# An Empirical Assessment of Performance of Data Balancing Techniques in Classification Task
## 4 Results and Discussion
### Performance of DBT for Varying Levels of IR in the Dataset  
Tables 15-20 show ranks of DBT for six different classifiers for varying levels of IR in the dataset. In order to assess the performance of DBT for varying levels of IR, we used Kendall's test statistics. The rows in the tables indicate the DB strategy and the columns \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & **DT** & **kNN** & **LR** & **NB** & **RF** & **SVM** & **Mean Rank** \\ \hline None & 7 & 7 & 7 & 7 & 7 & 7 \\ \hline US & 2 & 6 & 4 & 1 & 2 & 5 & 3.333333 \\ \hline OS & 5 & 1 & 2 & 4 & 5 & 3 & 3.333333 \\ \hline HS & 4 & 4 & 3 & 5 & 3 & 1 & 3.3333333 \\ \hline ROSE & 6 & 3 & 6 & 6 & 6 & 6 & 5.5 \\ \hline SMOTE & 3 & 2 & 1 & 2 & 4 & 4 & 2.666667 \\ \hline CBUS & 1 & 5 & 5 & 3 & 1 & 2 & 2.833333 \\ \hline Kendall’s statistics & & & & W = 0.562, chi-sq = 20.2, \(p\)-value = 0.00254 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 14: Ranks of DBT for different classifiers. indicate the range of IR in the dataset. The values in each cell indicate the rank of DBT for varying levels of IR in the dataset for a given classifier. The last row in each table shows the results of Kendall's test statistics. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **01–10** & **11–20** & **21–30** & **31–40** & **41–50** & **Mean** \\ \hline None & 5 & 7 & 7 & 7 & 7 & 6.6 \\ \hline US & 7 & 4 & 6 & 4 & 6 & 5.4 \\ \hline OS & 1 & 2 & 1 & 2 & 2.5 & 1.7 \\ \hline HS & 6 & 3 & 2.5 & 4 & 4 & 3.9 \\ \hline ROSE & 4 & 5 & 2.5 & 1 & 1 & 2.7 \\ \hline SMOTE & 2 & 1 & 4 & 4 & 5 & 3.2 \\ \hline CBUS & 3 & 6 & 5 & 6 & 2.5 & 4.5 \\ \hline Kendall’s statistics & & & W = 0.593, chi-sq = 17.8, \(p\)-value = 0.00679 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 16: Ranks of DBT for kNN for varying levels of IR. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **01–10** & **11–20** & **21–30** & **31–40** & **41–50** & **Mean** \\ \hline None & 6 & 5 & 7 & 7 & 7 & 6.4 \\ \hline US & 3 & 4 & 6 & 1 & 2 & 3.2 \\ \hline OS & 5 & 1 & 3.5 & 6 & 5 & 4.1 \\ \hline HS & 4 & 3 & 3.5 & 3 & 3.5 & 3.4 \\ \hline ROSE & 7 & 6.5 & 2 & 4 & 3.5 & 4.6 \\ \hline SMOTE & 1 & 2 & 1 & 5 & 1 & 2 \\ \hline CBUS & 2 & 6.5 & 5 & 2 & 6 & 4.3 \\ \hline Kendall’s statistics & & & W = 0.401, chi-sq = 12, \(p\)-value = 0.0615 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 17: Ranks of DBT for LR for varying levels of IR. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **01–10** & **11–20** & **21–30** & **31–40** & **41–50** & **Mean** \\ \hline None & 6 & 4 & 7 & 7 & 7 & 6.2 \\ \hline US & 3 & 5 & 2 & 5 & 1 & 3.2 \\ \hline OS & 1 & 1.5 & 6 & 4 & 6 & 3.7 \\ \hline HS & 5 & 3 & 3 & 6 & 4 & 4.2 \\ \hline ROSE & 7 & 7 & 4 & 2 & 3 & 4.6 \\ \hline SMOTE & 2 & 1.5 & 5 & 3 & 5 & 3.3 \\ \hline CBUS & 4 & 6 & 1 & 1 & 2 & 2.8 \\ \hline Kendall’s statistics & & & W = 0.282, chi-sq = 8.46, \(p\)-value = 0.206 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 15: Ranks of DBT for DT for varying levels of IR. From the results of Kendall's statistics, we can infer that:  
1. For the DT classifier, there is no agreement over the rankings of DBT as the \"\(p\)\" value is greater than 0.05. This means that for the DT classifier, the performance of the data balancing techniques was not consistent for varying imbalance-ratio percentages. 2. For the kNN classifier, there is agreement over the rankings of the data-balancing techniques as the \"\(p\)\" value is less than 0.05. However, the concordance value (w) is 0.593, which indicates that there is partial agreement over the rankings. From the ranks of DBT, it is observed that the performance of None seemed consistent, whereas the performance of other DBT was different for varying imbalance-ratio percentages. 3. For the LR classifier, there is no agreement over the rankings of data-balancing techniques as the \"\(p\)\" value is greater than 0.05. This means that for the LR classifier,