Appendix A. Tables and Figures
In this section, we report the power of various tests for normality using Monte Carlo simulations under alternative hypotheses. The simulations were performed in R. The sample sizes were small, moderate, and large, with n = 25, 50, 75, 100, 150, 200, 250, 500, and 1000. Although simulations were conducted for all stated sample sizes, the table includes only rows up to the first row where all criteria have a power of 1, to maintain shorter tables.
The null hypothesis is in almost all cases; exceptions are specified separately. As alternative hypotheses, we considered normal, log-normal, mixed normal, Student’s t, gamma, and uniform distributions.
Recall that the following procedure to estimate the power was used: 1000 samples with a given sample size were generated from the alternative hypothesis with specific parameters, and the ratio of the number of rejections of the null hypothesis to 1000 was calculated.
We used the notations and for Anderson–Darling and Cramér–von Mises tests respectively, where the parameters were replaced with their estimates (i.e., modifications for testing composite hypotheses).
Table A1.
The estimated power is reported when the null hypothesis is tested against samples simulated from the normal distribution . The last column contains the test power of the Fisher test for the null hypothesis where the variance is equal to 1.
Table A1.
The estimated power is reported when the null hypothesis is tested against samples simulated from the normal distribution . The last column contains the test power of the Fisher test for the null hypothesis where the variance is equal to 1.
| n | | | | | | Fisher |
---|
| 25 | 0.739 | 0.673 | 0.175 | 0.418 | 0.173 | 0.392 |
| 50 | 0.907 | 0.882 | 0.265 | 0.655 | 0.276 | 0.680 |
| 75 | 0.975 | 0.970 | 0.391 | 0.832 | 0.433 | 0.835 |
| 100 | 0.991 | 0.991 | 0.510 | 0.924 | 0.607 | 0.929 |
| 150 | 1 | 0.999 | 0.732 | 0.993 | 0.822 | 0.994 |
| 200 | 1 | 1 | 0.857 | 1 | 0.933 | 1 |
| 250 | 1 | 1 | 0.951 | 1 | 0.978 | 1 |
| 500 | 1 | 1 | 1 | 1 | 1 | 1 |
| 25 | 0.655 | 0.576 | 0.042 | 0.179 | 0.039 | 0.164 |
| 50 | 0.852 | 0.831 | 0.077 | 0.348 | 0.074 | 0.401 |
| 75 | 0.953 | 0.940 | 0.137 | 0.529 | 0.124 | 0.631 |
| 100 | 0.988 | 0.986 | 0.191 | 0.752 | 0.204 | 0.801 |
| 150 | 1 | 1 | 0.385 | 0.940 | 0.454 | 0.943 |
| 200 | 1 | 1 | 0.539 | 0.982 | 0.669 | 0.991 |
| 250 | 1 | 1 | 0.730 | 0.997 | 0.841 | 0.998 |
| 500 | 1 | 1 | 0.996 | 1 | 1 | 1 |
| 1000 | 1 | 1 | 1 | 1 | 1 | 1 |
Table A2.
The estimated power is reported when the null hypothesis is tested against samples simulated from the normal distribution . The two last columns contain the test powers of the Student and Welch statistics used to test whether the difference between the two means is statistically significant or not.
Table A2.
The estimated power is reported when the null hypothesis is tested against samples simulated from the normal distribution . The two last columns contain the test powers of the Student and Welch statistics used to test whether the difference between the two means is statistically significant or not.
| n | | | | | | Student | Welch |
---|
| 25 | 0.946 | 0.015 | 0.993 | 0.997 | 0.997 | 0.929 | 0.929 |
| 50 | 1 | 0.961 | 1 | 1 | 1 | 0.999 | 0.999 |
| 75 | 1 | 0.999 | 1 | 1 | 1 | 1 | 1 |
| 100 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 25 | 0.889 | 0.002 | 0.949 | 0.987 | 0.978 | 0.803 | 0.803 |
| 50 | 0.997 | 0.030 | 0.999 | 1 | 1 | 0.988 | 0.988 |
| 75 | 1 | 0.967 | 1 | 1 | 1 | 0.999 | 0.999 |
| 100 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
Table A3.
The null hypothesis is tested against data sampled from the Cauchy distribution.
Table A3.
The null hypothesis is tested against data sampled from the Cauchy distribution.
| n | | | | | | | | | | | |
---|
| 25 | 0.999 | 0.900 | 0.997 | 0.896 | 0.262 | 0.909 | 0.971 | 0.927 | 0.248 | 0.927 | 0.939 |
| 50 | 1 | 0.994 | 1 | 0.993 | 0.478 | 0.992 | 0.999 | 0.995 | 0.478 | 0.997 | 0.997 |
| 75 | 1 | 1 | 1 | 1 | 0.720 | 1 | 1 | 1 | 0.676 | 1 | 1 |
| 100 | 1 | 1 | 1 | 1 | 0.864 | 1 | 1 | 1 | 0.853 | 1 | 1 |
| 150 | 1 | 1 | 1 | 1 | 0.984 | 1 | 1 | 1 | 0.971 | 1 | 1 |
| 200 | 1 | 1 | 1 | 1 | 0.999 | 1 | 1 | 1 | 1 | 1 | 1 |
| 250 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 25 | 0.995 | 0.854 | 0.994 | 0.854 | 0.072 | 0.816 | 0.945 | 0.882 | 0.071 | 0.880 | 0.894 |
| 50 | 1 | 0.988 | 1 | 0.986 | 0.186 | 0.986 | 0.996 | 0.995 | 0.161 | 0.996 | 0.994 |
| 75 | 1 | 1 | 1 | 1 | 0.329 | 1 | 1 | 1 | 0.283 | 1 | 1 |
| 100 | 1 | 1 | 1 | 1 | 0.512 | 1 | 1 | 1 | 0.463 | 1 | 1 |
| 150 | 1 | 1 | 1 | 1 | 0.867 | 1 | 1 | 1 | 0.806 | 1 | 1 |
| 200 | 1 | 1 | 1 | 1 | 0.971 | 1 | 1 | 1 | 0.935 | 1 | 1 |
| 250 | 1 | 1 | 1 | 1 | 0.997 | 1 | 1 | 1 | 0.994 | 1 | 1 |
| 500 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
Table A4.
The null hypothesis is tested against data sampled from the Student’s t distribution with 5 degrees of freedom.
Table A4.
The null hypothesis is tested against data sampled from the Student’s t distribution with 5 degrees of freedom.
| n | | | | | | | | | | | |
---|
| 25 | 0.560 | 0.215 | 0.531 | 0.216 | 0.069 | 0.135 | 0.168 | 0.200 | 0.078 | 0.178 | 0.265 |
| 50 | 0.742 | 0.371 | 0.715 | 0.385 | 0.069 | 0.173 | 0.186 | 0.269 | 0.065 | 0.230 | 0.411 |
| 75 | 0.857 | 0.523 | 0.828 | 0.527 | 0.065 | 0.27 | 0.254 | 0.387 | 0.078 | 0.341 | 0.531 |
| 100 | 0.910 | 0.628 | 0.911 | 0.624 | 0.06 | 0.326 | 0.297 | 0.473 | 0.070 | 0.422 | 0.624 |
| 150 | 0.976 | 0.764 | 0.974 | 0.758 | 0.073 | 0.443 | 0.420 | 0.605 | 0.086 | 0.555 | 0.750 |
| 200 | 0.992 | 0.861 | 0.991 | 0.856 | 0.082 | 0.540 | 0.510 | 0.736 | 0.112 | 0.685 | 0.861 |
| 250 | 0.996 | 0.904 | 0.997 | 0.914 | 0.102 | 0.634 | 0.625 | 0.829 | 0.124 | 0.771 | 0.907 |
| 500 | 1 | 0.990 | 1 | 0.991 | 0.174 | 0.905 | 0.936 | 0.976 | 0.205 | 0.965 | 0.987 |
| 1000 | 1 | 1 | 1 | 1 | 0.480 | 0.998 | 1 | 1 | 0.497 | 1 | 1 |
| 25 | 0.506 | 0.138 | 0.459 | 0.148 | 0.012 | 0.057 | 0.053 | 0.097 | 0.016 | 0.081 | 0.136 |
| 50 | 0.66 | 0.285 | 0.647 | 0.288 | 0.011 | 0.078 | 0.066 | 0.153 | 0.013 | 0.129 | 0.235 |
| 75 | 0.803 | 0.421 | 0.803 | 0.442 | 0.007 | 0.124 | 0.077 | 0.247 | 0.011 | 0.191 | 0.385 |
| 100 | 0.882 | 0.504 | 0.875 | 0.517 | 0.008 | 0.158 | 0.094 | 0.287 | 0.013 | 0.248 | 0.450 |
| 150 | 0.96 | 0.702 | 0.95 | 0.698 | 0.013 | 0.264 | 0.163 | 0.462 | 0.024 | 0.407 | 0.644 |
| 200 | 0.986 | 0.789 | 0.983 | 0.793 | 0.020 | 0.346 | 0.240 | 0.575 | 0.023 | 0.512 | 0.744 |
| 250 | 0.991 | 0.865 | 0.991 | 0.873 | 0.022 | 0.388 | 0.313 | 0.672 | 0.026 | 0.596 | 0.840 |
| 500 | 1 | 0.990 | 1 | 0.992 | 0.035 | 0.750 | 0.716 | 0.940 | 0.040 | 0.902 | 0.986 |
| 1000 | 1 | 1 | 1 | 1 | 0.128 | 0.970 | 0.990 | 1 | 0.122 | 0.997 | 1 |
Table A5.
The null hypothesis is tested against data sampled from .
Table A5.
The null hypothesis is tested against data sampled from .
| n | | | | | | | | | | | |
---|
| 25 | 0.989 | 0 | 0.976 | 0.001 | 0.677 | 0.125 | 0.972 | 0.230 | 0.708 | 0.178 | 0.128 |
| 50 | 1 | 0 | 0.999 | 0.001 | 0.953 | 0.252 | 1 | 0.567 | 0.976 | 0.414 | 0.446 |
| 75 | 1 | 0.112 | 1 | 0.084 | 0.995 | 0.435 | 1 | 0.844 | 1 | 0.681 | 0.837 |
| 100 | 1 | 0.602 | 1 | 0.543 | 1 | 0.574 | 1 | 0.941 | 1 | 0.832 | 0.964 |
| 150 | 1 | 0.987 | 1 | 0.985 | 1 | 0.839 | 1 | 0.997 | 1 | 0.974 | 1 |
| 200 | 1 | 1 | 1 | 1 | 1 | 0.947 | 1 | 1 | 1 | 0.996 | 1 |
| 250 | 1 | 1 | 1 | 1 | 1 | 0.989 | 1 | 1 | 1 | 1 | 1 |
| 500 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 25 | 0.977 | 0 | 0.957 | 0 | 0.339 | 0.024 | 0.874 | 0.058 | 0.323 | 0.043 | 0.014 |
| 50 | 1 | 0 | 0.999 | 0 | 0.782 | 0.074 | 0.998 | 0.271 | 0.823 | 0.179 | 0.126 |
| 75 | 1 | 0 | 1 | 0 | 0.959 | 0.147 | 1 | 0.553 | 0.982 | 0.373 | 0.444 |
| 100 | 1 | 0.005 | 1 | 0.002 | 0.999 | 0.276 | 1 | 0.799 | 1 | 0.576 | 0.777 |
| 150 | 1 | 0.531 | 1 | 0.483 | 1 | 0.524 | 1 | 0.976 | 1 | 0.887 | 0.990 |
| 200 | 1 | 0.975 | 1 | 0.970 | 1 | 0.725 | 1 | 0.998 | 1 | 0.972 | 0.999 |
| 250 | 1 | 0.999 | 1 | 0.999 | 1 | 0.891 | 1 | 1 | 1 | 0.996 | 1 |
| 500 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
Table A6.
The null hypothesis is tested against data sampled from .
Table A6.
The null hypothesis is tested against data sampled from .
| n | | | | | | | | | | | |
---|
| 25 | 1 | 0.128 | 0.760 | 0.380 | 1 | 0.409 | 1 | 0.576 | 1 | 0.512 | 0.623 |
| 50 | 1 | 1 | 0.950 | 0.772 | 1 | 0.730 | 1 | 0.896 | 1 | 0.843 | 0.934 |
| 75 | 1 | 1 | 0.993 | 0.944 | 1 | 0.880 | 1 | 0.975 | 1 | 0.954 | 0.984 |
| 100 | 1 | 1 | 0.999 | 0.992 | 1 | 0.948 | 1 | 0.999 | 1 | 0.994 | 0.999 |
| 150 | 1 | 1 | 1 | 1 | 1 | 0.994 | 1 | 1 | 1 | 0.998 | 1 |
| 200 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 25 | 1 | 0.046 | 0.676 | 0.244 | 1 | 0.186 | 1 | 0.332 | 1 | 0.287 | 0.349 |
| 50 | 1 | 0.307 | 0.930 | 0.640 | 1 | 0.444 | 1 | 0.755 | 1 | 0.676 | 0.805 |
| 75 | 1 | 1 | 0.983 | 0.847 | 1 | 0.700 | 1 | 0.936 | 1 | 0.879 | 0.957 |
| 100 | 1 | 1 | 0.994 | 0.935 | 1 | 0.825 | 1 | 0.982 | 1 | 0.955 | 0.994 |
| 150 | 1 | 1 | 1 | 0.999 | 1 | 0.965 | 1 | 1 | 1 | 0.997 | 1 |
| 200 | 1 | 1 | 1 | 1 | 1 | 0.995 | 1 | 1 | 1 | 1 | 1 |
| 250 | 1 | 1 | 1 | 1 | 1 | 0.999 | 1 | 1 | 1 | 1 | 1 |
| 500 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
Table A7.
The null hypothesis is tested against data sampled from the log-normal distribution .
Table A7.
The null hypothesis is tested against data sampled from the log-normal distribution .
| n | | | | | | | | | | | |
---|
| 25 | 0.994 | 0.760 | 0.907 | 0.860 | 1 | 0.889 | 1 | 0.960 | 1 | 0.947 | 0.963 |
| 50 | 1 | 1 | 0.994 | 0.994 | 1 | 0.998 | 1 | 1 | 1 | 1 | 1 |
| 75 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | |
| 25 | 0.996 | 0.574 | 0.850 | 0.737 | 1 | 0.727 | 1 | 0.881 | 1 | 0.853 | 0.888 |
| 50 | 1 | 0.966 | 0.980 | 0.978 | 1 | 0.972 | 1 | 0.996 | 1 | 0.991 | 0.998 |
| 75 | 1 | 1 | 0.998 | 0.999 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 100 | 1 | 1 | 0.999 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 150 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 1 |
Table A8.
The null hypothesis is tested against data sampled from the , which is a mixture of the standard normal distribution and the normal distribution with equal mixture weights.
Table A8.
The null hypothesis is tested against data sampled from the , which is a mixture of the standard normal distribution and the normal distribution with equal mixture weights.
| n | | | | | | | | | | | |
---|
| 25 | 0.997 | 0.228 | 0.997 | 0.212 | 0.277 | 0.271 | 0.955 | 0.339 | 0.292 | 0.345 | 0.366 |
| 50 | 1 | 0.430 | 1 | 0.433 | 0.499 | 0.425 | 0.999 | 0.553 | 0.538 | 0.536 | 0.581 |
| 75 | 1 | 0.599 | 1 | 0.575 | 0.791 | 0.626 | 1 | 0.756 | 0.831 | 0.742 | 0.737 |
| 100 | 1 | 0.737 | 1 | 0.724 | 0.889 | 0.745 | 1 | 0.878 | 0.937 | 0.87 | 0.863 |
| 150 | 1 | 0.884 | 1 | 0.889 | 0.991 | 0.893 | 1 | 0.972 | 0.996 | 0.967 | 0.97 |
| 200 | 1 | 0.957 | 1 | 0.957 | 1 | 0.975 | 1 | 0.996 | 1 | 0.997 | 0.993 |
| 250 | 1 | 0.988 | 1 | 0.986 | 1 | 0.991 | 1 | 0.999 | 1 | 0.999 | 0.999 |
| 500 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 25 | 0.998 | 0.155 | 0.993 | 0.154 | 0.089 | 0.105 | 0.840 | 0.147 | 0.077 | 0.139 | 0.170 |
| 50 | 1 | 0.349 | 1 | 0.334 | 0.196 | 0.235 | 0.983 | 0.374 | 0.202 | 0.350 | 0.363 |
| 75 | 1 | 0.446 | 1 | 0.444 | 0.420 | 0.355 | 0.998 | 0.537 | 0.436 | 0.525 | 0.505 |
| 100 | 1 | 0.591 | 1 | 0.581 | 0.564 | 0.485 | 1 | 0.721 | 0.613 | 0.699 | 0.662 |
| 150 | 1 | 0.789 | 1 | 0.791 | 0.896 | 0.738 | 1 | 0.909 | 0.934 | 0.899 | 0.883 |
| 200 | 1 | 0.893 | 1 | 0.893 | 0.986 | 0.892 | 1 | 0.983 | 0.994 | 0.981 | 0.961 |
| 250 | 1 | 0.958 | 1 | 0.952 | 1 | 0.961 | 1 | 0.996 | 1 | 0.995 | 0.991 |
| 500 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
Table A9.
The null hypothesis is tested against data sampled from the gamma distribution.
Table A9.
The null hypothesis is tested against data sampled from the gamma distribution.
| n | | | | | | | | | | | |
---|
| 25 | 0.292 | 0.274 | 0.353 | 0.410 | 0.136 | 0.400 | 0.134 | 0.558 | 0.131 | 0.505 | 0.620 |
| 50 | 0.421 | 0.477 | 0.592 | 0.761 | 0.269 | 0.732 | 0.307 | 0.885 | 0.263 | 0.837 | 0.913 |
| 75 | 0.523 | 0.652 | 0.765 | 0.942 | 0.370 | 0.856 | 0.482 | 0.975 | 0.382 | 0.949 | 0.991 |
| 100 | 0.643 | 0.805 | 0.948 | 0.995 | 0.421 | 0.952 | 0.658 | 0.999 | 0.465 | 0.990 | 1 |
| 150 | 0.815 | 0.935 | 1 | 1 | 0.619 | 0.996 | 0.913 | 1 | 0.679 | 1 | 1 |
| 200 | 0.923 | 0.971 | 1 | 1 | 0.831 | 1 | 0.992 | 1 | 0.837 | 1 | 1 |
| 250 | 0.989 | 0.994 | 1 | 1 | 0.979 | 1 | 1 | 1 | 0.928 | 1 | 1 |
| 500 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 25 | 0.219 | 0.176 | 0.260 | 0.272 | 0.045 | 0.171 | 0.034 | 0.316 | 0.040 | 0.270 | 0.360 |
| 50 | 0.363 | 0.412 | 0.488 | 0.617 | 0.098 | 0.459 | 0.084 | 0.757 | 0.092 | 0.675 | 0.790 |
| 75 | 0.451 | 0.581 | 0.665 | 0.832 | 0.173 | 0.671 | 0.179 | 0.928 | 0.169 | 0.872 | 0.962 |
| 100 | 0.563 | 0.701 | 0.800 | 0.945 | 0.197 | 0.818 | 0.250 | 0.979 | 0.197 | 0.946 | 0.991 |
| 150 | 0.684 | 0.882 | 0.967 | 0.997 | 0.371 | 0.969 | 0.571 | 1 | 0.407 | 0.997 | 1 |
| 200 | 0.807 | 0.951 | 0.999 | 1 | 0.507 | 0.996 | 0.797 | 1 | 0.549 | 1 | 1 |
| 250 | 0.904 | 0.99 | 1 | 1 | 0.667 | 1 | 0.951 | 1 | 0.724 | 1 | 1 |
| 500 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0.992 | 1 | 1 |
| 1000 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
Table A10.
The null hypothesis is tested against data sampled from a mixture of a standard normal distribution (weight 0.9) and a sum of independent random variables—with a standard normal distribution and Poisson distribution with (weight 0.1).
Table A10.
The null hypothesis is tested against data sampled from a mixture of a standard normal distribution (weight 0.9) and a sum of independent random variables—with a standard normal distribution and Poisson distribution with (weight 0.1).
| n | | | | | | | | | | | |
---|
| 25 | 0.994 | 0.923 | 0.985 | 0.884 | 0.111 | 0.808 | 0.878 | 0.890 | 0.160 | 0.878 | 0.920 |
| 50 | 1 | 0.999 | 1 | 0.990 | 0.134 | 0.952 | 0.966 | 0.990 | 0.194 | 0.981 | 0.995 |
| 75 | 1 | 1 | 1 | 1 | 0.235 | 0.991 | 0.999 | 0.999 | 0.319 | 0.999 | 1 |
| 100 | 1 | 1 | 1 | 1 | 0.310 | 0.998 | 1 | 1 | 0.398 | 1 | 1 |
| 150 | 1 | 1 | 1 | 1 | 0.570 | 1 | 1 | 1 | 0.609 | 1 | 1 |
| 200 | 1 | 1 | 1 | 1 | 0.823 | 1 | 1 | 1 | 0.770 | 1 | 1 |
| 250 | 1 | 1 | 1 | 1 | 0.974 | 1 | 1 | 1 | 0.887 | 1 | 1 |
| 500 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0.999 | 1 | 1 |
| 1000 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 25 | 0.996 | 0.861 | 0.992 | 0.796 | 0.033 | 0.647 | 0.671 | 0.791 | 0.049 | 0.754 | 0.842 |
| 50 | 1 | 0.992 | 1 | 0.985 | 0.043 | 0.884 | 0.854 | 0.966 | 0.065 | 0.951 | 0.984 |
| 75 | 1 | 1 | 1 | 0.998 | 0.085 | 0.979 | 0.990 | 0.994 | 0.131 | 0.989 | 0.999 |
| 100 | 1 | 1 | 1 | 1 | 0.108 | 0.994 | 0.998 | 1 | 0.169 | 0.998 | 1 |
| 150 | 1 | 1 | 1 | 1 | 0.207 | 1 | 1 | 1 | 0.275 | 1 | 1 |
| 200 | 1 | 1 | 1 | 1 | 0.379 | 1 | 1 | 1 | 0.424 | 1 | 1 |
| 250 | 1 | 1 | 1 | 1 | 0.622 | 1 | 1 | 1 | 0.617 | 1 | 1 |
| 500 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0.972 | 1 | 1 |
| 1000 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
Figure A1.
The power for depending on the sample size n ( is tested against data sampled from the Student’s t distribution with 5 degrees of freedom. Figure created by S. Khrushchev and A. Yambartsev.
Figure A1.
The power for depending on the sample size n ( is tested against data sampled from the Student’s t distribution with 5 degrees of freedom. Figure created by S. Khrushchev and A. Yambartsev.
Figure A2.
The power for depending on the sample size n ( is tested against data sampled from the Student’s t distribution with 5 degrees of freedom. Figure created by S. Khrushchev and A. Yambartsev.
Figure A2.
The power for depending on the sample size n ( is tested against data sampled from the Student’s t distribution with 5 degrees of freedom. Figure created by S. Khrushchev and A. Yambartsev.