# Impact of Imbalanced Datasets Preprocessing in the Performance of Associative Classifiers
## 5 Experimental Results
### Statistical Analysis  
To establish whether the differences in the AUC founded in the previous section are significant or not, statistical tests were carried out. The Friedman tests applied did not reject the hypothesis of equal performance when comparing the AUC of the balancing methods for the HACT, with \(p\)-values of 0.9799 for oversampling, 0.2116 for undersampling, and 0.9212 for hybrid algorithms. In this case, it is possible to conclude, with 95% certainty, that using class balancing methods DOES NOT improve the performance of HACT classifier, in imbalanced datasets, belonging to the financial field. The test also did not reject the null hypothesis for oversampling and hybrid algorithms for NAC classifier (\(p\)-values of 0.2853 and 0.4980, respectively). For undersampling algorithms, the test did reject the null hypothesis, with a \(p\)-value of 0.0207. In the [PERSON] test, the best ranked algorithm was the original classifier, without instance sampling. For the undersampling algorithms, we applied the [PERSON]'s test (Table 21). [PERSON]'s procedure rejects those hypotheses that have an unadjusted \(p\)-value \(\leq 0.01\). As shown by the test, we can conclude with a 95% of certainty, that the sampling algorithms but SBC, DID NOT improve the performance of the NAC classifier, in financial imbalanced data. In addition, SBC algorithm decreases the NAC performance. Regarding the Extended Gamma classifier, the [PERSON]'s tests did reject the null hypothesis of equal performance for oversampling, undersampling and hybrid algorithms. The corresponding \(p\)-values were 0.000048, 0.015356 and 0.013584, respectively. The best ranked algorithms were ROS, TL and SPIDER2. In these cases, post-hoc tests were performed to determine among which algorithms the differences were. Tables 22-24 show the results of the tests applied for oversampling, undersampling and hybrid methods, respectively. The ROS algorithm had no significant differences with respect to the original classifier, nor with the SMOTE-SL algorithm. Then, we can conclude within a 95% confidence, that using oversampling algorithms DID NOT increase the performance of the Extended Gamma classifier, using imbalanced financial data. The best ranked undersampling algorithm, TL, had no significant difference in performance with none of the remaining undersampling algorithms but SBC, nor with respect using the original imbalanced dataset. The SBC algorithm was indeed significantly worse than TL, for the Extended Gamma Classifier performance. Again, we can conclude within a 95% confidence, that using undersampling algorithms DID NOT increase the performance of the Extended Gamma classifier, using imbalanced financial data. The best ranked hybrid algorithm SPIDER2, had no significant difference in performance with SPIDER and SMOTE-TL nor with respect using the original imbalanced dataset. The SMOTE-ENN algorithm was significantly worse than SPIDER2, for the Extended Gamma classifier performance. Again, we can conclude within a 95% confidence, that using hybrid algorithms DID NOT increase the performance of the Extended Gamma classifier, using imbalanced financial data. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**i** & **Algorithm** & **z** & **p** & **Holm** \\ \hline
6 & SBC & 2.768916 & 0.005624 & 0.008333 \\
5 & CNNTL & 1.861075 & 0.062734 & 0.01000 \\
4 & OSS & 1.770291 & 0.076679 & 0.012500 \\
3 & TL & 0.408529 & 0.682886 & 0.016667 \\
2 & NCL & 0.136176 & 0.891682 & 0.025000 \\
1 & RUS & 0.045392 & 0.963795 & 0.050000 \\ \hline \hline \end{tabular}
\end{table} 
Table 21: Results of the Holm test comparing the performance of the NAC classifier after undersampling algorithms. With respect the SNDAM classifier, the best ranked algorithms according to the Friedman tests were SMOTE, RUS and SMOTE-ENN. The results of the corresponding Holm's test for oversampling, undersampling and hybrid algorithms are showed in Tables 25-27.