## 3 Results  
Table 1 presents the average canal angles for each technique, measured before and after complete instrumentation at the Initial Apical File (IAF) and Master Apical File (MAF) stages. Additionally, the table includes the minimum and maximum values for each step, providing a more comprehensive understanding of the original root canal anatomy across the different techniques.  
From Table 1, it can be seen that the mean canal angles across different groups varied before and after full instrumentation at the Initial Apical File (IAF) and Master Apical File (MAF) stages. Initially, the STEP-BACK and PTN groups had the highest mean angles at the IAF stage, suggesting a greater initial canal curvature. In contrast, the RECIPROC, PTU,  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline  & \multicolumn{2}{c}{**Group**} & \multicolumn{2}{c}{**N**} & \multicolumn{2}{c}{**Mean**} & \multicolumn{2}{c}{**Median**} & \multicolumn{2}{c}{**SD**} & \multicolumn{2}{c}{**Minimum**} & \multicolumn{2}{c}{**Maximum**} \\ \hline IAF & STEP-BACK & 20 & 27.40 & 26.00 & 13.89 & 4 & 58 \\ \hline  & RECIPROC & 20 & 21.10 & 17.50 & 11.80 & 6 & 41 \\ \hline  & MTWO & 20 & 23.40 & 20.50 & 10.30 & 10 & 42 \\ \hline  & PTU & 20 & 22.60 & 22.00 & 10.37 & 6 & 52 \\ \hline  & PTN & 20 & 26.90 & 27.00 & 9.19 & 10 & 43 \\ \hline MAF & STEP-BACK & 20 & 21.70 & 21.50 & 10.45 & 4 & 40 \\ \hline  & RECIPROC & 20 & 18.40 & 16.00 & 10.55 & 4 & 38 \\ \hline  & MTWO & 20 & 18.40 & 17.50 & 7.70 & 8 & 35 \\ \hline  & PTU & 20 & 18.60 & 20.00 & 6.83 & 5 & 30 \\ \hline  & PTN & 20 & 21.40 & 24.00 & 10.08 & 4 & 40 \\ \hline \end{tabular}
\end{table}
Table 1: [PERSON]’s angles in the different groups. The values are given in degrees. IAF: Initial Apical File; MAF: Master Apical File.  
Figure 3: Schematic picture of reference points, lines and angles and root canal curvature. (M-mesial, D-distal)and MTWO groups showed lower mean angles, indicating a less severe canal curvature before instrumentation.  
The STEP-BACK group had the greatest variability, as indicated by the highest standard deviation (SD) at the IAF stage, reflecting diverse canal anatomies within this group. After instrumentation at the MAF stage, all groups demonstrated a reduction in mean angle, showing that each technique effectively reduced canal curvature. The STEP-BACK group continued to have a wider range of angles post instrumentation, while RECIPROC, PTU, and MTWO had more consistent results, characterized by lower SD values and narrower ranges. Although the initial curvatures in the STEP-BACK and PTN groups were somewhat larger, statistical analysis confirmed that these differences were not significant (\(\chi^{2}\) = 4.93, df = 4, \(p\) = 0.214), ensuring comparability across all study groups.  
Table 2 shows the average change in canal angles for each technique from IAF to MAF. The table demonstrates the degree of angulation change associated with each system, indicating the relative effectiveness of each technique in altering root canal curvature.  
Table 2 shows that the mean angle change from IAF to MAF varied across the different techniques. The STEP-BACK and PTN groups exhibited the highest mean angle changes (5.70\({}^{\circ}\) and 5.60\({}^{\circ}\), respectively), indicating more substantial modifications in canal curvature. Conversely, the RECIPROC group showed the lowest mean change (2.65\({}^{\circ}\)). The variability within groups, as indicated by the standard deviation (SD), was most pronounced in the PTU group (SD = 6.39), reflecting a wider range of angle changes in this technique.  
Despite these observed differences, the Kruskal-Wallis test did not reveal a statistically significant difference in the magnitude of angular change between the groups (\(\chi^{2}\) = 6.23, df = 4, \(p\) = 0.182).  
Finally, Table 3 shows the mean degree of angular change expressed as percentages.