## 3 Results
### Incisor (1.1)  
The ANOVA test is performed to verify, for each point, whether the mean force differs significantly among the aligners. In the case of a significant test (_p_-value < 0.05), it is concluded that at least one aligner has a mean value different from the others. Before the test, the homoscedasticity assumption was checked, and since it was not satisfied, the robust version of the ANOVA test by [PERSON] was chosen. For all points, it was found that at least one aligner exhibits a significant difference in force compared to the others (_p_-value < 0.001), with very large eta-squared values indicating highly pronounced differences among the aligners. Post hoc comparisons conducted using [PERSON]'s test reveal that all aligners, for each point, have significantly different force values. * At the gingival point, the NHVH aligner exerted the highest average force, followed by NHH, F22, NHZ, and AS;
* At the middle point, NHVH again showed the highest force, followed by NHH, NHZ, F22, and AS;
* At the incisal point, NHH had the highest force, followed by NHVH, NHZ, F22, and AS (Table 2). \begin{table}
\begin{tabular}{l l l l} \hline \hline  & **Force (N)** & **Force (N)** & **Force (N)** \\ \hline Inter-Item Correlation Matrix Gingival Incisor & 1.00 & 0.90 & 0.96 \\  & 0.90 & 1.00 & 0.92 \\  & 0.96 & 0.92 & 1.00 \\ \hline Inter-Item Correlation Matrix Middle Incisor & 1.00 & 0.94 & 0.94 \\  & 0.94 & 1.00 & 0.93 \\  & 0.94 & 0.93 & 1.00 \\ \hline Inter-Item Correlation Matrix Incisal Incisor & 1.00 & 0.94 & 0.96 \\  & 0.94 & 1.00 & 0.92 \\  & 0.96 & 0.92 & 1.00 \\ \hline Inter-Item Correlation Matrix Gingival Molar & 1.00 & 0.97 & 0.92 \\  & 0.97 & 1.00 & 0.93 \\  & 0.92 & 0.93 & 1.00 \\ \hline Inter-Item Correlation Matrix Middle Molar & 1.00 & 0.91 & 0.91 \\  & 0.91 & 1.00 & 0.92 \\  & 0.91 & 0.92 & 1.00 \\ \hline Inter-Item Correlation Matrix Oclusal Molar & 1.00 & 0.96 & 0.96 \\  & 0.96 & 1.00 & 0.96 \\  & 0.96 & 0.96 & 1.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Inter-Item Correlation Matrix. Additionally, when comparing the force across the three measurement points, it was found that for all aligners, the highest average force occurred at the incisal point, followed by the middle point, and finally the gingival point. This was consistent across all aligners, as confirmed by the robust ANOVA test and post hoc Tamhane comparisons, which showed significant differences between the points for each aligner. Regarding the initial and final force values, as well as the average percentage of stress decay, the mean values for each of the five aligners were calculated for the incisors (1.1). As for stress decay, the Kruskal-Wallis non-parametric test indicated no significant differences (\(p\)-value \(>\) 0.05) in stress relaxation between the aligners on the 1.1 tooth (Table 3). In Figure 5, the analysis of the force applied to the upper central incisor shows that aligners exhibited significantly different forces at each measured point. The highest forces at the gingival and middle points were observed with the NHVH model, followed by the NHH, F22, NHZ, and finally AS, which recorded much lower values. This highlights the effectiveness of the thickness gradients in stabilizing force in the gingival areas, where dissipation naturally occurs, confirming the design's efficacy. At the incisal point, the NHH generated the highest force (16.3 N), followed closely by the NHVH (14.7 N), with the AS showing significantly lower values. Despite the statistical significance, the difference between NHH and NHVH is minimal and within acceptable limits. In summary, NHVH achieves the highest forces at the gingival and middle points while maintaining adequate force at the incisal point. The highest average force was recorded at the incisal point, followed by the middle and gingival points, confirming natural force dissipation. Additionally, the NHZ aligners showed lower forces, particularly at the gingival point, likely due to their zenith cut geometry.