## 3 Results
the smallest variation in surface roughness. The position of the medians in the boxplot reveals that sodium bicarbonate tends to produce more extreme roughness values, while erythritol and glycine tend to produce more moderate and uniform values. Statistical analysis begins with [PERSON]'s test to verify the homogeneity of variances among the abrasive groups. The test result indicates that the variances are not homogeneous (\(p<0.001\)), suggesting that the groups have significantly different variances. Due to the lack of homogeneity of variances, [PERSON]'s test is performed instead of the standard ANOVA, as [PERSON]'s test is more robust in situations where variances among groups differ. [PERSON]'s test reveals a significant difference in mean roughness (Ra) among the abrasives (\(p<0.05\)). Following [PERSON]'s test, a Games-Howell post hoc test is conducted (Table 5) to identify where the differences among the groups are. The results show a significant difference between erythroid and glycine (\(p<0.05\)), while comparisons between sodium bicarbonate and erythroid, and between sodium bicarbonate and glycine, are not significant. This indicates that erythroid and glycine differ significantly in their impact on roughness, but sodium bicarbonate does not differ significantly from either. The roughness data for Fuji(tm) IX after 10 s of application with the different powders reveals significant variability, as shown in Figure 6. Erythritol causes relatively low and consistent roughness, with Ra values ranging from 0.35 to 0.62. In contrast, glycine produces greater variability, with Ra values ranging dramatically from 0.26 to 2.15, indicating a more aggressive or inconsistent effect on the material's surface. Sodium bicarbonate, in turn, presents intermediate variability, with Ra values ranging from 0.36 to 0.77, suggesting a moderate impact on roughness. Figure 5: Boxplot of composite roughness by abrasives (time 5s). \begin{table}
\begin{tabular}{c c c} \hline
**Description** & **Difference between Means** & \(p\)**-Value** \\ \hline Erythritol/Bicarbonate & \(-0.028\) & \(0.990\) \\ Glycine/Bicarbonate & \(-0.188\) & \(0.674\) \\ Glycine-/Eryrhritol & \(-0.160\) & \(0.010\) \\ \hline \end{tabular}
\end{table} 
Table 5: Games–Howell post hoc test results. The ANOVA conducted to compare the roughness (Ra) among the powders used on Fuji(tm) IX after 10 s does not reveal any statistically significant differences among the groups (F = 1.159, \(p\) = 0.357). This suggests that the observed variations in roughness among erythroid, glycine, and sodium bicarbonate are not large enough to be considered statistically significant, meaning that the Ra means among the different abrasives are similar within the adopted confidence level. Figure 7 presents roughness (Ra) values after 5 s of abrasion on Fuji(tm) IX using the three powders under study--sodium bicarbonate, erythroid, and glycine. The Ra measurements vary depending on the powder used. It is observed that, for sodium bicarbonate, Ra values range from 0.37 to 0.97, indicating a greater variability in roughness. Erythnitol shows more consistent Ra values, ranging from 0.36 to 0.58. Glycine, in turn, has the lowest Ra values, between 0.16 and 0.27, indicating less surface roughness after application. These data suggest that the type of powder used significantly influences the surface roughness of Fuji(tm) IX, with sodium bicarbonate producing the roughest surfaces and glycine the smoothest. Statistical analysis aims to compare the mean surface roughness (Ra) of Fuji(tm) IX after 5 s of abrasion with the three different powders--sodium bicarbonate, erythroid, and glycine. Initially, [PERSON]'s test is conducted to assess the homogeneity of variances among the groups. The test result indicates a _p_-value of 0.116, suggesting that the variances are homogeneous, as there is no significant difference between them (_p_ > 0.05). Based on this, it is appropriate to proceed with an analysis of variance (ANOVA) to compare the group means.