Table 2 Power estimated with the Raschpower procedure for different values of the sample size per group ( N g ), the group effect ( γ ), the variance of the item distribution \(\left (\sigma ^{2}_{\delta _{j}}\right)\) and the gap between the means of the two normal distributions ( a ) when the variance of the latent variable \(\sigma ^{2}_{\theta }\) =1 and the number of items J =7
N g | γ | \({\sigma ^{2}_{\delta _{j}}}\) | a=0 | \({a=\pm \frac {1}{4}\sigma _{\delta _{j}}}\) | \({a=\pm \frac {1}{2}\sigma _{\delta _{j}}}\) | \({a=\pm \frac {3}{4}\sigma _{\delta _{j}}}\) |
|---|---|---|---|---|---|---|
50 | 0.1 | 0.25 | 0.057 | 0.057 | 0.057 | 0.057 |
1 | 0.057 | 0.057 | 0.057 | 0.057 | ||
8 | 0.055 | 0.054 | 0.053 | 0.052 | ||
50 | 0.2 | 0.25 | 0.115 | 0.115 | 0.115 | 0.115 |
1 | 0.114 | 0.114 | 0.114 | 0.113 | ||
8 | 0.107 | 0.106 | 0.103 | 0.099 | ||
50 | 0.5 | 0.25 | 0.475 | 0.474 | 0.474 | 0.473 |
1 | 0.472 | 0.471 | 0.469 | 0.466 | ||
8 | 0.432 | 0.427 | 0.413 | 0.387 | ||
50 | 0.8 | 0.25 | 0.854 | 0.855 | 0.856 | 0.855 |
1 | 0.852 | 0.852 | 0.850 | 0.848 | ||
8 | 0.815 | 0.810 | 0.794 | 0.764 | ||
200 | 0.1 | 0.25 | 0.116 | 0.116 | 0.116 | 0.116 |
1 | 0.115 | 0.115 | 0.114 | 0.114 | ||
8 | 0.107 | 0.106 | 0.103 | 0.099 | ||
200 | 0.2 | 0.25 | 0.333 | 0.332 | 0.332 | 0.331 |
1 | 0.329 | 0.328 | 0.326 | 0.324 | ||
8 | 0.299 | 0.296 | 0.286 | 0.268 | ||
200 | 0.5 | 0.25 | 0.968 | 0.968 | 0.968 | 0.967 |
1 | 0.966 | 0.966 | 0.965 | 0.964 | ||
8 | 0.947 | 0.945 | 0.936 | 0.918 | ||
200 | 0.8 | 0.25 | 1.000 | 1.000 | 1.000 | 1.000 |
1 | 1.000 | 1.000 | 1.000 | 1.000 | ||
8 | 1.000 | 1.000 | 1.000 | 1.000 | ||
500 | 0.1 | 0.25 | 0.226 | 0.226 | 0.226 | 0.225 |
1 | 0.223 | 0.223 | 0.222 | 0.220 | ||
8 | 0.204 | 0.202 | 0.195 | 0.184 | ||
500 | 0.2 | 0.25 | 0.675 | 0.675 | 0.674 | 0.673 |
1 | 0.669 | 0.668 | 0.666 | 0.662 | ||
8 | 0.621 | 0.615 | 0.596 | 0.563 | ||
500 | 0.5 | 0.25 | 1.000 | 1.000 | 1.000 | 1.000 |
1 | 1.000 | 1.000 | 1.000 | 1.000 | ||
8 | 1.000 | 1.000 | 1.000 | 1.000 | ||
500 | 0.8 | 0.25 | 1.000 | 1.000 | 1.000 | 1.000 |
1 | 1.000 | 1.000 | 1.000 | 1.000 | ||
8 | 1.000 | 1.000 | 1.000 | 1.000 |