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. 2013 Feb 28;8(2):e57279. doi: 10.1371/journal.pone.0057279

Table 3. Power estimated in the simulation study (1−Inline graphic) and using the Cramer-Rao’s bound (1−Inline graphic) for different values of the sample size in each group (Inline graphic), the group effect (Inline graphic), the variance of the latent variable (Inline graphic), the spacing regularity of the items and the gap between the global mean of the latent variable and the mean of the distribution of the item difficulties (Inline graphic).

Normal distribution Mixture of normal distributions
Inline graphic Inline graphic Inline graphic Inline graphic Inline graphic Inline graphic
Inline graphic Inline graphic Inline graphic 1−Inline graphic/1−Inline graphic 1−Inline graphic/1−Inline graphic 1−Inline graphic/1−Inline graphic 1−Inline graphic/1−Inline graphic 1−Inline graphic/1−Inline graphic 1−Inline graphic/1−Inline graphic
50 0.2 0.25 0.172/0.155 0.175/0.151 0.194/0.138 0.164/0.153 0.153/0.150 0.155/0.140
1 0.116/0.104 0.110/0.099 0.085/0.086 0.113/0.102 0.096/0.099 0.095/0.089
4 0.077/0.062 0.061/0.059 0.066/0.051 0.071/0.061 0.081/0.060 0.090/0.054
9 0.073/0.048 0.056/0.046 0.055/0.041 0.067/0.048 0.058*/0.047 0.058/0.044
0.5 0.25 0.645/0.652 0.685/0.635 0.658/0.586 0.652/0.645 0.696/0.633 0.680/0.589
1 0.419/0.414 0.405/0.389 0.312/0.316 0.405/0.402 0.387/0.390 0.357/0.332
4 0.171/0.182 0.170/0.168 0.171/0.127 0.186/0.178 0.177/0.172 0.177/0.141
9 0.131/0.111 0.115/0.103 0.109/0.082 0.115/0.110 0.114*/0.106 0.112/0.091
0.8 0.25 0.974/0.962 0.973/0.955 0.964/0.933 0.971/0.959 0.967/0.954 0.966/0.936
1 0.796/0.794 0.794/0.762 0.672/0.660 0.772/0.780 0.758/0.764 0.685/0.682
4 0.387/0.390 0.386/0.356 0.404/0.261 0.412/0.382 0.389/0.368 0.398/0.293
9 0.211/0.218 0.233/0.198 0.224/0.146 0.215/0.215 0.250*/0.206 0.225/0.168
100 0.2 0.25 0.291/0.266 0.294/0.258 0.286/0.235 0.289/0.262 0.275/0.257 0.259/0.236
1 0.188/0.166 0.171/0.156 0.147/0.132 0.167/0.161 0.169/0.157 0.140/0.137
4 0.090/0.086 0.094/0.081 0.109/0.068 0.089/0.085 0.111/0.083 0.102/0.072
9 0.068/0.062 0.075/0.059 0.069/0.051 0.073/0.061 0.069/0.060 0.069/0.054
0.5 0.25 0.918/0.914 0.933/0.904 0.916/0.869 0.925/0.909 0.921/0.902 0.921/0.872
1 0.693/0.694 0.686/0.661 0.537/0.557 0.667/0.679 0.659/0.661 0.547/0.580
4 0.311/0.319 0.348/0.291 0.350/0.213 0.309/0.311 0.300/0.300 0.344/0.240
9 0.166/0.180 0.159/0.164 0.164/0.123 0.171/0.178 0.177/0.170 0.182/0.140
0.8 0.25 1.000/1.000 1.000/0.999 1.000/0.998 1.000/0.999 0.999/0.999 0.999/0.998
1 0.975/0.976 0.972/0.966 0.925/0.919 0.968/0.972 0.963/0.966 0.921/0.932
4 0.653/0.662 0.679/0.615 0.667/0.460 0.665/0.651 0.664/0.631 0.670/0.517
9 0.391/0.386 0.373/0.348 0.378/0.249 0.388/0.381 0.383/0.364 0.379/0.291
200 0.2 0.25 0.450/0.472 0.452/0.457 0.467/0.416 0.484/0.464 0.491/0.455 0.475/0.420
1 0.318/0.287 0.282/0.269 0.237/0.221 0.284/0.279 0.287/0.270 0.247/0.231
4 0.118/0.132 0.137/0.123 0.133/0.097 0.122/0.129 0.109/0.126 0.124/0.106
9 0.091/0.086 0.079/0.080 0.095/0.066 0.093/0.085 0.086/0.082 0.082/0.072
0.5 0.25 1.000/0.997 0.999/0.996 0.999/0.992 1.000/0.997 0.996/0.996 0.998/0.992
1 0.942/0.937 0.922/0.919 0.850/0.845 0.928/0.929 0.915/0.919 0.873/0.864
4 0.532/0.558 0.577/0.513 0.545/0.378 0.559/0.546 0.577/0.528 0.525/0.427
9 0.324/0.315 0.308/0.284 0.313/0.205 0.301/0.310 0.305/0.296 0.291/0.238
0.8 0.25 1.000/1.000 1.000/1.000 1.000/1.000 1.000/1.000 1.000/1.000 1.000/1.000
1 1.000/1.000 1.000/1.000 0.998/0.997 1.000/1.000 1.000/1.000 0.998/0.998
4 0.924/0.920 0.921/0.890 0.920/0.752 0.933/0.913 0.913/0.901 0.904/0.810
9 0.650/0.656 0.676/0.602 0.660/0.442 0.647/0.649 0.666/0.625 0.648/0.512
300 0.2 0.25 0.647/0.639 0.636/0.622 0.649/0.572 0.636/0.630 0.628/0.618 0.644/0.576
1 0.413/0.402 0.377/0.377 0.306/0.308 0.397/0.391 0.383/0.378 0.355/0.323
4 0.174*/0.177 0.189/0.163 0.193/0.125 0.175/0.173 0.176/0.167 0.176/0.138
9 0.131/0.108 0.117/0.100 0.097/0.080 0.112/0.107 0.110/0.103 0.098/0.089
0.5 0.25 1.000/1.000 1.000/1.000 1.000/1.000 1.000/1.000 1.000/1.000 1.000/1.000
1 0.993/0.990 0.986/0.984 0.944/0.954 0.988/0.987 0.979/0.984 0.966/0.963
4 0.728*/0.732 0.714/0.685 0.718/0.524 0.743/0.720 0.724/0.701 0.728/0.585
9 0.462/0.440 0.456/0.397 0.441/0.284 0.428/0.434 0.445/0.415 0.451/0.332
0.8 0.25 1.000/1.000 1.000/1.000 1.000/1.000 1.000/1.000 1.000/1.000 1.000/1.000
1 1.000/1.000 1.000/1.000 1.000/1.000 1.000/1.000 1.000/1.000 1.000/1.000
4 0.984*/0.985 0.988/0.974 0.982/0.898 0.988/0.982 0.988/0.978 0.985/0.935
9 0.825/0.825 0.835/0.776 0.834/0.603 0.828/0.819 0.824/0.797 0.833/0.684
500 0.2 0.25 0.824/0.848 0.859/0.834 0.851/0.789 0.853/0.841 0.864/0.831 0.854/0.793
1 0.587/0.599 0.546/0.566 0.458/0.470 0.600/0.584 0.585/0.567 0.469*/0.491
4 0.278/0.265 0.271/0.242 0.259/0.180 0.263/0.259 0.271/0.250 0.246/0.201
9 0.170/0.153 0.120/0.140 0.165/0.107 0.145/0.151 0.169/0.145 0.152/0.121
0.5 0.25 1.000/1.000 1.000/1.000 1.000/1.000 1.000/1.000 1.000/1.000 1.000/1.000
1 1.000/1.000 0.999/1.000 0.998/0.997 0.998/1.000 1.000/1.000 0.996*/0.998
4 0.913/0.915 0.917/0.883 0.925/0.742 0.900/0.907 0.932/0.895 0.909/0.801
9 0.660/0.647 0.672/0.593 0.639/0.435 0.647/0.639 0.626/0.615 0.634/0.504
0.8 0.25 1.000/1.000 1.000/1.000 1.000/1.000 1.000/1.000 1.000/1.000 1.000/1.000
1 1.000/1.000 1.000/1.000 1.000/1.000 1.000/1.000 1.000/1.000 1.000*/1.000
4 1.000/1.000 0.999/0.999 0.998/0.987 0.999/0.999 0.999/0.999 0.999/0.994
9 0.947/0.962 0.967/0.939 0.949/0.818 0.971/0.959 0.960/0.950 0.975/0.883

Results for a questionnaire composed of 5 items.

*

The 95% confidence interval of the type I error does not contain the expected value of 5%.