## 3 Results
### Statistical Tests
#### 3.4.7 Wilcoxon Non-Parametric Signed-Rank Test  
In addition to the parametric paired \(t\)-test, the Wilcoxon pairwise non-parametric signed-rank test was conducted to ensure more robust results, addressing potential violations of normality assumptions, small sample sizes, and the influence of outliers. Unlike the \(t\)-test, the Wilcoxon test operates on rank values rather than raw numerical differences, allowing it to capture consistent directional differences between models even when absolute values vary.  
The aggregated results are presented in Table 12, while the full set of detailed statistical results is available in Appendix A (Table A6). The results indicate a substantially higher number of statistically significant pairwise differences compared to the \(t\)-test. Notably, the test identified significant differences (in at least three metrics) for nearly all model pairs, with the sole exception of CB and XGB, where no statistically significant difference was detected.  
The sample for the Wilcoxon test was derived from repeated 10-fold cross-validation, resulting in 100 estimates. Initially, two approaches were considered: a standard 10-fold CV (yielding 10 estimates) and a repeated 10-fold CV (yielding 100 estimates). The latter was selected as it better aligns with the sample size requirements determined by statistical  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & **RF** & **ANN** & **LR** & **SVM** & **LGBM** & **CB** & **XGB** \\ \hline
**RF** & & & C & arfc & c & & PC & PC \\ \hline
**ANN** & 1 & & aprfc & Rc & & & \\ \hline
**LR** & 4 & 5 & & ARFC & APRFC & APRFC & APRFC \\ \hline
**SVM** & 1 & 2 & 4 & & rC & PrC & PrC \\ \hline
**LGBM** & & & 5 & 2 & & PC & P \\ \hline
**CB** & 2 & & 5 & 3 & 2 & & \\ \hline
**XGB** & 2 & & 5 & 3 & 1 & & \\ \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 11: Aggregate performance table of Corrected random resampled paired \(t\)-test.  
power analysis. With a sample size of only 10, the results were considerably more modest in terms of detecting statistically significant differences (higher Type II error).  
Which model performs better cannot be derived directly from the W value, as this is always a positive value (unlike the t value). Instead, the medians of the model outputs are compared in order to take account of the rank-based nature of the Wilcoxon test. From Table 12, it is evident that CB and XGB once again dominate across nearly all metrics and model comparisons, with the exception of the recall metric, where SVM, RF, and LGBM demonstrate stronger performance. As observed in previous analyses, SVM maintains its dominance in recall across all model pairs. Additionally, in the F1 metric, SVM outperforms all models except CB and XGB, where no statistically significant difference is observed, making it inconclusive which model has the advantage. ANN, RF, and exhibit mixed results, while LR consistently ranks as the weakest performer, surpassing only RF on a few metrics and ANN on ROC-AUC.