Table 1 Power estimated with the Raschpower procedure for different values of the variance of the latent variable ( \(\sigma ^{2}_{\theta }\) ), the number of items ( J ), the group effect ( γ ) and the sample size per group ( N g )
J | N g | γ | \({\sigma ^{2}_{\theta }=0.25}\) | \({\sigma ^{2}_{\theta }=0.5}\) | \({\sigma ^{2}_{\theta }=0.75}\) | \({\sigma ^{2}_{\theta }=1}\) | \({\sigma ^{2}_{\theta }=2}\) | \({\sigma ^{2}_{\theta }=4}\) | \({\sigma ^{2}_{\theta }=9}\) |
|---|---|---|---|---|---|---|---|---|---|
3 | 50 | 0.1 | 0.058 | 0.054 | 0.051 | 0.049 | 0.044 | 0.039 | 0.034 |
0.2 | 0.117 | 0.104 | 0.095 | 0.088 | 0.072 | 0.058 | 0.046 | ||
0.5 | 0.482 | 0.417 | 0.367 | 0.328 | 0.237 | 0.162 | 0.104 | ||
0.8 | 0.859 | 0.793 | 0.731 | 0.677 | 0.511 | 0.343 | 0.199 | ||
3 | 200 | 0.1 | 0.117 | 0.104 | 0.095 | 0.088 | 0.072 | 0.058 | 0.046 |
0.2 | 0.337 | 0.289 | 0.254 | 0.229 | 0.168 | 0.119 | 0.081 | ||
0.5 | 0.969 | 0.938 | 0.900 | 0.859 | 0.702 | 0.495 | 0.287 | ||
0.8 | 1.000 | 1.000 | 0.999 | 0.998 | 0.978 | 0.875 | 0.607 | ||
3 | 500 | 0.1 | 0.229 | 0.198 | 0.176 | 0.159 | 0.121 | 0.090 | 0.064 |
0.2 | 0.682 | 0.602 | 0.538 | 0.485 | 0.351 | 0.234 | 0.141 | ||
0.5 | 1.000 | 1.000 | 0.999 | 0.998 | 0.976 | 0.868 | 0.598 | ||
0.8 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 0.998 | 0.942 | ||
9 | 50 | 0.1 | 0.084 | 0.071 | 0.064 | 0.059 | 0.049 | 0.041 | 0.036 |
0.2 | 0.209 | 0.164 | 0.138 | 0.121 | 0.088 | 0.065 | 0.049 | ||
0.5 | 0.798 | 0.682 | 0.579 | 0.501 | 0.325 | 0.200 | 0.118 | ||
0.8 | 0.991 | 0.970 | 0.929 | 0.877 | 0.674 | 0.433 | 0.234 | ||
9 | 200 | 0.1 | 0.213 | 0.165 | 0.138 | 0.121 | 0.088 | 0.065 | 0.049 |
0.2 | 0.643 | 0.505 | 0.415 | 0.352 | 0.227 | 0.144 | 0.090 | ||
0.5 | 1.000 | 0.998 | 0.992 | 0.977 | 0.856 | 0.612 | 0.340 | ||
0.8 | 1.000 | 1.000 | 1.000 | 1.000 | 0.998 | 0.948 | 0.696 | ||
9 | 500 | 0.1 | 0.453 | 0.345 | 0.281 | 0.239 | 0.158 | 0.106 | 0.071 |
0.2 | 0.958 | 0.878 | 0.788 | 0.707 | 0.482 | 0.295 | 0.163 | ||
0.5 | 1.000 | 1.000 | 1.000 | 1.000 | 0.998 | 0.944 | 0.686 | ||
0.8 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 0.974 | ||
15 | 50 | 0.1 | 0.094 | 0.077 | 0.067 | 0.061 | 0.050 | 0.042 | 0.036 |
0.2 | 0.228 | 0.181 | 0.149 | 0.129 | 0.091 | 0.067 | 0.050 | ||
0.5 | 0.768 | 0.695 | 0.607 | 0.532 | 0.346 | 0.210 | 0.122 | ||
0.8 | 0.989 | 0.962 | 0.932 | 0.895 | 0.703 | 0.455 | 0.244 | ||
15 | 200 | 0.1 | 0.263 | 0.190 | 0.154 | 0.132 | 0.092 | 0.067 | 0.050 |
0.2 | 0.737 | 0.578 | 0.467 | 0.392 | 0.245 | 0.152 | 0.093 | ||
0.5 | 1.000 | 1.000 | 0.996 | 0.987 | 0.887 | 0.642 | 0.355 | ||
0.8 | 1.000 | 1.000 | 1.000 | 1.000 | 0.999 | 0.961 | 0.719 | ||
15 | 500 | 0.1 | 0.562 | 0.408 | 0.322 | 0.269 | 0.170 | 0.111 | 0.072 |
0.2 | 0.987 | 0.932 | 0.850 | 0.766 | 0.521 | 0.313 | 0.170 | ||
0.5 | 1.000 | 1.000 | 1.000 | 1.000 | 0.999 | 0.957 | 0.709 | ||
0.8 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 0.980 |