## 3 Results  
The interaction effect of bracket and adhesive types using a two-way ANOVA (Table 3) revealed significant differences for both the brackets and the adhesive types, separately. However, the effect of both variables together was not significant (\(p\) = 0.952). Pairwise comparison for the differences between the two types of brackets and two types of adhesives (Table 4) revealed significant differences in favor of ceramic brackets (\(\Delta\)E= 3.77 \(\pm\) 3.60; \(p\)= 0.009) and the Transbond XT adhesive system (\(\Delta\)E = 3.52 \(\pm\) 2.45; \(p\) = 0.008).  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Item** & & **N** & **Mean** & **SD** & **Mean Difference** & \begin{tabular}{c} **95\% CI of the Difference** \\ **Lower** \\ \end{tabular} & \begin{tabular}{c} **95\% CI of the Difference** \\ **Upper** \\ \end{tabular} & \
\begin{tabular}{c} **\(p\)*** \\ **\(p\)*** \\ \end{tabular} \\ \hline \multirow{2}{*}{
\begin{tabular}{c} Bracket Type \\ \end{tabular} } & Metal & 20 & 6.72 & 4.62 & \multirow{2}{*}{2.95} & \multirow{2}{*}{0.30} & \multirow{2}{*}{5.61} & \multirow{2}{*}{0.009 *} \\  & Ceramic & 20 & 3.77 & 3.60 & & & \\ \cline{1-1} \cline{3-7}  & Transbond XT & 20 & 3.52 & 2.45 & & & \\ \cline{1-1} \cline{3-7}  & U-Cem & 20 & 6.98 & 5.16 & & & \\ \hline \hline \end{tabular}
\end{table}
Table 4: Comparison of means and SDs of change in color (\(\Delta\)E) between metal and ceramic brackets and between Transbond XT and U-Cem adhesive systems using Mann-Whitney nonparametric test.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**NBS Units** & **Critical Remarks for Color Differences** \\ \hline
0.0–0.5 & Trace \\
0.5–1.5 & Slight \\
1.5–3.0 & Noticeable \\
3.0–6.0 & Apprecable \\
6.0–12.0 & Much \\ \(\geq\)12.0 & Very much \\ \hline \hline \end{tabular}
\end{table}
Table 2: National Bureau of Standards system of expressing color difference (NBS).  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Source** & **Type III Sum of Squares** & **df** & **Mean Square** & **F** & \(p\) \\ \hline \multirow{2}{*}{Corrected Model} & 206.898 & 3 & 68.966 & 4.660 & 0.007 \\  & 1101.135 & 1 & 1101.135 & 74.398 & 0.000 \\ \multirow{2}{*}{\begin{tabular}{c} Bracket type \\ \end{tabular} } & 87.232 & 1 & 87.232 & 5.894 & 0.020 * \\ \multirow{2}{*}{\begin{tabular}{c} Adhesive type \\ \end{tabular} } & 119.612 & 1 & 119.612 & 8.082 & 0.007 * \\ \multirow{2}{*}{\
\begin{tabular}{c} Bracket—Adhesive \\ \end{tabular} } & 0.054 & 1 & 0.054 & 0.004 & 0.952 \\ \multirow{2}{*}{
\begin{tabular}{c} Error \\ \end{tabular} } & 532.824 & 36 & 14.801 & & \\ \cline{1-1} \cline{3-7} Total & 1840.857 & 40 & & & \\ \cline{1-1} \cline{3-7} Corrected Total & 739.722 & 39 & & & \\ \hline \hline \end{tabular}  
* Statistically significant at \(p\) value \(<\) 0.05. R2 = 0.280; Adjusted R2 = 0.220.  
\end{table}
Table 3: Two-way ANOVA for the interaction effect of bracket and adhesive on change in tooth color (\(\Delta\)E).  
When analyzing the differences between the different groups tested, the Kruskal-Willis nonparametric test (Table 5) revealed a significant difference (\(p\) = 0.006) among the different groups, with group C having the least change in color (\(\Delta\)E= 2.00 \(\pm\) 0.89) and group B having the highest (\(\Delta\)E = 8.42 \(\pm\) 5.66). According to the NBS units, changes in group C were considered noticeable, while in all the other groups tested, changes in tooth color ranged from \"appreciable\" to \"much\" as in group B.  
Further multiple comparisons revealed that a significant difference was found between group C and group B (Table 6).