## 3 Results
### Correlation Between Protrusive and Opening Guidance Angles  
Statistical analysis (Table 2) revealed a moderate positive correlation between the condylar guidance angles measured in protrusion and those measured during mouth opening. Using each subject's mean bilateral angle for the two movements, the Pearson correlation coefficient was r = 0.57 (\(p\) < 0.001). This indicates that individuals with a relatively steep condylar guidance in one type of movement tended to also show a steep guidance angle in the other movement. In practical terms, a subject who exhibited a high protrusive inclination (for example, well above the average) often also had an above-average inclination during full opening, and vice versa for lower-angle cases. However, the correlation was far from perfect. The coefficient of determination was r\({}^{2}\approx\) 0.33, meaning only about 33% of the variance in opening angle can be statistically explained by the protrusive angle. The remaining \(\sim\)67% of variability is due to factors other than a simple linear relationship--in other words, there is substantial individual variation in how the condyle translates during opening versus protrusion. Figure 6 (scatterplot of protrusive vs. opening angles) illustrated this trend: while there is an upward slope to the data points (confirming a general positive association), the points are fairly widely scattered rather than falling tightly along a line. Some subjects with moderate protrusive angles had much steeper opening angles than expected, and a few with high protrusive angles still showed only moderate opening values.  
The clinical implication of this finding is that protrusive and opening condylar guidance angles, though related, are not interchangeable. A moderate correlation suggests that a clinician who calibrates an articulator using a protrusive record can expect the opening pathway inclination to be in a similar ballpark for many patients, but not with high preci  
Figure 7: Correlation between the condylar guidance angle during opening and protrusion.  
sion. The statistically significant relationship supports the idea that the steepness of the condylar path is partly a characteristic of the individual's joint anatomy (and thus influences all movements to some extent). Yet, the differences in movement patterns (protrusion being a mostly linear forward translation vs. opening involving rotation plus translation along a different condylar trajectory) result in divergence between the two measurements. From the study's primary objective standpoint, this result is notable: it confirms that there is a correlation between the two methods of determining sagittal condylar inclination, but also underscores that protrusive movement recordings are more reliable (given their lower variability) for articulator programming. The data demonstrated that protrusive measurements had tighter consistency (as described above), which, combined with the moderate correlation, suggests that articulators set using protrusive records would approximate the patient's functional movements more predictably than those set using maximal opening records. In summary, while a shared trend exists between the protrusive and opening guidance angles, the degree of scatter in the data reinforces the need to measure protrusive inclination directly for the most accurate result, rather than relying on mouth-opening values as a proxy.