# Detection of Pitt-Hopkins Syndrome Based on Morphological Facial Features
## 3 Results
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Feature** & **Population** & **N** & **Min** & **Q1** & **Median** & **Q3** & **Max** & **Mean** & **SD** \\ \hline RNose & \multirow{2}{*}{PTHS} & \multirow{2}{*}{32} & \multirow{2}{*}{15} & \multirow{2}{*}{21} & \multirow{2}{*}{22} & \multirow{2}{*}{24} & \multirow{2}{*}{30} & \multirow{2}{*}{22.41} & \multirow{2}{*}{3.35} \\ (Group 1) & & & & & & & & & \\ \hline RNose & \multirow{2}{*}{Control} & \multirow{2}{*}{29} & \multirow{2}{*}{21} & \multirow{2}{*}{23} & \multirow{2}{*}{25} & \multirow{2}{*}{26} & \multirow{2}{*}{30} & \multirow{2}{*}{24.79} & \multirow{2}{*}{2.13} \\ (Group 2) & & & & & & & & & \\ \hline RMouth & \multirow{2}{*}{PTHS} & \multirow{2}{*}{32} & \multirow{2}{*}{8} & \multirow{2}{*}{11} & \multirow{2}{*}{12.5} & \multirow{2}{*}{15} & \multirow{2}{*}{24} & \multirow{2}{*}{14} & \multirow{2}{*}{4.47} \\ (Group 3) & & & & & & & & & \\ \hline RMouth & \multirow{2}{*}{Control} & \multirow{2}{*}{29} & \multirow{2}{*}{8} & \multirow{2}{*}{9} & \multirow{2}{*}{9} & \multirow{2}{*}{10} & \multirow{2}{*}{11} & \multirow{2}{*}{9.38} & \multirow{2}{*}{0.78} \\ (Group 4) & & & & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Statistical comparison of area features (the ratio of nose area over face area (RNose) and second, the ratio of mouth area over face area (RMouth)) for both groups (PTHS and control). Figure 6: Box plots of angle features for both groups (PTHS and control). NoseAngle-PTHS = Group 1; NoseAngle-Control = Group 2. Following the statistical comparative analysis on the geometrical features, the relationships between the syndrome and the extracted geometrical features were investigated. The Pearson correlation coefficient matrix of the features is reported in Table 4.  
Pearson correlation coefficients \(r\) and the \(p\)-value (two-tailed) of geometrical features of the two groups for non-correlation testing were computed, and the details are reported in Table 5. Student's \(t\)-test and the \(p\)-value were used to evaluate the significance levels of each feature in the classification of PTHS individuals. The results reported suggest that moderate correlations (\(0.3<r<0.7\)) are present among almost all the features, and a strong correlation (\(r>0.7\)) is observed between R3 and R3, R3 and RNase. Moreover, RMouth and NoseAngle are the most statistically significant features in the discrimination between the two experimental groups. \begin{table}
\begin{tabular}{c c c c c c c} \hline  & **R1** & **R2** & **R3** & **NoseAngle** & **RNose** & **RMouth** & **C** \\ \hline R1 & \(1.000000\) & \(0.631856\) & \(0.565448\) & \(-0.123501\) & \(0.44860\) & \(0.234808\) & \(-0.099263\) \\ \hline R2 & \(0.631856\) & \(1.000000\) & \(0.767697\) & \(-0.184765\) & \(0.758548\) & \(0.277656\) & \(-0.048716\) \\ \hline R3 & \(0.565448\) & \(0.767697\) & \(1.000000\) & \(-0.131357\) & \(0.639932\) & \(0.438070\) & \(-0.171853\) \\ \hline RNose & \(-0.123501\) & \(-0.184765\) & \(-0.131357\) & \(1.000000\) & \(0.329132\) & \(-0.601934\) & \(0.708482\) \\ \hline RMouth & \(0.448690\) & \(0.758548\) & \(0.639932\) & \(0.329132\) & \(1.000000\) & \(-0.150740\) & \(0.234934\) \\ \hline NoseAngle & \(0.234808\) & \(0.277656\) & \(0.438070\) & \(-0.601934\) & \(-0.150740\) & \(1.000000\) & \(-0.675969\) \\ \hline C & \(-0.099263\) & \(-0.048716\) & \(-0.171853\) & \(0.708482\) & \(0.234934\) & \(-0.675969\) & \(1.000000\) \\ \hline \end{tabular} The class to predict PTHS is C.  
\end{table} 
Table 4: Pearson correlation coefficient matrix of the geometrical features.