## 4 Experimental Results
As can be seen from Table 6, the model factor is statistically significant. Thus, a detailed analysis will be performed now for each of the factors examined, using the Multiple Range Test for the two factors (model and filter) in which a multiple comparison procedure is carried out to determine which means are significantly different from which others. The method currently being used to discriminate among the means is [PERSON]'s least significant difference (LSD) procedure [36]. A summary of this procedure can be seen in Table 7. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Source** & \
\begin{tabular}{c} **Sum of** \\ **Squares** \\ \end{tabular} & **Df** &
\begin{tabular}{c} **Mean** \\ **Square** \\ \end{tabular} & **F-Ratio** & _p_**-Value** \\ \hline Main Effects & & & & \\ \hline A: Filter & 29.2101 & 9 & 3.24557 & 1.52 & 0.1460 \\ \hline B: Model & 95.588 & 4 & 23.897 & 11.21 & 0.0000 \\ \hline Residual & 289.987 & 136 & 2.13226 & & \\ \hline Total (Corrected) & 414.785 & 149 & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Analysis of Variance for the dependent variable that analyzes the AUC of the system when the model and the filter are modified. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Factors** & **Filter** & _Model_ \\ \hline Raw & VGG16 \\ Blur & VGG19 \\ CLAHE & ResNet50 \\ Contour & MobileNet \\
**Levels of the factors** & Detail & DenseNet121 \\ Edge Enhance & \\ Edge Enhance More & \\ FHE & \\ SHarpen & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Variables used in the statistical analysis. All the possible configurations of factors levels. From this test can be observed that there exist three homogenous groups (identified using columns of X's, with intersection) for the variable filter. All of the groups have intersections (therefore, different levels of these groups have the same behavior over the AUC variable). These groups are:  
* Contour, Sharpen, HE, Edge Enhance More, Blur, CLAHE, Edge Enhance, Raw
* Sharpen, HE, Edge Enhance More, BLUR, CLAHE, EDGE ENHANCE, raw, FHE
* HE, Edge Enhance More, BLUR, CLAHE, Edge Enhance, Raw, FHE, Detail  
The levels of these 3 groups are not significant from a statistical point of view (analyzing the behavior of the dependent output variable) having an intersection between all of them. This information can be graphically represented in Figure 3.  
On the other hand, with respect to the Model factor, there are three different groups without intersection. * DenseNet121
* MobileNet
* ResNet50, VGG16, VGG19  
The best group (best AUC) is the third. VGG19 obtains the best results. This factor is statistically significant. Figure 4 shows that, unlike the filter factor, the groups are well differentiated. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Factors** & & & Homogeneous \\ \hline Filter & Count & LS means & Ls sigma & Groups \\ \hline Contour & 15 & 92.1773 & 0.377028 & X \\ \hline Sharpen & 15 & 92.2287 & 0.377028 & X  X \\ \hline HE & 15 & 92.5227 & 0.377028 & X  X  X \\ \hline Edge Enhance & 15 & 92.776 & 0.377028 & X  X  X \\ More & 15 & 93.1107 & 0.377028 & X  X  X \\ \hline Blur & 15 & 93.1713 & 0.377028 & X  X  X \\ \hline CLAHE & 15 & 93.1793 & 0.377028 & X  X  X \\ \hline Edge Enhance & 15 & 93.1793 & 0.377028 & X  X  X \\ \hline Raw & 15 & 93.2287 & 0.377028 & X  X  X \\ \hline FHE & 15 & 93.238 & 0.377028 & X  X \\ \hline Detail & 15 & 93.5333 & 0.377028 & X  X \\ \hline Model & Count & LS means & Ls sigma &
\begin{tabular}{c} Homogeneous \\ Groups \\ \end{tabular} \\ \hline DenseNet121 & 30 & 91.5653 & 0.266599 & X \\ \hline MobileNet & 30 & 92.451 & 0.266599 & X \\ \hline ResNet50 & 30 & 93.374 & 0.266599 & X \\ \hline VGG16 & 30 & 93.5247 & 0.266599 & X \\ \hline VGG19 & 30 & 93.668 & 0.266599 & X \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Multiple Range Tests for the different factors. Method: 95.0 percent LSD. Figure 4: Multiple Range Tests for variable Model. Figure 3: Multiple Range Tests for variable Filter.