Table 1.
Power in settings with two endpoints. Power to reject both elementary hypotheses (H 1∪H 2), specifically H 1, H 2, or at least one elementary hypothesis (any H i) under alternatives with standardized effects δ = (δ 1,δ 2), assuming bivariate normal test statistics with variances equal to 1 and correlation ρ and global one‐sided level α = 0.025. The power is given in percent (100,000 simulation runs per scenario). The column Trimmed Simes refers to the diagonally trimmed Simes test.
| δ | ρ | Test | H 1∪H 2 | H 1 | H 2 | any H i |
|---|---|---|---|---|---|---|
| (3, 0) | 0 | Trimmed Simes/Hommel | 2.1/2.1 | 77.8/77.9 | 2.3/2.3 | 78.0/78.1 |
| Bonferroni–Holm/maxT | 2.0/1.9 | 77.8/76.5 | 2.2/2.1 | 78.0/76.8 | ||
| 0.5 | Trimmed Simes/Hommel | 2.5/2.5 | 77.6/77.7 | 2.5/2.5 | 77.6/77.7 | |
| Bonferroni–Holm/maxT | 2.5/2.5 | 77.7/77.3 | 2.5/2.5 | 77.7/77.3 | ||
| 0.75 | Trimmed Simes/Hommel | 2.5/2.5 | 77.8/77.9 | 2.5/2.5 | 77.8/77.9 | |
| Bonferroni–Holm/ maxT | 2.5/2.5 | 77.9/78.5 | 2.5/2.5 | 77.9/78.5 | ||
| 0.85 | Trimmed Simes/Hommel | 2.5/2.5 | 77.4/77.4 | 2.5/2.5 | 77.4/77.4 | |
| Bonferroni–Holm/maxT | 2.5/2.5 | 77.4/79.1 | 2.5/2.5 | 77.4/79.1 | ||
| 0.9 | Trimmed Simes/Hommel | 2.5/2.5 | 77.8/77.8 | 2.5/2.5 | 77.8/77.8 | |
| Bonferroni–Holm/maxT | 2.5/2.4 | 77.8/79.7 | 2.5/2.4 | 77.8/79.7 | ||
| (2, 3) | 0 | Trimmed Simes/Hommel | 44.0/44.0 | 50.1/50.1 | 81.4/81.4 | 87.4/87.4 |
| Bonferroni–Holm/maxT | 43.2/41.7 | 49.2/48.1 | 80.5/79.3 | 86.6/85.7 | ||
| 0.5 | Trimmed Simes/Hommel | 48.3/48.3 | 50.2/50.2 | 80.0/80.0 | 81.9/81.9 | |
| Bonferroni–Holm/maxT | 47.5/47.0 | 49.4/49.1 | 79.2/78.9 | 81.1/81.0 | ||
| 0.75 | Trimmed Simes/Hommel | 50.4/50.4 | 50.8/50.8 | 78.8/78.8 | 79.2/79.2 | |
| Bonferroni–Holm/maxT | 49.7/49.6 | 50.1/50.1 | 78.1/79.3 | 78.5/79.8 | ||
| 0.85 | Trimmed Simes/Hommel | 51.3/51.3 | 51.4/51.4 | 78.2/78.2 | 78.3/78.3 | |
| Bonferroni–Holm/maxT | 50.9/50.3 | 51.0/50.4 | 77.8/79.9 | 77.8/80.1 | ||
| 0.9 | Trimmed Simes/Hommel | 51.6/51.6 | 51.6/51.6 | 78.0/78.0 | 78.1/78.1 | |
| Bonferroni–Holm/maxT | 51.3/50.5 | 51.3/50.6 | 77.8/80.3 | 77.8/80.3 | ||
| (3, 3) | 0 | Trimmed Simes/Hommel | 72.5/72.5 | 84.1/84.1 | 83.9/83.9 | 95.5/95.5 |
| Bonferroni–Holm/maxT | 71.9/70.3 | 83.5/82.4 | 83.3/82.4 | 94.9/94.5 | ||
| 0.5 | Trimmed Simes/Hommel | 75.9/75.9 | 83.3/83.3 | 83.2/83.2 | 90.6/90.6 | |
| Bonferroni–Holm/maxT | 75.1/74.0 | 82.4/81.7 | 82.4/81.9 | 89.7/89.6 | ||
| 0.75 | Trimmed Simes/Hommel | 78.7/78.7 | 83.0/83.0 | 83.0/83.0 | 87.4/87.4 | |
| Bonferroni–Holm/maxT | 77.6/76.8 | 81.9/81.9 | 81.9/81.8 | 86.3/86.9 | ||
| 0.85 | Trimmed Simes/Hommel | 79.9/79.9 | 82.8/82.8 | 82.8/82.8 | 85.6/85.6 | |
| Bonferroni–Holm/maxT | 78.5/78.5 | 81.4/82.3 | 81.3/82.2 | 84.2/86.1 | ||
| 0.9 | Trimmed Simes/Hommel | 81.2/81.2 | 83.1/83.1 | 83.1/83.1 | 85.0/85.0 | |
| Bonferroni–Holm/maxT | 79.4/79.5 | 81.3/82.5 | 81.3/82.4 | 83.1/85.4 |