J | M | Ntrial | μ | γ = 0 | γ = 0.2 | ||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Type-I error | Power | Position bias | SD of the estimates | ||||||||||||||||
Non calibrated | Calibrated | Non calibrated | Calibrated | Non calibrated | Calibrated | Non calibrated | Calibrated | ||||||||||||
\(\hat{\gamma}\) | t test on \(\hat{\theta_i}\) | \(\hat{\gamma}\) | t test on \(\hat{\theta_i}\) | \(\hat{\gamma}\) | t test on \(\hat{\theta_i}\) | \(\hat{\gamma}\) | t test on \(\hat{\theta_i}\) | \(\hat{\gamma}\) | t test on \(\hat{\theta_i}\) | \(\hat{\gamma}\) | t test on \(\hat{\theta_i}\) | \(\hat{\gamma}\) | t test on \(\hat{\theta_i}\) | \(\hat{\gamma}\) | t test on \(\hat{\theta_i}\) | ||||
4 | 3 | 200 | 0 | 5.6 | 5.6 | 5.6 | 5.6 | 32.8 | 32.8 | 32.8 | 32.6 | 0.01 | 0.08 | 0.01 | 0.08 | 0.13 | 0.08 | 0.13 | 0.08 |
0.5 | 4.4 | 4.4 | 4.6 | 4.4 | 32.8 | 32.8 | 33.2 | 33.0 | 0.00 | 0.08 | 0.00 | 0.08 | 0.13 | 0.08 | 0.13 | 0.08 | |||
2 | 5.8 | 5.6 | 5.6 | 5.4 | 29.6 | 29.6 | 29.8 | 29.6 | 0.00 | 0.10 | 0.01 | 0.10 | 0.15 | 0.07 | 0.15 | 0.07 | |||
500 | 0 | 6.8 | 6.6 | 6.8 | 6.8 | 68.0 | 68.0 | 68.0 | 68.0 | 0.00 | 0.08 | 0.00 | 0.08 | 0.08 | 0.05 | 0.08 | 0.05 | ||
0.5 | 2.6 | 2.6 | 2.6 | 2.6 | 68.4 | 68.4 | 68.6 | 68.4 | 0.00 | 0.08 | 0.00 | 0.08 | 0.08 | 0.05 | 0.08 | 0.05 | |||
2 | 4.6 | 4.6 | 4.6 | 4.6 | 58.6 | 58.6 | 58.4 | 58.4 | 0.00 | 0.11 | 0.00 | 0.10 | 0.09 | 0.04 | 0.09 | 0.05 | |||
5 | 200 | 0 | 4.6 | 4.6 | 4.8 | 4.6 | 41.2 | 41.2 | 41.2 | 40.6 | 0.00 | 0.05 | 0.00 | 0.05 | 0.12 | 0.09 | 0.12 | 0.09 | |
0.5 | 4.6 | 4.6 | 4.6 | 4.4 | 40.8 | 40.8 | 40.6 | 40.4 | 0.00 | 0.05 | 0.00 | 0.05 | 0.12 | 0.09 | 0.12 | 0.09 | |||
2 | 5.4 | 5.4 | 5.6 | 5.4 | 32.2 | 32.4 | 32.6 | 32.4 | 0.00 | 0.08 | 0.00 | 0.07 | 0.13 | 0.08 | 0.13 | 0.08 | |||
500 | 0 | 5.2 | 5.2 | 5.2 | 5.2 | 76.6 | 76.6 | 76.8 | 76.6 | 0.00 | 0.05 | 0.00 | 0.05 | 0.07 | 0.06 | 0.07 | 0.06 | ||
0.5 | 4.6 | 4.6 | 4.6 | 4.6 | 75.6 | 75.6 | 75.8 | 75.8 | 0.00 | 0.05 | 0.00 | 0.05 | 0.08 | 0.06 | 0.08 | 0.06 | |||
2 | 4.2 | 4.2 | 4.2 | 4.2 | 69.8 | 69.8 | 69.4 | 69.4 | 0.00 | 0.08 | 0.00 | 0.07 | 0.08 | 0.05 | 0.08 | 0.05 | |||
7 | 3 | 200 | 0 | 7.6 | 7.2 | 7.4 | 7.2 | 40.8 | 40.8 | 40.8 | 40.8 | 0.00 | 0.05 | 0.00 | 0.05 | 0.12 | 0.09 | 0.12 | 0.09 |
0.5 | 5.4 | 5.2 | 5.6 | 5.2 | 40.0 | 40.0 | 40.2 | 40.0 | 0.00 | 0.06 | 0.00 | 0.06 | 0.12 | 0.08 | 0.12 | 0.08 | |||
2 | 5.2 | 5.2 | 5.2 | 5.2 | 36.6 | 36.6 | 36.6 | 36.4 | 0.01 | 0.08 | 0.01 | 0.08 | 0.13 | 0.08 | 0.13 | 0.08 | |||
500 | 0 | 5.2 | 5.2 | 5.2 | 5.2 | 76.8 | 76.6 | 77.0 | 76.8 | 0.00 | 0.05 | 0.00 | 0.05 | 0.07 | 0.05 | 0.07 | 0.05 | ||
0.5 | 5.2 | 5.2 | 5.2 | 5.2 | 75.0 | 75.0 | 75.0 | 75.0 | 0.00 | 0.05 | 0.00 | 0.05 | 0.08 | 0.06 | 0.08 | 0.06 | |||
2 | 3.6 | 3.6 | 3.6 | 3.6 | 67.8 | 67.8 | 67.8 | 67.8 | 0.00 | 0.08 | 0.00 | 0.08 | 0.08 | 0.05 | 0.09 | 0.05 | |||
5 | 200 | 0 | 5.2 | 5.2 | 5.2 | 5.2 | 42.6 | 42.6 | 42.8 | 42.6 | 0.00 | 0.03 | 0.00 | 0.03 | 0.11 | 0.09 | 0.11 | 0.09 | |
0.5 | 5.2 | 5.0 | 5.2 | 5.0 | 46.0 | 45.6 | 46.0 | 46.0 | 0.00 | 0.03 | 0.00 | 0.03 | 0.11 | 0.10 | 0.11 | 0.10 | |||
2 | 6.4 | 6.4 | 6.4 | 6.4 | 41.2 | 40.6 | 41.2 | 40.6 | 0.00 | 0.05 | 0.01 | 0.05 | 0.12 | 0.09 | 0.12 | 0.09 | |||
500 | 0 | 6.8 | 6.8 | 6.8 | 6.8 | 80.8 | 80.8 | 80.8 | 80.6 | 0.00 | 0.03 | 0.00 | 0.03 | 0.07 | 0.06 | 0.07 | 0.06 | ||
0.5 | 3.2 | 3.0 | 3.2 | 3.2 | 80.8 | 80.8 | 80.6 | 80.6 | 0.00 | 0.03 | 0.00 | 0.03 | 0.07 | 0.06 | 0.07 | 0.06 | |||
2 | 5.2 | 5.2 | 5.4 | 5.2 | 73.6 | 73.6 | 73.4 | 73.2 | 0.01 | 0.06 | 0.01 | 0.06 | 0.07 | 0.05 | 0.08 | 0.06 | |||
10 | 3 | 200 | 0 | 4.2 | 4.2 | 4.2 | 4.2 | 42.6 | 42.4 | 42.6 | 42.2 | 0.00 | 0.04 | 0.00 | 0.04 | 0.11 | 0.09 | 0.12 | 0.09 |
0.5 | 5.2 | 5.2 | 5.2 | 5.2 | 42.0 | 41.6 | 42.2 | 41.6 | 0.00 | 0.04 | 0.00 | 0.04 | 0.11 | 0.09 | 0.11 | 0.09 | |||
2 | 4.0 | 3.6 | 4.0 | 3.6 | 39.2 | 39.0 | 39.2 | 39.0 | 0.00 | 0.07 | 0.00 | 0.07 | 0.13 | 0.08 | 0.13 | 0.09 | |||
500 | 0 | 4.8 | 4.4 | 4.6 | 4.4 | 79.4 | 79.2 | 79.4 | 79.2 | 0.00 | 0.04 | 0.00 | 0.04 | 0.07 | 0.06 | 0.07 | 0.06 | ||
0.5 | 6.2 | 6.2 | 6.2 | 6.2 | 78.8 | 78.8 | 78.8 | 78.8 | 0.00 | 0.04 | 0.00 | 0.04 | 0.07 | 0.06 | 0.07 | 0.06 | |||
2 | 8.2 | 8.2 | 8.2 | 8.2 | 76.0 | 75.8 | 75.8 | 75.6 | 0.00 | 0.07 | 0.00 | 0.06 | 0.08 | 0.05 | 0.08 | 0.05 | |||
5 | 200 | 0 | 5.0 | 5.0 | 5.2 | 5.0 | 46.0 | 45.8 | 45.4 | 45.4 | 0.00 | 0.02 | 0.00 | 0.02 | 0.10 | 0.09 | 0.10 | 0.09 | |
0.5 | 5.6 | 5.6 | 6.0 | 5.6 | 47.2 | 46.8 | 47.2 | 46.4 | 0.00 | 0.02 | 0.00 | 0.02 | 0.11 | 0.09 | 0.11 | 0.10 | |||
2 | 4.4 | 4.2 | 4.4 | 4.0 | 42.0 | 41.6 | 42.0 | 41.6 | 0.00 | 0.04 | 0.00 | 0.04 | 0.11 | 0.09 | 0.11 | 0.09 | |||
500 | 0 | 5.6 | 5.4 | 5.6 | 5.6 | 84.4 | 84.2 | 84.4 | 84.2 | 0.00 | 0.02 | 0.00 | 0.02 | 0.07 | 0.06 | 0.07 | 0.06 | ||
0.5 | 6.2 | 6.2 | 6.2 | 6.2 | 83.8 | 83.8 | 84.2 | 83.8 | 0.00 | 0.02 | 0.00 | 0.02 | 0.07 | 0.06 | 0.07 | 0.06 | |||
2 | 6.6 | 6.4 | 6.6 | 6.4 | 81.8 | 81.6 | 81.8 | 81.6 | 0.00 | 0.04 | 0.00 | 0.04 | 0.07 | 0.06 | 0.07 | 0.06 |