## 2 Materials and Methods
### Statistical Analysis  
The difference among the groups were analyzed for significance using a variance analysis. The Kolmogorov-Smirnov test was performed to determine the variable distribution. A statistical normal distribution was recorded for all measurements, apart from the variable area and volume, which showed a non-normal distribution. For the comparison between Class I and Class II, a t-student test was used for the parametric variables (Table 3) and a Mann-Whitney test for the non-parametric variables (Table 4). Figure 2: (**a**) The connection of the most apical points of the dental–gingival junction of all erupted teeth; (**b**) the isolation of the previously selected palatine vault; (**c**) an illustration of palatal vault placement on the reference grid for the measurement of palatal area and volume; (**d**) a palatal section, with the sagittal plane passing through the median palatine suture; (**e**) the palatal length measured on the divided scan obtained. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Variables** & **Hypodivergent** & \multicolumn{2}{c}{**Normaldivergent**} & \multicolumn{2}{c}{**Hyperdivergent**} & \multicolumn{1}{c}{\(p\)**} \\ \hline  & **Mean** & **SD** & **Mean** & **SD** & **Mean** & **SD** & \\ \hline Intercanine distance (mm) & 24.97 & 2.31 & 25.17 & 2.09 & 24.16 & 2.28 & 0.122 \\ Interpremolar distance (mm) & 27.56 & 2.31 & 27.33 & 2.13 & 26.48 & 2.67 & 0.142 \\ Interpolar distance (mm) & 34.36 & 2.34 & 33.39 & 2.72 & 32.59 & 2.71 & 0.026 \\ Palatal depth (mm) & 31.42 & 2.78 & 31.44 & 3.38 & 31.35 & 2.31 & 0.991 \\ Palatal anterior height (mm) & 4.67 & 1.62 & 5.27 & 1.98 & 5.06 & 1.96 & 0.336 \\ Palatal posterior height (mm) & 16.37 & 2.26 & 16.07 & 2.45 & 16.81 & 2.89 & 0.422 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Descriptive statistics and statistical comparisons on palatal area and volume between hypodivergent, normodivergent, and hyperdivergent Class II subjects. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Variables** & **Class I** & \multicolumn{2}{c}{**Class II**} & \multicolumn{1}{c}{\(p\)**} \\ \hline  & **Mean** & **SD** & **Mean** & **SD** & \\ \hline Intercanine distance (mm) & 25.12 & 1.91 & 24.87 & 2.22 & 0.411 a \\ Interpremolar distance(mm) & 26.93 & 1.85 & 27.19 & 2.34 & 0.384 b \\ Interpolar distance (mm) & 33.34 & 2.82 & 33.48 & 2.67 & 0.742 a \\ Palatal depth (mm) & 31.99 & 2.07 & 31.41 & 2.96 & 0.113 b \\ Anterior palatal height (mm) & 4.65 & 1.82 & 5.05 & 1.88 & 0.143 a \\ Posterior palatal height (mm) & 15.54 & 2.04 & 16.34 & 2.51 & 0.021 a \\ \hline \hline \end{tabular}  
* a: The \(p\)-values of the \(t\)-student test with equal variances assumed; b: The \(p\)-values of the \(t\)-student test with equal variances not assumed.  
\end{table} 
Table 3: Descriptive statistics and statistical comparisons on bidimensional values between Class I and Class II subjects. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Variables** & **Class I** & \multicolumn{2}{c}{**Class II**} & \multicolumn{1}{c}{\(p\)**} \\ \hline  & **Median (min;max)** & \multicolumn{2}{c}{**Median (min;max)**} & \multicolumn{2}{c}{} \\ \hline Area (mm\({}^{2}\)) & 1290.09 (841.17;1561.94) & 1235.44 (827.11;10,001.50) & 0.026 \\ Volume (mm\({}^{3}\)) & 5995.08 (3411.47;8999.72) & 5865.62 (2416.07;59,844.61) & 0.386 \\ \hline \hline \end{tabular}  
* For the comparison between hypodivergent, normodivergent, and hyperdivergent subjects in Class II, an Anova test was used for the parametric variables (Table 5) and a Kruskal–Wallis test for the non-parametric values (Table 6).  
\end{table} 
Table 4: Descriptive statistics and statistical comparisons of palatal area and volume between Class I and Class II.