## 3 Results
### Performance Evaluation on Test Data
The results from the DeLong significance test are presented in Table 14, using a threshold \(p\)-value \(<\) 0.05 to indicate a significant difference in performance. On the original dataset, all pairwise comparisons between LR and other models reported statistically significant differences in AUC values (\(p\) < 0.001), while z-statistics reported relatively high magnitudes (e.g., z = \(-\)14.42 for LR vs. RF; z = \(-\)16.24 for LR vs. GBM). We note that the difference between LR and the ANN, although significant, reported a relatively low magnitude (z = \(-\)7.98). Nonetheless, the highest magnitudes in significance \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \multicolumn{2}{c}{**Model**} & \multicolumn{5}{c}{**Original Data**} & \multicolumn{5}{c}{**Augmented Data**} \\ \multicolumn{2}{c}{**Comparison**} & **AUC1** & **AUC2** & \(p\)**-Value** & **z-Stat** & **AUC1** & **AUC2** & \(p\)**-Value** & **z-Stat** \\ \hline LR & SVM & 0.86 & 0.74 & \(<\)0.001 & \(-\)14.50 & 0.86 & 0.77 & \(<\)0.001 & \(-\)14.56 \\ LR & RF & 0.86 & 0.92 & \(<\)0.001 & \(-\)14.42 & 0.86 & 0.95 & \(<\)0.001 & \(-\)25.76 \\ LR & GBM & 0.86 & 0.94 & \(<\)0.001 & \(-\)16.24 & 0.86 & 0.94 & \(<\)0.001 & \(-\)23.38 \\ LR & XGB & 0.86 & 0.94 & \(<\)0.001 & \(-\)15.75 & 0.86 & 0.95 & \(<\)0.001 & \(-\)25.07 \\ LR & ANN & 0.86 & 0.88 & \(<\)0.001 & \(-\)7.98 & 0.86 & 0.93 & \(<\)0.001 & \(-\)20.67 \\ SVM & RF & 0.74 & 0.92 & \(<\)0.001 & \(-\)22.71 & 0.77 & 0.95 & \(<\)0.001 & \(-\)32.44 \\ SVM & GBM & 0.74 & 0.94 & \(<\)0.001 & \(-\)24.77 & 0.77 & 0.94 & \(<\)0.001 & \(-\)31.22 \\ SVM & XGB & 0.74 & 0.94 & \(<\)0.001 & \(-\)24.73 & 0.77 & 0.95 & \(<\)0.001 & \(-\)32.93 \\ SVM & ANN & 0.74 & 0.88 & \(<\)0.001 & \(-\)18.58 & 0.77 & 0.93 & \(<\)0.001 & \(-\)28.87 \\ RF & GBM & 0.92 & 0.94 & \(<\)0.001 & \(-\)7.54 & 0.95 & 0.94 & \(<\)0.001 & \(-\)7.386 \\ RF & XGB & 0.92 & 0.94 & \(<\)0.001 & \(-\)6.10 & 0.95 & 0.95 & 0.342 & \(-\)0.950 \\ RF & ANN & 0.92 & 0.88 & \(<\)0.000 & \(-\)10.72 & 0.95 & 0.93 & \(<\)0.001 & \(-\)9.799 \\ GBM & XGB & 0.94 & 0.94 & 0.451 & \(-\)0.75 & 0.94 & 0.95 & \(<\)0.001 & \(-\)10.941 \\ GBM & ANN & 0.94 & 0.88 & \(<\)0.001 & \(-\)13.62 & 0.94 & 0.93 & \(<\)0.001 & \(-\)5.120 \\ XGB & ANN & 0.94 & 0.88 & \(<\)0.001 & \(-\)13.25 & 0.95 & 0.93 & \(<\)0.001 & \(-\)9.919 \\ \hline \end{tabular}
\end{table} 
Table 14: A table showing the significance test result for the models evaluated. Figure 9: Comparing the ROC curves and AUCs of the original and augmented datasets. The image on the right shows the ROC curves and AUCs generated from the original data, while the image on the left shows the ROC curves and AUCs generated from the augmented data. The dash line is the diagonal random-classifier line (AUC = 0.5) against which the ROC curves of the models are compared to determine how significantly the algorithms performed against random guessing. were observed on pairwise comparisons between the SVM and the ensemble decision tree classifiers (e.g., z = \(-\)24.77 for SVM vs. GBM; z = \(-\)22.71 for SVM vs. RF), with all differences being significant. Among the ensemble classifiers, differences between AUC values of RF and the GBM as well as between RF and XGB were statistically significant but with a low magnitude ((\(p\) < 0.001, z = \(-\)7.54) and (\(p\) < 0.001, z = \(-\)6.10), respectively). There was no significant difference observed between the GBM and XGB (\(p\) = 0.451, z= \(-\)0.75) in the original dataset. After data augmentation, comparisons between LR and all other models remained significant (\(p\) < 0.001), with increased z-statistics for the ensemble classifiers (e.g., z = \(-\)25.76 for LR vs. RF, z = \(-\)25.07 for LR vs. XGB). However, the difference in AUC values between the GBM and XGB was significant, while the value difference between RF and XGB was no longer significant (\(p\) = 0.342). The RF and XGB models reported the highest AUC (0.995) compared to all other models, with significant differences recorded against the GBM (\(p\) < 0.001) and the ANN (\(p\) < 0.001) models.