## 3 Results  
Table 4 summarizes the inferential analysis of the cranial landmarks used for the present study. It was shown that none of the variables tested resulted in statistical significance (\(p>0.05\)) regarding all three directions of space (x, y, and z axes). Thus, the reliability of RFo, LFo, ELSA, RPo, and LPo was confirmed providing a stable three-dimensional reference system for maxillary dental and skeletal measurements.  
Table 5 shows the starting forms comparison between Hyrax and Haas groups. Based on the fact that none of the skeletal measurements were statistically significant (\(p>0.05\)) between groups before the treatment start (T0), it can be postulated that there was homogeneity among the compared groups; statistically significant differences between dental measurements of the two groups, except for 6 + 6 distance, could be correlated to a different compensation of dental structures, and were irrelevant since the main outcome of the study was the observation of skeletal expansion.  
Finally, Table 6 shows the results of the inferential analysis of the differences within the same group and between the Hyrax and Hass group in the interval T1-T0.  
\begin{table}
\begin{tabular}{l c c c c c c c c c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Transversal (x)**} & \multicolumn{4}{c}{**Sagittal (y)**} & \multicolumn{4}{c}{**Vertical (z)**} \\  & \multicolumn{3}{c}{**Hyrax**} & \multicolumn{3}{c}{**Haas**} & \multicolumn{3}{c}{**Hyrax**} & \multicolumn{3}{c}{**Haas**} & \multicolumn{3}{c}{**Hyrax**} & \multicolumn{3}{c}{**Haas**} \\ \cline{2-19}  & **Mean** & **SD** & \(p\) & **Mean** & **SD** & \(p\) & **Mean** & **SD** & \(p\) & **Mean** & **SD** & \(p\) & **Mean** & **SD** & \(p\) & **Mean** & **SD** & \(p\) \\ \hline RFs & 0.13 & 0.41 & 0.11 & 0.02 & 0.72 & 0.89 & \(-\)0.43 & 1.11 & 0.99 & \(-\)0.61 & 1.98 & 0.54 & \(-\)0.69 & 0.82 & 0.36 & \(-\)0.08 & 0.70 & 0.75 \\ LFs & \(-\)0.33 & 0.48 & 0.09 & 0.05 & 0.90 & 0.88 & 0.16 & 1.09 & 0.70 & 0.61 & 1.61 & 0.32 & \(-\)0.29 & 0.62 & 0.23 & \(-\)0.11 & 0.66 & 0.38 \\ ELSA & 0.03 & 0.30 & 0.76 & \(-\)0.07 & 0.27 & 0.49 & \(-\)0.13 & 0.15 & 0.06 & 0.05 & 0.25 & 0.57 & \(-\)0.05 & 0.30 & 0.63 & \(-\)0.05 & 0.31 & 0.63 \\ RPo & 0.00 & 0.05 & 0.13 & 0.01 & 0.05 & 0.55 & 0.40 & 1.14 & 0.35 & \(-\)0.06 & 2.35 & 0.95 & 0.30 & 0.50 & 0.13 & 0.33 & 0.73 & 0.24 \\ LPo & \(-\)0.11 & 0.26 & 0.29 & \(-\)0.09 & 0.25 & 0.32 & 0.06 & 0.73 & 0.83 & 0.39 & 1.32 & 0.43 & 0.32 & 0.83 & 0.31 & 0.39 & 1.32 & 0.43 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Intragroup comparison of cranial references observed in all three directions of space (x, y, and z axes) for both Hyrax and Haas group (\(p<0.05\)).  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{1}{c}{**Landmark**} & \multicolumn{1}{c}{**Axis**} & \multicolumn{1}{c}{**X**} & \multicolumn{1}{c}{**Y**} & \multicolumn{1}{c}{**X**} \\ \hline Cranial & & & & \\ RFs & 0.39 & 4.18 & 0.28 \\ LFs & 0.32 & 4.04 & 0.27 \\ ELSA & 0.29 & 0.24 & 0.19 \\ Rpo & 0.31 & 5.57 & 0.37 \\ Lpo & 0.27 & 0.12 & 0.64 \\ \hline Skeletal & & & \\ RNF & 0.29 & 0.61 & 0.23 \\ LNF & 0.17 & 0.43 & 0.23 \\ RLpt & 0.07 & 0.35 & 0.37 \\ LLpt & 0.03 & 0.27 & 0.36 \\ \hline Dental & & & \\ PC 1.6 & 0.21 & 0.43 & 0.29 \\ PC 2.6 & 0.21 & 0.24 & 0.19 \\ PC 5.5 & 0.27 & 0.33 & 0.29 \\ PC 6.5 & 0.25 & 0.17 & 0.29 \\ FURCA 1.6 & 0.41 & 0.19 \\ FURCA 2.6 & 0.32 & 0.28 & 0.22 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Intraoperator error on x, y, and z axes.