## 3 Statistical Analysis  
For statistical analysis, SPSS (version 23.0, SPSS Inc., Chicago, IL, USA) was used. A two-way mixed Intraclass Correlation Coefficient (ICC) was used to evaluate measuring reliability (intra- and inter-examiner) with a significance threshold set at 0.05. Inter-examiner reliability was assessed with 37.5% of the sample, and intra-examiner reliability was evaluated for examiners 1 and 2 with the complete sample.  
Intra-examiner Intraclass Correlation Coefficient (average measures) was calculated for every coordinate of every landmark, with and without orientation with the Acta plane (Table 4). Reliability was considered poor (ICC < 0.50), moderate (between 0.50 and 0.75), good (between 0.75 and 0.90), or excellent (ICC > 0.90) [33].  
Distribution of the ICCs per landmark was tested using the Shapiro-Wilk normality test (\(p<0.05\)) and the exact sign test to compare the differences in reliability with the two orientations.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Landmark** & **X** & **X\({}^{\prime}\)ACTA** & **Y** & **Y\({}^{\prime}\)ACTA** & **Z** & **Z\({}^{\prime}\)ACTA** \\ \hline \hline Nasion & 0.997 * & 0.9980 * & 0.999 * & 1.000 * & 0.997 * & 0.999 * \\ \hline Sella & 0.985 * & 0.997 * & 0.998 * & 1.000 * & 0.999 * & 1.000 * \\ \hline \hline Basion & 0.894 * & 0.999 * & 0.880 * & 1.000 * & 0.429 & 1.000 * \\ \hline Pogonion & 0.996 * & 0.998 * & 1.000 * & 1.000 * & 0.953 * & 0.996 * \\ \hline Gonion.R & 0.991 * & 0.994 * & 0.991 * & 0.986 * & 0.974 * & 0.997 * \\ \hline Gonion.L & 0.997 * & 0.935 * & 0.995 * & 0.879 * & 0.990 * & 0.804 * \\ \hline MFR & 0.986 * & 0.990 * & 0.987 * & 0.999 * & 0.999 * & 1.000 * \\ \hline MFL & 0.992 * & 0.992 * & 0.994 * & 1.000 * & 0.999 * & 1.000 * \\ \hline Orbita.R & 0.985 * & 0.980 * & 0.974 * & 1.000 * & 0.979 * & 0.992 * \\ \hline Orbita.L & 0.958 * & 0.975 * & 0.975 * & 0.997 * & 0.949 * & 0.990 * \\ \hline OrbitaLat.R & 0.774 * & 0.997 * & 0.495 & 1.000 * & 0.183 & 0.998 * \\ \hline OrbitaLat.L & 0.774 * & 0.999 * & 0.502 & 1.000 * & 0.634 * & 0.998 * \\ \hline Porion.R & 0.938 * & 0.928 * & 0.978 * & 0.989 * & 0.959 * & 0.780 * \\ \hline Porion.L & 0.899 * & 0.931 * & 0.980 * & 0.996 * & 0.987 * & 0.991 * \\ \hline Roottip.R & 0.997 * & 0.993 * & 0.995 * & 1.000 * & 0.987 * & 0.999 * \\ \hline Roottip.L & 0.987 * & 0.997 * & 0.989 * & 0.999 * & 0.975 * & 1.000 * \\ \hline \hline \end{tabular}  
* Reliability: ICC < 0.50 is poor, between 0.50 and 0.75 is moderate, between 0.75 and 0.90 is good, and ICC > 0.90 it is excellent [30]. The asterisk (*) used indicates that the result is statistically significant at a significance level of \(p<0.05\).  
\end{table}
Table 3: Transformation matrix.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Cos(a) \(\bullet\) Cos(e)** & **Cos(a) \(\bullet\) Sin(e) \(\bullet\) Sin(r) \(-\) Sin(a) \(\bullet\) Cos(r)** & **Cos(a) \(\bullet\) Sin(e) \(\bullet\) Cos(r) + Sin(a) \(\bullet\)Sin(r)** & **0** \\ \hline Sin(a) \(\bullet\) Cos(e) & Cos(a) \(\bullet\) Cos(r) + Sin(a) \(\bullet\) Sin(e) \(\bullet\) Sin(r) & Sin(a) \(\bullet\) Sin(e) \(\bullet\) Cos(r) \(-\) Cos(a) \(\bullet\) Sin(r) & 0 \\ \hline \(-\)Sin(e) & Cos(e) \(\bullet\) Sin(r) & Cos(e) \(\bullet\) Cos(r) & 0 \\ \hline
0 & 0 & 0 & 1 \\ \hline \hline \end{tabular}  
* with Cos(a) = cosinus (azimuth), Sin(a) = sinus (azimuth), Cos(e) = cosinus (elevation), Sin(e) = sinus (elevation), Cos(r) = cosinus (roll), Sin(r) = sinus (roll).  
\end{table}
Table 3: Transformation matrix.  
Four measurements (linear and angular) were also evaluated for normality using the Shapiro-Wilk test. Either a paired \(t\)-test or a sign test was performed to assess the influence of orientation with the Acta plane in performing measurements (Table 5).