## 3 Results  
Five measurements were made for each sample, but in different locations. Please check Table 3 for further clarification.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline  & **Ra1** & **Raz** & **Ra3** & **Ra4** & **Ra5** & **Media** & **Standard Deviation** \\ \hline
1 & 0.4778 & 0.4683 & 0.4508 & 0.4375 & 0.513 & 0.46948 & 0.02888022 \\
2 & 1.9845 & 2.0159 & 1.9518 & 2.3981 & 2.5405 & 2.17816 & 0.27144762 \\
3 & 0.9504 & 0.8388 & 0.8195 & 1.0379 & 1.0858 & 0.94648 & 0.11779426 \\
4 & 0.9042 & 1.1652 & 1.0916 & 0.9886 & 0.9196 & 1.01384 & 0.11235617 \\
5 & 0.9337 & 0.6827 & 0.5569 & 0.565 & 0.5016 & 0.64798 & 0.17280751 \\
6 & 1.118 & 0.9084 & 0.8817 & 1.0521 & 1.3365 & 1.05934 & 0.18347338 \\
7 & 0.7099 & 0.7319 & 0.8403 & 0.8248 & 1.002 & 0.82178 & 0.11557131 \\
8 & 1.5126 & 1.7345 & 1.4272 & 0.9311 & 1.0254 & 1.32616 & 0.33846695 \\ \hline \end{tabular}
\end{table}
Table 3: Profilometer measurements.  
Statistical analysis was carried out using R Statistical Software. Figure 1 shows the boxplot of the eight treatments considered in this study. It is possible to observe that the G2 group differed from the other groups with regard to the roughness, having the highest value. The group with the second highest roughness was G8. Among all groups, G2 and G8 exhibited greater variability than the others. Regarding G1, it can be noted that it had the lowest values, while G5 was the only group that had an outlier point. The other groups had relatively similar behaviors.  
In Table 4, the results with the \(p\)-value of each test are reported. It may be underlined that the values highlighted in red represent the groups that had a statistically significant difference, considering the \(p\)-value of \(\alpha\) = 0,10.  
Therefore, it can be concluded, for example, that the G1 treatment presented a significant difference compared to the G2, G6 and G8 groups. In particular, G1 had on average a lower roughness value than groups \"2\", \"6\" and \"8\"; however, there was no statistically significant difference between group \"1\" and groups \"3\", \"4\", \"5\" and \"7\".  
Moreover, G2 was statistically different when groups \"5\" and \"7\" were compared, showing on average a higher value than groups \"5\" and \"7\".  
Finally, as far as the \(p\)-values between the other groups are concerned, it can be noted that these values were greater than 0.10, so the null hypothesis is not rejected, since there was no significant difference in the roughness found in the tooth.  
The SEM images show the differences between the surfaces, even at higher magnification levels (Figure 2).  
\begin{table}
\begin{tabular}{c c c c c c c} \hline  & **G1** & **G2** & **G3** & **G4** & **G5** & **G6** & **G7** \\ \hline G2 & 0.0001 & & & & & \\ \hline G3 & 0.4000 & 0.3632 & & & & \\ \hline G4 & 0.1227 & 0.9314 & 1.0000 & & & \\ \hline G5 & 1.0000 & 0.0041 & 1.0000 & 0.9916 & & \\ \hline G6 & 0.0912 & 1.0000 & 1.0000 & 0.9138 & 0.8695 & \\ \hline G7 & 1.0000 & 0.0388 & 1.0000 & 1.0000 & 1.0000 & 1.0000 & \\ \hline G8 & 0.0103 & 1.0000 & 1.0000 & 1.0000 & 0.1913 & 1.0000 & 0.8613 \\ \hline \end{tabular}
\end{table}
Table 4: \(p\)-value following the Dunnet \(t\)-test.  
Figure 1: Boxplot of the treatments considered in the study.  
The first null hypothesis is therefore confirmed, as no statistically significant difference between the two toothpastes and the fluoride varnish in terms of erosion prevention was reported.  
Figure 2: SEM observations divided by treatment group and magnification level—600X, 1500X and 3000X.  
The second null hypothesis is rejected, as in terms of protection from a second acid attack, the fluoride toothpaste and the fluoride varnish seemed to be more effective than the non-fluoride toothpaste