## 3 Results
### Statistical Tests
#### 3.4.8 Non-Parametric Friedman Test
In terms of accuracy, precision, and ROC-AUC, the best performing models are CB (2.71, 2.39, 1.90) and XGB, which have slightly higher rankings. ANN follows closely behind, with an average value of rankings around 3. However, SVM is the best model for recall and F1, followed by CB and XGB. These findings align with previous observations regarding recall (Tables 8-11) and F1 (Table 12), reinforcing the overall ranking trends. Additionally, RF demonstrated strong performance in recall and F1 metrics, securing second and third place rankings, respectively. The rankings in Table 15, in contrast to those in Table 14, are average ranks without statistical tests or significance analyzes. To conclude this evaluation, the [PERSON] statistical test followed by the post-hoc Nemenyi test is graphically presented in Figure 5 in the form of critical difference (CD) diagrams, providing a visual comparison of model performance across multiple metrics. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Chi-Square** & \(p\)**-Value** \\ \hline accuracy & 513.846 & \textless{}0.001 \\ \hline precision & 510.167 & \textless{}0.001 \\ \hline recall & 481.602 & \textless{}0.001 \\ \hline F1 & 504.781 & \textless{}0.001 \\ \hline ROC-AUC & 568.358 & \textless{}0.001 \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Results of Friedman test across multiple metrics. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **RF** & **ANN** & **LR** & **SVM** & **LGBM** & **CB** & **XGB** \\ \hline
**RF** & & C & aprfc & c & rC & APFC & PC \\ \hline
**ANN** & 1 & & aprfc & pRc & P & \\ \hline
**LR** & 5 & 5 & & APRFC & APRFC & APRFC & APRFC \\ \hline
**SVM** & 1 & 3 & 5 & & rfC & APrC & PrC \\ \hline
**LGBM** & 2 & 1 & 5 & 3 & & APFC & APC \\ \hline
**CB** & 4 & & 5 & 4 & 4 & \\ \hline
**XGB** & 2 & & 5 & 3 & & \\ \hline \hline \end{tabular}  
* A: Accuracy, P: Precision, R: Recall, F: F1-score, C: ROC-AUC. The colors represent the intensity of the statistically significant differences. Dark green indicates differences identified across all performance metrics (regardless of direction), while no color indicates differences identified on one or no metrics. The yellow diagonal separates the lower triangle (number of significant differences) from the upper triangle (metrics where significant differences is identified).  
\end{table} 
Table 14: Summary performance table for Friedman non-parametric pairwise test (100 estimates). In the critical difference (CD) diagram for accuracy (Figure 5), four distinct performance groups of ML models can be observed. The top-performing group consists of CB and XGB (positioned on the right side of the scale), followed by a middle group comprising SVM and ANN. A lower-middle group includes RF and LGBM, while LR stands as a clear outlier on the far-left side of the chart, indicating the worst performance. For precision, three performance groups can be identified: CB, XGB, and ANN as the top-performing models; RF, SVM, and LGBM forming a middle-tier group; and LR again positioned as the lowest-performing model on the far left. The ROC-AUC metric follows a similar grouping pattern, except that SVM shifts from the middle group to the lower-performing group alongside LR, while RF and LGBM remain in the middle tier. In recall, LR continues to exhibit the worst performance, whereas SVM emerges as the best-performing model by a significant margin. The middle-tier models are more evenly distributed, with RF and LGBM showing the strongest results, followed by CB and XGB. ANN, in contrast, performs poorly on this metric. For F1, the top-performing group consists of SVM, CB, and XGB, while RF, LGBM, and ANN cluster closely together in the middle tier. As expected, LR remains the worst-performing model.