0.757 0.907 0.970 0.992 0.998 1.0001.8 0.165 0.463 0.731 0.891 0.964 0.990 0.997 0.999 1.0001.9 0.150 0.434 0.704 0.875 0.956 0.987 0.997 0.999 1.0002.0 0.135 0.406 0.677 0.857 0.947 0.983 0.995 0.999 1.000
844 Appendix 3 Tables
Table 3 (Continued )
aλ 0 1 2 3 4 5 6 7 8 9
2.2 0.111 0.355 0.623 0.819 0.928 0.975 0.993 0.998 1.0002.4 0.091 0.308 0.570 0.779 0.904 0.964 0.988 0.997 0.999 1.0002.6 0.074 0.267 0.518 0.736 0.877 0.951 0.983 0.995 0.999 1.0002.8 0.061 0.231 0.469 0.692 0.848 0.935 0.976 0.992 0.998 0.9993.0 0.050 0.199 0.423 0.647 0.815 0.916 0.966 0.988 0.996 0.999
3.2 0.041 0.171 0.380 0.603 0.781 0.895 0.955 0.983 0.994 0.9983.4 0.033 0.147 0.340 0.558 0.744 0.871 0.942 0.977 0.992 0.9973.6 0.027 0.126 0.303 0.515 0.706 0.844 0.927 0.969 0.988 0.9963.8 0.022 0.107 0.269 0.473 0.668 0.816 0.909 0.960 0.984 0.9944.0 0.018 0.092 0.238 0.433 0.629 0.785 0.889 0.949 0.979 0.992
4.2 0.015 0.078 0.210 0.395 0.590 0.753 0.867 0.936 0.972 0.9894.4 0.012 0.066 0.185 0.359 0.551 0.720 0.844 0.921 0.964 0.9854.6 0.010 0.056 0.163 0.326 0.513 0.686 0.818 0.905 0.955 0.9804.8 0.008 0.048 0.143 0.294 0.476 0.651 0.791 0.887 0.944 0.9755.0 0.007 0.040 0.125 0.265 0.440 0.616 0.762 0.867 0.932 0.968
5.2 0.006 0.034 0.109 0.238 0.406 0.581 0.732 0.845 0.918 0.9605.4 0.005 0.029 0.095 0.213 0.373 0.546 0.702 0.822 0.903 0.9515.6 0.004 0.024 0.082 0.191 0.342 0.512 0.670 0.797 0.886 0.9415.8 0.003 0.021 0.072 0.170 0.313 0.478 0.638 0.771 0.867 0.9296.0 0.002 0.017 0.062 0.151 0.285 0.446 0.606 0.744 0.847 0.916
10 11 12 13 14 15 16
2.8 1.0003.0 1.0003.2 1.0003.4 0.999 1.0003.6 0.999 1.0003.8 0.998 0.999 1.0004.0 0.997 0.999 1.000
4.2 0.996 0.999 1.0004.4 0.994 0.998 0.999 1.0004.6 0.992 0.997 0.999 1.0004.8 0.990 0.996 0.999 1.0005.0 0.986 0.995 0.998 0.999 1.000
5.2 0.982 0.993 0.997 0.999 1.0005.4 0.977 0.990 0.996 0.999 1.0005.6 0.972 0.988 0.995 0.998 0.999 1.0005.8 0.965 0.984 0.993 0.997 0.999 1.0006.0 0.957 0.980 0.991 0.996 0.999 0.999 1.000
Tables 845
Table 3 (Continued )
aλ 0 1 2 3 4 5 6 7 8 9
6.2 0.002 0.015 0.054 0.134 0.259 0.414 0.574 0.716 0.826 0.9026.4 0.002 0.012 0.046 0.119 0.235 0.384 0.542 0.687 0.803 0.8866.6 0.001 0.010 0.040 0.105 0.213 0.355 0.511 0.658 0.780 0.8696.8 0.001 0.009 0.034 0.093 0.192 0.327 0.480 0.628 0.755 0.8507.0 0.001 0.007 0.030 0.082 0.173 0.301 0.450 0.599 0.729 0.830
7.2 0.001 0.006 0.025 0.072 0.156 0.276 0.420 0.569 0.703 0.8107.4 0.001 0.005 0.022 0.063 0.140 0.253 0.392 0.539 0.676 0.7887.6 0.001 0.004 0.019 0.055 0.125 0.231 0.365 0.510 0.648 0.7657.8 0.000 0.004 0.016 0.048 0.112 0.210 0.338 0.481 0.620 0.741
8.0 0.000 0.003 0.014 0.042 0.100 0.191 0.313 0.453 0.593 0.7178.5 0.000 0.002 0.009 0.030 0.074 0.150 0.256 0.386 0.523 0.6539.0 0.000 0.001 0.006 0.021 0.055 0.116 0.207 0.324 0.456 0.5879.5 0.000 0.001 0.004 0.015 0.040 0.089 0.165 0.269 0.392 0.522
10.0 0.000 0.000 0.003 0.010 0.029 0.067 0.130 0.220 0.333 0.458
10 11 12 13 14 15 16 17 18 19
6.2 0.949 0.975 0.989 0.995 0.998 0.999 1.0006.4 0.939 0.969 0.986 0.994 0.997 0.999 1.0006.6 0.927 0.963 0.982 0.992 0.997 0.999 0.999 1.0006.8 0.915 0.955 0.978 0.990 0.996 0.998 0.999 1.0007.0 0.901 0.947 0.973 0.987 0.994 0.998 0.999 1.000
7.2 0.887 0.937 0.967 0.984 0.993 0.997 0.999 0.999 1.0007.4 0.871 0.926 0.961 0.980 0.991 0.996 0.998 0.999 1.0007.6 0.854 0.915 0.954 0.976 0.989 0.995 0.998 0.999 1.0007.8 0.835 0.902 0.945 0.971 0.986 0.993 0.997 0.999 1.000
8.0 0.816 0.888 0.936 0.966 0.983 0.992 0.996 0.998 0.999 1.0008.5 0.763 0.849 0.909 0.949 0.973 0.986 0.993 0.997 0.999 0.9999.0 0.706 0.803 0.876 0.926 0.959 0.978 0.989 0.995 0.998 0.9999.5 0.645 0.752 0.836 0.898 0.940 0.967 0.982 0.991 0.996 0.998
10.0 0.583 0.697 0.792 0.864 0.917 0.951 0.973 0.986 0.993 0.997
20 21 22
8.5 1.0009.0 1.0009.5 0.999 1.000
10.0 0.998 0.999 1.000
846 Appendix 3 Tables
Table 3 (Continued )
aλ 0 1 2 3 4 5 6 7 8 9
10.5 0.000 0.000 0.002 0.007 0.021 0.050 0.102 0.179 0.279 0.39711.0 0.000 0.000 0.001 0.005 0.015 0.038 0.079 0.143 0.232 0.34111.5 0.000 0.000 0.001 0.003 0.011 0.028 0.060 0.114 0.191 0.28912.0 0.000 0.000 0.001 0.002 0.008 0.020 0.046 0.090 0.155 0.24212.5 0.000 0.000 0.000 0.002 0.005 0.015 0.035 0.070 0.125 0.201
13.0 0.000 0.000 0.000 0.001 0.004 0.011 0.026 0.054 0.100 0.16613.5 0.000 0.000 0.000 0.001 0.003 0.008 0.019 0.041 0.079 0.13514.0 0.000 0.000 0.000 0.000 0.002 0.006 0.014 0.032 0.062 0.10914.5 0.000 0.000 0.000 0.000 0.001 0.004 0.010 0.024 0.048 0.08815.0 0.000 0.000 0.000 0.000 0.001 0.003 0.008 0.018 0.037 0.070
10 11 12 13 14 15 16 17 18 19
10.5 0.521 0.639 0.742 0.825 0.888 0.932 0.960 0.978 0.988 0.99411.0 0.460 0.579 0.689 0.781 0.854 0.907 0.944 0.968 0.982 0.99111.5 0.402 0.520 0.633 0.733 0.815 0.878 0.924 0.954 0.974 0.98612.0 0.347 0.462 0.576 0.682 0.772 0.844 0.899 0.937 0.963 0.97912.5 0.297 0.406 0.519 0.628 0.725 0.806 0.869 0.916 0.948 0.969
13.0 0.252 0.353 0.463 0.573 0.675 0.764 0.835 0.890 0.930 0.95713.5 0.211 0.304 0.409 0.518 0.623 0.718 0.798 0.861 0.908 0.94214.0 0.176 0.260 0.358 0.464 0.570 0.669 0.756 0.827 0.883 0.92314.5 0.145 0.220 0.311 0.413 0.518 0.619 0.711 0.790 0.853 0.90115.0 0.118 0.185 0.268 0.363 0.466 0.568 0.664 0.749 0.819 0.875
20 21 22 23 24 25 26 27 28 29
10.5 0.997 0.999 0.999 1.00011.0 0.995 0.998 0.999 1.00011.5 0.992 0.996 0.998 0.999 1.00012.0 0.988 0.994 0.997 0.999 0.999 1.00012.5 0.983 0.991 0.995 0.998 0.999 0.999 1.000
13.0 0.975 0.986 0.992 0.996 0.998 0.999 1.00013.5 0.965 0.980 0.989 0.994 0.997 0.998 0.999 1.00014.0 0.952 0.971 0.983 0.991 0.995 0.997 0.999 0.999 1.00014.5 0.936 0.960 0.976 0.986 0.992 0.996 0.998 0.999 0.999 1.00015.0 0.917 0.947 0.967 0.981 0.989 0.994 0.997 0.998 0.999 1.000
Tables 847
Table 3 (Continued )
aλ 4 5 6 7 8 9 10 11 12 13
16 0.000 0.001 0.004 0.010 0.022 0.043 0.077 0.127 0.193 0.27517 0.000 0.001 0.002 0.005 0.013 0.026 0.049 0.085 0.135 0.20118 0.000 0.000 0.001 0.003 0.007 0.015 0.030 0.055 0.092 0.14319 0.000 0.000 0.001 0.002 0.004 0.009 0.018 0.035 0.061 0.09820 0.000 0.000 0.000 0.001 0.002 0.005 0.011 0.021 0.039 0.06621 0.000 0.000 0.000 0.000 0.001 0.003 0.006 0.013 0.025 0.04322 0.000 0.000 0.000 0.000 0.001 0.002 0.004 0.008 0.015 0.02823 0.000 0.000 0.000 0.000 0.000 0.001 0.002 0.004 0.009 0.01724 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.003 0.005 0.01125 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.001 0.003 0.006
14 15 16 17 18 19 20 21 22 23
16 0.368 0.467 0.566 0.659 0.742 0.812 0.868 0.911 0.942 0.96317 0.281 0.371 0.468 0.564 0.655 0.736 0.805 0.861 0.905 0.93718 0.208 0.287 0.375 0.469 0.562 0.651 0.731 0.799 0.855 0.89919 0.150 0.215 0.292 0.378 0.469 0.561 0.647 0.725 0.793 0.84920 0.105 0.157 0.221 0.297 0.381 0.470 0.559 0.644 0.721 0.78721 0.072 0.111 0.163 0.227 0.302 0.384 0.471 0.558 0.640 0.71622 0.048 0.077 0.117 0.169 0.232 0.306 0.387 0.472 0.556 0.63723 0.031 0.052 0.082 0.123 0.175 0.238 0.310 0.389 0.472 0.55524 0.020 0.034 0.056 0.087 0.128 0.180 0.243 0.314 0.392 0.47325 0.012 0.022 0.038 0.060 0.092 0.134 0.185 0.247 0.318 0.394
24 25 26 27 28 29 30 31 32 33
16 0.978 0.987 0.993 0.996 0.998 0.999 0.999 1.00017 0.959 0.975 0.985 0.991 0.995 0.997 0.999 0.999 1.00018 0.932 0.955 0.972 0.983 0.990 0.994 0.997 0.998 0.999 1.00019 0.893 0.927 0.951 0.969 0.980 0.988 0.993 0.996 0.998 0.99920 0.843 0.888 0.922 0.948 0.966 0.978 0.987 0.992 0.995 0.99721 0.782 0.838 0.883 0.917 0.944 0.963 0.976 0.985 0.991 0.99422 0.712 0.777 0.832 0.877 0.913 0.940 0.959 0.973 0.983 0.98923 0.635 0.708 0.772 0.827 0.873 0.908 0.936 0.956 0.971 0.98124 0.554 0.632 0.704 0.768 0.823 0.868 0.904 0.932 0.953 0.96925 0.473 0.553 0.629 0.700 0.763 0.818 0.863 0.900 0.929 0.950
34 35 36 37 38 39 40 41 42 43
19 0.999 1.00020 0.999 0.999 1.00021 0.997 0.998 0.999 0.999 1.00022 0.994 0.996 0.998 0.999 0.999 1.00023 0.988 0.993 0.996 0.997 0.999 0.999 1.00024 0.979 0.987 0.992 0.995 0.997 0.998 0.999 0.999 1.00025 0.966 0.978 0.985 0.991 0.991 0.997 0.998 0.999 0.999 1.000
848 Appendix 3 Tables
Table 4 Normal Curve AreasStandard normal probability in right-hand tail(for negative values of z, areas are found by symmetry)
0 z
Area
Second decimal place of z
z .00 .01 .02 .03 .04 .05 .06 .07 .08 .09
0.0 .5000 .4960 .4920 .4880 .4840 .4801 .4761 .4721 .4681 .46410.1 .4602 .4562 .4522 .4483 .4443 .4404 .4364 .4325 .4286 .42470.2 .4207 .4168 .4129 .4090 .4052 .4013 .3974 .3936 .3897 .38590.3 .3821 .3783 .3745 .3707 .3669 .3632 .3594 .3557 .3520 .34830.4 .3446 .3409 .3372 .3336 .3300 .3264 .3228 .3192 .3156 .3121
0.5 .3085 .3050 .3015 .2981 .2946 .2912 .2877 .2843 .2810 .27760.6 .2743 .2709 .2676 .2643 .2611 .2578 .2546 .2514 .2483 .24510.7 .2420 .2389 .2358 .2327 .2296 .2266 .2236 .2206 .2177 .21480.8 .2119 .2090 .2061 .2033 .2005 .1977 .1949 .1922 .1894 .18670.9 .1841 .1814 .1788 .1762 .1736 .1711 .1685 .1660 .1635 .1611
1.0 .1587 .1562 .1539 .1515 .1492 .1469 .1446 .1423 .1401 .13791.1 .1357 .1335 .1314 .1292 .1271 .1251 .1230 .1210 .1190 .11701.2 .1151 .1131 .1112 .1093 .1075 .1056 .1038 .1020 .1003 .09851.3 .0968 .0951 .0934 .0918 .0901 .0885 .0869 .0853 .0838 .08231.4 .0808 .0793 .0778 .0764 .0749 .0735 .0722 .0708 .0694 .0681
1.5 .0668 .0655 .0643 .0630 .0618 .0606 .0594 .0582 .0571 .05591.6 .0548 .0537 .0526 .0516 .0505 .0495 .0485 .0475 .0465 .04551.7 .0446 .0436 .0427 .0418 .0409 .0401 .0392 .0384 .0375 .03671.8 .0359 .0352 .0344 .0336 .0329 .0322 .0314 .0307 .0301 .02941.9 .0287 .0281 .0274 .0268 .0262 .0256 .0250 .0244 .0239 .0233
2.0 .0228 .0222 .0217 .0212 .0207 .0202 .0197 .0192 .0188 .01832.1 .0179 .0174 .0170 .0166 .0162 .0158 .0154 .0150 .0146 .01432.2 .0139 .0136 .0132 .0129 .0125 .0122 .0119 .0116 .0113 .01102.3 .0107 .0104 .0102 .0099 .0096 .0094 .0091 .0089 .0087 .00842.4 .0082 .0080 .0078 .0075 .0073 .0071 .0069 .0068 .0066 .0064
2.5 .0062 .0060 .0059 .0057 .0055 .0054 .0052 .0051 .0049 .00482.6 .0047 .0045 .0044 .0043 .0041 .0040 .0039 .0038 .0037 .00362.7 .0035 .0034 .0033 .0032 .0031 .0030 .0029 .0028 .0027 .00262.8 .0026 .0025 .0024 .0023 .0023 .0022 .0021 .0021 .0020 .00192.9 .0019 .0018 .0017 .0017 .0016 .0016 .0015 .0015 .0014 .0014
3.0 .001353.5 .000 2334.0 .000 031 74.5 .000 003 405.0 .000 000 287
From R. E. Walpole, Introduction to Statistics (New York: Macmillan, 1968).
Tables 849
Table 5 Percentage Points of the t Distributions
taa
t.100 t.050 t.025 t.010 t.005 df
3.078 6.314 12.706 31.821 63.657 11.886 2.920 4.303 6.965 9.925 21.638 2.353 3.182 4.541 5.841 31.533 2.132 2.776 3.747 4.604 4
1.476 2.015 2.571 3.365 4.032 51.440 1.943 2.447 3.143 3.707 61.415 1.895 2.365 2.998 3.499 71.397 1.860 2.306 2.896 3.355 81.383 1.833 2.262 2.821 3.250 9
1.372 1.812 2.228 2.764 3.169 101.363 1.796 2.201 2.718 3.106 111.356 1.782 2.179 2.681 3.055 121.350 1.771 2.160 2.650 3.012 131.345 1.761 2.145 2.624 2.977 141.341 1.753 2.131 2.602 2.947 15
1.337 1.746 2.120 2.583 2.921 161.333 1.740 2.110 2.567 2.898 171.330 1.734 2.101 2.552 2.878 181.328 1.729 2.093 2.539 2.861 191.325 1.725 2.086 2.528 2.845 20
1.323 1.721 2.080 2.518 2.831 211.321 1.717 2.074 2.508 2.819 221.319 1.714 2.069 2.500 2.807 231.318 1.711 2.064 2.492 2.797 241.316 1.708 2.060 2.485 2.787 25
1.315 1.706 2.056 2.479 2.779 261.314 1.703 2.052 2.473 2.771 271.313 1.701 2.048 2.467 2.763 281.311 1.699 2.045 2.462 2.756 291.282 1.645 1.960 2.326 2.576 inf.
From “Table of Percentage Points of the t-Distribution.” Computed byMaxine Merrington, Biometrika, Vol. 32 (1941), p. 300.
850 Appendix 3 Tables
Table 6 Percentage Points of the χ2 Distributions
0 c2a
a
df χ 20.995 χ2
0.990 χ20.975 χ 2
0.950 χ20.900
1 0.0000393 0.0001571 0.0009821 0.0039321 0.01579082 0.0100251 0.0201007 0.0506356 0.102587 0.2107203 0.0717212 0.114832 0.215795 0.351846 0.5843754 0.206990 0.297110 0.484419 0.710721 1.063623
5 0.411740 0.554300 0.831211 1.145476 1.610316 0.675727 0.872085 1.237347 1.63539 2.204137 0.989265 1.239043 1.68987 2.16735 2.833118 1.344419 1.646482 2.17973 2.73264 3.489549 1.734926 2.087912 2.70039 3.32511 4.16816
10 2.15585 2.55821 3.24697 3.94030 4.8651811 2.60321 3.05347 3.81575 4.57481 5.5777912 3.07382 3.57056 4.40379 5.22603 6.3038013 3.56503 4.10691 5.00874 5.89186 7.0415014 4.07468 4.66043 5.62872 6.57063 7.78953
15 4.60094 5.22935 6.26214 7.26094 8.5467516 5.14224 5.81221 6.90766 7.96164 9.3122317 5.69724 6.40776 7.56418 8.67176 10.085218 6.26481 7.01491 8.23075 9.39046 10.864919 6.84398 7.63273 8.90655 10.1170 11.6509
20 7.43386 8.26040 9.59083 10.8508 12.442621 8.03366 8.89720 10.28293 11.5913 13.239622 8.64272 9.54249 10.9823 12.3380 14.041523 9.26042 10.19567 11.6885 13.0905 14.847924 9.88623 10.8564 12.4011 13.8484 15.6587
25 10.5197 11.5240 13.1197 14.6114 16.473426 11.1603 12.1981 13.8439 15.3791 17.291927 11.8076 12.8786 14.5733 16.1513 18.113828 12.4613 13.5648 15.3079 16.9279 18.939229 13.1211 14.2565 16.0471 17.7083 19.7677
30 13.7867 14.9535 16.7908 18.4926 20.599240 20.7065 22.1643 24.4331 26.5093 29.050550 27.9907 29.7067 32.3574 34.7642 37.688660 35.5346 37.4848 40.4817 43.1879 46.4589
70 43.2752 45.4418 48.7576 51.7393 55.329080 51.1720 53.5400 57.1532 60.3915 64.277890 59.1963 61.7541 65.6466 69.1260 73.2912
100 67.3276 70.0648 74.2219 77.9295 82.3581
Tables 851
Table 6 (Continued )
χ20.100 χ 2
0.050 χ 20.025 χ2
0.010 χ20.005 df
2.70554 3.84146 5.02389 6.63490 7.87944 14.60517 5.99147 7.37776 9.21034 10.5966 26.25139 7.81473 9.34840 11.3449 12.8381 37.77944 9.48773 11.1433 13.2767 14.8602 4
9.23635 11.0705 12.8325 15.0863 16.7496 510.6446 12.5916 14.4494 16.8119 18.5476 612.0170 14.0671 16.0128 18.4753 20.2777 713.3616 15.5073 17.5346 20.0902 21.9550 814.6837 16.9190 19.0228 21.6660 23.5893 9
15.9871 18.3070 20.4831 23.2093 25.1882 1017.2750 19.6751 21.9200 24.7250 26.7569 1118.5494 21.0261 23.3367 26.2170 28.2995 1219.8119 22.3621 24.7356 27.6883 29.8194 1321.0642 23.6848 26.1190 29.1413 31.3193 14
22.3072 24.9958 27.4884 30.5779 32.8013 1523.5418 26.2962 28.8454 31.9999 34.2672 1624.7690 27.5871 30.1910 33.4087 35.7185 1725.9894 28.8693 31.5264 34.8053 37.1564 1827.2036 30.1435 32.8523 36.1908 38.5822 19
28.4120 31.4104 34.1696 37.5662 39.9968 2029.6151 32.6705 35.4789 38.9321 41.4010 2130.8133 33.9244 36.7807 40.2894 42.7956 2232.0069 35.1725 38.0757 41.6384 44.1813 2333.1963 36.4151 39.3641 42.9798 45.5585 24
34.3816 37.6525 40.6465 44.3141 46.9278 2535.5631 38.8852 41.9232 45.6417 48.2899 2636.7412 40.1133 43.1944 46.9630 49.6449 2737.9159 41.3372 44.4607 48.2782 50.9933 2839.0875 42.5569 45.7222 49.5879 52.3356 29
40.2560 43.7729 46.9792 50.8922 53.6720 3051.8050 55.7585 59.3417 63.6907 66.7659 4063.1671 67.5048 71.4202 76.1539 79.4900 5074.3970 79.0819 83.2976 88.3794 91.9517 60
85.5271 90.5312 95.0231 100.425 104.215 7096.5782 101.879 106.629 112.329 116.321 80
107.565 113.145 118.136 124.116 128.299 90118.498 124.342 129.561 135.807 140.169 100
From “Tables of the Percentage Points of the χ2-Distribution.” Biometrika, Vol. 32(1941), pp. 188–189, by Catherine M. Thompson.
852 Appendix 3 Tables
Table 7 Percentage Points of the F Distributions
0 Fa
a
Numerator dfDenominator
df α 1 2 3 4 5 6 7 8 9
1 .100 39.86 49.50 53.59 55.83 57.24 58.20 58.91 59.44 59.86.050 161.4 199.5 215.7 224.6 230.2 234.0 236.8 238.9 240.5.025 647.8 799.5 864.2 899.6 921.8 937.1 948.2 956.7 963.3.010 4052 4999.5 5403 5625 5764 5859 5928 5982 6022.005 16211 20000 21615 22500 23056 23437 23715 23925 24091
2 .100 8.53 9.00 9.16 9.24 9.29 9.33 9.35 9.37 9.38.050 18.51 19.00 19.16 19.25 19.30 19.33 19.35 19.37 19.38.025 38.51 39.00 39.17 39.25 39.30 39.33 39.36 39.37 39.39.010 98.50 99.00 99.17 99.25 99.30 99.33 99.36 99.37 99.39.005 198.5 199.0 199.2 199.2 199.3 199.3 199.4 199.4 199.4
3 .100 5.54 5.46 5.39 5.34 5.31 5.28 5.27 5.25 5.24.050 10.13 9.55 9.28 9.12 9.01 8.94 8.89 8.85 8.81.025 17.44 16.04 15.44 15.10 14.88 14.73 14.62 14.54 14.47.010 34.12 30.82 29.46 28.71 28.24 27.91 27.67 27.49 27.35.005 55.55 49.80 47.47 46.19 45.39 44.84 44.43 44.13 43.88
4 .100 4.54 4.32 4.19 4.11 4.05 4.01 3.98 3.95 3.94.050 7.71 6.94 6.59 6.39 6.26 6.16 6.09 6.04 6.00.025 12.22 10.65 9.98 9.60 9.36 9.20 9.07 8.98 8.90.010 21.20 18.00 16.69 15.98 15.52 15.21 14.98 14.80 14.66.005 31.33 26.28 24.26 23.15 22.46 21.97 21.62 21.35 21.14
5 .100 4.06 3.78 3.62 3.52 3.45 3.40 3.37 3.34 3.32.050 6.61 5.79 5.41 5.19 5.05 4.95 4.88 4.82 4.77.025 10.01 8.43 7.76 7.39 7.15 6.98 6.85 6.76 6.68.010 16.26 13.27 12.06 11.39 10.97 10.67 10.46 10.29 10.16.005 22.78 18.31 16.53 15.56 14.94 14.51 14.20 13.96 13.77
6 .100 3.78 3.46 3.29 3.18 3.11 3.05 3.01 2.98 2.96.050 5.99 5.14 4.76 4.53 4.39 4.28 4.21 4.15 4.10.025 8.81 7.26 6.60 6.23 5.99 5.82 5.70 5.60 5.52.010 13.75 10.92 9.78 9.15 8.75 8.47 8.26 8.10 7.98.005 18.63 14.54 12.92 12.03 11.46 11.07 10.79 10.57 10.39
7 .100 3.59 3.26 3.07 2.96 2.88 2.83 2.78 2.75 2.72.050 5.59 4.74 4.35 4.12 3.97 3.87 3.79 3.73 3.68.025 8.07 6.54 5.89 5.52 5.29 5.12 4.99 4.90 4.82.010 12.25 9.55 8.45 7.85 7.46 7.19 6.99 6.84 6.72.005 16.24 12.40 10.88 10.05 9.52 9.16 8.89 8.68 8.51
Tables 853
Table 7 (Continued )Fα
Numerator df
10 12 15 20 24 30 40 60 120 ∞ α df
60.19 60.71 61.22 61.74 62.00 62.26 62.53 62.79 63.06 63.33 .100 1241.9 243.9 245.9 248.0 249.1 250.1 251.1 252.2 253.3 254.3 .050968.6 976.7 984.9 993.1 997.2 1001 1006 1010 1014 1018 .025
6056 6106 6157 6209 6235 6261 6287 6313 6339 6366 .01024224 24426 24630 24836 24940 25044 25148 25253 25359 25465 .005
9.39 9.41 9.42 9.44 9.45 9.46 9.47 9.47 9.48 9.49 .100 219.40 19.41 19.43 19.45 19.45 19.45 19.47 19.48 19.49 19.50 .05039.40 39.41 39.43 39.45 39.46 39.46 39.47 39.48 39.49 39.50 .02599.40 99.42 99.43 99.45 99.46 99.47 99.47 99.48 99.49 99.50 .010
199.4 199.4 199.4 199.4 199.5 199.5 199.5 199.5 199.5 199.5 .005
5.23 5.22 5.20 5.18 5.18 5.17 5.16 5.15 5.14 5.13 .100 38.79 8.74 8.70 8.66 8.64 8.62 8.59 8.57 8.55 8.53 .050
14.42 14.34 14.25 14.17 14.12 14.08 14.04 13.99 13.95 13.90 .02527.23 27.05 26.87 26.69 26.60 26.50 26.41 26.32 26.22 26.13 .01043.69 43.39 43.08 42.78 42.62 42.47 42.31 42.15 41.99 41.83 .005
3.92 3.90 3.87 3.84 3.83 3.82 3.80 3.79 3.78 3.76 .100 45.96 5.91 5.86 5.80 5.77 5.75 5.72 5.69 5.66 5.63 .0508.84 8.75 8.66 8.56 8.51 8.46 8.41 8.36 8.31 8.26 .025
14.55 14.37 14.20 14.02 13.93 13.84 13.75 13.65 13.56 13.46 .01020.97 20.70 20.44 20.17 20.03 19.89 19.75 19.61 19.47 19.32 .005
3.30 3.27 3.24 3.21 3.19 3.17 3.16 3.14 3.12 3.10 .100 54.74 4.68 4.62 4.56 4.53 4.50 4.46 4.43 4.40 4.36 .0506.62 6.52 6.43 6.33 6.28 6.23 6.18 6.12 6.07 6.02 .025
10.05 9.89 9.72 9.55 9.47 9.38 9.29 9.20 9.11 9.02 .01013.62 13.38 13.15 12.90 12.78 12.66 12.53 12.40 12.27 12.14 .005
2.94 2.90 2.87 2.84 2.82 2.80 2.78 2.76 2.74 2.72 .100 64.06 4.00 3.94 3.87 3.84 3.81 3.77 3.74 3.70 3.67 .0505.46 5.37 5.27 5.17 5.12 5.07 5.01 4.96 4.90 4.85 .0257.87 7.72 7.56 7.40 7.31 7.23 7.14 7.06 6.97 6.88 .010
10.25 10.03 9.81 9.59 9.47 9.36 9.24 9.12 9.00 8.88 .005
2.70 2.67 2.63 2.59 2.58 2.56 2.54 2.51 2.49 2.47 .100 73.64 3.57 3.51 3.44 3.41 3.38 3.34 3.30 3.27 3.23 .0504.76 4.67 4.57 4.47 4.42 4.36 4.31 4.25 4.20 4.14 .0256.62 6.47 6.31 6.16 6.07 5.99 5.91 5.82 5.74 5.65 .0108.38 8.18 7.97 7.75 7.65 7.53 7.42 7.31 7.19 7.08 .005
854 Appendix 3 Tables
Table 7 (Continued )Fα
Numerator dfDenominator
df α 1 2 3 4 5 6 7 8 9
8 .100 3.46 3.11 2.92 2.81 2.73 2.67 2.62 2.59 2.56.050 5.32 4.46 4.07 3.84 3.69 3.58 3.50 3.44 3.39.025 7.57 6.06 5.42 5.05 4.82 4.65 4.53 4.43 4.36.010 11.26 8.65 7.59 7.01 6.63 6.37 6.18 6.03 5.91.005 14.69 11.04 9.60 8.81 8.30 7.95 7.69 7.50 7.34
9 .100 3.36 3.01 2.81 2.69 2.61 2.55 2.51 2.47 2.44.050 5.12 4.26 3.86 3.63 3.48 3.37 3.29 3.23 3.18.025 7.21 5.71 5.08 4.72 4.48 4.32 4.20 4.10 4.03.010 10.56 8.02 6.99 6.42 6.06 5.80 5.61 5.47 5.35.005 13.61 10.11 8.72 7.96 7.47 7.13 6.88 6.69 6.54
10 .100 3.29 2.92 2.73 2.61 2.52 2.46 2.41 2.38 2.35.050 4.96 4.10 3.71 3.48 3.33 3.22 3.14 3.07 3.02.025 6.94 5.46 4.83 4.47 4.24 4.07 3.95 3.85 3.78.010 10.04 7.56 6.55 5.99 5.64 5.39 5.20 5.06 4.94.005 12.83 9.43 8.08 7.34 6.87 6.54 6.30 6.12 5.97
11 .100 3.23 2.86 2.66 2.54 2.45 2.39 2.34 2.30 2.27.050 4.84 3.98 3.59 3.36 3.20 3.09 3.01 2.95 2.90.025 6.72 5.26 4.63 4.28 4.04 3.88 3.76 3.66 3.59.010 9.65 7.21 6.22 5.67 5.32 5.07 4.89 4.74 4.63.005 12.23 8.91 7.60 6.88 6.42 6.10 5.86 5.68 5.54
12 .100 3.18 2.81 2.61 2.48 2.39 2.33 2.28 2.24 2.21.050 4.75 3.89 3.49 3.26 3.11 3.00 2.91 2.85 2.80.025 6.55 5.10 4.47 4.12 3.89 3.73 3.61 3.51 3.44.010 9.33 6.93 5.95 5.41 5.06 4.82 4.64 4.50 4.39.005 11.75 8.51 7.23 6.52 6.07 5.76 5.52 5.35 5.20
13 .100 3.14 2.76 2.56 2.43 2.35 2.28 2.23 2.20 2.16.050 4.67 3.81 3.41 3.18 3.03 2.92 2.83 2.77 2.71.025 6.41 4.97 4.35 4.00 3.77 3.60 3.48 3.39 3.31.010 9.07 6.70 5.74 5.21 4.86 4.62 4.44 4.30 4.19.005 11.37 8.19 6.93 6.23 5.79 5.48 5.25 5.08 4.94
14 .100 3.10 2.73 2.52 2.39 2.31 2.24 2.19 2.15 2.12.050 4.60 3.74 3.34 3.11 2.96 2.85 2.76 2.70 2.65.025 6.30 4.86 4.24 3.89 3.66 3.50 3.38 3.29 3.21.010 8.86 6.51 5.56 5.04 4.69 4.46 4.28 4.14 4.03.005 11.06 7.92 6.68 6.00 5.56 5.26 5.03 4.86 4.72
Tables 855
Table 7 (Continued )Fα
Numerator df
10 12 15 20 24 30 40 60 120 ∞ α df
2.54 2.50 2.46 2.42 2.40 2.38 2.36 2.34 2.32 2.29 .100 83.35 3.28 3.22 3.15 3.12 3.08 3.04 3.01 2.97 2.93 .0504.30 4.20 4.10 4.00 3.95 3.89 3.84 3.78 3.73 3.67 .0255.81 5.67 5.52 5.36 5.28 5.20 5.12 5.03 4.95 4.86 .0107.21 7.01 6.81 6.61 6.50 6.40 6.29 6.18 6.06 5.95 .005
2.42 2.38 2.34 2.30 2.28 2.25 2.23 2.21 2.18 2.16 .100 93.14 3.07 3.01 2.94 2.90 2.86 2.83 2.79 2.75 2.71 .0503.96 3.87 3.77 3.67 3.61 3.56 3.51 3.45 3.39 3.33 .0255.26 5.11 4.96 4.81 4.73 4.65 4.57 4.48 4.40 4.31 .0106.42 6.23 6.03 5.83 5.73 5.62 5.52 5.41 5.30 5.19 .005
2.32 2.28 2.24 2.20 2.18 2.16 2.13 2.11 2.08 2.06 .100 102.98 2.91 2.85 2.77 2.74 2.70 2.66 2.62 2.58 2.54 .0503.72 3.62 3.52 3.42 3.37 3.31 3.26 3.20 3.14 3.08 .0254.85 4.71 4.56 4.41 4.33 4.25 4.17 4.08 4.00 3.91 .0105.85 5.66 5.47 5.27 5.17 5.07 4.97 4.86 4.75 4.64 .005
2.25 2.21 2.17 2.12 2.10 2.08 2.05 2.03 2.00 1.97 .100 112.85 2.79 2.72 2.65 2.61 2.57 2.53 2.49 2.45 2.40 .0503.53 3.43 3.33 3.23 3.17 3.12 3.06 3.00 2.94 2.88 .0254.54 4.40 4.25 4.10 4.02 3.94 3.86 3.78 3.69 3.60 .0105.42 5.24 5.05 4.86 4.76 4.65 4.55 4.44 4.34 4.23 .005
2.19 2.15 2.10 2.06 2.04 2.01 1.99 1.96 1.93 1.90 .100 122.75 2.69 2.62 2.54 2.51 2.47 2.43 2.38 2.34 2.30 .0503.37 3.28 3.18 3.07 3.02 2.96 2.91 2.85 2.79 2.72 .0254.30 4.16 4.01 3.86 3.78 3.70 3.62 3.54 3.45 3.36 .0105.09 4.91 4.72 4.53 4.43 4.33 4.23 4.12 4.01 3.90 .005
2.14 2.10 2.05 2.01 1.98 1.96 1.93 1.90 1.88 1.85 .100 132.67 2.60 2.53 2.46 2.42 2.38 2.34 2.30 2.25 2.21 .0503.25 3.15 3.05 2.95 2.89 2.84 2.78 2.72 2.66 2.60 .0254.10 3.96 3.82 3.66 3.59 3.51 3.43 3.34 3.25 3.17 .0104.82 4.64 4.46 4.27 4.17 4.07 3.97 3.87 3.76 3.65 .005
2.10 2.05 2.01 1.96 1.94 1.91 1.89 1.86 1.83 1.80 .100 142.60 2.53 2.46 2.39 2.35 2.31 2.27 2.22 2.18 2.13 .0503.15 3.05 2.95 2.84 2.79 2.73 2.67 2.61 2.55 2.49 .0253.94 3.80 3.66 3.51 3.43 3.35 3.27 3.18 3.09 3.00 .0104.60 4.43 4.25 4.06 3.96 3.86 3.76 3.66 3.55 3.44 .005
856 Appendix 3 Tables
Table 7 (Continued )Fα
Numerator dfDenominator
df α 1 2 3 4 5 6 7 8 9
15 .100 3.07 2.70 2.49 2.36 2.27 2.21 2.16 2.12 2.09.050 4.54 3.68 3.29 3.06 2.90 2.79 2.71 2.64 2.59.025 6.20 4.77 4.15 3.80 3.58 3.41 3.29 3.20 3.12.010 8.68 6.36 5.42 4.89 4.56 4.32 4.14 4.00 3.89.005 10.80 7.70 6.48 5.80 5.37 5.07 4.85 4.67 4.54
16 .100 3.05 2.67 2.46 2.33 2.24 2.18 2.13 2.09 2.06.050 4.49 3.63 3.24 3.01 2.85 2.74 2.66 2.59 2.54.025 6.12 4.69 4.08 3.73 3.50 3.34 3.22 3.12 3.05.010 8.53 6.23 5.29 4.77 4.44 4.20 4.03 3.89 3.78.005 10.58 7.51 6.30 5.64 5.21 4.91 4.69 4.52 4.38
17 .100 3.03 2.64 2.44 2.31 2.22 2.15 2.10 2.06 2.03.050 4.45 3.59 3.20 2.96 2.81 2.70 2.61 2.55 2.49.025 6.04 4.62 4.01 3.66 3.44 3.28 3.16 3.06 2.98.010 8.40 6.11 5.18 4.67 4.34 4.10 3.93 3.79 3.68.005 10.38 7.35 6.16 5.50 5.07 4.78 4.56 4.39 4.25
18 .100 3.01 2.62 2.42 2.29 2.20 2.13 2.08 2.04 2.00.050 4.41 3.55 3.16 2.93 2.77 2.66 2.58 2.51 2.46.025 5.98 4.56 3.95 3.61 3.38 3.22 3.10 3.01 2.93.010 8.29 6.01 5.09 4.58 4.25 4.01 3.84 3.71 3.60.005 10.22 7.21 6.03 5.37 4.96 4.66 4.44 4.28 4.14
19 .100 2.99 2.61 2.40 2.27 2.18 2.11 2.06 2.02 1.98.050 4.38 3.52 3.13 2.90 2.74 2.63 2.54 2.48 2.42.025 5.92 4.51 3.90 3.56 3.33 3.17 3.05 2.96 2.88.010 8.18 5.93 5.01 4.50 4.17 3.94 3.77 3.63 3.52.005 10.07 7.09 5.92 5.27 4.85 4.56 4.34 4.18 4.04
20 .100 2.97 2.59 2.38 2.25 2.16 2.09 2.04 2.00 1.96.050 4.35 3.49 3.10 2.87 2.71 2.60 2.51 2.45 2.39.025 5.87 4.46 3.86 3.51 3.29 3.13 3.01 2.91 2.84.010 8.10 5.85 4.94 4.43 4.10 3.87 3.70 3.56 3.46.005 9.94 6.99 5.82 5.17 4.76 4.47 4.26 4.09 3.96
21 .100 2.96 2.57 2.36 2.23 2.14 2.08 2.02 1.98 1.95.050 4.32 3.47 3.07 2.84 2.68 2.57 2.49 2.42 2.37.025 5.83 4.42 3.82 3.48 3.25 3.09 2.97 2.87 2.80.010 8.02 5.78 4.87 4.37 4.04 3.81 3.64 3.51 3.40.005 9.83 6.89 5.73 5.09 4.68 4.39 4.18 4.01 3.88
Tables 857
Table 7 (Continued )Fα
Numerator df
10 12 15 20 24 30 40 60 120 ∞ α df
2.06 2.02 1.97 1.92 1.90 1.87 1.85 1.82 1.79 1.76 .100 152.54 2.48 2.40 2.33 2.29 2.25 2.20 2.16 2.11 2.07 .0503.06 2.96 2.86 2.76 2.70 2.64 2.59 2.52 2.46 2.40 .0253.80 3.67 3.52 3.37 3.29 3.21 3.13 3.05 2.96 2.87 .0104.42 4.25 4.07 3.88 3.79 3.69 3.58 3.48 3.37 3.26 .005
2.03 1.99 1.94 1.89 1.87 1.84 1.81 1.78 1.75 1.72 .100 162.49 2.42 2.35 2.28 2.24 2.19 2.15 2.11 2.06 2.01 .0502.99 2.89 2.79 2.68 2.63 2.57 2.51 2.45 2.38 2.32 .0253.69 3.55 3.41 3.26 3.18 3.10 3.02 2.93 2.84 2.75 .0104.27 4.10 3.92 3.73 3.64 3.54 3.44 3.33 3.22 3.11 .005
2.00 1.96 1.91 1.86 1.84 1.81 1.78 1.75 1.72 1.69 .100 172.45 2.38 2.31 2.23 2.19 2.15 2.10 2.06 2.01 1.96 .0502.92 2.82 2.72 2.62 2.56 2.50 2.44 2.38 2.32 2.25 .0253.59 3.46 3.31 3.16 3.08 3.00 2.92 2.83 2.75 2.65 .0104.14 3.97 3.79 3.61 3.51 3.41 3.31 3.21 3.10 2.98 .005
1.98 1.93 1.89 1.84 1.81 1.78 1.75 1.72 1.69 1.66 .100 182.41 2.34 2.27 2.19 2.15 2.11 2.06 2.02 1.97 1.92 .0502.87 2.77 2.67 2.56 2.50 2.44 2.38 2.32 2.26 2.19 .0253.51 3.37 3.23 3.08 3.00 2.92 2.84 2.75 2.66 2.57 .0104.03 3.86 3.68 3.50 3.40 3.30 3.20 3.10 2.99 2.87 .005
1.96 1.91 1.86 1.81 1.79 1.76 1.73 1.70 1.67 1.63 .100 192.38 2.31 2.23 2.16 2.11 2.07 2.03 1.98 1.93 1.88 .0502.82 2.72 2.62 2.51 2.45 2.39 2.33 2.27 2.20 2.13 .0253.43 3.30 3.15 3.00 2.92 2.84 2.76 2.67 2.58 2.49 .0103.93 3.76 3.59 3.40 3.31 3.21 3.11 3.00 2.89 2.78 .005
1.94 1.89 1.84 1.79 1.77 1.74 1.71 1.68 1.64 1.61 .100 202.35 2.28 2.20 2.12 2.08 2.04 1.99 1.95 1.90 1.84 .0502.77 2.68 2.57 2.46 2.41 2.35 2.29 2.22 2.16 2.09 .0253.37 3.23 3.09 2.94 2.86 2.78 2.69 2.61 2.52 2.42 .0103.85 3.68 3.50 3.32 3.22 3.12 3.02 2.92 2.81 2.69 .005
1.92 1.87 1.83 1.78 1.75 1.72 1.69 1.66 1.62 1.59 .100 212.32 2.25 2.18 2.10 2.05 2.01 1.96 1.92 1.87 1.81 .0502.73 2.64 2.53 2.42 2.37 2.31 2.25 2.18 2.11 2.04 .0253.31 3.17 3.03 2.88 2.80 2.72 2.64 2.55 2.46 2.36 .0103.77 3.60 3.43 3.24 3.15 3.05 2.95 2.84 2.73 2.61 .005
858 Appendix 3 Tables
Table 7 (Continued )Fα
Numerator dfDenominatordf α 1 2 3 4 5 6 7 8 9
22 .100 2.95 2.56 2.35 2.22 2.13 2.06 2.01 1.97 1.93.050 4.30 3.44 3.05 2.82 2.66 2.55 2.46 2.40 2.34.025 5.79 4.38 3.78 3.44 3.22 3.05 2.93 2.84 2.76.010 7.95 5.72 4.82 4.31 3.99 3.76 3.59 3.45 3.35.005 9.73 6.81 5.65 5.02 4.61 4.32 4.11 3.94 3.81
23 .100 2.94 2.55 2.34 2.21 2.11 2.05 1.99 1.95 1.92.050 4.28 3.42 3.03 2.80 2.64 2.53 2.44 2.37 2.32.025 5.75 4.35 3.75 3.41 3.18 3.02 2.90 2.81 2.73.010 7.88 5.66 4.76 4.26 3.94 3.71 3.54 3.41 3.30.005 9.63 6.73 5.58 4.95 4.54 4.26 4.05 3.88 3.75
24 .100 2.93 2.54 2.33 2.19 2.10 2.04 1.98 1.94 1.91.050 4.26 3.40 3.01 2.78 2.62 2.51 2.42 2.36 2.30.025 5.72 4.32 3.72 3.38 3.15 2.99 2.87 2.78 2.70.010 7.82 5.61 4.72 4.22 3.90 3.67 3.50 3.36 3.26.005 9.55 6.66 5.52 4.89 4.49 4.20 3.99 3.83 3.69
25 .100 2.92 2.53 2.32 2.18 2.09 2.02 1.97 1.93 1.89.050 4.24 3.39 2.99 2.76 2.60 2.49 2.40 2.34 2.28.025 5.69 4.29 3.69 3.35 3.13 2.97 2.85 2.75 2.68.010 7.77 5.57 4.68 4.18 3.85 3.63 3.46 3.32 3.22.005 9.48 6.60 5.46 4.84 4.43 4.15 3.94 3.78 3.64
26 .100 2.91 2.52 2.31 2.17 2.08 2.01 1.96 1.92 1.88.050 4.23 3.37 2.98 2.74 2.59 2.47 2.39 2.32 2.27.025 5.66 4.27 3.67 3.33 3.10 2.94 2.82 2.73 2.65.010 7.72 5.53 4.64 4.14 3.82 3.59 3.42 3.29 3.18.005 9.41 6.54 5.41 4.79 4.38 4.10 3.89 3.73 3.60
27 .100 2.90 2.51 2.30 2.17 2.07 2.00 1.95 1.91 1.87.050 4.21 3.35 2.96 2.73 2.57 2.46 2.37 2.31 2.25.025 5.63 4.24 3.65 3.31 3.08 2.92 2.80 2.71 2.63.010 7.68 5.49 4.60 4.11 3.78 3.56 3.39 3.26 3.15.005 9.34 6.49 5.36 4.74 4.34 4.06 3.85 3.69 3.56
28 .100 2.89 2.50 2.29 2.16 2.06 2.00 1.94 1.90 1.87.050 4.20 3.34 2.95 2.71 2.56 2.45 2.36 2.29 2.24.025 5.61 4.22 3.63 3.29 3.06 2.90 2.78 2.69 2.61.010 7.64 5.45 4.57 4.07 3.75 3.53 3.36 3.23 3.12.005 9.28 6.44 5.32 4.70 4.30 4.02 3.81 3.65 3.52
Tables 859
Table 7 (Continued )Fα
Numerator df
10 12 15 20 24 30 40 60 120 ∞ α df
1.90 1.86 1.81 1.76 1.73 1.70 1.67 1.64 1.60 1.57 .100 222.30 2.23 2.15 2.07 2.03 1.98 1.94 1.89 1.84 1.78 .0502.70 2.60 2.50 2.39 2.33 2.27 2.21 2.14 2.08 2.00 .0253.26 3.12 2.98 2.83 2.75 2.67 2.58 2.50 2.40 2.31 .0103.70 3.54 3.36 3.18 3.08 2.98 2.88 2.77 2.66 2.55 .005
1.89 1.84 1.80 1.74 1.72 1.69 1.66 1.62 1.59 1.55 .100 232.27 2.20 2.13 2.05 2.01 1.96 1.91 1.86 1.81 1.76 .0502.67 2.57 2.47 2.36 2.30 2.24 2.18 2.11 2.04 1.97 .0253.21 3.07 2.93 2.78 2.70 2.62 2.54 2.45 2.35 2.26 .0103.64 3.47 3.30 3.12 3.02 2.92 2.82 2.71 2.60 2.48 .005
1.88 1.83 1.78 1.73 1.70 1.67 1.64 1.61 1.57 1.53 .100 242.25 2.18 2.11 2.03 1.98 1.94 1.89 1.84 1.79 1.73 .0502.64 2.54 2.44 2.33 2.27 2.21 2.15 2.08 2.01 1.94 .0253.17 3.03 2.89 2.74 2.66 2.58 2.49 2.40 2.31 2.21 .0103.59 3.42 3.25 3.06 2.97 2.87 2.77 2.66 2.55 2.43 .005
1.87 1.82 1.77 1.72 1.69 1.66 1.63 1.59 1.56 1.52 .100 252.24 2.16 2.09 2.01 1.96 1.92 1.87 1.82 1.77 1.71 .0502.61 2.51 2.41 2.30 2.24 2.18 2.12 2.05 1.98 1.91 .0253.13 2.99 2.85 2.70 2.62 2.54 2.45 2.36 2.27 2.17 .0103.54 3.37 3.20 3.01 2.92 2.82 2.72 2.61 2.50 2.38 .005
1.86 1.81 1.76 1.71 1.68 1.65 1.61 1.58 1.54 1.50 .100 262.22 2.15 2.07 1.99 1.95 1.90 1.85 1.80 1.75 1.69 .0502.59 2.49 2.39 2.28 2.22 2.16 2.09 2.03 1.95 1.88 .0253.09 2.96 2.81 2.66 2.58 2.50 2.42 2.33 2.23 2.13 .0103.49 3.33 3.15 2.97 2.87 2.77 2.67 2.56 2.45 2.33 .005
1.85 1.80 1.75 1.70 1.67 1.64 1.60 1.57 1.53 1.49 .100 272.20 2.13 2.06 1.97 1.93 1.88 1.84 1.79 1.73 1.67 .0502.57 2.47 2.36 2.25 2.19 2.13 2.07 2.00 1.93 1.85 .0253.06 2.93 2.78 2.63 2.55 2.47 2.38 2.29 2.20 2.10 .0103.45 3.28 3.11 2.93 2.83 2.73 2.63 2.52 2.41 2.29 .005
1.84 1.79 1.74 1.69 1.66 1.63 1.59 1.56 1.52 1.48 .100 282.19 2.12 2.04 1.96 1.91 1.87 1.82 1.77 1.71 1.65 .0502.55 2.45 2.34 2.23 2.17 2.11 2.05 1.98 1.91 1.83 .0253.03 2.90 2.75 2.60 2.52 2.44 2.35 2.26 2.17 2.06 .0103.41 3.25 3.07 2.89 2.79 2.69 2.59 2.48 2.37 2.25 .005
860 Appendix 3 Tables
Table 7 (Continued )Fα
Numerator dfDenominatordf α 1 2 3 4 5 6 7 8 9
29 .100 2.89 2.50 2.28 2.15 2.06 1.99 1.93 1.89 1.86.050 4.18 3.33 2.93 2.70 2.55 2.43 2.35 2.28 2.22.025 5.59 4.20 3.61 3.27 3.04 2.88 2.76 2.67 2.59.010 7.60 5.42 4.54 4.04 3.73 3.50 3.33 3.20 3.09.005 9.23 6.40 5.28 4.66 4.26 3.98 3.77 3.61 3.48
30 .100 2.88 2.49 2.28 2.14 2.05 1.98 1.93 1.88 1.85.050 4.17 3.32 2.92 2.69 2.53 2.42 2.33 2.27 2.21.025 5.57 4.18 3.59 3.25 3.03 2.87 2.75 2.65 2.57.010 7.56 5.39 4.51 4.02 3.70 3.47 3.30 3.17 3.07.005 9.18 6.35 5.24 4.62 4.23 3.95 3.74 3.58 3.45
40 .100 2.84 2.44 2.23 2.09 2.00 1.93 1.87 1.83 1.79.050 4.08 3.23 2.84 2.61 2.45 2.34 2.25 2.18 2.12.025 5.42 4.05 3.46 3.13 2.90 2.74 2.62 2.53 2.45.010 7.31 5.18 4.31 3.83 3.51 3.29 3.12 2.99 2.89.005 8.83 6.07 4.98 4.37 3.99 3.71 3.51 3.35 3.22
60 .100 2.79 2.39 2.18 2.04 1.95 1.87 1.82 1.77 1.74.050 4.00 3.15 2.76 2.53 2.37 2.25 2.17 2.10 2.04.025 5.29 3.93 3.34 3.01 2.79 2.63 2.51 2.41 2.33.010 7.08 4.98 4.13 3.65 3.34 3.12 2.95 2.82 2.72.005 8.49 5.79 4.73 4.14 3.76 3.49 3.29 3.13 3.01
120 .100 2.75 2.35 2.13 1.99 1.90 1.82 1.77 1.72 1.68.050 3.92 3.07 2.68 2.45 2.29 2.17 2.09 2.02 1.96.025 5.15 3.80 3.23 2.89 2.67 2.52 2.39 2.30 2.22.010 6.85 4.79 3.95 3.48 3.17 2.96 2.79 2.66 2.56.005 8.18 5.54 4.50 3.92 3.55 3.28 3.09 2.93 2.81
∞ .100 2.71 2.30 2.08 1.94 1.85 1.77 1.72 1.67 1.63.050 3.84 3.00 2.60 2.37 2.21 2.10 2.01 1.94 1.88.025 5.02 3.69 3.12 2.79 2.57 2.41 2.29 2.19 2.11.010 6.63 4.61 3.78 3.32 3.02 2.80 2.64 2.51 2.41.005 7.88 5.30 4.28 3.72 3.35 3.09 2.90 2.74 2.62
From “Tables of percentage points of the inverted beta (F) distribution.” Biometrika, Vol. 33 (1943) by M. Merrington and C. M.Thompson and from Table 18 of Biometrika Tables for Statisticians, Vol. 1, Cambridge University Press, 1954, edited by E. S.Pearson and H. O. Hartley.
Tables 861
Table 7 (Continued )Fα
Numerator df
10 12 15 20 24 30 40 60 120 ∞ α df
1.83 1.78 1.73 1.68 1.65 1.62 1.58 1.55 1.51 1.47 .100 292.18 2.10 2.03 1.94 1.90 1.85 1.81 1.75 1.70 1.64 .0502.53 2.43 2.32 2.21 2.15 2.09 2.03 1.96 1.89 1.81 .0253.00 2.87 2.73 2.57 2.49 2.41 2.33 2.23 2.14 2.03 .0103.38 3.21 3.04 2.86 2.76 2.66 2.56 2.45 2.33 2.21 .005
1.82 1.77 1.72 1.67 1.64 1.61 1.57 1.54 1.50 1.46 .100 302.16 2.09 2.01 1.93 1.89 1.84 1.79 1.74 1.68 1.62 .0502.51 2.41 2.31 2.20 2.14 2.07 2.01 1.94 1.87 1.79 .0252.98 2.84 2.70 2.55 2.47 2.39 2.30 2.21 2.11 2.01 .0103.34 3.18 3.01 2.82 2.73 2.63 2.52 2.42 2.30 2.18 .005
1.76 1.71 1.66 1.61 1.57 1.54 1.51 1.47 1.42 1.38 .100 402.08 2.00 1.92 1.84 1.79 1.74 1.69 1.64 1.58 1.51 .0502.39 2.29 2.18 2.07 2.01 1.94 1.88 1.80 1.72 1.64 .0252.80 2.66 2.52 2.37 2.29 2.20 2.11 2.02 1.92 1.80 .0103.12 2.95 2.78 2.60 2.50 2.40 2.30 2.18 2.06 1.93 .005
1.71 1.66 1.60 1.54 1.51 1.48 1.44 1.40 1.35 1.29 .100 601.99 1.92 1.84 1.75 1.70 1.65 1.59 1.53 1.47 1.39 .0502.27 2.17 2.06 1.94 1.88 1.82 1.74 1.67 1.58 1.48 .0252.63 2.50 2.35 2.20 2.12 2.03 1.94 1.84 1.73 1.60 .0102.90 2.74 2.57 2.39 2.29 2.19 2.08 1.96 1.83 1.69 .005
1.65 1.60 1.55 1.48 1.45 1.41 1.37 1.32 1.26 1.19 .100 1201.91 1.83 1.75 1.66 1.61 1.55 1.50 1.43 1.35 1.25 .0502.16 2.05 1.94 1.82 1.76 1.69 1.61 1.53 1.43 1.31 .0252.47 2.34 2.19 2.03 1.95 1.86 1.76 1.66 1.53 1.38 .0102.71 2.54 2.37 2.19 2.09 1.98 1.87 1.75 1.61 1.43 .005
1.60 1.55 1.49 1.42 1.38 1.34 1.30 1.24 1.17 1.00 .100 ∞1.83 1.75 1.67 1.57 1.52 1.46 1.39 1.32 1.22 1.00 .0502.05 1.94 1.83 1.71 1.64 1.57 1.48 1.39 1.27 1.00 .0252.32 2.18 2.04 1.88 1.79 1.70 1.59 1.47 1.32 1.00 .0102.52 2.36 2.19 2.00 1.90 1.79 1.67 1.53 1.36 1.00 .005
862 Appendix 3 Tables
Table 8 Distribution Function of U
P(U ≤ U0); U0 is theargument; n1 ≤ n2;3 ≤ n2 ≤ 10.
n2 = 3
n1
U0 1 2 3
0 .25 .10 .051 .50 .20 .102 .40 .203 .60 .354 .50
n2 = 4
n1
U0 1 2 3 4
0 .2000 .0667 .0286 .01431 .4000 .1333 .0571 .02862 .6000 .2667 .1143 .05713 .4000 .2000 .10004 .6000 .3143 .17145 .4286 .24296 .5714 .34297 .44298 .5571
Tables 863
Table 8 (Continued )
n2 = 5
n1
U0 1 2 3 4 5
0 .1667 .0476 .0179 .0079 .00401 .3333 .0952 .0357 .0159 .00792 .5000 .1905 .0714 .0317 .01593 .2857 .1250 .0556 .02784 .4286 .1964 .0952 .04765 .5714 .2857 .1429 .07546 .3929 .2063 .11117 .5000 .2778 .15488 .3651 .21039 .4524 .2738
10 .5476 .345211 .420612 .5000
n2 = 6
n1
U0 1 2 3 4 5 6
0 .1429 .0357 .0119 .0048 .0022 .00111 .2857 .0714 .0238 .0095 .0043 .00222 .4286 .1429 .0476 .0190 .0087 .00433 .5714 .2143 .0833 .0333 .0152 .00764 .3214 .1310 .0571 .0260 .01305 .4286 .1905 .0857 .0411 .02066 .5714 .2738 .1286 .0628 .03257 .3571 .1762 .0887 .04658 .4524 .2381 .1234 .06609 .5476 .3048 .1645 .0898
10 .3810 .2143 .120111 .4571 .2684 .154812 .5429 .3312 .197013 .3961 .242414 .4654 .294415 .5346 .349616 .409117 .468618 .5314
864 Appendix 3 Tables
Table 8 (Continued )
n2 = 7
n1
U0 1 2 3 4 5 6 7
0 .1250 .0278 .0083 .0030 .0013 .0006 .00031 .2500 .0556 .0167 .0061 .0025 .0012 .00062 .3750 .1111 .0333 .0121 .0051 .0023 .00123 .5000 .1667 .0583 .0212 .0088 .0041 .00204 .2500 .0917 .0364 .0152 .0070 .00355 .3333 .1333 .0545 .0240 .0111 .00556 .4444 .1917 .0818 .0366 .0175 .00877 .5556 .2583 .1152 .0530 .0256 .01318 .3333 .1576 .0745 .0367 .01899 .4167 .2061 .1010 .0507 .0265
10 .5000 .2636 .1338 .0688 .036411 .3242 .1717 .0903 .048712 .3939 .2159 .1171 .064113 .4636 .2652 .1474 .082514 .5364 .3194 .1830 .104315 .3775 .2226 .129716 .4381 .2669 .158817 .5000 .3141 .191418 .3654 .227919 .4178 .267520 .4726 .310021 .5274 .355222 .402423 .450824 .5000
Tables 865
Table 8 (Continued )
n2 = 8
n1
U0 1 2 3 4 5 6 7 8
0 .1111 .0222 .0061 .0020 .0008 .0003 .0002 .00011 .2222 .0444 .0121 .0040 .0016 .0007 .0003 .00022 .3333 .0889 .0242 .0081 .0031 .0013 .0006 .00033 .4444 .1333 .0424 .0141 .0054 .0023 .0011 .00054 .5556 .2000 .0667 .0242 .0093 .0040 .0019 .00095 .2667 .0970 .0364 .0148 .0063 .0030 .00156 .3556 .1394 .0545 .0225 .0100 .0047 .00237 .4444 .1879 .0768 .0326 .0147 .0070 .00358 .5556 .2485 .1071 .0466 .0213 .0103 .00529 .3152 .1414 .0637 .0296 .0145 .0074
10 .3879 .1838 .0855 .0406 .0200 .010311 .4606 .2303 .1111 .0539 .0270 .014112 .5394 .2848 .1422 .0709 .0361 .019013 .3414 .1772 .0906 .0469 .024914 .4040 .2176 .1142 .0603 .032515 .4667 .2618 .1412 .0760 .041516 .5333 .3108 .1725 .0946 .052417 .3621 .2068 .1159 .065218 .4165 .2454 .1405 .080319 .4716 .2864 .1678 .097420 .5284 .3310 .1984 .117221 .3773 .2317 .139322 .4259 .2679 .164123 .4749 .3063 .191124 .5251 .3472 .220925 .3894 .252726 .4333 .286927 .4775 .322728 .5225 .360529 .399230 .439231 .479632 .5204
866 Appendix 3 Tables
Table 8 (Continued )
n2 = 9
n1
U0 1 2 3 4 5 6 7 8 9
0 .1000 .0182 .0045 .0014 .0005 .0002 .0001 .0000 .00001 .2000 .0364 .0091 .0028 .0010 .0004 .0002 .0001 .00002 .3000 .0727 .0182 .0056 .0020 .0008 .0003 .0002 .00013 .4000 .1091 .0318 .0098 .0035 .0014 .0006 .0003 .00014 .5000 .1636 .0500 .0168 .0060 .0024 .0010 .0005 .00025 .2182 .0727 .0252 .0095 .0038 .0017 .0008 .00046 .2909 .1045 .0378 .0145 .0060 .0026 .0012 .00067 .3636 .1409 .0531 .0210 .0088 .0039 .0019 .00098 .4545 .1864 .0741 .0300 .0128 .0058 .0028 .00149 .5455 .2409 .0993 .0415 .0180 .0082 .0039 .0020
10 .3000 .1301 .0559 .0248 .0115 .0056 .002811 .3636 .1650 .0734 .0332 .0156 .0076 .003912 .4318 .2070 .0949 .0440 .0209 .0103 .005313 .5000 .2517 .1199 .0567 .0274 .0137 .007114 .3021 .1489 .0723 .0356 .0180 .009415 .3552 .1818 .0905 .0454 .0232 .012216 .4126 .2188 .1119 .0571 .0296 .015717 .4699 .2592 .1361 .0708 .0372 .020018 .5301 .3032 .1638 .0869 .0464 .025219 .3497 .1942 .1052 .0570 .031320 .3986 .2280 .1261 .0694 .038521 .4491 .2643 .1496 .0836 .047022 .5000 .3035 .1755 .0998 .056723 .3445 .2039 .1179 .068024 .3878 .2349 .1383 .080725 .4320 .2680 .1606 .095126 .4773 .3032 .1852 .111227 .5227 .3403 .2117 .129028 .3788 .2404 .148729 .4185 .2707 .170130 .4591 .3029 .193331 .5000 .3365 .218132 .3715 .244733 .4074 .272934 .4442 .302435 .4813 .333236 .5187 .365237 .398138 .431739 .465740 .5000
Tables 867
Table 8 (Continued )
n2 = 10
n1
U0 1 2 3 4 5 6 7 8 9 10
0 .0909 .0152 .0035 .0010 .0003 .0001 .0001 .0000 .0000 .00001 .1818 .0303 .0070 .0020 .0007 .0002 .0001 .0000 .0000 .00002 .2727 .0606 .0140 .0040 .0013 .0005 .0002 .0001 .0000 .00003 .3636 .0909 .0245 .0070 .0023 .0009 .0004 .0002 .0001 .00004 .4545 .1364 .0385 .0120 .0040 .0015 .0006 .0003 .0001 .00015 .5455 .1818 .0559 .0180 .0063 .0024 .0010 .0004 .0002 .00016 .2424 .0804 .0270 .0097 .0037 .0015 .0007 .0003 .00027 .3030 .1084 .0380 .0140 .0055 .0023 .0010 .0005 .00028 .3788 .1434 .0529 .0200 .0080 .0034 .0015 .0007 .00049 .4545 .1853 .0709 .0276 .0112 .0048 .0022 .0011 .0005
10 .5455 .2343 .0939 .0376 .0156 .0068 .0031 .0015 .000811 .2867 .1199 .0496 .0210 .0093 .0043 .0021 .001012 .3462 .1518 .0646 .0280 .0125 .0058 .0028 .001413 .4056 .1868 .0823 .0363 .0165 .0078 .0038 .001914 .4685 .2268 .1032 .0467 .0215 .0103 .0051 .002615 .5315 .2697 .1272 .0589 .0277 .0133 .0066 .003416 .3177 .1548 .0736 .0351 .0171 .0086 .004517 .3666 .1855 .0903 .0439 .0217 .0110 .005718 .4196 .2198 .1099 .0544 .0273 .0140 .007319 .4725 .2567 .1317 .0665 .0338 .0175 .009320 .5275 .2970 .1566 .0806 .0416 .0217 .011621 .3393 .1838 .0966 .0506 .0267 .014422 .3839 .2139 .1148 .0610 .0326 .017723 .4296 .2461 .1349 .0729 .0394 .021624 .4765 .2811 .1574 .0864 .0474 .026225 .5235 .3177 .1819 .1015 .0564 .031526 .3564 .2087 .1185 .0667 .037627 .3962 .2374 .1371 .0782 .044628 .4374 .2681 .1577 .0912 .052629 .4789 .3004 .1800 .1055 .061530 .5211 .3345 .2041 .1214 .071631 .3698 .2299 .1388 .082732 .4063 .2574 .1577 .095233 .4434 .2863 .1781 .108834 .4811 .3167 .2001 .123735 .5189 .3482 .2235 .139936 .3809 .2483 .157537 .4143 .2745 .176338 .4484 .3019 .196539 .4827 .3304 .2179
868 Appendix 3 Tables
Table 8 (Continued )
n2 = 10
n1
U0 1 2 3 4 5 6 7 8 9 10
40 .5173 .3598 .240641 .3901 .264442 .4211 .289443 .4524 .315344 .4841 .342145 .5159 .369746 .398047 .426748 .455949 .485350 .5147
Computed by M. Pagano, Department of Statistics, University of Florida.
Table 9 Critical Values of T in the Wilcoxon Matched-Pairs, Signed-Ranks Test; n = 5(1)50
One-sided Two-sided n = 5 n = 6 n = 7 n = 8 n = 9 n = 10
P = .05 P = .10 1 2 4 6 8 11P = .025 P = .05 1 2 4 6 8P = .01 P = .02 0 2 3 5P = .005 P = .01 0 2 3
One-sided Two-sided n = 11 n = 12 n = 13 n = 14 n = 15 n = 16
P = .05 P = .10 14 17 21 26 30 36P = .025 P = .05 11 14 17 21 25 30P = .01 P = .02 7 10 13 16 20 24P = .005 P = .01 5 7 10 13 16 19
One-sided Two-sided n = 17 n = 18 n = 19 n = 20 n = 21 n = 22
P = .05 P = .10 41 47 54 60 68 75P = .025 P = .05 35 40 46 52 59 66P = .01 P = .02 28 33 38 43 49 56P = .005 P = .01 23 28 32 37 43 49
One-sided Two-sided n = 23 n = 24 n = 25 n = 26 n = 27 n = 28
P = .05 P = .10 83 92 101 110 120 130P = .025 P = .05 73 81 90 98 107 117P = .01 P = .02 62 69 77 85 93 102P = .005 P = .01 55 68 68 76 84 92
Tables 869
Table 9 (Continued )
One-sided Two-sided n = 29 n = 30 n = 31 n = 32 n = 33 n = 34
P = .05 P = .10 141 152 163 175 188 201P = .025 P = .05 127 137 148 159 171 183P = .01 P = .02 111 120 130 141 151 162P = .005 P = .01 100 109 118 128 138 149
One-sided Two-sided n = 35 n = 36 n = 37 n = 38 n = 39
P = .05 P = .10 214 228 242 256 271P = .025 P = .05 195 208 222 235 250P = .01 P = .02 174 186 198 211 224P = .005 P = .01 160 171 183 195 208
One-sided Two-sided n = 40 n = 41 n = 42 n = 43 n = 44 n = 45
P = .05 P = .10 287 303 319 336 353 371P = .025 P = .05 264 279 295 311 327 344P = .01 P = .02 238 252 267 281 297 313P = .005 P = .01 221 234 248 262 277 292
One-sided Two-sided n = 46 n = 47 n = 48 n = 49 n = 50
P = .05 P = .10 389 408 427 446 466P = .025 P = .05 361 379 397 415 434P = .01 P = .02 329 345 362 380 398P = .005 P = .01 307 323 339 356 373
From “Some Rapid Approximate Statistical Procedures” (1964), 28, F. Wilcoxon and R. A. Wilcox.
870 Appendix 3 Tables
Table 10 Distribution of the Total Number of Runs R in Samples of Size (n1, n2); P(R ≤ a)
a
(n1, n2) 2 3 4 5 6 7 8 9 10
(2, 3) .200 .500 .900 1.000(2, 4) .133 .400 .800 1.000(2, 5) .095 .333 .714 1.000(2, 6) .071 .286 .643 1.000(2, 7) .056 .250 .583 1.000(2, 8) .044 .222 .533 1.000(2, 9) .036 .200 .491 1.000(2, 10) .030 .182 .455 1.000
(3, 3) .100 .300 .700 .900 1.000(3, 4) .057 .200 .543 .800 .971 1.000(3, 5) .036 .143 .429 .714 .929 1.000(3, 6) .024 .107 .345 .643 .881 1.000(3, 7) .017 .083 .283 .583 .833 1.000(3, 8) .012 .067 .236 .533 .788 1.000(3, 9) .009 .055 .200 .491 .745 1.000(3, 10) .007 .045 .171 .455 .706 1.000
(4, 4) .029 .114 .371 .629 .886 .971 1.000(4, 5) .016 .071 .262 .500 .786 .929 .992 1.000(4, 6) .010 .048 .190 .405 .690 .881 .976 1.000(4, 7) .006 .033 .142 .333 .606 .833 .954 1.000(4, 8) .004 .024 .109 .279 .533 .788 .929 1.000(4, 9) .003 .018 .085 .236 .471 .745 .902 1.000(4, 10) .002 .014 .068 .203 .419 .706 .874 1.000
(5, 5) .008 .040 .167 .357 .643 .833 .960 .992 1.000(5, 6) .004 .024 .110 .262 .522 .738 .911 .976 .998(5, 7) .003 .015 .076 .197 .424 .652 .854 .955 .992(5, 8) .002 .010 .054 .152 .347 .576 .793 .929 .984(5, 9) .001 .007 .039 .119 .287 .510 .734 .902 .972(5, 10) .001 .005 .029 .095 .239 .455 .678 .874 .958
(6, 6) .002 .013 .067 .175 .392 .608 .825 .933 .987(6, 7) .001 .008 .043 .121 .296 .500 .733 .879 .966(6, 8) .001 .005 .028 .086 .226 .413 .646 .821 .937(6, 9) .000 .003 .019 .063 .175 .343 .566 .762 .902(6, 10) .000 .002 .013 .047 .137 .288 .497 .706 .864
(7, 7) .001 .004 .025 .078 .209 .383 .617 .791 .922(7, 8) .000 .002 .015 .051 .149 .296 .514 .704 .867(7, 9) .000 .001 .010 .035 .108 .231 .427 .622 .806(7, 10) .000 .001 .006 .024 .080 .182 .355 .549 .743
(8, 8) .000 .001 .009 .032 .100 .214 .405 .595 .786(8, 9) .000 .001 .005 .020 .069 .157 .319 .500 .702(8, 10) .000 .000 .003 .013 .048 .117 .251 .419 .621
(9, 9) .000 .000 .003 .012 .044 .109 .238 .399 .601(9, 10) .000 .000 .002 .008 .029 .077 .179 .319 .510(10, 10) .000 .000 .001 .004 .019 .051 .128 .242 .414
Tables 871
Table 10 (Continued )
a
(n1, n2) 11 12 13 14 15 16 17 18 19 20
(2, 3)(2, 4)(2, 5)(2, 6)(2, 7)(2, 8)(2, 9)(2, 10)
(3, 3)(3, 4)(3, 5)(3, 6)(3, 7)(3, 8)(3, 9)(3, 10)
(4, 4)(4, 5)(4, 6)(4, 7)(4, 8)(4, 9)(4, 10)
(5, 5)(5, 6) 1.000(5, 7) 1.000(5, 8) 1.000(5, 9) 1.000(5, 10) 1.000
(6, 6) .998 1.000(6, 7) .992 .999 1.000(6, 8) .984 .998 1.000(6, 9) .972 .994 1.000(6, 10) .958 .990 1.000
(7, 7) .975 .996 .999 1.000(7, 8) .949 .988 .998 1.000 1.000(7, 9) .916 .975 .994 .999 1.000(7, 10) .879 .957 .990 .998 1.000
(8, 8) .900 .968 .991 .999 1.000 1.000(8, 9) .843 .939 .980 .996 .999 1.000 1.000(8, 10) .782 .903 .964 .990 .998 1.000 1.000
(9, 9) .762 .891 .956 .988 .997 1.000 1.000 1.000(9, 10) .681 .834 .923 .974 .992 .999 1.000 1.000 1.000(10, 10) .586 .758 .872 .949 .981 .996 .999 1.000 1.000 1.000
From “Tables for Testing Randomness of Grouping in a Sequence of Alternatives,” C. Eisenhart andF. Swed, Annals of Mathematical Statistics, Volume 14 (1943).
872 Appendix 3 Tables
Table 11 Critical Values of Spearman’s Rank CorrelationCoefficient
n α = .05 α = .025 α = .01 α = .005
5 0.900 — — —6 0.829 0.886 0.943 —7 0.714 0.786 0.893 —8 0.643 0.738 0.833 0.8819 0.600 0.683 0.783 0.833
10 0.564 0.648 0.745 0.794
11 0.523 0.623 0.736 0.81812 0.497 0.591 0.703 0.78013 0.475 0.566 0.673 0.74514 0.457 0.545 0.646 0.71615 0.441 0.525 0.623 0.689
16 0.425 0.507 0.601 0.66617 0.412 0.490 0.582 0.64518 0.399 0.476 0.564 0.62519 0.388 0.462 0.549 0.60820 0.377 0.450 0.534 0.591
21 0.368 0.438 0.521 0.57622 0.359 0.428 0.508 0.56223 0.351 0.418 0.496 0.54924 0.343 0.409 0.485 0.53725 0.336 0.400 0.475 0.526
26 0.329 0.392 0.465 0.51527 0.323 0.385 0.456 0.50528 0.317 0.377 0.448 0.49629 0.311 0.370 0.440 0.48730 0.305 0.364 0.432 0.478
From “Distribution of Sums of Squares of Rank Differ-ences for Small Samples,” E. G. Olds, Annals of Mathe-matical Statistics, Volume 9 (1938).
Tables 873
Tabl
e12
Ran
dom
Num
bers
Lin
e/C
ol.
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
(13)
(14)
110
480
1501
101
536
0201
181
647
9164
669
179
1419
462
590
3620
720
969
9957
091
291
9070
02
2236
846
573
2559
585
393
3099
589
198
2798
253
402
9396
534
095
5266
619
174
3961
599
505
324
130
4836
022
527
9726
576
393
6480
915
179
2483
049
340
3208
130
680
1965
563
348
5862
94
4216
793
003
0624
361
680
0785
616
376
3944
053
537
7134
157
004
0084
974
917
9775
816
379
537
570
3997
581
837
1665
606
121
9178
260
468
8130
549
684
6067
214
110
0692
701
263
5461
3
677
921
0690
711
008
4275
127
756
5349
818
602
7065
990
655
1505
321
916
8182
544
394
4288
07
9956
272
095
5642
069
994
9887
231
016
7119
418
738
4401
348
840
6321
321
069
1063
412
952
896
301
9197
705
463
0797
218
876
2092
294
595
5686
969
014
6004
518
425
8490
342
508
3230
79
8957
914
342
6366
110
281
1745
318
103
5774
084
378
2533
112
566
5867
844
947
0558
556
941
1085
475
3685
753
342
5398
853
060
5953
338
867
6230
008
158
1798
316
439
1145
818
593
6495
2
1128
918
6957
888
231
3327
670
997
7993
656
865
0585
990
106
3159
501
547
8559
091
610
7818
812
6355
340
961
4823
503
427
4962
669
445
1866
372
695
5218
020
847
1223
490
511
3370
390
322
1309
429
9396
952
636
9273
788
974
3348
836
320
1761
730
015
0827
284
115
2715
630
613
7495
214
1036
561
129
8752
985
689
4823
752
267
6768
993
394
0151
126
358
8510
420
285
2997
589
868
1507
119
9733
671
048
0817
877
233
1391
647
564
8105
697
735
8597
729
372
7446
128
551
9070
7
1651
085
1276
551
821
5125
977
452
1630
860
756
9214
449
442
5390
070
960
6399
075
601
4071
917
0236
821
382
5240
460
268
8936
819
885
5532
244
819
0118
865
255
6483
544
919
0594
455
157
1801
011
5409
233
362
9490
431
273
0414
618
594
2985
271
585
8503
051
132
0191
592
747
6495
119
5216
253
916
4636
958
586
2321
614
513
8314
998
736
2349
564
350
9473
817
752
3515
635
749
2007
056
9762
833
787
0999
842
698
0669
176
988
1360
251
851
4610
488
916
1950
925
625
5810
4
2148
663
9124
585
828
1434
609
172
3016
890
229
0473
459
193
2217
830
421
6166
699
904
3281
222
5416
458
492
2242
174
103
4707
025
306
7646
826
384
5815
106
646
2152
415
227
9690
944
592
2332
639
3236
305
597
2420
013
363
3800
594
342
2872
835
806
0691
217
012
6416
118
296
2285
124
2933
427
001
8763
787
308
5873
100
256
4583
415
398
4655
741
135
1036
707
684
3618
818
510
2502
488
3306
228
834
0735
119
731
9242
060
952
6128
050
001
6765
832
586
8667
950
720
9495
3
874 Appendix 3 Tables
Tabl
e12
(Con
tinu
ed)
Lin
e/C
ol.
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
(13)
(14)
2681
525
7229
504
839
9642
324
878
8265
166
566
1477
876
797
1478
013
300
8707
479
666
9572
527
2967
620
591
6808
626
432
4690
120
849
8976
881
536
8664
512
659
9225
957
102
8042
825
280
2800
742
5739
239
064
6643
284
673
4002
732
832
6136
298
947
9606
764
760
6458
496
096
9825
329
0536
604
213
2566
926
422
4440
744
048
3793
763
904
4576
666
134
7547
066
520
3469
390
449
3091
921
2641
864
117
9430
526
766
2594
039
972
2220
971
500
6456
891
402
4241
607
844
6961
831
0058
204
711
8791
777
341
4220
635
126
7408
799
547
8181
742
607
4380
876
655
6202
876
630
3200
725
6988
462
797
5617
086
324
8807
276
222
3608
684
637
9316
176
038
6585
577
919
8800
633
6901
165
795
9587
655
293
1898
827
354
2657
508
625
4080
159
920
2984
180
150
1277
748
501
3425
976
5794
829
888
8860
467
917
4870
818
912
8227
165
424
6977
433
611
5426
285
963
0354
735
0976
383
473
7357
712
908
3088
318
317
2829
035
797
0599
841
688
3495
237
888
3891
788
050
3691
567
4259
527
958
3013
404
024
8638
529
880
9973
055
536
8485
529
080
0925
079
656
7321
137
1795
556
349
9099
949
127
2004
459
931
0611
520
542
1805
902
008
7370
883
517
3610
342
791
3846
503
1858
418
845
4961
802
304
5103
820
655
5872
728
168
1547
556
942
5338
920
562
8733
839
9215
789
634
9482
478
171
8461
082
834
0992
225
417
4413
748
413
2555
521
246
3550
920
468
4014
577
6276
535
605
8126
339
667
4735
856
873
5630
761
607
4951
889
656
2010
377
490
1806
241
9842
707
523
3336
264
270
0163
892
477
6696
998
420
0488
045
585
4656
504
102
4688
045
709
4234
914
6397
688
720
8276
534
476
1703
287
589
4083
632
427
7000
270
663
8886
377
775
6934
843
7006
028
277
3947
546
473
2321
953
416
9497
025
832
6997
594
884
1966
172
828
0010
266
794
4453
976
5491
406
990
6724
568
350
8294
811
398
4287
880
287
8826
747
363
4663
406
541
9780
945
7607
229
515
4098
007
391
5874
525
774
2298
780
059
3991
196
189
4115
114
222
6069
759
583
4690
725
5221
083
974
2999
265
831
3885
750
490
8376
555
657
1436
131
720
5737
556
228
4154
647
6436
467
412
3333
931
926
1488
324
413
5974
492
351
9747
389
286
3593
104
110
2372
651
900
4808
962
0035
831
662
2538
861
642
3407
281
249
3564
856
891
6935
248
373
4557
878
547
8178
849
9501
268
379
9352
670
765
1059
204
542
7646
354
328
0234
917
247
2886
514
777
6273
092
277
5015
664
1049
320
492
3839
191
132
2199
959
516
8165
227
195
4822
346
751
2292
332
261
8565
3
Tables 875
Tabl
e12
(Con
tinu
ed)
Lin
e/C
ol.
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
(13)
(14)
5116
408
8189
904
153
5338
179
401
2143
883
035
9235
036
693
3123
859
649
9175
472
772
0233
852
1862
981
953
0552
091
962
0473
913
092
9766
224
822
9473
006
496
3509
004
822
8677
498
289
5373
115
3510
147
498
8763
799
016
7106
088
824
7101
318
735
2028
623
153
7292
435
165
4304
054
5749
116
703
2316
749
323
4502
133
132
1254
441
035
8078
045
393
4481
212
515
9893
191
202
5530
405
8394
623
792
1442
215
059
4579
922
716
1979
209
983
7435
368
668
3042
970
735
2549
9
5616
631
3500
685
900
9827
532
388
5239
016
815
6929
882
732
3848
073
817
3252
341
961
4443
757
9677
320
206
4255
978
985
0530
022
164
2436
954
224
3508
319
687
1105
291
491
6038
319
746
5838
935
6420
214
349
8267
466
523
4413
300
697
3555
235
970
1912
463
318
2968
603
387
5984
659
3162
476
384
1740
353
363
4416
764
486
6475
875
366
7655
431
601
1261
433
072
6033
292
325
6078
919
1947
423
632
2788
947
914
0258
437
680
2080
172
152
3933
934
806
0893
085
001
8782
0
6103
931
3330
957
047
7421
163
445
1736
162
825
3990
805
607
9128
468
833
2557
038
818
4692
062
7442
633
278
4397
210
119
8991
715
665
5287
273
823
7314
488
662
8897
074
492
5180
599
378
6309
066
0090
320
795
9545
292
648
4545
409
552
8881
516
553
5112
579
375
9759
616
296
6609
264
4223
812
426
8702
514
267
2097
904
508
6453
531
355
8606
429
472
4768
905
974
5246
816
834
6516
153
0800
226
504
4174
481
959
6564
274
240
5630
200
033
6710
777
510
7062
528
725
3419
1
6621
457
4074
229
820
9678
329
400
2184
015
035
3453
733
310
0611
695
240
1595
716
572
0600
467
2158
157
802
0205
089
728
1793
737
621
4707
542
080
9740
348
626
6899
543
805
3338
621
597
6855
612
7809
583
197
3373
205
810
2481
386
902
6039
716
489
0326
488
525
4278
605
269
9253
269
4465
766
999
9932
451
281
8446
360
563
7931
293
454
6887
625
471
9391
125
650
1268
273
572
7091
340
8497
946
949
8197
337
949
6102
343
997
1526
380
644
4394
289
203
7179
599
533
5050
1
7191
227
2119
931
935
2702
284
067
0546
235
216
1448
629
891
6860
741
867
1495
191
696
8506
572
5000
138
140
6632
119
924
7216
309
538
1215
106
878
9190
318
749
3440
556
087
8279
070
925
7365
390
0522
472
958
2860
981
406
3914
725
549
4854
242
627
4523
357
202
9461
723
772
0789
674
2750
496
131
8394
441
575
1057
308
619
6448
273
923
3615
205
184
9414
225
299
8438
734
925
7537
169
9485
139
117
8963
200
959
1648
765
536
4907
139
782
1709
502
330
7430
100
275
4828
0
876 Appendix 3 Tables
Tabl
e12
(Con
tinu
ed)
Lin
e/C
ol.
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
(13)
(14)
7611
508
7022
551
111
3835
119
444
6649
971
945
0542
213
442
7867
584
081
6693
893
654
5989
477
3744
930
362
0669
454
690
0405
253
115
6275
795
348
7866
211
163
8165
150
245
3497
152
924
7846
515
7033
185
922
3832
957
015
1576
597
161
1786
945
349
6179
666
345
8107
349
106
7986
079
3098
681
223
4241
658
353
2153
230
502
3230
586
482
0517
407
901
5433
958
861
7481
846
942
8063
798
6499
546
583
0978
544
160
7812
883
991
4288
592
520
8353
180
377
3590
981
250
5423
8
8182
486
8484
699
254
6763
243
218
5007
621
361
6481
651
202
8812
441
870
5268
951
275
8355
682
2188
532
906
9243
109
060
6429
751
674
6412
662
570
2612
305
155
5919
452
799
2822
585
762
8360
336
9878
207
408
5345
813
564
5908
926
445
2978
985
205
4100
112
535
1213
314
645
2354
184
4393
746
891
2401
025
560
8635
533
941
2578
654
990
7189
915
475
9543
498
227
2182
419
585
8597
656
6317
589
303
1627
507
100
9206
321
942
1861
147
348
2020
318
534
0386
278
095
5013
6
8603
299
0122
105
418
3898
255
758
9223
726
759
8636
721
216
9844
208
303
5661
391
511
7592
887
7962
606
486
0357
417
668
0778
576
020
7992
425
651
8332
588
428
8507
672
811
2271
750
585
8885
636
6833
547
539
0312
965
651
1197
702
510
2611
399
447
6864
534
327
1515
255
230
9344
889
1803
914
367
6133
706
177
1214
346
609
3298
974
014
6470
800
533
3539
858
408
1326
147
908
9008
362
1565
660
627
3647
865
648
1676
453
412
0901
307
832
4157
417
639
8216
360
859
7556
7
9179
556
2906
804
142
1626
815
387
1285
666
227
3835
822
478
7337
388
732
0944
382
558
0525
092
9260
882
674
2707
232
534
1707
527
698
9820
463
863
1195
134
648
8802
256
148
3492
557
031
9323
982
2583
540
055
6700
612
293
0275
314
827
2323
535
071
9970
437
543
1160
135
503
8517
194
0991
596
306
0590
897
901
2839
514
186
0082
180
703
7042
675
647
7631
088
717
3789
040
129
9559
037
3330
026
695
6224
769
927
7612
350
842
4383
486
654
7095
979
725
9387
228
117
1923
3
9642
488
7807
769
882
6165
734
136
7918
097
526
4309
204
098
7357
180
799
7653
671
255
6423
997
4676
486
273
6300
393
017
3120
436
692
4020
235
275
5730
655
543
5320
318
098
4762
588
684
9803
237
4543
055
417
6328
290
816
1734
988
298
9018
336
600
7840
606
216
9578
742
579
9073
099
8659
181
482
5266
761
582
1497
290
053
8953
476
036
4919
943
716
9754
804
379
4637
028
672
100
3853
401
715
9496
487
288
6568
043
772
3956
012
918
8653
762
738
1963
651
132
2573
956
947
Abr
idge
dfr
omH
andb
ook
ofTa
bles
for
Pro
babi
lity
and
Stat
isti
cs,2
nded
ition
,edi
ted
byW
illia
mH
.B
eyer
(Cle
vela
nd:T
heC
hem
ical
Rub
ber
Com
pany
,196
8).