# Impact of Imbalanced Datasets Preprocessing in the Performance of Associative Classifiers
## 5 Experimental Results
### Statistical Analysis
The SMOTE algorithm did not have significant differences with respect the SMOTE-BL, ADASYN and ADOMS algorithms, due to the null hypothesis were not rejected for such cases. However, SMOTE showed a significantly better performance than SMOTE-SL, ROS and the original classifier without instance selection. The statistical tests allow us to state that using oversampling techniques such as SMOTE, DID increase the Area under the ROC curve of the SNDAM classifier, over imbalanced financial data. Such improvement came with the additional computational cost of creating artificial instances and therefore increasing the cardinality of the datasets. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**i** & **Algorithm** & **z** & **P** & **Holm** \\ \hline
6 & SDC & 3.404405 & 0.000663 & 0.008333 \\
5 & RUS & 1.361762 & 0.173273 & 0.010000 \\
4 & CNNTL & 0.817057 & 0.413896 & 0.012500 \\
3 & OSS & 0.635489 & 0.52511 & 0.016667 \\
2 & Original & 0.499313 & 0.617559 & 0.025000 \\
1 & NCL & 0.272352 & 0.785351 & 0.05 \\ \hline \hline \end{tabular}
\end{table} 
Table 23: Results of the Holm test comparing the performance of the Extended Gamma classifier after undersampling algorithms. The test rejects the hypothesis having an unadjusted \(p\)-value \(\leq\) 0.01. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**i** & **Algorithm** & **z** & **P** & **Holm** \\ \hline
6 & Original & 2.995876 & 0.002737 & 0.008333 \\ \hline
5 & ROS & 2.995876 & 0.002737 & 0.010000 \\ \hline
4 & SMOTE-SL & 2.814308 & 0.004888 & 0.012500 \\ \hline
3 & ADOMS & 1.225586 & 0.220355 & 0.016667 \\ \hline
2 & ADASYN & 0.22696 & 0.820455 & 0.025000 \\ \hline
1 & SMOTE-BL & 0.22696 & 0.820455 & 0.05000 \\ \hline \hline \end{tabular}
\end{table} 
Table 25: Results of the Holm test comparing the performance of the SNDAM classifier after oversampling algorithms. The test rejects the hypothesis having an unadjusted \(p\)-value \(\leq\) 0.016667. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**i** & **Algorithm** & **z** & **P** & **Holm** \\ \hline
6 & ADOMS & 3.994502 & 0.000065 & 0.008333 \\
5 & SMOTE & 3.041268 & 0.002356 & 0.010000 \\
4 & ADASYN & 2.995876 & 0.002737 & 0.012500 \\
3 & SMOTE-BL & 2.496564 & 0.01254 & 0.016667 \\
2 & SMOTE-SL & 0.998625 & 0.317976 & 0.025000 \\
1 & Original & 0.136176 & 0.891682 & 0.050000 \\ \hline \hline \end{tabular}
\end{table} 
Table 22: Results of the Holm test comparing the performance of the Extended Gamma classifier after oversampling algorithms. The test rejects the hypothesis having an unadjusted \(p\)-value \(\leq\) 0.025. The best ranked undersampling algorithm, RUS, had no significant difference in performance with none of the remaining undersampling algorithms but SBC, nor with respect using the original imbalanced dataset. Again, we can conclude within a 95% confidence, that using undersampling algorithms DID NOT increase the performance of the SNDAM classifier, using imbalanced financial data. The [PERSON]'s test did not found significant differences in performance between the SMOTE-ENN and SMOTE-TL algorithms. However, the test did found SMOTE-ENN being significantly better than SPIDER2, SPIDER and the original classifier without instance sampling. Then, can conclude within a 95% confidence, that using oversampling algorithms such as SMOTE-ENN DID increase the performance of the SNDAM classifier, using imbalanced financial data. From the experiments performed, it is possible to establish that the HACT, Extended Gamma and NAC classifiers DO NOT benefit from data balancing. On the other hand, the SNDAM classifier DOES obtain improvements in its performance by balancing the datasets using oversampling (as SMOTE) and hybrid (as SMOTE-ENN) algorithms. Undersampling algorithms DO NOT improve the performance of the SNDAM classifier over imbalanced financial data.