## 4 Discussion  
The accuracy of slot height reproduction is one of the many aspects of brackets that must be thoroughly investigated if their reliability is to be assured and their routine use endorsed. This study demonstrated that, across a sample comprising metal, ceramic, and resin brackets, the percentage difference between the real and nominal slot heights ranges from \(-0.36\%\) to \(+4.30\%\). Specifically, the slots of all brackets investigated, except the 3D-printed ones, were significantly oversized with respect to the nominal values declared by the manufacturers (from \(+1.08\%\) to \(+4.30\%\)). This rejects our null hypothesis, i.e., that there would be no difference in this regard between commercially available brackets and those 3D-printed in-house  
Although an increase of \(+4.30\%\) may seem small, the application of [PERSON] et al. 's formula highlights how this leads to considerable increases, about \(19^{\circ}\), in the archive-slot play [22]. The results of this study are in agreement with those presented in the literature [18, 22, 23, 24, 25, 26], although smaller than the dimensional variation found by other authors. For instance, [PERSON] et al. reported that slot height tends to be oversized by between \(+5\%\) and \(+24\%\)[25]. Similarly, [PERSON] et al. found that lingual and vestibular bracket slot heights are between \(+0.56\%\) and \(+11.6\%\) oversized [18], a conclusion shared by [PERSON] et al., who reported vertical oversizing ranging from \(1\%\) to \(7\%\) as compared with the nominal values [24]. The manufacture of metal brackets mainly relies on metal injection moulding (MIM) and milling, while ceramic brackets are usually made via ceramic injection moulding (CIM) [27, 28]. The literature reveals differences in precision both among and within brands and suggests that inaccuracies can be introduced at different stages during the process of manufacturing metal brackets. Inaccuracies may be introduced during slot milling, which can be affected by the size and extent of the vibration of the cutter and the subsequent stages of finishing and polishing. The precise reproduction of injection-moulded brackets, on the other hand, will depend on the accuracy of the mould. Like the metal brackets on the market, ceramic bracket slots also tend to be oversized. As with the MIM process, the CIM process also has the same production steps at which errors can accumulate [28], and firing may also be responsible for altering slot size and shape. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Groups** & **Test Statistic** & **SE** & **Std. Test Statistic** & \(p\)**-Value** \\ \hline Group 3 vs. Group 2 & 5.1 & 7.832 & 0.651 & 0.515 \\ \hline Group 3 vs. Group 1 & 8.525 & 7.832 & 1.089 & 0.276 \\ \hline Group 3 vs. Group 4 & \(-40.45\) & 7.832 & \(-5.165\) & \(<\)0.001 * \\ \hline Group 2 vs. Group 1 & 3.425 & 6.394 & 0.536 & 0.592 \\ \hline Group 2 vs. Group 4 & \(-35.35\) & 6.394 & \(-5.528\) & \(<\)0.001 * \\ \hline Group 1 vs. Group 4 & \(-31.925\) & 6.394 & \(-4.993\) & \(<\)0.001 * \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Pairwise Dunn–Bonferroni comparative analysis of slot height in the four groups investigated (\(p<0.05\)*). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Groups** & **Typology of Bracket** & \(p\)**-Value** \\ \hline
**Group 1** & PRIMO SWM & Legend Mini & 0.010 * \\ \hline
**Group 2** & Damon Q2 & Carriere SLX 3D & 0.102 \\ \hline
**Group 4** & IH3 DB 1 & IH3 DB 2 & 0.157 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: [PERSON]’s within-group comparative analysis of the bracket types 1, 2, and 4 (\(p<0.05\)*). In fact, [PERSON] et al. [25], who measured the slot heights of 0.022-inch metal brackets from six different manufacturers, found a range of inaccuracy of 5-24%, with four types of brackets showing parallel slot walls, five having converging slot walls, and two with divergent slots.