Table 5.
Power of six global tests of correlated P-values (The correlation coefficient for Beta random variables isρ. Uniform distributions have random correlation matrices)
| Correlated 0.9Uniform (0,1) ± 0.1Beta (0.4,6), | ||||||
|---|---|---|---|---|---|---|
|
n |
KS |
Inverse chi |
Inverse norm |
Tippett |
Wilcoxon |
Logit |
| 20 |
0.176 |
0.359 |
0.259 |
0.332 |
0.191 |
0.294 |
| 50 |
0.27 |
0.576 |
0.418 |
0.505 |
0.303 |
0.464 |
| 100 |
0.407 |
0.824 |
0.599 |
0.652 |
0.456 |
0.672 |
| 200 |
0.645 |
0.967 |
0.827 |
0.791 |
0.657 |
0.877 |
| 300 |
0.808 |
0.995 |
0.92 |
0.861 |
0.785 |
0.941 |
| 400 |
0.896 |
0.997 |
0.966 |
0.896 |
0.861 |
0.979 |
| 500 |
0.949 |
0.999 |
0.984 |
0.933 |
0.926 |
0.993 |
|
Correlated 0.6 Uniform (0,1) ± 0.4Beta (0.4,6), | ||||||
|
n |
KS |
Inverse chi |
Inverse norm |
Tippett |
Wilcoxon |
Logit |
| 20 |
0.797 |
0.957 |
0.896 |
0.784 |
0.815 |
0.918 |
| 50 |
0.987 |
1 |
0.997 |
0.939 |
0.983 |
1 |
| 100 |
1 |
1 |
1 |
0.972 |
1 |
1 |
| 200 |
1 |
1 |
1 |
0.998 |
1 |
1 |
| 300 |
1 |
1 |
1 |
1 |
1 |
1 |
| 400 |
1 |
1 |
1 |
0.999 |
1 |
1 |
| 500 |
1 |
1 |
1 |
0.999 |
1 |
1 |
|
Correlated 0.9 Uniform (0,1) ± 0.1Beta (0.5,4.5), | ||||||
|
n |
KS |
Inverse chi |
Inverse norm |
Tippett |
Wilcoxon |
Logit |
| 20 |
0.151 |
0.266 |
0.207 |
0.225 |
0.183 |
0.221 |
| 50 |
0.227 |
0.466 |
0.336 |
0.326 |
0.264 |
0.369 |
| 100 |
0.343 |
0.664 |
0.493 |
0.437 |
0.397 |
0.534 |
| 200 |
0.545 |
0.863 |
0.709 |
0.537 |
0.595 |
0.757 |
| 300 |
0.706 |
0.944 |
0.832 |
0.587 |
0.719 |
0.863 |
| 400 |
0.811 |
0.982 |
0.913 |
0.632 |
0.81 |
0.933 |
| 500 |
0.89 |
0.992 |
0.951 |
0.695 |
0.887 |
0.966 |
|
Correlated 0.6 Uniform (0,1) ± 0.4Beta (0.5,4.5), | ||||||
|
n |
KS |
Inverse chi |
Inverse norm |
Tippett |
Wilcoxon |
Logit |
| 20 |
0.161 |
0.291 |
0.212 |
0.225 |
0.173 |
0.237 |
| 50 |
0.251 |
0.475 |
0.362 |
0.302 |
0.292 |
0.385 |
| 100 |
0.322 |
0.64 |
0.504 |
0.397 |
0.39 |
0.528 |
| 200 |
0.517 |
0.882 |
0.701 |
0.527 |
0.58 |
0.743 |
| 300 |
0.726 |
0.952 |
0.845 |
0.568 |
0.731 |
0.873 |
| 400 |
0.806 |
0.976 |
0.894 |
0.607 |
0.805 |
0.917 |
| 500 |
0.895 |
0.998 |
0.95 |
0.676 |
0.883 |
0.965 |
|
Correlated 0.9 Uniform (0,1) ± 0.1Beta (1,5), | ||||||
|
n |
KS |
Inverse chi |
Inverse norm |
Tippett |
Wilcoxon |
Logit |
| 20 |
0.127 |
0.118 |
0.139 |
0.056 |
0.144 |
0.136 |
| 50 |
0.203 |
0.199 |
0.211 |
0.063 |
0.235 |
0.206 |
| 100 |
0.248 |
0.272 |
0.28 |
0.064 |
0.271 |
0.269 |
| 200 |
0.406 |
0.448 |
0.453 |
0.06 |
0.446 |
0.438 |
| 300 |
0.535 |
0.559 |
0.541 |
0.073 |
0.542 |
0.535 |
| 400 |
0.619 |
0.657 |
0.649 |
0.07 |
0.657 |
0.631 |
| 500 |
0.725 |
0.743 |
0.729 |
0.071 |
0.731 |
0.715 |
|
Correlated 0.6 Uniform (0,1) ± 0.4Beta (1,5), | ||||||
|
n |
KS |
Inverse chi |
Inverse norm |
Tippett |
Wilcoxon |
Logit |
| 20 |
0.572 |
0.56 |
0.599 |
0.117 |
0.611 |
0.587 |
| 50 |
0.893 |
0.864 |
0.904 |
0.104 |
0.917 |
0.891 |
| 100 |
0.991 |
0.981 |
0.986 |
0.114 |
0.991 |
0.981 |
| 200 |
1 |
1 |
0.999 |
0.091 |
1 |
0.999 |
| 300 |
1 |
1 |
1 |
0.109 |
1 |
1 |
| 400 |
1 |
1 |
1 |
0.111 |
1 |
1 |
| 500 | 1 | 1 | 1 | 0.085 | 1 | 1 |