Alternate View
a. n=5 |
p
k |
.01 |
.05 |
.10 |
.20 |
.30 |
.40 |
.50 |
.60 |
.70 |
.80 |
.90 |
.95 |
.99 |
0 |
.951 |
.774 |
.590 |
.328 |
.168 |
.078 |
.031 |
.010 |
.002 |
.000 |
.000 |
.000 |
.000 |
1 |
.999 |
.977 |
.919 |
.737 |
.528 |
.337 |
.188 |
.087 |
.031 |
.007 |
.000 |
.000 |
.000 |
2 |
1.000 |
.999 |
.991 |
.942 |
.837 |
.683 |
.500 |
.317 |
.163 |
.058 |
.009 |
.001 |
.000 |
3 |
1.000 |
1.000 |
1.000 |
.993 |
.969 |
.913 |
.812 |
.663 |
.472 |
.263 |
.081 |
.023 |
.001 |
4 |
1.000 |
1.000 |
1.000 |
1.000 |
.998 |
.990 |
.969 |
.922 |
.832 |
.672 |
.410 |
.226 |
.049 |
b. n=6 |
p
k |
.01 |
.05 |
.10 |
.20 |
.30 |
.40 |
.50 |
.60 |
.70 |
.80 |
.90 |
.95 |
.99 |
0 |
.941 |
.735 |
.531 |
.262 |
.118 |
.047 |
.016 |
.004 |
.001 |
.000 |
.000 |
.000 |
.000 |
1 |
.999 |
.967 |
.886 |
.655 |
.420 |
.233 |
.109 |
.041 |
.011 |
.002 |
.000 |
.000 |
.000 |
2 |
1.000 |
.998 |
.984 |
.901 |
.744 |
.544 |
.344 |
.179 |
.070 |
.017 |
.001 |
.000 |
.000 |
3 |
1.000 |
1.000 |
.999 |
.983 |
.930 |
.821 |
.656 |
.456 |
.256 |
.099 |
.016 |
.002 |
.000 |
4 |
1.000 |
1.000 |
1.000 |
.998 |
.989 |
.959 |
.891 |
.767 |
.580 |
.345 |
.114 |
.033 |
.001 |
5 |
1.000 |
1.000 |
1.000 |
1.000 |
.999 |
.996 |
.984 |
.953 |
.882 |
.738 |
.469 |
.265 |
.059 |
c. n=7 |
p
k |
.01 |
.05 |
.10 |
.20 |
.30 |
.40 |
.50 |
.60 |
.70 |
.80 |
.90 |
.95 |
.99 |
0 |
.932 |
.698 |
.478 |
.210 |
.082 |
.028 |
.008 |
.002 |
.000 |
.000 |
.000 |
.000 |
.000 |
1 |
.998 |
.956 |
.850 |
.577 |
.329 |
.159 |
.063 |
.019 |
.004 |
.000 |
.000 |
.000 |
.000 |
2 |
1.000 |
.996 |
.974 |
.852 |
.647 |
.420 |
.227 |
.096 |
.029 |
.005 |
.000 |
.000 |
.000 |
3 |
1.000 |
1.000 |
.997 |
.967 |
.874 |
.710 |
.500 |
.290 |
.126 |
.033 |
.003 |
.000 |
.000 |
4 |
1.000 |
1.000 |
1.000 |
.995 |
.971 |
.904 |
.773 |
.580 |
.353 |
.148 |
.026 |
.004 |
.000 |
5 |
1.000 |
1.000 |
1.000 |
1.000 |
.996 |
.981 |
.937 |
.841 |
.671 |
.423 |
.150 |
.044 |
.002 |
6 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
.998 |
.992 |
.972 |
.918 |
.790 |
.522 |
.302 |
.068 |
d. n=8 |
p
k |
.01 |
.05 |
.10 |
.20 |
.30 |
.40 |
.50 |
.60 |
.70 |
.80 |
.90 |
.95 |
.99 |
0 |
.923 |
.663 |
.430 |
.168 |
.058 |
.017 |
.004 |
.001 |
.000 |
.000 |
.000 |
.000 |
.000 |
1 |
.997 |
.943 |
.813 |
.503 |
.255 |
.106 |
.035 |
.009 |
.001 |
.000 |
.000 |
.000 |
.000 |
2 |
1.000 |
.994 |
.962 |
.797 |
.552 |
.315 |
.145 |
.050 |
.011 |
.001 |
.000 |
.000 |
.000 |
3 |
1.000 |
1.000 |
.995 |
.944 |
.806 |
.594 |
.363 |
.174 |
.058 |
.010 |
.000 |
.000 |
.000 |
4 |
1.000 |
1.000 |
1.000 |
.990 |
.942 |
.826 |
.637 |
.406 |
.194 |
.056 |
.005 |
.000 |
.000 |
5 |
1.000 |
1.000 |
1.000 |
.999 |
.989 |
.950 |
.855 |
.685 |
.448 |
.203 |
.038 |
.006 |
.000 |
6 |
1.000 |
1.000 |
1.000 |
1.000 |
.999 |
.991 |
.965 |
.894 |
.745 |
.497 |
.187 |
.057 |
.003 |
7 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
.999 |
.996 |
.983 |
.942 |
.832 |
.570 |
.337 |
.077 |
e. n=9 |
p
k |
.01 |
.05 |
.10 |
.20 |
.30 |
.40 |
.50 |
.60 |
.70 |
.80 |
.90 |
.95 |
.99 |
0 |
.914 |
.630 |
.387 |
.134 |
.040 |
.010 |
.002 |
.000 |
.000 |
.000 |
.000 |
.000 |
.000 |
1 |
.997 |
.929 |
.775 |
.436 |
.196 |
.071 |
.020 |
.004 |
.000 |
.000 |
.000 |
.000 |
.000 |
2 |
1.000 |
.992 |
.947 |
.738 |
.463 |
.232 |
.090 |
.025 |
.004 |
.000 |
.000 |
.000 |
.000 |
3 |
1.000 |
.999 |
.992 |
.914 |
.730 |
.483 |
.254 |
.099 |
.025 |
.003 |
.000 |
.000 |
.000 |
4 |
1.000 |
1.000 |
.999 |
.980 |
.901 |
.733 |
.500 |
.267 |
.099 |
.020 |
.001 |
.000 |
.000 |
5 |
1.000 |
1.000 |
1.000 |
.997 |
.975 |
.901 |
.746 |
.517 |
.270 |
.086 |
.008 |
.001 |
.000 |
6 |
1.000 |
1.000 |
1.000 |
1.000 |
.996 |
.975 |
.910 |
.768 |
.537 |
.262 |
.053 |
.008 |
.000 |
7 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
.996 |
.980 |
.929 |
.804 |
.564 |
.225 |
.071 |
.003 |
8 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
.998 |
.990 |
.960 |
.866 |
.613 |
.370 |
.086 |
f. n=10 |
p
k |
.01 |
.05 |
.10 |
.20 |
.30 |
.40 |
.50 |
.60 |
.70 |
.80 |
.90 |
.95 |
.99 |
0 |
.904 |
.599 |
.349 |
.107 |
.028 |
.006 |
.001 |
.000 |
.000 |
.000 |
.000 |
.000 |
.000 |
1 |
.996 |
.914 |
.736 |
.376 |
.149 |
.046 |
.011 |
.002 |
.000 |
.000 |
.000 |
.000 |
.000 |
2 |
1.000 |
.988 |
.930 |
.678 |
.383 |
.167 |
.055 |
.012 |
.002 |
.000 |
.000 |
.000 |
.000 |
3 |
1.000 |
.999 |
.987 |
.879 |
.650 |
.382 |
.172 |
.055 |
.011 |
.001 |
.000 |
.000 |
.000 |
4 |
1.000 |
1.000 |
.998 |
.967 |
.850 |
.633 |
.377 |
.166 |
.047 |
.006 |
.000 |
.000 |
.000 |
5 |
1.000 |
1.000 |
1.000 |
.994 |
.953 |
.834 |
.623 |
.367 |
.150 |
.033 |
.002 |
.000 |
.000 |
6 |
1.000 |
1.000 |
1.000 |
.999 |
.989 |
.945 |
.828 |
.618 |
.350 |
.121 |
.013 |
.001 |
.000 |
7 |
1.000 |
1.000 |
1.000 |
1.000 |
.998 |
.988 |
.945 |
.833 |
.617 |
.322 |
.070 |
.012 |
.000 |
8 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
.998 |
.989 |
.954 |
.851 |
.624 |
.264 |
.086 |
.004 |
9 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
.999 |
.994 |
.972 |
.893 |
.651 |
.401 |
.096 |
g. n=15 |
p
k |
.01 |
.05 |
.10 |
.20 |
.30 |
.40 |
.50 |
.60 |
.70 |
.80 |
.90 |
.95 |
.99 |
0 |
.860 |
.463 |
.206 |
.035 |
.005 |
.000 |
.000 |
.000 |
.000 |
.000 |
.000 |
.000 |
.000 |
1 |
.990 |
.829 |
.549 |
.167 |
.035 |
.005 |
.000 |
.000 |
.000 |
.000 |
.000 |
.000 |
.000 |
2 |
1.000 |
.964 |
.816 |
.398 |
.127 |
.027 |
.004 |
.000 |
.000 |
.000 |
.000 |
.000 |
.000 |
3 |
1.000 |
.995 |
.944 |
.648 |
.297 |
.091 |
.018 |
.002 |
.000 |
.000 |
.000 |
.000 |
.000 |
4 |
1.000 |
.999 |
.987 |
.838 |
.515 |
.217 |
.059 |
.009 |
.001 |
.000 |
.000 |
.000 |
.000 |
5 |
1.000 |
1.000 |
.998 |
.939 |
.722 |
.403 |
.151 |
.034 |
.004 |
.000 |
.000 |
.000 |
.000 |
6 |
1.000 |
1.000 |
1.000 |
.982 |
.869 |
.610 |
.304 |
.095 |
.015 |
.001 |
.000 |
.000 |
.000 |
7 |
1.000 |
1.000 |
1.000 |
.996 |
.950 |
.787 |
.500 |
.213 |
.050 |
.004 |
.000 |
.000 |
.000 |
8 |
1.000 |
1.000 |
1.000 |
.999 |
.985 |
.905 |
.696 |
.390 |
.131 |
.018 |
.000 |
.000 |
.000 |
9 |
1.000 |
1.000 |
1.000 |
1.000 |
.996 |
.966 |
.849 |
.597 |
.278 |
.061 |
.002 |
.000 |
.000 |
10 |
1.000 |
1.000 |
1.000 |
1.000 |
.999 |
.991 |
.941 |
.783 |
.485 |
.164 |
.013 |
.001 |
.000 |
11 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
.998 |
.982 |
.909 |
.703 |
.352 |
.056 |
.005 |
.000 |
12 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
.996 |
.973 |
.873 |
.602 |
.184 |
.036 |
.000 |
13 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
.995 |
.965 |
.833 |
.451 |
.171 |
.010 |
14 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
.995 |
.965 |
.794 |
.537 |
.140 |
h. n=20 |
p
k |
.01 |
.05 |
.10 |
.20 |
.30 |
.40 |
.50 |
.60 |
.70 |
.80 |
.90 |
.95 |
.99 |
0 |
.818 |
.358 |
.122 |
.012 |
.001 |
.000 |
.000 |
.000 |
.000 |
.000 |
.000 |
.000 |
.000 |
1 |
.983 |
.736 |
.392 |
.069 |
.008 |
.001 |
.000 |
.000 |
.000 |
.000 |
.000 |
.000 |
.000 |
2 |
.999 |
.925 |
.677 |
.206 |
.035 |
.004 |
.000 |
.000 |
.000 |
.000 |
.000 |
.000 |
.000 |
3 |
1.000 |
.984 |
.867 |
.411 |
.107 |
.016 |
.001 |
.000 |
.000 |
.000 |
.000 |
.000 |
.000 |
4 |
1.000 |
.997 |
.957 |
.630 |
.238 |
.051 |
.006 |
.000 |
.000 |
.000 |
.000 |
.000 |
.000 |
5 |
1.000 |
1.000 |
.989 |
.804 |
.416 |
.126 |
.021 |
.002 |
.000 |
.000 |
.000 |
.000 |
.000 |
6 |
1.000 |
1.000 |
.998 |
.913 |
.608 |
.250 |
.058 |
.006 |
.000 |
.000 |
.000 |
.000 |
.000 |
7 |
1.000 |
1.000 |
1.000 |
.968 |
.772 |
.416 |
.132 |
.021 |
.001 |
.000 |
.000 |
.000 |
.000 |
8 |
1.000 |
1.000 |
1.000 |
.990 |
.887 |
.596 |
.252 |
.057 |
.005 |
.000 |
.000 |
.000 |
.000 |
9 |
1.000 |
1.000 |
1.000 |
.997 |
.952 |
.755 |
.412 |
.128 |
.017 |
.001 |
.000 |
.000 |
.000 |
10 |
1.000 |
1.000 |
1.000 |
.999 |
.983 |
.872 |
.588 |
.245 |
.048 |
.003 |
.000 |
.000 |
.000 |
11 |
1.000 |
1.000 |
1.000 |
1.000 |
.995 |
.943 |
.748 |
.404 |
.113 |
.010 |
.000 |
.000 |
.000 |
12 |
1.000 |
1.000 |
1.000 |
1.000 |
.999 |
.979 |
.868 |
.584 |
.228 |
.032 |
.000 |
.000 |
.000 |
13 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
.994 |
.942 |
.750 |
.392 |
.087 |
.002 |
.000 |
.000 |
14 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
.998 |
.979 |
.874 |
.584 |
.196 |
.011 |
.000 |
.000 |
15 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
.994 |
.949 |
.762 |
.370 |
.043 |
.003 |
.000 |
16 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
.999 |
.984 |
.893 |
.589 |
.133 |
.016 |
.000 |
17 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
.996 |
.965 |
.794 |
.323 |
.075 |
.001 |
18 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
.999 |
.992 |
.931 |
.608 |
.264 |
.017 |
19 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
.999 |
.988 |
.878 |
.642 |
.182 |
i. n=25 |
p
k |
.01 |
.05 |
.10 |
.20 |
.30 |
.40 |
.50 |
.60 |
.70 |
.80 |
.90 |
.95 |
.99 |
0 |
.778 |
.277 |
.072 |
.004 |
.000 |
.000 |
.000 |
.000 |
.000 |
.000 |
.000 |
.000 |
.000 |
1 |
.974 |
.642 |
.271 |
.027 |
.002 |
.000 |
.000 |
.000 |
.000 |
.000 |
.000 |
.000 |
.000 |
2 |
.998 |
.873 |
.537 |
.098 |
.009 |
.000 |
.000 |
.000 |
.000 |
.000 |
.000 |
.000 |
.000 |
3 |
1.000 |
.966 |
.764 |
.234 |
.033 |
.002 |
.000 |
.000 |
.000 |
.000 |
.000 |
.000 |
.000 |
4 |
1.000 |
.993 |
.902 |
.421 |
.090 |
.009 |
.000 |
.000 |
.000 |
.000 |
.000 |
.000 |
.000 |
5 |
1.000 |
.999 |
.967 |
.617 |
.193 |
.029 |
.002 |
.000 |
.000 |
.000 |
.000 |
.000 |
.000 |
6 |
1.000 |
1.000 |
.991 |
.780 |
.341 |
.074 |
.007 |
.000 |
.000 |
.000 |
.000 |
.000 |
.000 |
7 |
1.000 |
1.000 |
.998 |
.891 |
.512 |
.154 |
.022 |
.001 |
.000 |
.000 |
.000 |
.000 |
.000 |
8 |
1.000 |
1.000 |
1.000 |
.953 |
.677 |
.274 |
.054 |
.004 |
.000 |
.000 |
.000 |
.000 |
.000 |
9 |
1.000 |
1.000 |
1.000 |
.983 |
.811 |
.425 |
.115 |
.013 |
.000 |
.000 |
.000 |
.000 |
.000 |
10 |
1.000 |
1.000 |
1.000 |
.994 |
.902 |
.586 |
.212 |
.034 |
.002 |
.000 |
.000 |
.000 |
.000 |
11 |
1.000 |
1.000 |
1.000 |
.998 |
.956 |
.732 |
.345 |
.078 |
.006 |
.000 |
.000 |
.000 |
.000 |
12 |
1.000 |
1.000 |
1.000 |
1.000 |
.983 |
.846 |
.500 |
.154 |
.017 |
.000 |
.000 |
.000 |
.000 |
13 |
1.000 |
1.000 |
1.000 |
1.000 |
.994 |
.922 |
.655 |
.268 |
.044 |
.002 |
.000 |
.000 |
.000 |
14 |
1.000 |
1.000 |
1.000 |
1.000 |
.998 |
.966 |
.788 |
.414 |
.098 |
.006 |
.000 |
.000 |
.000 |
15 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
.987 |
.885 |
.575 |
.189 |
.017 |
.000 |
.000 |
.000 |
16 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
.996 |
.946 |
.726 |
.323 |
.047 |
.000 |
.000 |
.000 |
17 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
.999 |
.978 |
.846 |
.488 |
.109 |
.002 |
.000 |
.000 |
18 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
.993 |
.926 |
.659 |
.220 |
.009 |
.000 |
.000 |
19 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
.998 |
.971 |
.807 |
.383 |
.033 |
.001 |
.000 |
20 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
.991 |
.910 |
.579 |
.098 |
.007 |
.000 |
21 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
.998 |
.967 |
.766 |
.236 |
.034 |
.000 |
22 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
.991 |
.902 |
.463 |
.127 |
.002 |
23 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
.998 |
.973 |
.729 |
.358 |
.026 |
24 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
.996 |
.928 |
.723 |
.222 |
Table II Normal Curve Areas
Alternate View
z |
.00 |
.01 |
.02 |
.03 |
.04 |
.05 |
.06 |
.07 |
.08 |
.09 |
.0 |
.0000 |
.0040 |
.0080 |
.0120 |
.0160 |
.0199 |
.0239 |
.0279 |
.0319 |
.0359 |
.1 |
.0398 |
.0438 |
.0478 |
.0517 |
.0557 |
.0596 |
.0636 |
.0675 |
.0714 |
.0753 |
.2 |
.0793 |
.0832 |
.0871 |
.0910 |
.0948 |
.0987 |
.1026 |
.1064 |
.1103 |
.1141 |
.3 |
.1179 |
.1217 |
.1255 |
.1293 |
.1331 |
.1368 |
.1406 |
.1443 |
.1480 |
.1517 |
.4 |
.1554 |
.1591 |
.1628 |
.1664 |
.1700 |
.1736 |
.1772 |
.1808 |
.1844 |
.1879 |
.5 |
.1915 |
.1950 |
.1985 |
.2019 |
.2054 |
.2088 |
.2123 |
.2157 |
.2190 |
.2224 |
.6 |
.2257 |
.2291 |
.2324 |
.2357 |
.2389 |
.2422 |
.2454 |
.2486 |
.2517 |
.2549 |
.7 |
.2580 |
.2611 |
.2642 |
.2673 |
.2704 |
.2734 |
.2764 |
.2794 |
.2823 |
.2852 |
.8 |
.2881 |
.2910 |
.2939 |
.2967 |
.2995 |
.3023 |
.3051 |
.3078 |
.3106 |
.3133 |
.9 |
.3159 |
.3186 |
.3212 |
.3238 |
.3264 |
.3289 |
.3315 |
.3340 |
.3365 |
.3389 |
1.0 |
.3413 |
.3438 |
.3461 |
.3485 |
.3508 |
.3531 |
.3554 |
.3577 |
.3599 |
.3621 |
1.1 |
.3643 |
.3665 |
.3686 |
.3708 |
.3729 |
.3749 |
.3770 |
.3790 |
.3810 |
.3830 |
1.2 |
.3849 |
.3869 |
.3888 |
.3907 |
.3925 |
.3944 |
.3962 |
.3980 |
.3997 |
.4015 |
1.3 |
.4032 |
.4049 |
.4066 |
.4082 |
.4099 |
.4115 |
.4131 |
.4147 |
.4162 |
.4177 |
1.4 |
.4192 |
.4207 |
.4222 |
.4236 |
.4251 |
.4265 |
.4279 |
.4292 |
.4306 |
.4319 |
1.5 |
.4332 |
.4345 |
.4357 |
.4370 |
.4382 |
.4394 |
.4406 |
.4418 |
.4429 |
.4441 |
1.6 |
.4452 |
.4463 |
.4474 |
.4484 |
.4495 |
.4505 |
.4515 |
.4525 |
.4535 |
.4545 |
1.7 |
.4554 |
.4564 |
.4573 |
.4582 |
.4591 |
.4599 |
.4608 |
.4616 |
.4625 |
.4633 |
1.8 |
.4641 |
.4649 |
.4656 |
.4664 |
.4671 |
.4678 |
.4686 |
.4693 |
.4699 |
.4706 |
1.9 |
.4713 |
.4719 |
.4726 |
.4732 |
.4738 |
.4744 |
.4750 |
.4756 |
.4761 |
.4767 |
2.0 |
.4772 |
.4778 |
.4783 |
.4788 |
.4793 |
.4798 |
.4803 |
.4808 |
.4812 |
.4817 |
2.1 |
.4821 |
.4826 |
.4830 |
.4834 |
.4838 |
.4842 |
.4846 |
.4850 |
.4854 |
.4857 |
2.2 |
.4861 |
.4864 |
.4868 |
.4871 |
.4875 |
.4878 |
.4881 |
.4884 |
.4887 |
.4890 |
2.3 |
.4893 |
.4896 |
.4898 |
.4901 |
.4904 |
.4906 |
.4909 |
.4911 |
.4913 |
.4916 |
2.4 |
.4918 |
.4920 |
.4922 |
.4925 |
.4927 |
.4929 |
.4931 |
.4932 |
.4934 |
.4936 |
2.5 |
.4938 |
.4940 |
.4941 |
.4943 |
.4945 |
.4946 |
.4948 |
.4949 |
.4951 |
.4952 |
2.6 |
.4953 |
.4955 |
.4956 |
.4957 |
.4959 |
.4960 |
.4961 |
.4962 |
.4963 |
.4964 |
2.7 |
.4965 |
.4966 |
.4967 |
.4968 |
.4969 |
.4970 |
.4971 |
.4972 |
.4973 |
.4974 |
2.8 |
.4974 |
.4975 |
.4976 |
.4977 |
.4977 |
.4978 |
.4979 |
.4979 |
.4980 |
.4981 |
2.9 |
.4981 |
.4982 |
.4982 |
.4983 |
.4984 |
.4984 |
.4985 |
.4985 |
.4986 |
.4986 |
3.0 |
.4987 |
.4987 |
.4987 |
.4988 |
.4988 |
.4989 |
.4989 |
.4989 |
.4990 |
.4990 |
Source: Abridged from Table I of A. Hald, Statistical Tables and Formulas (New York: Wiley), 1952.
Table III Critical Values of t
Alternate View
|
Degrees of Freedom |
t.100 |
t.050 |
t.025 |
t.010 |
t.005 |
t.001 |
t.0005 |
1 |
3.078 |
6.314 |
12.706 |
31.821 |
63.657 |
318.31 |
636.62 |
2 |
1.886 |
2.920 |
4.303 |
6.965 |
9.925 |
22.326 |
31.598 |
3 |
1.638 |
2.353 |
3.182 |
4.541 |
5.841 |
10.213 |
12.924 |
4 |
1.533 |
2.132 |
2.776 |
3.747 |
4.604 |
7.173 |
8.610 |
5 |
1.476 |
2.015 |
2.571 |
3.365 |
4.032 |
5.893 |
6.869 |
6 |
1.440 |
1.943 |
2.447 |
3.143 |
3.707 |
5.208 |
5.959 |
7 |
1.415 |
1.895 |
2.365 |
2.998 |
3.499 |
4.785 |
5.408 |
8 |
1.397 |
1.860 |
2.306 |
2.896 |
3.355 |
4.501 |
5.041 |
9 |
1.383 |
1.833 |
2.262 |
2.821 |
3.250 |
4.297 |
4.781 |
10 |
1.372 |
1.812 |
2.228 |
2.764 |
3.169 |
4.144 |
4.587 |
11 |
1.363 |
1.796 |
2.201 |
2.718 |
3.106 |
4.025 |
4.437 |
12 |
1.356 |
1.782 |
2.179 |
2.681 |
3.055 |
3.930 |
4.318 |
13 |
1.350 |
1.771 |
2.160 |
2.650 |
3.012 |
3.852 |
4.221 |
14 |
1.345 |
1.761 |
2.145 |
2.624 |
2.977 |
3.787 |
4.140 |
15 |
1.341 |
1.753 |
2.131 |
2.602 |
2.947 |
3.733 |
4.073 |
16 |
1.337 |
1.746 |
2.120 |
2.583 |
2.921 |
3.686 |
4.015 |
17 |
1.333 |
1.740 |
2.110 |
2.567 |
2.898 |
3.646 |
3.965 |
18 |
1.330 |
1.734 |
2.101 |
2.552 |
2.878 |
3.610 |
3.922 |
19 |
1.328 |
1.729 |
2.093 |
2.539 |
2.861 |
3.579 |
3.883 |
20 |
1.325 |
1.725 |
2.086 |
2.528 |
2.845 |
3.552 |
3.850 |
21 |
1.323 |
1.721 |
2.080 |
2.518 |
2.831 |
3.527 |
3.819 |
22 |
1.321 |
1.717 |
2.074 |
2.508 |
2.819 |
3.505 |
3.792 |
23 |
1.319 |
1.714 |
2.069 |
2.500 |
2.807 |
3.485 |
3.767 |
24 |
1.318 |
1.711 |
2.064 |
2.492 |
2.797 |
3.467 |
3.745 |
25 |
1.316 |
1.708 |
2.060 |
2.485 |
2.787 |
3.450 |
3.725 |
26 |
1.315 |
1.706 |
2.056 |
2.479 |
2.779 |
3.435 |
3.707 |
27 |
1.314 |
1.703 |
2.052 |
2.473 |
2.771 |
3.421 |
3.690 |
28 |
1.313 |
1.701 |
2.048 |
2.467 |
2.763 |
3.408 |
3.674 |
29 |
1.311 |
1.699 |
2.045 |
2.462 |
2.756 |
3.396 |
3.659 |
30 |
1.310 |
1.697 |
2.042 |
2.457 |
2.750 |
3.385 |
3.646 |
40 |
1.303 |
1.684 |
2.021 |
2.423 |
2.704 |
3.307 |
3.551 |
60 |
1.296 |
1.671 |
2.000 |
2.390 |
2.660 |
3.232 |
3.460 |
120 |
1.289 |
1.658 |
1.980 |
2.358 |
2.617 |
3.160 |
3.373 |
∞ |
1.282 |
1.645 |
1.960 |
2.326 |
2.576 |
3.090 |
3.291 |
Alternate View
Degrees of Freedom |
χ2.995 |
χ2.990 |
χ2.975 |
χ2.950 |
χ2.900 |
1 |
.0000393 |
.0001571 |
.0009821 |
.0039321 |
.0157908 |
2 |
.0100251 |
.0201007 |
.0506356 |
.102587 |
.210720 |
3 |
.0717212 |
.114832 |
.215795 |
.351846 |
.584375 |
4 |
.206990 |
.297110 |
.484419 |
.710721 |
1.063623 |
5 |
.411740 |
.554300 |
.831211 |
1.145476 |
1.61031 |
6 |
.675727 |
.872085 |
1.237347 |
1.63539 |
2.20413 |
7 |
.989265 |
1.239043 |
1.68987 |
2.16735 |
2.83311 |
8 |
1.344419 |
1.646482 |
2.17973 |
2.73264 |
3.48954 |
9 |
1.734926 |
2.087912 |
2.70039 |
3.32511 |
4.16816 |
10 |
2.15585 |
2.55821 |
3.24697 |
3.94030 |
4.86518 |
11 |
2.60321 |
3.05347 |
3.81575 |
4.57481 |
5.57779 |
12 |
3.07382 |
3.57056 |
4.40379 |
5.22603 |
6.30380 |
13 |
3.56503 |
4.10691 |
5.00874 |
5.89186 |
7.04150 |
14 |
4.07468 |
4.66043 |
5.62872 |
6.57063 |
7.78953 |
15 |
4.60094 |
5.22935 |
6.26214 |
7.26094 |
8.54675 |
16 |
5.14224 |
5.81221 |
6.90766 |
7.96164 |
9.31223 |
17 |
5.69724 |
6.40776 |
7.56418 |
8.67176 |
10.0852 |
18 |
6.26481 |
7.01491 |
8.23075 |
9.39046 |
10.8649 |
19 |
6.84398 |
7.63273 |
8.90655 |
10.1170 |
11.6509 |
20 |
7.43386 |
8.26040 |
9.59083 |
10.8508 |
12.4426 |
21 |
8.03366 |
8.89720 |
10.28293 |
11.5913 |
13.2396 |
22 |
8.64272 |
9.54249 |
10.9823 |
12.3380 |
14.0415 |
23 |
9.26042 |
10.19567 |
11.6885 |
13.0905 |
14.8479 |
24 |
9.88623 |
10.8564 |
12.4011 |
13.8484 |
15.6587 |
25 |
10.5197 |
11.5240 |
13.1197 |
14.6114 |
16.4734 |
26 |
11.1603 |
12.1981 |
13.8439 |
15.3791 |
17.2919 |
27 |
11.8076 |
12.8786 |
14.5733 |
16.1513 |
18.1138 |
28 |
12.4613 |
13.5648 |
15.3079 |
16.9279 |
18.9392 |
29 |
13.1211 |
14.2565 |
16.0471 |
17.7083 |
19.7677 |
30 |
13.7867 |
14.9535 |
16.7908 |
18.4926 |
20.5992 |
40 |
20.7065 |
22.1643 |
24.4331 |
26.5093 |
29.0505 |
50 |
27.9907 |
29.7067 |
32.3574 |
34.7642 |
37.6886 |
60 |
35.5346 |
37.4848 |
40.4817 |
43.1879 |
46.4589 |
70 |
43.2752 |
45.4418 |
48.7576 |
51.7393 |
55.3290 |
80 |
51.1720 |
53.5400 |
57.1532 |
60.3915 |
64.2778 |
90 |
59.1963 |
61.7541 |
65.6466 |
69.1260 |
73.2912 |
100 |
67.3276 |
70.0648 |
74.2219 |
77.9295 |
82.3581 |
Degrees of Freedom |
χ2.100 |
χ2.050 |
χ2.025 |
χ2.010 |
χ2.005 |
1 |
2.70554 |
3.84146 |
5.02389 |
6.63490 |
7.87944 |
2 |
4.60517 |
5.99147 |
7.37776 |
9.21034 |
10.5966 |
3 |
6.25139 |
7.81473 |
9.34840 |
11.3449 |
12.8381 |
4 |
7.77944 |
9.48773 |
11.1433 |
13.2767 |
14.8602 |
5 |
9.23635 |
11.0705 |
12.8325 |
15.0863 |
16.7496 |
6 |
10.6446 |
12.5916 |
14.4494 |
16.8119 |
18.5476 |
7 |
12.0170 |
14.0671 |
16.0128 |
18.4753 |
20.2777 |
8 |
13.3616 |
15.5073 |
17.5346 |
20.0902 |
21.9550 |
9 |
14.6837 |
16.9190 |
19.0228 |
21.6660 |
23.5893 |
10 |
15.9871 |
18.3070 |
20.4831 |
23.2093 |
25.1882 |
11 |
17.2750 |
19.6751 |
21.9200 |
24.7250 |
26.7569 |
12 |
18.5494 |
21.0261 |
23.3367 |
26.2170 |
28.2995 |
13 |
19.8119 |
22.3621 |
24.7356 |
27.6883 |
29.8194 |
14 |
21.0642 |
23.6848 |
26.1190 |
29.1413 |
31.3193 |
15 |
22.3072 |
24.9958 |
27.4884 |
30.5779 |
32.8013 |
16 |
23.5418 |
26.2962 |
28.8454 |
31.9999 |
34.2672 |
17 |
24.7690 |
27.5871 |
30.1910 |
33.4087 |
35.7185 |
18 |
25.9894 |
28.8693 |
31.5264 |
34.8053 |
37.1564 |
19 |
27.2036 |
30.1435 |
32.8523 |
36.1908 |
38.5822 |
20 |
28.4120 |
31.4104 |
34.1696 |
37.5662 |
39.9968 |
21 |
29.6151 |
32.6705 |
35.4789 |
38.9321 |
41.4010 |
22 |
30.8133 |
33.9244 |
36.7807 |
40.2894 |
42.7956 |
23 |
32.0069 |
35.1725 |
38.0757 |
41.6384 |
44.1813 |
24 |
33.1963 |
36.4151 |
39.3641 |
42.9798 |
45.5585 |
25 |
34.3816 |
37.6525 |
40.6465 |
44.3141 |
46.9278 |
26 |
35.5631 |
38.8852 |
41.9232 |
45.6417 |
48.2899 |
27 |
36.7412 |
40.1133 |
43.1944 |
46.9630 |
49.6449 |
28 |
37.9159 |
41.3372 |
44.4607 |
48.2782 |
50.9933 |
29 |
39.0875 |
42.5569 |
45.7222 |
49.5879 |
52.3356 |
30 |
40.2560 |
43.7729 |
46.9792 |
50.8922 |
53.6720 |
40 |
51.8050 |
55.7585 |
59.3417 |
63.6907 |
66.7659 |
50 |
63.1671 |
67.5048 |
71.4202 |
76.1539 |
79.4900 |
60 |
74.3970 |
79.0819 |
83.2976 |
88.3794 |
91.9517 |
70 |
85.5271 |
90.5312 |
95.0231 |
100.425 |
104.215 |
80 |
96.5782 |
101.879 |
106.629 |
112.329 |
116.321 |
90 |
107.565 |
113.145 |
118.136 |
124.116 |
128.299 |
100 |
118.498 |
124.342 |
129.561 |
135.807 |
140.169 |
Table V Critical Values of TL and TU for the Wilcoxon Rank Sum Test
Test statistic is the rank sum associated with the smaller sample (if equal sample sizes, either rank sum can be used).
Alternate View
a. α=.025 one-tailed; α=.05 two-tailed |
n1 n2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
TL |
TU |
TL |
TU |
TL |
TU |
TL |
TU |
TL |
TU |
TL |
TU |
TL |
TU |
TL |
TU |
3 |
5 |
16 |
6 |
18 |
6 |
21 |
7 |
23 |
7 |
26 |
8 |
28 |
8 |
31 |
9 |
33 |
4 |
6 |
18 |
11 |
25 |
12 |
28 |
12 |
32 |
13 |
35 |
14 |
38 |
15 |
41 |
16 |
44 |
5 |
6 |
21 |
12 |
28 |
18 |
37 |
19 |
41 |
20 |
45 |
21 |
49 |
22 |
53 |
24 |
56 |
6 |
7 |
23 |
12 |
32 |
19 |
41 |
26 |
52 |
28 |
56 |
29 |
61 |
31 |
65 |
32 |
70 |
7 |
7 |
26 |
13 |
35 |
20 |
45 |
28 |
56 |
37 |
68 |
39 |
73 |
41 |
78 |
43 |
83 |
8 |
8 |
28 |
14 |
38 |
21 |
49 |
29 |
61 |
39 |
73 |
49 |
87 |
51 |
93 |
54 |
98 |
9 |
8 |
31 |
15 |
41 |
22 |
53 |
31 |
65 |
41 |
78 |
51 |
93 |
63 |
108 |
66 |
114 |
10 |
9 |
33 |
16 |
44 |
24 |
56 |
32 |
70 |
43 |
83 |
54 |
98 |
66 |
114 |
79 |
131 |
b. α=.05 one-tailed; α=.10 two-tailed |
n1 n2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
|
TL |
TU |
TL |
TU |
TL |
TU |
TL |
TU |
TL |
TU |
TL |
TU |
TL |
TU |
TL |
TU |
3 |
6 |
15 |
7 |
17 |
7 |
20 |
8 |
22 |
9 |
24 |
9 |
27 |
10 |
29 |
11 |
31 |
4 |
7 |
17 |
12 |
24 |
13 |
27 |
14 |
30 |
15 |
33 |
16 |
36 |
17 |
39 |
18 |
42 |
5 |
7 |
20 |
13 |
27 |
19 |
36 |
20 |
40 |
22 |
43 |
24 |
46 |
25 |
50 |
26 |
54 |
6 |
8 |
22 |
14 |
30 |
20 |
40 |
28 |
50 |
30 |
54 |
32 |
58 |
33 |
63 |
35 |
67 |
7 |
9 |
24 |
15 |
33 |
22 |
43 |
30 |
54 |
39 |
66 |
41 |
71 |
43 |
76 |
46 |
80 |
8 |
9 |
27 |
16 |
36 |
24 |
46 |
32 |
58 |
41 |
71 |
52 |
84 |
54 |
90 |
57 |
95 |
9 |
10 |
29 |
17 |
39 |
25 |
50 |
33 |
63 |
43 |
76 |
54 |
90 |
66 |
105 |
69 |
111 |
10 |
11 |
31 |
18 |
42 |
26 |
54 |
35 |
67 |
46 |
80 |
57 |
95 |
69 |
111 |
83 |
127 |
Source: From F. Wilcoxon and R. A. Wilcox, “Some Rapid Approximate Statistical Procedures,” 1964, 20–23.
Table VI Critical Values of T0 in the Wilcoxon Signed Rank Test
Alternate View
One-Tailed |
Two-Tailed |
n=5 |
n=6 |
n=7 |
n=8 |
n=9 |
n=10 |
α=.05 |
α=.10 |
1 |
2 |
4 |
6 |
8 |
11 |
α=.025 |
α=.05 |
|
1 |
2 |
4 |
6 |
8 |
α=.01 |
α=.02 |
|
|
0 |
2 |
3 |
5 |
α=.005 |
α=.01 |
|
|
|
0 |
2 |
3 |
|
|
n=11 |
n=12 |
n=13 |
n=14 |
n=15 |
n=16 |
α=.05 |
α=.10 |
14 |
17 |
21 |
26 |
30 |
36 |
α=.025 |
α=.05 |
11 |
14 |
17 |
21 |
25 |
30 |
α=.01 |
α=.02 |
7 |
10 |
13 |
16 |
20 |
24 |
α=.005 |
α=.01 |
5 |
7 |
10 |
13 |
16 |
19 |
|
|
n=17 |
n=18 |
n=19 |
n=20 |
n=21 |
n=22 |
α=.05 |
α=.10 |
41 |
47 |
54 |
60 |
68 |
75 |
α=.025 |
α=.05 |
35 |
40 |
46 |
52 |
59 |
66 |
α=.01 |
α=.02 |
28 |
33 |
38 |
43 |
49 |
56 |
α=.005 |
α=.01 |
23 |
28 |
32 |
37 |
43 |
49 |
|
|
n=23 |
n=24 |
n=25 |
n=26 |
n=27 |
n=28 |
α=.05 |
α=.10 |
83 |
92 |
101 |
110 |
120 |
130 |
α=.025 |
α=.05 |
73 |
81 |
90 |
98 |
107 |
117 |
α=.01 |
α=.02 |
62 |
69 |
77 |
85 |
93 |
102 |
α=.005 |
α=.01 |
55 |
61 |
68 |
76 |
84 |
92 |
|
|
n=29 |
n=30 |
n=31 |
n=32 |
n=33 |
n=34 |
α=.05 |
α=.10 |
141 |
152 |
163 |
175 |
188 |
201 |
α=.025 |
α=.05 |
127 |
137 |
148 |
159 |
171 |
183 |
α=.01 |
α=.02 |
111 |
120 |
130 |
141 |
151 |
162 |
α=.005 |
α=.01 |
100 |
109 |
118 |
128 |
138 |
149 |
|
|
n=35 |
n=36 |
n=37 |
n=38 |
n=39 |
|
α=.05 |
α=.10 |
214 |
228 |
242 |
256 |
271 |
|
α=.025 |
α=.05 |
195 |
208 |
222 |
235 |
250 |
|
α=.01 |
α=.02 |
174 |
186 |
198 |
211 |
224 |
|
α=.005 |
α=.01 |
160 |
171 |
183 |
195 |
208 |
|
|
|
n=40 |
n=41 |
n=42 |
n=43 |
n=44 |
n=45 |
α=.05 |
α=.10 |
287 |
303 |
319 |
336 |
353 |
371 |
α=.025 |
α=.05 |
264 |
279 |
295 |
311 |
327 |
344 |
α=.01 |
α=.02 |
238 |
252 |
267 |
281 |
297 |
313 |
α=.005 |
α=.01 |
221 |
234 |
248 |
262 |
277 |
292 |
|
|
n=46 |
n=47 |
n=48 |
n=49 |
n=50 |
|
α=.05 |
α=.10 |
389 |
408 |
427 |
446 |
466 |
|
α=.025 |
α=.05 |
361 |
379 |
397 |
415 |
434 |
|
α=.01 |
α=.02 |
329 |
345 |
362 |
380 |
398 |
|
α=.005 |
α=.01 |
307 |
323 |
339 |
356 |
373 |
|
Source: From F. Wilcoxon and R. A. Wilcox, “Some Rapid Approximate Statistical Procedures,” 1964, p. 28
Alternate View
v1 |
Numerator Degrees of Freedom |
v2 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
1 |
39.86 |
49.50 |
53.59 |
55.83 |
57.24 |
58.20 |
58.91 |
59.44 |
59.86 |
2 |
8.53 |
9.00 |
9.16 |
9.24 |
9.29 |
9.33 |
9.35 |
9.37 |
9.38 |
3 |
5.54 |
5.46 |
5.39 |
5.34 |
5.31 |
5.28 |
5.27 |
5.25 |
5.24 |
4 |
4.54 |
4.32 |
4.19 |
4.11 |
4.05 |
4.01 |
3.98 |
3.95 |
3.94 |
5 |
4.06 |
3.78 |
3.62 |
3.52 |
3.45 |
3.40 |
3.37 |
3.34 |
3.32 |
6 |
3.78 |
3.46 |
3.29 |
3.18 |
3.11 |
3.05 |
3.01 |
2.98 |
2.96 |
7 |
3.59 |
3.26 |
3.07 |
2.96 |
2.88 |
2.83 |
2.78 |
2.75 |
2.72 |
8 |
3.46 |
3.11 |
2.92 |
2.81 |
2.73 |
2.67 |
2.62 |
2.59 |
2.56 |
9 |
3.36 |
3.01 |
2.81 |
2.69 |
2.61 |
2.55 |
2.51 |
2.47 |
2.44 |
10 |
3.29 |
2.92 |
2.73 |
2.61 |
2.52 |
2.46 |
2.41 |
2.38 |
2.35 |
11 |
3.23 |
2.86 |
2.66 |
2.54 |
2.45 |
2.39 |
2.34 |
2.30 |
2.27 |
12 |
3.18 |
2.81 |
2.61 |
2.48 |
2.39 |
2.33 |
2.28 |
2.24 |
2.21 |
13 |
3.14 |
2.76 |
2.56 |
2.43 |
2.35 |
2.28 |
2.23 |
2.20 |
2.16 |
14 |
3.10 |
2.73 |
2.52 |
2.39 |
2.31 |
2.24 |
2.19 |
2.15 |
2.12 |
15 |
3.07 |
2.70 |
2.49 |
2.36 |
2.27 |
2.21 |
2.16 |
2.12 |
2.09 |
16 |
3.05 |
2.67 |
2.46 |
2.33 |
2.24 |
2.18 |
2.13 |
2.09 |
2.06 |
17 |
3.03 |
2.64 |
2.44 |
2.31 |
2.22 |
2.15 |
2.10 |
2.06 |
2.03 |
18 |
3.01 |
2.62 |
2.42 |
2.29 |
2.20 |
2.13 |
2.08 |
2.04 |
2.00 |
19 |
2.99 |
2.61 |
2.40 |
2.27 |
2.18 |
2.11 |
2.06 |
2.02 |
1.98 |
20 |
2.97 |
2.59 |
2.38 |
2.25 |
2.16 |
2.09 |
2.04 |
2.00 |
1.96 |
21 |
2.96 |
2.57 |
2.36 |
2.23 |
2.14 |
2.08 |
2.02 |
1.98 |
1.95 |
22 |
2.95 |
2.56 |
2.35 |
2.22 |
2.13 |
2.06 |
2.01 |
1.97 |
1.93 |
23 |
2.94 |
2.55 |
2.34 |
2.21 |
2.11 |
2.05 |
1.99 |
1.95 |
1.92 |
24 |
2.93 |
2.54 |
2.33 |
2.19 |
2.10 |
2.04 |
1.98 |
1.94 |
1.91 |
25 |
2.92 |
2.53 |
2.32 |
2.18 |
2.09 |
2.02 |
1.97 |
1.93 |
1.89 |
26 |
2.91 |
2.52 |
2.31 |
2.17 |
2.08 |
2.01 |
1.96 |
1.92 |
1.88 |
27 |
2.90 |
2.51 |
2.30 |
2.17 |
2.07 |
2.00 |
1.95 |
1.91 |
1.87 |
28 |
2.89 |
2.50 |
2.29 |
2.16 |
2.06 |
2.00 |
1.94 |
1.90 |
1.87 |
29 |
2.89 |
2.50 |
2.28 |
2.15 |
2.06 |
1.99 |
1.93 |
1.89 |
1.86 |
30 |
2.88 |
2.49 |
2.28 |
2.14 |
2.05 |
1.98 |
1.93 |
1.88 |
1.85 |
40 |
2.84 |
2.44 |
2.23 |
2.09 |
2.00 |
1.93 |
1.87 |
1.83 |
1.79 |
60 |
2.79 |
2.39 |
2.18 |
2.04 |
1.95 |
1.87 |
1.82 |
1.77 |
1.74 |
120 |
2.75 |
2.35 |
2.13 |
1.99 |
1.90 |
1.82 |
1.77 |
1.72 |
1.68 |
∞ |
2.71 |
2.30 |
2.08 |
1.94 |
1.85 |
1.77 |
1.72 |
1.67 |
1.63 |
v1 |
Numerator Degrees of Freedom |
v2 |
10 |
12 |
15 |
20 |
24 |
30 |
40 |
60 |
120 |
∞ |
1 |
60.19 |
60.71 |
61.22 |
61.74 |
62.00 |
62.26 |
62.53 |
62.79 |
63.06 |
63.33 |
2 |
9.39 |
9.41 |
9.42 |
9.44 |
9.45 |
9.46 |
9.47 |
9.47 |
9.48 |
9.49 |
3 |
5.23 |
5.22 |
5.20 |
5.18 |
5.18 |
5.17 |
5.16 |
5.15 |
5.14 |
5.13 |
4 |
3.92 |
3.90 |
3.87 |
3.84 |
3.83 |
3.82 |
3.80 |
3.79 |
3.78 |
3.76 |
5 |
3.30 |
3.27 |
3.24 |
3.21 |
3.19 |
3.17 |
3.16 |
3.14 |
3.12 |
3.10 |
6 |
2.94 |
2.90 |
2.87 |
2.84 |
2.82 |
2.80 |
2.78 |
2.76 |
2.74 |
2.72 |
7 |
2.70 |
2.67 |
2.63 |
2.59 |
2.58 |
2.56 |
2.54 |
2.51 |
2.49 |
2.47 |
8 |
2.54 |
2.50 |
2.46 |
2.42 |
2.40 |
2.38 |
2.36 |
2.34 |
2.32 |
2.29 |
9 |
2.42 |
2.38 |
2.34 |
2.30 |
2.28 |
2.25 |
2.23 |
2.21 |
2.18 |
2.16 |
10 |
2.32 |
2.28 |
2.24 |
2.20 |
2.18 |
2.16 |
2.13 |
2.11 |
2.08 |
2.06 |
11 |
2.25 |
2.21 |
2.17 |
2.12 |
2.10 |
2.08 |
2.05 |
2.03 |
2.00 |
1.97 |
12 |
2.19 |
2.15 |
2.10 |
2.06 |
2.04 |
2.01 |
1.99 |
1.96 |
1.93 |
1.90 |
13 |
2.14 |
2.10 |
2.05 |
2.01 |
1.98 |
1.96 |
1.93 |
1.90 |
1.88 |
1.85 |
14 |
2.10 |
2.05 |
2.01 |
1.96 |
1.94 |
1.91 |
1.89 |
1.86 |
1.83 |
1.80 |
15 |
2.06 |
2.02 |
1.97 |
1.92 |
1.90 |
1.87 |
1.85 |
1.82 |
1.79 |
1.76 |
16 |
2.03 |
1.99 |
1.94 |
1.89 |
1.87 |
1.84 |
1.81 |
1.78 |
1.75 |
1.72 |
17 |
2.00 |
1.96 |
1.91 |
1.86 |
1.84 |
1.81 |
1.78 |
1.75 |
1.72 |
1.69 |
18 |
1.98 |
1.93 |
1.89 |
1.84 |
1.81 |
1.78 |
1.75 |
1.72 |
1.69 |
1.66 |
19 |
1.96 |
1.91 |
1.86 |
1.81 |
1.79 |
1.76 |
1.73 |
1.70 |
1.67 |
1.63 |
20 |
1.94 |
1.89 |
1.84 |
1.79 |
1.77 |
1.74 |
1.71 |
1.68 |
1.64 |
1.61 |
21 |
1.92 |
1.87 |
1.83 |
1.78 |
1.75 |
1.72 |
1.69 |
1.66 |
1.62 |
1.59 |
22 |
1.90 |
1.86 |
1.81 |
1.76 |
1.73 |
1.70 |
1.67 |
1.64 |
1.60 |
1.57 |
23 |
1.89 |
1.84 |
1.80 |
1.74 |
1.72 |
1.69 |
1.66 |
1.62 |
1.59 |
1.55 |
24 |
1.88 |
1.83 |
1.78 |
1.73 |
1.70 |
1.67 |
1.64 |
1.61 |
1.57 |
1.53 |
25 |
1.87 |
1.82 |
1.77 |
1.72 |
1.69 |
1.66 |
1.63 |
1.59 |
1.56 |
1.52 |
26 |
1.86 |
1.81 |
1.76 |
1.71 |
1.68 |
1.65 |
1.61 |
1.58 |
1.54 |
1.50 |
27 |
1.85 |
1.80 |
1.75 |
1.70 |
1.67 |
1.64 |
1.60 |
1.57 |
1.53 |
1.49 |
28 |
1.84 |
1.79 |
1.74 |
1.69 |
1.66 |
1.63 |
1.59 |
1.56 |
1.52 |
1.48 |
29 |
1.83 |
1.78 |
1.73 |
1.68 |
1.65 |
1.62 |
1.58 |
1.55 |
1.51 |
1.47 |
30 |
1.82 |
1.77 |
1.72 |
1.67 |
1.64 |
1.61 |
1.57 |
1.54 |
1.50 |
1.46 |
40 |
1.76 |
1.71 |
1.66 |
1.61 |
1.57 |
1.54 |
1.51 |
1.47 |
1.42 |
1.38 |
60 |
1.71 |
1.66 |
1.60 |
1.54 |
1.51 |
1.48 |
1.44 |
1.40 |
1.35 |
1.29 |
120 |
1.65 |
1.60 |
1.55 |
1.48 |
1.45 |
1.41 |
1.37 |
1.32 |
1.26 |
1.19 |
∞ |
1.60 |
1.55 |
1.49 |
1.42 |
1.38 |
1.34 |
1.30 |
1.24 |
1.17 |
1.00 |
Denominator Degrees of Freedom |
Alternate View
v1 |
Numerator Degrees of Freedom |
v2 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
1 |
161.4 |
199.5 |
215.7 |
224.6 |
230.2 |
234.0 |
236.8 |
238.9 |
240.5 |
2 |
18.51 |
19.00 |
19.16 |
19.25 |
19.30 |
19.33 |
19.35 |
19.37 |
19.38 |
3 |
10.13 |
9.55 |
9.28 |
9.12 |
9.01 |
8.94 |
8.89 |
8.85 |
8.81 |
4 |
7.71 |
6.94 |
6.59 |
6.39 |
6.26 |
6.16 |
6.09 |
6.04 |
6.00 |
5 |
6.61 |
5.79 |
5.41 |
5.19 |
5.05 |
4.95 |
4.88 |
4.82 |
4.77 |
6 |
5.99 |
5.14 |
4.76 |
4.53 |
4.39 |
4.28 |
4.21 |
4.15 |
4.10 |
7 |
5.59 |
4.74 |
4.35 |
4.12 |
3.97 |
3.87 |
3.79 |
3.73 |
3.68 |
8 |
5.32 |
4.46 |
4.07 |
3.84 |
3.69 |
3.58 |
3.50 |
3.44 |
3.39 |
9 |
5.12 |
4.26 |
3.86 |
3.63 |
3.48 |
3.37 |
3.29 |
3.23 |
3.18 |
10 |
4.96 |
4.10 |
3.71 |
3.48 |
3.33 |
3.22 |
3.14 |
3.07 |
3.02 |
11 |
4.84 |
3.98 |
3.59 |
3.36 |
3.20 |
3.09 |
3.01 |
2.95 |
2.90 |
12 |
4.75 |
3.89 |
3.49 |
3.26 |
3.11 |
3.00 |
2.91 |
2.85 |
2.80 |
13 |
4.67 |
3.81 |
3.41 |
3.18 |
3.03 |
2.92 |
2.83 |
2.77 |
2.71 |
14 |
4.60 |
3.74 |
3.34 |
3.11 |
2.96 |
2.85 |
2.76 |
2.70 |
2.65 |
15 |
4.54 |
3.68 |
3.29 |
3.06 |
2.90 |
2.79 |
2.71 |
2.64 |
2.59 |
16 |
4.49 |
3.63 |
3.24 |
3.01 |
2.85 |
2.74 |
2.66 |
2.59 |
2.54 |
17 |
4.45 |
3.59 |
3.20 |
2.96 |
2.81 |
2.70 |
2.61 |
2.55 |
2.49 |
18 |
4.41 |
3.55 |
3.16 |
2.93 |
2.77 |
2.66 |
2.58 |
2.51 |
2.46 |
19 |
4.38 |
3.52 |
3.13 |
2.90 |
2.74 |
2.63 |
2.54 |
2.48 |
2.42 |
20 |
4.35 |
3.49 |
3.10 |
2.87 |
2.71 |
2.60 |
2.51 |
2.45 |
2.39 |
21 |
4.32 |
3.47 |
3.07 |
2.84 |
2.68 |
2.57 |
2.49 |
2.42 |
2.37 |
22 |
4.30 |
3.44 |
3.05 |
2.82 |
2.66 |
2.55 |
2.46 |
2.40 |
2.34 |
23 |
4.28 |
3.42 |
3.03 |
2.80 |
2.64 |
2.53 |
2.44 |
2.37 |
2.32 |
24 |
4.26 |
3.40 |
3.01 |
2.78 |
2.62 |
2.51 |
2.42 |
2.36 |
2.30 |
25 |
4.24 |
3.39 |
2.99 |
2.76 |
2.60 |
2.49 |
2.40 |
2.34 |
2.28 |
26 |
4.23 |
3.37 |
2.98 |
2.74 |
2.59 |
2.47 |
2.39 |
2.32 |
2.77 |
27 |
4.21 |
3.35 |
2.96 |
2.73 |
2.57 |
2.46 |
2.37 |
2.31 |
2.25 |
28 |
4.20 |
3.34 |
2.95 |
2.71 |
2.56 |
2.45 |
2.36 |
2.29 |
2.24 |
29 |
4.18 |
3.33 |
2.93 |
2.70 |
2.55 |
2.43 |
2.35 |
2.28 |
2.22 |
30 |
4.17 |
3.32 |
2.92 |
2.69 |
2.53 |
2.42 |
2.33 |
2.27 |
2.21 |
40 |
4.08 |
3.23 |
2.84 |
2.61 |
2.45 |
2.34 |
2.25 |
2.18 |
2.12 |
60 |
4.00 |
3.15 |
2.76 |
2.53 |
2.37 |
2.25 |
2.17 |
2.10 |
2.04 |
120 |
3.92 |
3.07 |
2.68 |
2.45 |
2.29 |
2.17 |
2.09 |
2.02 |
1.96 |
∞ |
3.84 |
3.00 |
2.60 |
2.37 |
2.21 |
2.10 |
2.01 |
1.94 |
1.88 |
v1 |
Numerator Degrees of Freedom |
v2 |
10 |
12 |
15 |
20 |
24 |
30 |
40 |
60 |
120 |
∞ |
1 |
241.9 |
243.9 |
245.9 |
248.0 |
249.1 |
250.1 |
251.1 |
252.2 |
253.3 |
254.3 |
2 |
19.40 |
19.41 |
19.43 |
19.45 |
19.45 |
19.46 |
19.47 |
19.48 |
19.49 |
19.50 |
3 |
8.79 |
8.74 |
8.70 |
8.66 |
8.64 |
8.62 |
8.59 |
8.57 |
8.55 |
8.53 |
4 |
5.96 |
5.91 |
5.86 |
5.80 |
5.77 |
5.75 |
5.72 |
5.69 |
5.66 |
5.63 |
5 |
4.74 |
4.68 |
4.62 |
4.56 |
4.53 |
4.50 |
4.46 |
4.43 |
4.40 |
4.36 |
6 |
4.06 |
4.00 |
3.94 |
3.87 |
3.84 |
3.81 |
3.77 |
3.74 |
3.70 |
3.67 |
7 |
3.64 |
3.57 |
3.51 |
3.44 |
3.41 |
3.38 |
3.34 |
3.30 |
3.27 |
3.23 |
8 |
3.35 |
3.28 |
3.22 |
3.15 |
3.12 |
3.08 |
3.04 |
3.01 |
2.97 |
2.93 |
9 |
3.14 |
3.07 |
3.01 |
2.94 |
2.90 |
2.86 |
2.83 |
2.79 |
2.75 |
2.71 |
10 |
2.98 |
2.91 |
2.85 |
2.77 |
2.74 |
2.70 |
2.66 |
2.62 |
2.58 |
2.54 |
11 |
2.85 |
2.79 |
2.72 |
2.65 |
2.61 |
2.57 |
2.53 |
2.49 |
2.45 |
2.40 |
12 |
2.75 |
2.69 |
2.62 |
2.54 |
2.51 |
2.47 |
2.43 |
2.38 |
2.34 |
2.30 |
13 |
2.67 |
2.60 |
2.53 |
2.46 |
2.42 |
2.38 |
2.34 |
2.30 |
2.25 |
2.21 |
14 |
2.60 |
2.53 |
2.46 |
2.39 |
2.35 |
2.31 |
2.27 |
2.22 |
2.18 |
2.13 |
15 |
2.54 |
2.48 |
2.40 |
2.33 |
2.29 |
2.25 |
2.20 |
2.16 |
2.11 |
2.07 |
16 |
2.49 |
2.42 |
2.35 |
2.28 |
2.24 |
2.19 |
2.15 |
2.11 |
2.06 |
2.01 |
17 |
2.45 |
2.38 |
2.31 |
2.23 |
2.19 |
2.15 |
2.10 |
2.06 |
2.01 |
1.96 |
18 |
2.41 |
2.34 |
2.27 |
2.19 |
2.15 |
2.11 |
2.06 |
2.02 |
1.97 |
1.92 |
19 |
2.38 |
2.31 |
2.23 |
2.16 |
2.11 |
2.07 |
2.03 |
1.98 |
1.93 |
1.88 |
20 |
2.35 |
2.28 |
2.20 |
2.12 |
2.08 |
2.04 |
1.99 |
1.95 |
1.90 |
1.84 |
21 |
2.32 |
2.25 |
2.18 |
2.10 |
2.05 |
2.01 |
1.96 |
1.92 |
1.87 |
1.81 |
22 |
2.30 |
2.23 |
2.15 |
2.07 |
2.03 |
1.98 |
1.94 |
1.89 |
1.84 |
1.78 |
23 |
2.27 |
2.20 |
2.13 |
2.05 |
2.01 |
1.96 |
1.91 |
1.86 |
1.81 |
1.76 |
24 |
2.25 |
2.18 |
2.11 |
2.03 |
1.98 |
1.94 |
1.89 |
1.84 |
1.79 |
1.73 |
25 |
2.24 |
2.16 |
2.09 |
2.01 |
1.96 |
1.92 |
1.87 |
1.82 |
1.77 |
1.71 |
26 |
2.22 |
2.15 |
2.07 |
1.99 |
1.95 |
1.90 |
1.85 |
1.80 |
1.75 |
1.69 |
27 |
2.20 |
2.13 |
2.06 |
1.97 |
1.93 |
1.88 |
1.84 |
1.79 |
1.73 |
1.67 |
28 |
2.19 |
2.12 |
2.04 |
1.96 |
1.91 |
1.87 |
1.82 |
1.77 |
1.71 |
1.65 |
29 |
2.18 |
2.10 |
2.03 |
1.94 |
1.90 |
1.85 |
1.81 |
1.75 |
1.70 |
1.64 |
30 |
2.16 |
2.09 |
2.01 |
1.93 |
1.89 |
1.84 |
1.79 |
1.74 |
1.68 |
1.62 |
40 |
2.08 |
2.00 |
1.92 |
1.84 |
1.79 |
1.74 |
1.69 |
1.64 |
1.58 |
1.51 |
60 |
1.99 |
1.92 |
1.84 |
1.75 |
1.70 |
1.65 |
1.59 |
1.53 |
1.47 |
1.39 |
120 |
1.91 |
1.83 |
1.75 |
1.66 |
1.61 |
1.55 |
1.50 |
1.43 |
1.35 |
1.25 |
∞ |
1.83 |
1.75 |
1.67 |
1.57 |
1.52 |
1.46 |
1.39 |
1.32 |
1.22 |
1.00 |
Denominator Degrees of Freedom |
Alternate View
v1 |
Numerator Degrees of Freedom |
v2 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
1 |
647.8 |
799.5 |
864.2 |
899.6 |
921.8 |
937.1 |
948.2 |
956.7 |
963.3 |
2 |
38.51 |
39.00 |
39.17 |
39.25 |
39.30 |
39.33 |
39.36 |
39.37 |
39.39 |
3 |
17.44 |
16.04 |
15.44 |
15.10 |
14.88 |
14.73 |
14.62 |
14.54 |
14.47 |
4 |
12.22 |
10.65 |
9.98 |
9.60 |
9.36 |
9.20 |
9.07 |
8.98 |
8.90 |
5 |
10.01 |
8.43 |
7.76 |
7.39 |
7.15 |
6.98 |
6.85 |
6.76 |
6.68 |
6 |
8.81 |
7.26 |
6.60 |
6.23 |
5.99 |
5.82 |
5.70 |
5.60 |
5.52 |
7 |
8.07 |
6.54 |
5.89 |
5.52 |
5.29 |
5.12 |
4.99 |
4.90 |
4.82 |
8 |
7.57 |
6.06 |
5.42 |
5.05 |
4.82 |
4.65 |
4.53 |
4.43 |
4.36 |
9 |
7.21 |
5.71 |
5.08 |
4.72 |
4.48 |
4.32 |
4.20 |
4.10 |
4.03 |
10 |
6.94 |
5.46 |
4.83 |
4.47 |
4.24 |
4.07 |
3.95 |
3.85 |
3.78 |
11 |
6.72 |
5.26 |
4.63 |
4.28 |
4.04 |
3.88 |
3.76 |
3.66 |
3.59 |
12 |
6.55 |
5.10 |
4.47 |
4.12 |
3.89 |
3.73 |
3.61 |
3.51 |
3.44 |
13 |
6.41 |
4.97 |
4.35 |
4.00 |
3.77 |
3.60 |
3.48 |
3.39 |
3.31 |
14 |
6.30 |
4.86 |
4.24 |
3.89 |
3.66 |
3.50 |
3.38 |
3.29 |
3.21 |
15 |
6.20 |
4.77 |
4.15 |
3.80 |
3.58 |
3.41 |
3.29 |
3.20 |
3.12 |
16 |
6.12 |
4.69 |
4.08 |
3.73 |
3.50 |
3.34 |
3.22 |
3.12 |
3.05 |
17 |
6.04 |
4.62 |
4.01 |
3.66 |
3.44 |
3.28 |
3.16 |
3.06 |
2.98 |
18 |
5.98 |
4.56 |
3.95 |
3.61 |
3.38 |
3.22 |
3.10 |
3.01 |
2.93 |
19 |
5.92 |
4.51 |
3.90 |
3.56 |
3.33 |
3.17 |
3.05 |
2.96 |
2.88 |
20 |
5.87 |
4.46 |
3.86 |
3.51 |
3.29 |
3.13 |
3.01 |
2.91 |
2.84 |
21 |
5.83 |
4.42 |
3.82 |
3.48 |
3.25 |
3.09 |
2.97 |
2.87 |
2.80 |
22 |
5.79 |
4.38 |
3.78 |
3.44 |
3.22 |
3.05 |
2.93 |
2.84 |
2.76 |
23 |
5.75 |
4.35 |
3.75 |
3.41 |
3.18 |
3.02 |
2.90 |
2.81 |
2.73 |
24 |
5.72 |
4.32 |
3.72 |
3.38 |
3.15 |
2.99 |
2.87 |
2.78 |
2.70 |
25 |
5.69 |
4.29 |
3.69 |
3.35 |
3.13 |
2.97 |
2.85 |
2.75 |
2.68 |
26 |
5.66 |
4.27 |
3.67 |
3.33 |
3.10 |
2.94 |
2.82 |
2.73 |
2.65 |
27 |
5.63 |
4.24 |
3.65 |
3.31 |
3.08 |
2.92 |
2.80 |
2.71 |
2.63 |
28 |
5.61 |
4.22 |
3.63 |
3.29 |
3.06 |
2.90 |
2.78 |
2.69 |
2.61 |
29 |
5.59 |
4.20 |
3.61 |
3.27 |
3.04 |
2.88 |
2.76 |
2.67 |
2.59 |
30 |
5.57 |
4.18 |
3.59 |
3.25 |
3.03 |
2.87 |
2.75 |
2.65 |
2.57 |
40 |
5.42 |
4.05 |
3.46 |
3.13 |
2.90 |
2.74 |
2.62 |
2.53 |
2.45 |
60 |
5.29 |
3.93 |
3.34 |
3.01 |
2.79 |
2.63 |
2.51 |
2.41 |
2.33 |
120 |
5.15 |
3.80 |
3.23 |
2.89 |
2.67 |
2.52 |
2.39 |
2.30 |
2.22 |
∞ |
5.02 |
3.69 |
3.12 |
2.79 |
2.57 |
2.41 |
2.29 |
2.19 |
2.11 |
v1 |
Numerator Degrees of Freedom |
v2 |
10 |
12 |
15 |
20 |
24 |
30 |
40 |
60 |
120 |
∞ |
1 |
968.6 |
976.7 |
984.9 |
993.1 |
997.2 |
1,001 |
1,006 |
1,010 |
1,014 |
1,018 |
2 |
39.40 |
39.41 |
39.43 |
39.45 |
39.46 |
39.46 |
39.47 |
39.48 |
39.49 |
39.50 |
3 |
14.42 |
14.34 |
14.25 |
14.17 |
14.12 |
14.08 |
14.04 |
13.99 |
13.95 |
13.90 |
4 |
8.84 |
8.75 |
8.66 |
8.56 |
8.51 |
8.46 |
8.41 |
8.36 |
8.31 |
8.26 |
5 |
6.62 |
6.52 |
6.43 |
6.33 |
6.28 |
6.23 |
6.18 |
6.12 |
6.07 |
6.02 |
6 |
5.46 |
5.37 |
5.27 |
5.17 |
5.12 |
5.07 |
5.01 |
4.96 |
4.90 |
4.85 |
7 |
4.76 |
4.67 |
4.57 |
4.47 |
4.42 |
4.36 |
4.31 |
4.25 |
4.20 |
4.14 |
8 |
4.30 |
4.20 |
4.10 |
4.00 |
3.95 |
3.89 |
3.84 |
3.78 |
3.73 |
3.67 |
9 |
3.96 |
3.87 |
3.77 |
3.67 |
3.61 |
3.56 |
3.51 |
3.45 |
3.39 |
3.33 |
10 |
3.72 |
3.62 |
3.52 |
3.42 |
3.37 |
3.31 |
3.26 |
3.20 |
3.14 |
3.08 |
11 |
3.53 |
3.43 |
3.33 |
3.23 |
3.17 |
3.12 |
3.06 |
3.00 |
2.94 |
2.88 |
12 |
3.37 |
3.28 |
3.18 |
3.07 |
3.02 |
2.96 |
2.91 |
2.85 |
2.79 |
2.72 |
13 |
3.25 |
3.15 |
3.05 |
2.95 |
2.89 |
2.84 |
2.78 |
2.72 |
2.66 |
2.60 |
14 |
3.15 |
3.05 |
2.95 |
2.84 |
2.79 |
2.73 |
2.67 |
2.61 |
2.55 |
2.49 |
15 |
3.06 |
2.96 |
2.86 |
2.76 |
2.70 |
2.64 |
2.59 |
2.52 |
2.46 |
2.40 |
16 |
2.99 |
2.89 |
2.79 |
2.68 |
2.63 |
2.57 |
2.51 |
2.45 |
2.38 |
2.32 |
17 |
2.92 |
2.82 |
2.72 |
2.62 |
2.56 |
2.50 |
2.44 |
2.38 |
2.32 |
2.25 |
18 |
2.87 |
2.77 |
2.67 |
2.56 |
2.50 |
2.44 |
2.38 |
2.32 |
2.26 |
2.19 |
19 |
2.82 |
2.72 |
2.62 |
2.51 |
2.45 |
2.39 |
2.33 |
2.27 |
2.20 |
2.13 |
20 |
2.77 |
2.68 |
2.57 |
2.46 |
2.41 |
2.35 |
2.29 |
2.22 |
2.16 |
2.09 |
21 |
2.73 |
2.64 |
2.53 |
2.42 |
2.37 |
2.31 |
2.25 |
2.18 |
2.11 |
2.04 |
22 |
2.70 |
2.60 |
2.50 |
2.39 |
2.33 |
2.27 |
2.21 |
2.14 |
2.08 |
2.00 |
23 |
2.67 |
2.57 |
2.47 |
2.36 |
2.30 |
2.24 |
2.18 |
2.11 |
2.04 |
1.97 |
24 |
2.64 |
2.54 |
2.44 |
2.33 |
2.27 |
2.21 |
2.15 |
2.08 |
2.01 |
1.94 |
25 |
2.61 |
2.51 |
2.41 |
2.30 |
2.24 |
2.18 |
2.12 |
2.05 |
1.98 |
1.91 |
26 |
2.59 |
2.49 |
2.39 |
2.28 |
2.22 |
2.16 |
2.09 |
2.03 |
1.95 |
1.88 |
27 |
2.57 |
2.47 |
2.36 |
2.25 |
2.19 |
2.13 |
2.07 |
2.00 |
1.93 |
1.85 |
28 |
2.55 |
2.45 |
2.34 |
2.23 |
2.17 |
2.11 |
2.05 |
1.98 |
1.91 |
1.83 |
29 |
2.53 |
2.43 |
2.32 |
2.21 |
2.15 |
2.09 |
2.03 |
1.96 |
1.89 |
1.81 |
30 |
2.51 |
2.41 |
2.31 |
2.20 |
2.14 |
2.07 |
2.01 |
1.94 |
1.87 |
1.79 |
40 |
2.39 |
2.29 |
2.18 |
2.07 |
2.01 |
1.94 |
1.88 |
1.80 |
1.72 |
1.64 |
60 |
2.27 |
2.17 |
2.06 |
1.94 |
1.88 |
1.82 |
1.74 |
1.67 |
1.58 |
1.48 |
120 |
2.16 |
2.05 |
1.94 |
1.82 |
1.76 |
1.69 |
1.61 |
1.53 |
1.43 |
1.31 |
∞ |
2.05 |
1.94 |
1.83 |
1.71 |
1.64 |
1.57 |
1.48 |
1.39 |
1.27 |
1.00 |
Denominator Degrees of Freedom |
Alternate View
v1 |
Numerator Degrees of Freedom |
v2 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
1 |
4,052 |
4,999.5 |
5,403 |
5,625 |
5,764 |
5,859 |
5,928 |
5,982 |
6,022 |
2 |
98.50 |
99.00 |
99.17 |
99.25 |
99.30 |
99.33 |
99.36 |
99.37 |
99.39 |
3 |
34.12 |
30.82 |
29.46 |
28.71 |
28.24 |
27.91 |
27.67 |
27.49 |
27.35 |
4 |
21.20 |
18.00 |
16.69 |
15.98 |
15.52 |
15.21 |
14.98 |
14.80 |
14.66 |
5 |
16.26 |
13.27 |
12.06 |
11.39 |
10.97 |
10.67 |
10.46 |
10.29 |
10.16 |
6 |
13.75 |
10.92 |
9.78 |
9.15 |
8.75 |
8.47 |
8.26 |
8.10 |
7.98 |
7 |
12.25 |
9.55 |
8.45 |
7.85 |
7.46 |
7.19 |
6.99 |
6.84 |
6.72 |
8 |
11.26 |
8.65 |
7.59 |
7.01 |
6.63 |
6.37 |
6.18 |
6.03 |
5.91 |
9 |
10.56 |
8.02 |
6.99 |
6.42 |
6.06 |
5.80 |
5.61 |
5.47 |
5.35 |
10 |
10.04 |
7.56 |
6.55 |
5.99 |
5.64 |
5.39 |
5.20 |
5.06 |
4.94 |
11 |
9.65 |
7.21 |
6.22 |
5.67 |
5.32 |
5.07 |
4.89 |
4.74 |
4.63 |
12 |
9.33 |
6.93 |
5.95 |
5.41 |
5.06 |
4.82 |
4.64 |
4.50 |
4.39 |
13 |
9.07 |
6.70 |
5.74 |
5.21 |
4.86 |
4.62 |
4.44 |
4.30 |
4.19 |
14 |
8.86 |
6.51 |
5.56 |
5.04 |
4.69 |
4.46 |
4.28 |
4.14 |
4.03 |
15 |
8.68 |
6.36 |
5.42 |
4.89 |
4.56 |
4.32 |
4.14 |
4.00 |
3.89 |
16 |
8.53 |
6.23 |
5.29 |
4.77 |
4.44 |
4.20 |
4.03 |
3.89 |
3.78 |
17 |
8.40 |
6.11 |
5.18 |
4.67 |
4.34 |
4.10 |
3.93 |
3.79 |
3.68 |
18 |
8.29 |
6.01 |
5.09 |
4.58 |
4.25 |
4.01 |
3.84 |
3.71 |
3.60 |
19 |
8.18 |
5.93 |
5.01 |
4.50 |
4.17 |
3.94 |
3.77 |
3.63 |
3.52 |
20 |
8.10 |
5.85 |
4.94 |
4.43 |
4.10 |
3.87 |
3.70 |
3.56 |
3.46 |
21 |
8.02 |
5.78 |
4.87 |
4.37 |
4.04 |
3.81 |
3.64 |
3.51 |
3.40 |
22 |
7.95 |
5.72 |
4.82 |
4.31 |
3.99 |
3.76 |
3.59 |
3.45 |
3.35 |
23 |
7.88 |
5.66 |
4.76 |
4.26 |
3.94 |
3.71 |
3.54 |
3.41 |
3.30 |
24 |
7.82 |
5.61 |
4.72 |
4.22 |
3.90 |
3.67 |
3.50 |
3.36 |
3.26 |
25 |
7.77 |
5.57 |
4.68 |
4.18 |
3.85 |
3.63 |
3.46 |
3.32 |
3.22 |
26 |
7.72 |
5.53 |
4.64 |
4.14 |
3.82 |
3.59 |
3.42 |
3.29 |
3.18 |
27 |
7.68 |
5.49 |
4.60 |
4.11 |
3.78 |
3.56 |
3.39 |
3.26 |
3.15 |
28 |
7.64 |
5.45 |
4.57 |
4.07 |
3.75 |
3.53 |
3.36 |
3.23 |
3.12 |
29 |
7.60 |
5.42 |
4.54 |
4.04 |
3.73 |
3.50 |
3.33 |
3.20 |
3.09 |
30 |
7.56 |
5.39 |
4.51 |
4.02 |
3.70 |
3.47 |
3.30 |
3.17 |
3.07 |
40 |
7.31 |
5.18 |
4.31 |
3.83 |
3.51 |
3.29 |
3.12 |
2.99 |
2.89 |
60 |
7.08 |
4.98 |
4.13 |
3.65 |
3.34 |
3.12 |
2.95 |
2.82 |
2.72 |
120 |
6.85 |
4.79 |
3.95 |
3.48 |
3.17 |
2.96 |
2.79 |
2.66 |
2.56 |
∞ |
6.63 |
4.61 |
3.78 |
3.32 |
3.02 |
2.80 |
2.64 |
2.51 |
2.41 |
v1 |
Numerator Degrees of Freedom |
v2 |
10 |
12 |
15 |
20 |
24 |
30 |
40 |
60 |
120 |
∞ |
1 |
6,056 |
6,106 |
6,157 |
6,209 |
6,235 |
6,261 |
6,287 |
6,313 |
6,339 |
6,366 |
2 |
99.40 |
99.42 |
99.43 |
99.45 |
99.46 |
99.47 |
99.47 |
99.48 |
99.49 |
99.50 |
3 |
27.23 |
27.05 |
26.87 |
26.69 |
26.60 |
26.50 |
26.41 |
26.32 |
26.22 |
26.13 |
4 |
14.55 |
14.37 |
14.20 |
14.02 |
13.93 |
13.84 |
13.75 |
13.65 |
13.56 |
13.46 |
5 |
10.05 |
9.89 |
9.72 |
9.55 |
9.47 |
9.38 |
9.29 |
9.20 |
9.11 |
9.02 |
6 |
7.87 |
7.72 |
7.56 |
7.40 |
7.31 |
7.23 |
7.14 |
7.06 |
6.97 |
6.88 |
7 |
6.62 |
6.47 |
6.31 |
6.16 |
6.07 |
5.99 |
5.91 |
5.82 |
5.74 |
5.65 |
8 |
5.81 |
5.67 |
5.52 |
5.36 |
5.28 |
5.20 |
5.12 |
5.03 |
4.95 |
4.86 |
9 |
5.26 |
5.11 |
4.96 |
4.81 |
4.73 |
4.65 |
4.57 |
4.48 |
4.40 |
4.31 |
10 |
4.85 |
4.71 |
4.56 |
4.41 |
4.33 |
4.25 |
4.17 |
4.08 |
4.00 |
3.91 |
11 |
4.54 |
4.40 |
4.25 |
4.10 |
4.02 |
3.94 |
3.86 |
3.78 |
3.69 |
3.60 |
12 |
4.30 |
4.16 |
4.01 |
3.86 |
3.78 |
3.70 |
3.62 |
3.54 |
3.45 |
3.36 |
13 |
4.10 |
3.96 |
3.82 |
3.66 |
3.59 |
3.51 |
3.43 |
3.34 |
3.25 |
3.17 |
14 |
3.94 |
3.80 |
3.66 |
3.51 |
3.43 |
3.35 |
3.27 |
3.18 |
3.09 |
3.00 |
15 |
3.80 |
3.67 |
3.52 |
3.37 |
3.29 |
3.21 |
3.13 |
3.05 |
2.96 |
2.87 |
16 |
3.69 |
3.55 |
3.41 |
3.26 |
3.18 |
3.10 |
3.02 |
2.93 |
2.84 |
2.75 |
17 |
3.59 |
3.46 |
3.31 |
3.16 |
3.08 |
3.00 |
2.92 |
2.83 |
2.75 |
2.65 |
18 |
3.51 |
3.37 |
3.23 |
3.08 |
3.00 |
2.92 |
2.84 |
2.75 |
2.66 |
2.57 |
19 |
3.43 |
3.30 |
3.15 |
3.00 |
2.92 |
2.84 |
2.76 |
2.67 |
2.58 |
2.49 |
20 |
3.37 |
3.23 |
3.09 |
2.94 |
2.86 |
2.78 |
2.69 |
2.61 |
2.52 |
2.42 |
21 |
3.31 |
3.17 |
3.03 |
2.88 |
2.80 |
2.72 |
2.64 |
2.55 |
2.46 |
2.36 |
22 |
3.26 |
3.12 |
2.98 |
2.83 |
2.75 |
2.67 |
2.58 |
2.50 |
2.40 |
2.31 |
23 |
3.21 |
3.07 |
2.93 |
2.78 |
2.70 |
2.62 |
2.54 |
2.45 |
2.35 |
2.26 |
24 |
3.17 |
3.03 |
2.89 |
2.74 |
2.66 |
2.58 |
2.49 |
2.40 |
2.31 |
2.21 |
25 |
3.13 |
2.99 |
2.85 |
2.70 |
2.62 |
2.54 |
2.45 |
2.36 |
2.27 |
2.17 |
26 |
3.09 |
2.96 |
2.81 |
2.66 |
2.58 |
2.50 |
2.42 |
2.33 |
2.23 |
2.13 |
27 |
3.06 |
2.93 |
2.78 |
2.63 |
2.55 |
2.47 |
2.38 |
2.29 |
2.20 |
2.10 |
28 |
3.03 |
2.90 |
2.75 |
2.60 |
2.52 |
2.44 |
2.35 |
2.26 |
2.17 |
2.06 |
29 |
3.00 |
2.87 |
2.73 |
2.57 |
2.49 |
2.41 |
2.33 |
2.23 |
2.14 |
2.03 |
30 |
2.98 |
2.84 |
2.70 |
2.55 |
2.47 |
2.39 |
2.30 |
2.21 |
2.11 |
2.01 |
40 |
2.80 |
2.66 |
2.52 |
2.37 |
2.29 |
2.20 |
2.11 |
2.02 |
1.92 |
1.80 |
60 |
2.63 |
2.50 |
2.35 |
2.20 |
2.12 |
2.03 |
1.94 |
1.84 |
1.73 |
1.60 |
120 |
2.47 |
2.34 |
2.19 |
2.03 |
1.95 |
1.86 |
1.76 |
1.66 |
1.53 |
1.38 |
∞ |
2.32 |
2.18 |
2.04 |
1.88 |
1.79 |
1.70 |
1.59 |
1.47 |
1.32 |
1.00 |
Denominator Degrees of Freedom |
Table XI Critical Values of Spearman’s Rank Correlation Coefficient
The α values correspond to a one-tailed test of H0:ρ=0. The value should be doubled for two-tailed tests.
Alternate View
n |
α=.05 |
α=.025 |
α=.01 |
α=.005 |
n |
α=.05 |
α=.025 |
α=.01 |
α=.005 |
5 |
.900 |
− |
− |
− |
18 |
.399 |
.476 |
.564 |
.625 |
6 |
.829 |
.886 |
.943 |
− |
19 |
.388 |
.462 |
.549 |
.608 |
7 |
.714 |
.786 |
.893 |
− |
20 |
.377 |
.450 |
.534 |
.591 |
8 |
.643 |
.738 |
.833 |
.881 |
21 |
.368 |
.438 |
.521 |
.576 |
9 |
.600 |
.683 |
.783 |
.833 |
22 |
.359 |
.428 |
.508 |
.562 |
10 |
.564 |
.648 |
.745 |
.794 |
23 |
.351 |
.418 |
.496 |
.549 |
11 |
.523 |
.623 |
.736 |
.818 |
24 |
.343 |
.409 |
.485 |
.537 |
12 |
.497 |
.591 |
.703 |
.780 |
25 |
.336 |
.400 |
.475 |
.526 |
13 |
.475 |
.566 |
.673 |
.745 |
26 |
.329 |
.392 |
.465 |
.515 |
14 |
.457 |
.545 |
.646 |
.716 |
27 |
.323 |
.385 |
.456 |
.505 |
15 |
.441 |
.525 |
.623 |
.689 |
28 |
.317 |
.377 |
.448 |
.496 |
16 |
.425 |
.507 |
.601 |
.666 |
29 |
.311 |
.370 |
.440 |
.487 |
17 |
.412 |
.490 |
.582 |
.645 |
30 |
.305 |
.364 |
.432 |
.478 |
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