## 3 Results
### Statistical Tests
#### 3.4.8 Non-Parametric Friedman Test  
All previously applied statistical methods have been pairwise comparison tests, aiming to identify statistically significant differences between specific model pairs. The results were presented in tables, each populated with the outcomes of all possible two-model comparisons. In contrast, the Friedman test employs a multiple-model comparison approach, simultaneously evaluating all models to provide a broader perspective on their relative performance. As a non-parametric test, the [PERSON] test imposes no prior assumptions about the input distribution. Its results indicate whether a statistically significant difference exists among the tested models; however, it does not specify which models differ. To determine specific pairwise differences, a post-hoc test, such as [PERSON]'s test, is required. The [PERSON] test was performed using 100 estimates per metric, obtained through a repeated cross-validation procedure to ensure alignment with the required sample size. The statistical results, including chi-square values and \(p\)-values, are presented in Table 13. Across all metrics, statistical significance was achieved with \(p<0.001\), and the large chi-square values (>480) provide strong evidence of performance differences among models. The highest chi-square value was observed for ROC-AUC (568.36), while the lowest was recorded for the recall metric (481.6). Table 14 presents a summary of performance results across multiple metrics in the same format as previously shown. The results closely resemble those obtained from the corrected repeated cross-validation \(t\)-test (Table 10) and the corrected resampled \(t\)-test (Table 11). The most statistically significant differences were identified for the LR model, \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **RF** & **ANN** & **LR** & **SVM** & **LGBM** & **CB** & **XGB** \\ \hline
**RF** & & APrC & apRFC & ARFc & PrC & APrFC & APrC \\ \hline
**ANN** & **4** & & aprfC & pRFc & apRc & ARFC & ARFC \\ \hline
**LR** & **5** & **5** & & APRFC & APRFC & APRFC & APRFC \\ \hline
**SVM** & **4** & **4** & **5** & & APfrC & APrC \\ \hline
**LGBM** & **3** & **4** & **5** & **5** & & APrFC & APrFC \\ \hline
**CB** & **5** & **4** & **5** & **4** & **5** & & \\ \hline
**XGB** & **4** & **4** & **5** & **4** & **5** & & \\ \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 12: Aggregate performance table for non-parametric Wilcoxon signed-rank test (100 estimates) results across multiple metrics. followed by SVM, LGBM, and RF. The table further highlights the dominance of CB and XGB across most metrics, except for recall, while LR consistently underperforms across all metrics. Additionally, SVM maintains its superiority in recall over all models except RF, where no statistically significant difference was observed. A complete set of results for all model-metric combinations, including exact \(p\)-values from [PERSON]'s post-hoc test, is provided in Table 17 (Appendix A). Table 15 presents a summary of the average rankings of different classification models across various metrics. Each model was evaluated 100 times, with the corresponding metric computed in each iteration. Rather than using raw scores, models were ranked per iteration, with 1 assigned to the best-performing model for a given metric and 7 to the worst. After 100 iterations, the average rankings were calculated and are displayed in Table 15. The results indicate that LR is the poorest-performing model, consistently ranking above 6 across all metrics.