正規分布表Ⅰ
\(\displaystyle P=P_r(Z≧u)= \frac{1}{\sqrt{2π}}\int_{u}^∞e^{\frac{-u^2}{2}du}\)
u | *=0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
0.0.* | 0.500 | 0.496 | 0.492 | 0.488 | 0.484 | 0.480 | 0.476 | 0.47 | 0.468 | 0.46 |
0.1.* | 0.460 | 0.456 | 0.452 | 0.448 | 0.444 | 0.44 | 0.436 | 0.432 | 0.428 | 0.424 |
0.2.* | 0.420 | 0.416 | 0.412 | 0.409 | 0.405 | 0.401 | 0.397 | 0.393 | 0.389 | 0.385 |
0.3.* | 0.382 | 0.378 | 0.374 | 0.370 | 0.366 | 0.363 | 0.359 | 0.355 | 0.351 | 0.348 |
0.4.* | 0.344 | 0.340 | 0.337 | 0.333 | 0.329 | 0.326 | 0.32 | 0.319 | 0.315 | 0.312 |
0.5.* | 0.308 | 0.305 | 0.301 | 0.298 | 0.294 | 0.291 | 0.287 | 0.284 | 0.280 | 0.277 |
0.6* | 0.274 | 0.270 | 0.267 | 0.264 | 0.261 | 0.257 | 0.254 | 0.251 | 0.248 | 0.245 |
0.7* | 0.241 | 0.238 | 0.235 | 0.232 | 0.229 | 0.226 | 0.223 | 0.220 | 0.217 | 0.214 |
0.8* | 0.211 | 0.208 | 0.206 | 0.203 | 0.200 | 0.197 | 0.194 | 0.192 | 0.189 | 0.186 |
0.9* | 0.184 | 0.181 | 0.178 | 0.176 | 0.173 | 0.171 | 0.168 | 0.166 | 0.163 | 0.161 |
1.0* | 0.158 | 0.156 | 0.153 | 0.151 | 0.149 | 0.146 | 0.144 | 0.142 | 0.140 | 0.137 |
1.1* | 0.135 | 0.133 | 0.131 | 0.129 | 0.127 | 0.125 | 0.123 | 0.121 | 0.119 | 0.117 |
1.2* | 0.115 | 0.113 | 0.111 | 0.109 | 0.107 | 0.105 | 0.103 | 0.102 | 0.100 | 0.098 |
1.3* | 0.096 | 0.095 | 0.093 | 0.091 | 0.090 | 0.088 | 0.086 | 0.085 | 0.083 | 0.082 |
1.4* | 0.080 | 0.079 | 0.077 | 0.076 | 0.074 | 0.073 | 0.072 | 0.070 | 0.069 | 0.068 |
1.5* | 0.066 | 0.065 | 0.064 | 0.063 | 0.061 | 0.060 | 0.059 | 0.058 | 0.057 | 0.055 |
1.6* | 0.054 | 0.053 | 0.052 | 0.051 | 0.050 | 0.049 | 0.048 | 0.047 | 0.046 | 0.045 |
1.7* | 0.044 | 0.043 | 0.042 | 0.041 | 0.040 | 0.040 | 0.039 | 0.038 | 0.037 | 0.036 |
1.8* | 0.035 | 0.035 | 0.034 | 0.033 | 0.032 | 0.032 | 0.031 | 0.030 | 0.030 | 0.029 |
1.9* | 0.028 | 0.028 | 0.027 | 0.026 | 0.026 | 0.025 | 0.025 | 0.024 | 0.023 | 0.023 |
2.0* | 0.022 | 0.022 | 0.021 | 0.021 | 0.020 | 0.020 | 0.019 | 0.019 | 0.018 | 0.018 |
2.1* | 0.017 | 0.017 | 0.017 | 0.016 | 0.016 | 0.015 | 0.015 | 0.015 | 0.014 | 0.014 |
2.2* | 0.013 | 0.013 | 0.013 | 0.012 | 0.012 | 0.012 | 0.011 | 0.011 | 0.011 | 0.011 |
2.3* | 0.01 | 0.01 | 0.01 | 0.009 | 0.009 | 0.009 | 0.009 | 0.008 | 0.008 | 0.008 |
2.4* | 0.008 | 0.007 | 0.007 | 0.007 | 0.007 | 0.007 | 0.006 | 0.006 | 0.006 | 0.006 |
2.5* | 0.006 | 0.006 | 0.005 | 0.005 | 0.005 | 0.005 | 0.005 | 0.005 | 0.004 | 0.004 |
2.6* | 0.004 | 0.004 | 0.004 | 0.004 | 0.004 | 0.004 | 0.003 | 0.003 | 0.003 | 0.003 |
2.7* | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.002 | 0.002 | 0.002 | 0.002 | 0.002 |
2.8* | 0.002 | 0.002 | 0.002 | 0.002 | 0.002 | 0.002 | 0.002 | 0.002 | 0.001 | 0.001 |
2.9* | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 |
3.0* | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 |
4.0* | 0.00003 | 0.00003 | 0.00003 | 0.00003 | 0.00003 | 0.00002 | 0.00002 | 0.00002 | 0.00002 | 0.00002 |
正規分布表Ⅱ
P | 0.001 | 0.005 | 0.01 | 0.025 | 0.05 | 0.1 | 0.2 | 0.3 | 0.4 |
u | 3.09 | 2.576 | 2.376 | 1.96 | 1.645 | 1.282 | 0.845 | 0.524 | 0.253 |
\(χ^2\)表
\(自由度Φ,片側上限確率Pからχ^2(Φ,P)\)を求める表
Φ/P | 0.995 | 0.99 | 0.975 | 0.95 | 0.5 | 0.1 | 0.05 | 0.025 | 0.01 | 0.005 |
1 | 0.00004 | 0.0002 | 0.001 | 0.0039 | 0.455 | 2.710 | 3.84 | 5.02 | 6.63 | 7.88 |
2 | 0.01003 | 0.02010 | 0.0506 | 0.1026 | 1.386 | 4.61 | 5.99 | 7.38 | 9.21 | 10.6 |
3 | 0.07172 | 0.1148 | 0.2158 | 0.352 | 2.37 | 6.25 | 7.81 | 9.35 | 11.3 | 12.8 |
4 | 0.2070 | 0.2971 | 0.484 | 0.711 | 3.36 | 7.78 | 9.49 | 11.1 | 13.3 | 14.9 |
5 | 0.4117 | 0.554 | 0.831 | 1.15 | 4.35 | 9.24 | 11.07 | 12.8 | 15.1 | 16.8 |
6 | 0.676 | 0.872 | 1.24 | 1.64 | 5.35 | 10.64 | 12.6 | 14.5 | 16.8 | 18.6 |
7 | 0.989 | 1.24 | 1.69 | 2.17 | 6.35 | 12.02 | 14.1 | 16.0 | 18.5 | 20.3 |
8 | 1.34 | 1.65 | 2.18 | 2.73 | 7.34 | 13.4 | 15.5 | 17.5 | 20.1 | 22.0 |
9 | 1.73 | 2.09 | 2.70 | 3.33 | 8.34 | 14.7 | 16.9 | 19.0 | 21.7 | 23.6 |
10 | 2.16 | 2.56 | 3.25 | 3.94 | 9.34 | 16.0 | 18.3 | 20.5 | 23.2 | 25.2 |
11 | 2.60 | 3.05 | 3.82 | 4.57 | 10.3 | 17.3 | 19.7 | 21.9 | 24.7 | 26.8 |
12 | 3.07 | 3.57 | 4.40 | 5.23 | 11.3 | 18.6 | 21.0 | 23.3 | 26.2 | 28.3 |
13 | 3.57 | 4.11 | 5.01 | 5.89 | 12.3 | 19.8 | 22.4 | 24.7 | 27.7 | 29.8 |
14 | 4.07 | 4.66 | 5.63 | 6.57 | 13.3 | 21.1 | 23.7 | 26.1 | 29.1 | 31.3 |
15 | 4.60 | 5.23 | 6.26 | 7.26 | 14.3 | 22.3 | 25.0 | 27.5 | 30.6 | 32.8 |
16 | 5.14 | 5.81 | 6.91 | 7.96 | 15.3 | 23.5 | 26.3 | 28.9 | 32.0 | 34.3 |
17 | 5.70 | 6.41 | 7.56 | 8.67 | 16.3 | 24.8 | 27.6 | 30.2 | 33.4 | 35.7 |
18 | 6.26 | 7.01 | 8.23 | 9.39 | 17.3 | 26.0 | 28.9 | 31.5 | 34.8 | 37.2 |
19 | 6.84 | 7.63 | 8.91 | 10.1 | 18.3 | 27.2 | 30.1 | 32.9 | 36.2 | 38.6 |
20 | 7.43 | 8.26 | 9.59 | 10.9 | 19.3 | 28.4 | 31.4 | 34.2 | 37.6 | 40.0 |
21 | 8.03 | 8.90 | 10.3 | 11.6 | 20.3 | 29.6 | 32.7 | 35.5 | 38.9 | 41.4 |
22 | 8.64 | 9.54 | 11.0 | 12.3 | 21.3 | 30.8 | 33.9 | 36.8 | 40.3 | 42.8 |
23 | 9.26 | 10.2 | 11.7 | 13.1 | 22.3 | 32.0 | 35.2 | 38.1 | 41.6 | 44.2 |
24 | 9.89 | 10.9 | 12.4 | 13.9 | 23.3 | 33.2 | 36.4 | 39.4 | 43.0 | 45.6 |
25 | 10.5 | 11.5 | 13.1 | 14.6 | 24.3 | 34.4 | 37.7 | 40.7 | 44.3 | 46.9 |
26 | 11.2 | 12.2 | 13.8 | 15.4 | 25.3 | 35.6 | 38.9 | 41.9 | 45.6 | 48.3 |
27 | 11.8 | 12.9 | 14.6 | 16.2 | 26.3 | 36.7 | 40.1 | 43.2 | 47.0 | 49.6 |
28 | 12.5 | 13.6 | 15.3 | 16.9 | 27.3 | 37.9 | 41.3 | 44.5 | 48.3 | 51.0 |
29 | 13.1 | 14.3 | 16.1 | 17.7 | 28.3 | 39.1 | 42.6 | 45.7 | 49.6 | 52.3 |
30 | 13.8 | 15.0 | 16.8 | 18.5 | 29.3 | 40.3 | 43.8 | 47.0 | 50.9 | 53.7 |
40 | 20.7 | 22.2 | 24.4 | 26.5 | 39.3 | 51.8 | 55.8 | 59.3 | 63.7 | 66.8 |
50 | 28.0 | 29.7 | 32.4 | 34.8 | 49.3 | 63.2 | 67.5 | 71.4 | 76.2 | 79.5 |
60 | 35.5 | 37.5 | 40.5 | 43.2 | 59.3 | 74.4 | 79.1 | 83.3 | 88.4 | 92.0 |
80 | 51.2 | 53.5 | 57.2 | 60.4 | 79.3 | 96.6 | 101.9 | 106.6 | 112.3 | 116.3 |
100 | 67.3 | 70.1 | 74.2 | 77.9 | 99.3 | 118.5 | 124.3 | 129.6 | 135.8 | 140.2 |
t 表
\(t(Φ,P)\)
\(自由度Φと両側確率Pからtを求める表\)
Φ/P | 0.5 | 0.4 | 0.3 | 0.2 | 0.1 | 0.05 | 0.02 | 0.01 | 0.001 |
1 | 1.000 | 1.376 | 1.963 | 3.078 | 6.314 | 12.706 | 31.821 | 63.657 | 636.619 |
2 | 0.816 | 1.0061 | 1.386 | 1.886 | 2.920 | 4.303 | 6.965 | 9.925 | 31.599 |
3 | 0.765 | 0.978 | 1.25 | 1.638 | 2.353 | 3.182 | 4.541 | 5.841 | 12.924 |
4 | 0.741 | 0.941 | 1.190 | 1.533 | 2.132 | 2.776 | 3.747 | 4.604 | 8.610 |
5 | 0.727 | 0.920 | 1.156 | 1.476 | 2.015 | 2.571 | 3.365 | 4.032 | 6.869 |
6 | 0.718 | 0.906 | 1.134 | 1.440 | 1.943 | 2.447 | 3.143 | 3.707 | 5.959 |
7 | 0.711 | 0.896 | 1.119 | 1.415 | 1.895 | 2.365 | 2.998 | 3.499 | 5.408 |
8 | 0.706 | 0.889 | 1.108 | 1.397 | 1.860 | 2.306 | 2.896 | 3.355 | 5.041 |
9 | 0.703 | 0.883 | 1.100 | 1.383 | 1.833 | 2.262 | 2.821 | 3.250 | 4.781 |
10 | 0.700 | 0.879 | 1.093 | 1.372 | 1.812 | 2.228 | 2.764 | 3.169 | 4.587 |
11 | 0.697 | 0.876 | 1.088 | 1.363 | 1.796 | 2.201 | 2.718 | 3.106 | 4.437 |
12 | 0.695 | 0.873 | 1.083 | 1.356 | 1.782 | 2.179 | 2.681 | 3.055 | 4.318 |
13 | 0.694 | 0.870 | 1.079 | 1.350 | 1.771 | 2.160 | 2.650 | 3.012 | 4.221 |
14 | 0.692 | 0.868 | 1.076 | 1.345 | 1.761 | 2.145 | 2.624 | 2.977 | 4.140 |
15 | 0.691 | 0.866 | 1.074 | 1.341 | 1.753 | 2.131 | 2.602 | 2.947 | 4.073 |
16 | 0.69 | 0.865 | 1.071 | 1.337 | 1.746 | 2.120 | 2.583 | 2.921 | 4.015 |
17 | 0.689 | 0.863 | 1.069 | 1.333 | 1.740 | 2.110 | 2.567 | 2.898 | 3.965 |
18 | 0.688 | 0.862 | 1.067 | 1.330 | 1.734 | 2.101 | 2.552 | 2.878 | 3.922 |
19 | 0.688 | 0.861 | 1.066 | 1.328 | 1.729 | 2.093 | 2.539 | 2.861 | 3.883 |
20 | 0.687 | 0.860 | 1.064 | 1.325 | 1.725 | 2.086 | 2.528 | 2.845 | 3.850 |
21 | 0.686 | 0.859 | 1.063 | 1.323 | 1.721 | 2.080 | 2.518 | 2.831 | 2.819 |
22 | 0.686 | 0.858 | 1.061 | 1.321 | 1.717 | 2.074 | 2.508 | 2.819 | 3.792 |
23 | 0.685 | 0.858 | 1.060 | 1.319 | 1.714 | 2.069 | 2.500 | 2.807 | 3.768 |
24 | 0.685 | 0.857 | 1.059 | 1.318 | 1.711 | 2.064 | 2.492 | 2.797 | 3.745 |
25 | 0.684 | 0.856 | 1.058 | 1.316 | 1.708 | 2.060 | 2.485 | 2.787 | 3.725 |
26 | 0.684 | 0.856 | 1.057 | 1.315 | 1.706 | 2.056 | 2.479 | 2.779 | 3.707 |
27 | 0.684 | 0.855 | 1.056 | 1.314 | 1.703 | 2.052 | 2.473 | 2.771 | 3.690 |
28 | 0.683 | 0.855 | 1.056 | 1.313 | 1.701 | 2.048 | 2.467 | 2.763 | 3.674 |
29 | 0.683 | 0.854 | 1.055 | 1.311 | 1.699 | 2.045 | 2.462 | 2.756 | 3.659 |
30 | 0.683 | 0.854 | 1.055 | 1.310 | 1.697 | 2.042 | 2.457 | 2.750 | 3.646 |
40 | 0.681 | 0.851 | 1.050 | 1.303 | 1.684 | 2.021 | 2.423 | 2.704 | 3.551 |
60 | 0.679 | 0.848 | 1.045 | 1.296 | 1.671 | 2.000 | 2.390 | 2.660 | 3.460 |
120 | 0.677 | 0.845 | 1.041 | 1.289 | 1.658 | 1.980 | 2.358 | 2.617 | 3.373 |
∞ | 0.674 | 0.842 | 1.036 | 1.282 | 1.645 | 1.960 | 2.326 | 2.576 | 3.291 |
F表(5%,1%)
\(F(Φ_1,Φ_2:P)\)
P=0.05・・細字
P=0.01・・青太字
上側確率5%と1%を求める表
Φ2/Φ1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 12 | 15 | 20 | 24 | 30 | 40 | 60 | 120 | ∞ |
1 | 161 4052 | 200 5000 | 216 5403 | 225 5625 | 230 5764 | 234 5859 | 237 5928 | 239 5981 | 241 6022 | 242 6056 | 244 6106 | 246 6157 | 248 6209 | 249 6235 | 250 6261 | 251 6287 | 252 6313 | 253 6339 | 254 6366 |
2 | 18.5 98.5 | 19.0 99.0 | 19.2 99.2 | 19.2 99.2 | 19.3 99.3 | 19.3 99.3 | 19.4 99.4 | 19.4 99.4 | 19.4 99.4 | 19.4 99.4 | 19.4 99.4 | 19.4 99.4 | 19.4 99.4 | 19.5 99.5 | 19.5 99.5 | 19.5 99.5 | 19.5 99.5 | 19.5 99.5 | 19.5 99.5 |
3 | 10.1 34.1 | 9.55 30.8 | 9.28 29.5 | 9.12 28.7 | 9.01 28.2 | 8.94 29.5 | 8.89 28.7 | 8.85 28.2 | 8.81 27.9 | 8.79 27.7 | 8.74 27.5 | 8.7 27.3 | 8.66 26.7 | 8.64 26.6 | 8.62 26.5 | 8.59 26.4 | 8.57 26.3 | 8.55 26.2 | 8.53 26.1 |
4 | 7.71 21.2 | 6.94 18.0 | 6.59 16.7 | 6.39 16.0 | 6.26 15.5 | 6.16 15.2 | 6.09 15.0 | 6.04 14.8 | 6.00 14.7 | 5.96 14.5 | 5.91 14.4 | 5.86 14.2 | 5.8 14.0 | 5.77 13.9 | 5.75 13.8 | 5.72 13.7 | 5.69 13.7 | 5.66 13.6 | 5.63 13.5 |
5 | 6.61 16.3 | 5.79 5.41 | 5.41 12.1 | 5.19 11.4 | 5.05 11.0 | 4.95 10.7 | 4.88 10.5 | 4.82 10.3 | 4.77 10.2 | 4.74 10.1 | 4.68 9.89 | 4.62 9.72 | 4.56 9.55 | 4.53 9.47 | 4.5 9.38 | 4.46 9.29 | 4.43 9.2 | 4.4 9.11 | 4.36 9.02 |
6 | 5.99 13.7 | 5.14 10.9 | 4.76 9.78 | 4.53 9.15 | 4.39 8.75 | 4.28 8.47 | 4.21 8.26 | 4.15 8.10 | 4.10 7.98 | 4.06 7.87 | 4.00 7.72 | 3.94 7.56 | 3.87 7.40 | 3.84 7.31 | 3.81 7.23 | 3.77 7.14 | 3.74 7.06 | 3.70 6.97 | 3.67 6.88 |
7 | 5.59 13.7 | 4.74 9.55 | 4.35 8.45 | 4.12 7.85 | 3.97 7.46 | 3.87 7.19 | 3.79 6.99 | 3.73 6.84 | 3.68 6.72 | 3.64 6.62 | 3.57 6.47 | 3.51 6.31 | 3.44 6.16 | 3.41 6.07 | 3.38 5.99 | 3.34 5.91 | 3.30 5.82 | 3.27 5.74 | 3.23 5.65 |
8 | 5.32 11.3 | 4.46 8.65 | 4.07 7.59 | 3.84 7.01 | 3.69 6.63 | 3.58 6.37 | 3.50 6.18 | 3.44 6.03 | 3.39 5.91 | 3.35 5.81 | 3.28 5.67 | 3.22 5.52 | 3.15 5.36 | 3.12 5.28 | 3.08 5.20 | 3.04 5.12 | 3.01 5.03 | 2.97 4.95 | 2.93 4.86 |
9 | 5.12 10.6 | 4.26 8.02 | 3.86 6.99 | 3.63 6.42 | 3.48 6.06 | 3.37 5.80 | 3.29 5.61 | 3.23 5.43 | 3.18 5.35 | 3.14 5.26 | 3.07 5.11 | 3.01 4.96 | 2.94 4.81 | 2.90 4.73 | 2.86 4.65 | 2.83 4.57 | 2.79 4.48 | 2.75 4.40 | 2.71 4.31 |
10 | 4.96 10.0 | 4.10 7.56 | 3.71 6.55 | 3.48 5.99 | 3.33 5.64 | 3.22 5.39 | 3.14 5.20 | 3.07 5.06 | 3.02 4.94 | 2.98 4.85 | 2.91 4.71 | 2.85 4.56 | 2.77 4.41 | 2.74 4.33 | 2.70 4.25 | 2.66 4.17 | 2.62 4.08 | 2.58 4.00 | 2.54 3.91 |
11 | 4.84 9.65 | 3.98 7.21 | 3.59 6.22 | 3.36 5.67 | 3.20 5.32 | 3.09 5.07 | 3.01 4.89 | 2.95 4.74 | 2.90 4.63 | 2.85 4.54 | 2.79 4.40 | 2.72 4.25 | 2.65 4.10 | 2.61 4.02 | 2.57 3.94 | 2.53 3.86 | 2.49 3.78 | 2.45 3.69 | 2.40 3.60 |
12 | 4.75 9.33 | 3.89 6.93 | 3.49 5.95 | 3.26 5.41 | 3.11 5.06 | 3.00 4.82 | 2.91 4.64 | 2.85 4.50 | 2.80 4.39 | 2.75 4.30 | 2.69 4.16 | 2.62 4.01 | 2.54 3.86 | 2.51 3.78 | 2.47 3.70 | 2.43 3.62 | 2.38 3.54 | 2.34 3.45 | 2.30 3.36 |
13 | 4.67 9.07 | 3.81 6.70 | 3.41 5.74 | 3.18 5.21 | 3.03 4.86 | 2.92 4.62 | 2.83 4.44 | 2.77 4.3 | 2.71 4.19 | 2.67 4.10 | 2.60 3.96 | 2.53 3.85 | 2.46 3.66 | 2.42 3.59 | 2.38 3.51 | 2.34 3.43 | 2.30 3.34 | 2.25 3.25 | 2.21 3.17 |
14 | 4.60 8.86 | 3.74 6.51 | 3.34 5.56 | 3.11 5.04 | 2.96 4.69 | 2.85 4.46 | 2.76 4.28 | 2.70 4.14 | 2.65 3.94 | 2.60 3.94 | 2.53 3.80 | 2.46 3.66 | 2.39 3.51 | 2.35 3.43 | 2.31 3.35 | 2.27 3.27 | 2.22 3.18 | 2.18 3.09 | 2.13 3.00 |
15 | 4.54 8.68 | 3.68 6.36 | 3.29 5.42 | 3.06 4.86 | 2.90 4.56 | 2.79 4.32 | 2.71 4.14 | 2.64 4.00 | 2.59 3.89 | 2.54 3.80 | 2.48 3.67 | 2.40 3.52 | 2.33 3.37 | 2.29 3.29 | 2.25 3.21 | 2.20 3.13 | 2.16 3.05 | 2.11 2.96 | 2.07 2.87 |
16 | 4.49 8.53 | 3.63 6.23 | 3.24 5.29 | 3.01 4.77 | 2.85 4.44 | 2.74 4.20 | 2.66 4.03 | 2.59 3.89 | 2.54 3.78 | 2.49 3.69 | 2.42 3.69 | 2.35 3.41 | 2.28 3.26 | 2.24 3.18 | 2.19 3.10 | 2.15 3.02 | 2.11 2.93 | 2.06 2.84 | 2.01 2.75 |
17 | 4.45 8.40 | 3.59 6.11 | 3.20 5.18 | 2.96 4.67 | 2.81 4.34 | 2.70 4.10 | 2.61 3.93 | 2.55 3.79 | 2.49 3.68 | 2.45 3.45 | 2.38 3.46 | 2.31 3.31 | 2.23 3.15 | 2.19 3.08 | 2.15 3.00 | 2.10 2.92 | 2.06 2.83 | 2.01 2.75 | 1.96 2.65 |
18 | 4.41 8.29 | 3.55 6.01 | 3.16 5.09 | 2.93 4.58 | 2.77 4.25 | 2.66 4.01 | 2.58 3.84 | 2.51 3.71 | 2.46 3.60 | 2.41 3.51 | 2.34 3.60 | 2.27 3.23 | 2.19 3.08 | 2.15 3.00 | 2.11 2.92 | 2.06 2.84 | 2.02 2.75 | 1.97 2.66 | 1.92 2.57 |
19 | 4.38 8.18 | 3.52 5.93 | 3.13 5.01 | 2.90 4.50 | 2.74 4.17 | 2.63 3.94 | 2.54 3.77 | 2.48 3.63 | 2.42 3.52 | 2.38 3.43 | 2.31 3.30 | 2.23 3.15 | 2.16 3.00 | 2.11 2.93 | 2.07 2.84 | 2.03 2.76 | 1.98 2.67 | 1.93 2.58 | 1.88 2.49 |
20 | 4.35 8.10 | 3.49 5.85 | 3.10 4.94 | 2.87 4.43 | 2.71 4.10 | 2.60 3.87 | 2.51 3.70 | 2.45 3.56 | 2.39 3.46 | 2.35 3.37 | 2.28 3.23 | 2.20 3.09 | 2.12 2.94 | 2.08 2.86 | 2.04 2.78 | 1.99 2.69 | 1.95 2.61 | 1.90 2.52 | 1.84 2.42 |
21 | 4.32 8.02 | 3.47 5.78 | 3.07 4.87 | 2.84 4.37 | 2.68 4.04 | 2.57 3.81 | 2.49 3.64 | 2.42 3.52 | 2.37 3.40 | 2.32 3.31 | 2.25 3.17 | 2.18 3.03 | 2.10 2.88 | 2.05 2.80 | 2.01 2.72 | 1.96 2.64 | 1.92 2.55 | 1.87 2.46 | 1.81 2.36 |
22 | 4.30 7.95 | 3.44 5.72 | 3.05 4.82 | 2.82 4.31 | 2.66 3.99 | 2.55 3.76 | 2.46 3.59 | 2.40 3.45 | 2.34 3.35 | 2.30 3.26 | 2.23 3.12 | 2.15 2.98 | 2.07 2.83 | 2.03 2.75 | 1.98 2.67 | 1.94 2.58 | 1.89 2.50 | 1.84 2.40 | 1.78 2.31 |
23 | 4.28 7.88 | 3.42 5.66 | 3.03 4.76 | 2.80 4.260 | 2.64 3.94 | 2.53 3.71 | 2.44 3.54 | 2.37 3.41 | 2.32 3.30 | 2.27 3.21 | 2.20 3.20 | 2.13 2.93 | 2.05 2.78 | 2.01 2.70 | 1.96 2.62 | 1.91 2.54 | 1.86 2.45 | 1.81 2.35 | 1.76 2.26 |
24 | 4.26 7.82 | 3.40 5.61 | 3.01 4.72 | 2.78 4.22 | 2.62 3.90 | 2.51 3.67 | 2.42 3.51 | 2.36 3.36 | 2.30 3.26 | 2.25 3.17 | 2.18 3.03 | 2.11 2.89 | 2.03 2.74 | 1.98 2.66 | 1.94 2.58 | 1.89 2.49 | 1.84 2.40 | 1.79 2.31 | 1.73 2.21 |
25 | 4.24 7.77 | 3.39 5.57 | 2.99 4.68 | 2.76 4.18 | 2.60 3.85 | 2.49 3.63 | 2.40 3.46 | 2.34 3.32 | 2.28 3.22 | 2.24 3.13 | 2.16 2.99 | 2.09 2.85 | 2.01 2.70 | 1.96 2.62 | 1.92 2.54 | 1.87 2.45 | 1.82 2.36 | 1.77 2.27 | 1.71 2.17 |
26 | 4.23 7.72 | 3.37 5.56 | 2.98 4.64 | 2.74 4.14 | 2.59 3.82 | 2.47 3.59 | 2.39 3.42 | 2.32 3.29 | 2.27 3.18 | 2.22 3.09 | 2.15 2.96 | 2.07 2.81 | 1.99 2.66 | 1.95 2.58 | 1.90 2.50 | 1.85 2.42 | 1.80 2.33 | 1.75 2.23 | 1.69 2.13 |
27 | 4.21 7.68 | 3.35 5.49 | 2.96 4.60 | 2.73 4.11 | 2.57 3.78 | 2.46 3.56 | 2.37 3.39 | 2.31 3.26 | 2.25 3.15 | 2.20 3.06 | 2.13 2.90 | 2.06 2.78 | 1.97 2.63 | 1.93 2.55 | 1.88 2.47 | 1.84 2.38 | 1.79 2.29 | 1.73 2.20 | 1.67 2.10 |
28 | 4.20 7.64 | 3.34 5.45 | 2.95 4.57 | 2.71 4.07 | 2.56 3.75 | 2.45 3.53 | 2.36 3.36 | 2.29 3.23 | 2.24 3.12 | 2.19 3.03 | 2.12 2.90 | 2.04 2.75 | 1.96 2.60 | 1.91 2.52 | 1.87 2.44 | 1.82 2.35 | 1.77 2.26 | 1.71 2.17 | 1.65 2.06 |
29 | 4.18 7.60 | 3.33 5.42 | 2.93 4.54 | 2.70 4.04 | 2.55 3.73 | 2.43 3.50 | 2.35 3.33 | 2.28 3.20 | 2.22 3.09 | 2.18 3.00 | 2.10 2.87 | 2.03 2.73 | 1.94 2.57 | 1.90 2.49 | 1.85 2.41 | 1.81 2.33 | 1.75 2.23 | 1.70 2.14 | 1.64 2.03 |
30 | 4.17 7.56 | 3.32 5.39 | 2.92 4.51 | 2.69 4.02 | 2.53 3.70 | 2.42 3.47 | 2.33 3.30 | 2.27 3.17 | 2.21 3.07 | 2.16 2.98 | 2.09 2.84 | 2.01 2.70 | 1.93 2.55 | 1.89 2.47 | 1.84 2.37 | 1.79 2.30 | 1.74 2.21 | 1.68 2.11 | 1.62 2.01 |
40 | 4.08 7.31 | 3.23 5.18 | 2.84 4.31 | 2.61 3.83 | 2.45 3.51 | 2.34 3.29 | 2.25 3.12 | 2.18 2.99 | 2.12 2.89 | 2.08 2.80 | 2.00 2.66 | 1.92 2.52 | 1.84 2.37 | 1.79 2.29 | 1.74 2.20 | 1.69 2.11 | 1.64 2.02 | 1.58 1.92 | 1.51 1.80 |
60 | 4.00 7.08 | 3.15 4.98 | 2.76 4.13 | 2.53 3.65 | 2.37 3.34 | 2.25 3.12 | 2.17 2.95 | 2.10 2.82 | 2.04 2.72 | 1.99 2.63 | 1.92 2.50 | 1.84 2.35 | 1.75 2.20 | 1.70 2.12 | 1.65 2.03 | 1.59 1.94 | 1.53 1.84 | 1.47 1.73 | 1.39 1.60 |
120 | 3.92 6.85 | 3.07 4.79 | 2.68 3.95 | 2.45 3.48 | 2.29 3.17 | 2.18 2.96 | 2.09 2.79 | 2.02 2.66 | 1.96 2.56 | 1.91 2.47 | 1.83 2.34 | 1.75 2.19 | 1.66 2.03 | 1.61 1.95 | 1.55 1.86 | 1.50 1.76 | 1.43 1.66 | 1.35 1.53 | 1.25 1.38 |
∞ | 3.84 6.63 | 3.00 4.61 | 3.00 3.78 | 2.37 3.32 | 2.21 3.02 | 2.10 2.80 | 2.01 2.64 | 1.94 2.51 | 1.88 2.41 | 1.83 2.32 | 1.75 2.18 | 1.67 2.04 | 1.57 1.88 | 1.52 1.79 | 1.46 1.70 | 1.39 1.59 | 1.32 1.47 | 1.22 1.32 | 1.0 1.0 |
F表(10%)
Φ2/Φ1 | 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 | |||
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 | ||||||||||||||||||||||||||||||
40 | ||||||||||||||||||||||||||||||
60 | ||||||||||||||||||||||||||||||
120 | ||||||||||||||||||||||||||||||
∞ |
R表
\(Φ/P\) | 0.1 | 0.05 | 0.02 | 0.01 |
10 | 0.497 | 0.5760 | 0.6581 | 0.7029 |
11 | 0.4762 | 0.5529 | 0.6339 | 0.6835 |
12 | 0.4745 | 0.5324 | 0.6120 | 0.6614 |
13 | 0.4409 | 0.5140 | 0.5923 | 0.6411 |
14 | 0.4259 | 0.4973 | 0.5742 | 0.6226 |
15 | 0.4124 | 0.4821 | 0.5577 | 0.6055 |
16 | 0.4000 | 0.4683 | 0.5425 | 0.5897 |
17 | 0.3887 | 0.4555 | 0.5285 | 0.5751 |
18 | 0.3783 | 0.4438 | 0.5155 | 0.5614 |
19 | 0.3687 | 0.4329 | 0.5034 | 0.5487 |
20 | 0.3598 | 0.4227 | 0.4921 | 0.5368 |
25 | 0.3233 | 0.3809 | 0.4451 | 0.4869 |
30 | 0.2960 | 0.3494 | 0.4093 | 0.4487 |
35 | 0.2746 | 0.3246 | 0.3810 | 0.4182 |
40 | 0.2573 | 0.3044 | 0.3578 | 0.3932 |
50 | 0.2306 | 0.2732 | 0.3218 | 0.3542 |
60 | 0.2108 | 0.2500 | 0.2948 | 0.3248 |
70 | 0.1954 | 0.2319 | 0.2737 | 0.3017 |
80 | 0.1829 | 0.2172 | 0.2565 | 0.2830 |
90 | 0.1726 | 0.2050 | 0.2422 | 0.2673 |
100 | 0.1638 | 0.1946 | 0.2301 | 0.2540 |
近似式 | \(\displaystyle \frac{1.645}{\sqrt{Φ+1}}\) | \(\displaystyle \frac{1.960}{\sqrt{Φ+1}}\) | \(\displaystyle \frac{2.326}{\sqrt{Φ+1}}\) | \(\displaystyle \frac{2.576}{\sqrt{Φ+1}}\) |