## 4 Results and Discussion
### Balanced and Imbalanced Data Stream with Incremental Drift
\begin{table}
\begin{tabular}{l c c c c c c c c c c c} \hline \hline
**DS** & **NoCD** & **DDM** & **EDDM** & **Cusum** & **HDDM\_A** & **HDDM\_W** & **GMA** & **PH** & **RDDM** & **STEPD** & **EWMAC** \\ \hline B-S & **75.6318** & 73.5086 & 72.5561 & 72.9715 & 72.4036 & 70.4254 & **75.6318** & 72.3253 & 73.5527 & 70.7199 & 66.8582 \\ I-S & 71.501 & 71.7858 & 70.5645 & 70.5466 & **72.0156** & 68.4061 & 71.501 & 70.6462 & 70.6549 & 67.034 & 64.3249 \\ B-G & 73.7541 & 77.1057 & **77.8197** & 77.0541 & 73.9509 & 71.1709 & 73.7541 & 77.6869 & 77.0689 & 70.7089 & **77.8197** \\ I-G & 70.555 & **75.9551** & 75.1269 & 74.0852 & 75.0977 & 69.9959 & 70.555 & 75.4099 & 74.8177 & 66.9283 & 65.5907 \\ B-I & 58.9903 & 58.9247 & 60.2054 & 59.9613 & 58.0969 & 57.5035 & 58.9903 & **61.3183** & 60.1062 & 57.228 & 56.6787 \\ I-I & 56.6491 & **57.9251** & 56.9282 & 56.7571 & 57.5149 & 54.966 & 56.6491 & 57.1908 & 56.8511 & 55.7872 & 53.9512 \\ \hline \hline \end{tabular}
\begin{tabular}{l c c c c c c c c c} \hline \hline
**DS**: Data Stream; **NoCD**: No Change Detection Method; **B-S**: Balanced Stream with Sudden Drift; **I-S**: Balanced Stream with Sudden Drift; **B-G**: Balanced Stream with Gradual Drift; **I-G**: Imbalanced Stream with Gradual Drift; **B-I**: Balanced Stream with Incremental Drift; **I-I**: Imbalanced Stream with Incremental Drift.  
\end{table} 
Table 5: Overall F1 score of HT classifier with different drift detection methods. Therefore, from Table 5, we generated the ranking of the methods on each data stream and calculated the overall ranking same can be seen in Table 6. In this study, one base classifier is tested with 10 drift detections and one without the drift detection method, so the best ranking is 1, and the worst ranking is 11. The rankings were calculated using the RANK.EQ function available in Microsoft excel. The results show that the DDM produced the best average ranking which is 3.17. Both EDDM and PH produced the 2 nd best average ranking with 3.83. RDDM produced the 3 rd best average ranking with 4.33. 4, respectively. The STEP_D, EWMAC, and HDDM_W remained the poorest performers with 9.83, 9.33, and 9.5, respectively. On imbalance data streams specifically, the DDM produced the best ranking, i.e., ranked 2 nd on I-S, ranked 1 st on I-G, and ranked 1 st on I-I. The ranking of GMA is the ranking of the base classifier because GMA showed no effect on the performance of HT as the base classifier. _Statistical analysis_: Results of all drift detection methods are statistically analyzed to identify the performance significance. We used the [PERSON] test [52] to compare the results of all the methods investigated across six data streams. The [PERSON] test function FriedmanisquareResult of python was used to run the test. [PERSON]'s test result with statistic = 32.94 and \(p\) = 0.00028 rejects the null hypothesis (all drift detection methods produce the same performance) as \(p\) < 0.05. Still, it is not clear which of the compared methods performed significantly differently. To achieve this the Bonferroni-Dunn post hoc test [53] is used to determine which algorithms are statistically distinct. The result of the Bonferroni test is shown in Figure 12. The methods which are not significantly different (at \(p\) = 0.05) are connected.