# A Mixed Method with Effective Color Reduction
## 4 Results and Discussion
### Statistical Significance of the Results  
To conclude the comparison of the methods, the Wilcoxon test [53] was applied in order to determine the statistical significance of the improvement obtained by the proposed method. This test compares the results of two methods to determine that there is no significant difference between both methods.  
To compare BS+ITATCQ3 to the iterative methods, the results of iteration 25 of all the methods were used. Nevertheless, when the noniterative methods were compared, the results of BS+ITATCQ3 used were those corresponding to iteration 5. The Wilcoxon test, with a significance level of 0.05, was applied to compare both the MSE values and the execution time. The results of the tests appear in Table 1. The \(p\)-value (probability value corresponding to the \(Z\)-value) is not included in the table because it is the same in all cases (\(<\)0.00001). This value indicates that the differences between each pair of methods compared are significant in all cases. In addition, the sums of the ranks included in the table allow us to determine which of the two methods compared is better. If the results corresponding to the MSE values are analyzed, it is observed that the proposed method is significantly better than all the other methods, except ABC+ATCQ and BSKM. On the other hand, when analyzing the results for the execution time, the noniterative methods are significantly faster than BS+ITATCQ3. As far as the iterative methods are concerned, the proposed method is significantly faster than all of them, except ITATCQ.  
In summary, the results obtained from the Wilcoxon test confirm the conclusions previously presented in this section.  
\begin{table}
\begin{tabular}{l r r r r r r} \hline \hline  & \multicolumn{3}{c}{**MSE**} & \multicolumn{3}{c}{**Execution Time**} \\ \cline{2-7}
**Method** & \multicolumn{1}{c}{**Z-Value**} & \multicolumn{1}{c}{\(sum+\)} & \multicolumn{1}{c}{\(sum-\)} & \multicolumn{1}{c}{\(Z\)-Value**} & \multicolumn{1}{c}{\(sum+\)} & \multicolumn{1}{c}{\(sum-\)} \\ \hline WU & \(-8.5072\) & 0 & 4656 & \(-8.5072\) & 4656 & 0 \\ OC & \(-8.5072\) & 0 & 4656 & \(-8.5072\) & 4656 & 0 \\ VB & \(-8.5072\) & 0 & 4656 & \(-8.5072\) & 4656 & 0 \\ MC & \(-8.5072\) & 0 & 4656 & \(-8.5072\) & 4656 & 0 \\ NQ & \(-8.5072\) & 0 & 4656 & \(-8.2496\) & 4585.5 & 70.5 \\ BS & \(-8.5072\) & 0 & 4656 & \(-8.5072\) & 4656 & 0 \\ WATCQ & \(-5.4486\) & 837 & 3819 & \(-8.5072\) & 4656 & 0 \\ BS+ATCQ & \(-8.5072\) & 0 & 4656 & \(-8.5072\) & 4656 & 0 \\ ITATCQ & \(-8.5072\) & 0 & 4656 & \(-8.5072\) & 4656 & 0 \\ SFLA & \(-5.3172\) & 847.5 & 3712.5 & \(-7.7252\) & 214 & 4442 \\ ATCQ+FA & \(-8.5072\) & 0 & 4656 & \(-8.5072\) & 0 & 4656 \\ KM & \(-7.7946\) & 195 & 4461 & \(-8.5072\) & 0 & 4656 \\ BSKM & \(-6.1648\) & 4015 & 641 & \(-8.5072\) & 0 & 4656 \\ ABC+ATCQ & \(-4.7122\) & 3549.5 & 1010.5 & \(-8.5072\) & 0 & 4656 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Results of the Wilcoxon test that compares BS+ITATCQ3 to other methods. (\(Z\)-value: value of the test statistic; \(sum+\): sum of positive ranks; \(sum-\): sum of negative ranks).