## 4 Discussion  
The primary aim of the present study was to verify the reliability of a new method to analyze the three-dimensional accuracy of complete-arch impressions. In addition, the second aim was to compare the accuracy of conventional and intraoral digital impressions using the new method. The CMM used in the present study has a 0.7-\(\upmu\)m accuracy, with a 0.55-\(\upmu\)m repeatability, and the geometric analysis software is reported to have less than \(10^{-4}\) microns and \(10^{-4}\) arc second of separation or tilt for cylinders and planes [29; 30]. Therefore, the CMM and the geometric software were accurate enough to measure the physical models (master model and definitive casts) and the digital models. In the present study, a new coordinate system was set using the three reference centroids, therefore, all 13 centroids' coordinates, except the origin (#11C), were influenced by any deviation of the reference centroids. The results show that each ICC of \(\Delta\)x, \(\Delta\)y, and \(\Delta\)z resulted in the value of 1 for the master model, definitive casts, as well as the digital models, therefore, the first null hypothesis was rejected. [PERSON] and [PERSON] classified the degree of reliability into five categories, which were slight (0.00 \(<\) ICC \(\leq\) 0.20), fair (0.21 \(<\) ICC \(\leq\) 0.40), moderate (0.41 \(<\) ICC \(\leq\) 0.60), substantial (0.61 \(<\) ICC \(\leq\) 0.80), and almost perfect (0.81 \(<\) ICC \(\leq\) 1) [26]. The ICC value of 1 for the physical and digital models in the present study meant that the new method had an almost perfect reliability to evaluate the accuracy of complete-arch impressions. The inter-operator reliability test also showed that the new method had an almost perfect reliability between different operators. The present study applied three-dimensional metrology to assess the position of each tooth. To the authors' knowledge, this is the first study to evaluate the three-dimensional distortion of each tooth position using the metrology concept. Natural tooth has an irregular freeform configuration; therefore, coordinate measurements cannot be applied to locate tooth positions. In the present study, a basic geometrical shape, a cylinder, was used to represent each tooth; therefore, coordinate measurements could be used to assess  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{\(\Delta\)x} & \multicolumn{2}{c}{\(\Delta\)y} & \multicolumn{2}{c}{\(\Delta\)z} \\ \hline
**Position** & **Group CI** & **Group IOS** & \(p\) & **Group CI** & **Group IOS** & \(p\) & **Group CI** & **Group IOS** & \(p\) \\ \hline
917C & 0.026 \(\pm\) 0.023 & 0.032 \(\pm\) 0.023 & 0.004 & & & & & \\
916C & 0.018 \(\pm\) 0.018 & 0.026 \(\pm\) 0.019 & \textless{}0.001 & 0  
the three-dimensional position of each cylinder centroid and the displacement of each centroid in the X, Y, and Z axes. The new method presented in this study can exclude the inherent superimposition errors of best fit alignment, which was frequently used to compare the accuracy between digital models. In addition, it also excluded the inherent errors in converting the master model and definitive casts to digital models. This new method can be applied to evaluate the accuracy of any physical or digital model; therefore, it is possible to apply it to a wide variety of fields. The method can be applied to evaluate the accuracy of newly developed impression materials, as well as stereolithography models fabricated using different types of three-dimensional printers. Further, researchers can also analyze the amount of distortion in each impression step by scanning an impression before pouring any modeling stone. Then, the amount of distortion can be divided into the distortion from polymerization shrinkage of impression materials from the setting expansion of modeling stone. A linear mixed model is an analytical method that can be analyzed while taking intra-subject correlations that are characteristic of repeated measurement data into account.