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. 2024 Sep 8;14:20900. doi: 10.1038/s41598-024-71262-0

Table 7.

Estimated marginal means and 95% CIs for the categorical variables within the hierarchical mixed-model regression framework calculated for each specialty.

Factor Level Layperson Orthodontist Prostho-Resto
Mean SE 95% CI Mean SE 95% CI Mean SE 95% CI
Judge’s Sex Female 4.964 0.125 4.719 5.209 4.543 0.278 3.986 5.100 4.226 0.258 3.708 4.745
Male 4.801 0.205 4.397 5.205 5.587 0.331 4.922 6.251 4.999 0.429 4.128 5.870
Facial index 80% (Euryprosopic) 4.622 0.127 4.372 4.871 4.834 0.227 4.382 5.285 4.341 0.259 3.821 4.861
86% (Mesoprosopic) 5.101* 0.127 4.852 5.351 5.243* 0.227 4.792 5.695 4.846* 0.259 4.325 5.366
94% (Leptoprosopic) 4.925 0.127 4.676 5.174 5.118* 0.226 4.667 5.569 4.651* 0.259 4.132 5.171
Midline deviation 4 mm to the left 3.854 0.142 3.576 4.133 3.576 0.253 3.076 4.076 3.101 0.290 2.523 3.678
3 mm to the left 4.363 0.142 4.085 4.642 4.127 0.253 3.627 4.627 3.777 0.290 3.199 4.355
2 mm to the left 4.468 0.138 4.196 4.739 4.780 0.246 4.292 5.269 4.110 0.283 3.546 4.674
1 mm to the left 5.580* 0.142 5.301 5.859 6.039* 0.253 5.538 6.539 5.605* 0.290 5.028 6.183
No midline deviation 5.767* 0.113 5.544 5.989 6.385* 0.203 5.977 6.794 6.129* 0.231 5.659 6.599
1 mm to the right 5.871* 0.142 5.592 6.149 6.290* 0.253 5.790 6.791 5.863* 0.290 5.285 6.440
2 mm to the right 5.166 0.142 4.887 5.444 5.739 0.253 5.239 6.240 5.158 0.290 4.580 5.736
3 mm to the right 4.701 0.142 4.422 4.979 4.719 0.253 4.218 5.219 4.272 0.290 3.694 4.850
4 mm to the right 4.175 0.142 3.897 4.454 3.930 0.253 3.429 4.430 3.501 0.290 2.923 4.078
Midline roll 15° to the left 4.429 0.142 4.150 4.709 4.565 0.253 4.063 5.066 4.071 0.291 3.492 4.651
10° to the left 4.325 0.142 4.046 4.605 4.401 0.253 3.899 4.903 3.747 0.291 3.168 4.327
5° to the left 4.534 0.142 4.254 4.813 5.102 0.253 4.600 5.604 4.367 0.291 3.787 4.946
No midline roll 5.567* 0.112 5.345 5.788 5.979* 0.202 5.573 6.386 5.652* 0.230 5.184 6.120
5° to the right 5.132 0.142 4.852 5.411 5.292 0.253 4.791 5.794 4.805 0.291 4.225 5.384
10° to the right 4.948 0.142 4.668 5.227 5.041 0.253 4.539 5.543 4.738 0.291 4.158 5.317
15° to the right 5.244 0.142 4.965 5.524 5.075 0.253 4.573 5.577 4.909 0.291 4.330 5.489

SE, standard error; CI, confidence interval. Within each factor (categorical predictor), asterisks highlight the highest beauty score as well as features that are not significantly different from the top score according to the Bonferroni post hoc test at a 0.008 level of significance; in other words, a number of asterisks in a predictor section mark the zone of acceptability. A lack of asterisks within the ‘sex’ variable means non-significant main effects estimated using the mixed-model regression analyses.