# Co-Operative Binary Bat Optimizer with Rough Set Reducts for Text Feature Selection
## 5 Results and Discussion
### Internal Evaluation
#### 5.1.3 Statistical Test
The \(t\)-tests of BRE in the selected generations with BBA\({}_{\text{LHS}}\) and BBA\({}_{\text{CO}}\) are shown in Table 5.  
Observing the values of \(t\)_State_ and \(t\)_Critical two-tail_ in Table 5, it is clear that the BRE of the populations of BBA\({}_{\text{CO}}\) are significantly higher in the beginning of the search process, in both datasets. By the end of the first half (i.e., generation 50), the difference between BRE in the two groups of results reveals no significance in both of the datasets. By the later generations of the search process (i.e., generations 80 and 100), the BRE with BBA\({}_{\text{CO}}\) reduced and became significantly less than that of BBA\({}_{\text{LHS}}\) in both datasets. The results of the statistical test for BRE indicate that in the beginning of the search process, the best solution in BBA\({}_{\text{LHS}}\) outperforms that of BBA\({}_{\text{CO}}\). Then, with the progress of the search process, the best solution of BBA\({}_{\text{CO}}\) improves until it outperforms that of BBA\({}_{\text{LHS}}\). This shows that BBA\({}_{\text{CO}}\) is less subjected to stagnation than BBA\({}_{\text{LHS}}\). The \(t\)-test of ARE in the selected generations with BBA\({}_{\text{LHS}}\) and BBA\({}_{\text{CO}}\) are shown in Table 6. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Dataset** & \multicolumn{2}{c}{**Reuters**} & \multicolumn{2}{c}{**WebKB**} \\ \hline
**Method** & \(\text{BBA}_{\text{CO}}\) & \(\text{BBA}_{\text{LHS}}\) & \(\text{BBA}_{\text{CO}}\) & \(\text{BBA}_{\text{LHS}}\) \\ \hline \multicolumn{5}{c}{generation 1} \\ \hline Mean & 37.28 & 44.66 & 32.08 & 45.86 \\ \(p\)-Value & 0.39 & 0.35 & 0.26 & 0.31 \\ \(t\) State & \(-7.60\) & & \(-18.59\) & \\ \(t\) Critical two-tail & & 2.02 & & 2.00 \\ \hline \multicolumn{5}{c}{generation 20} \\ \hline Mean & 52.33 & 55.36 & 56.48 & 64.28 \\ \(p\)-Value & 0.32 & 0.16 & 0.13 & 0.36 \\ \(t\) State & \(-3.26\) & & \(-7.38\) & \\ \(t\) Critical two-tail & & 2.04 & & 2.04 \\ \hline \multicolumn{5}{c}{generation 50} \\ \hline Mean & 60.23 & 57.54 & 64.15 & 70.78 \\ \(p\)-Value & 0.64 & 0.06 & 0.19 & 0.15 \\ \(t\) State & & 2.14 & & \(-8.38\) & \\ \(t\) Critical two-tail & & 2.00 & & 2.04 \\ \hline \multicolumn{5}{c}{generation 80} \\ \hline Mean & 72.98 & 70.83 & 73.09 & 71.47 \\ \(p\)-Value & 0.43 & 0.13 & 0.16 & 0.29 \\ \(t\) State & & 3.48 & & 2.58 \\ \(t\) Critical two-tail & & 2.03 & & 2.03 \\ \hline \multicolumn{5}{c}{generation 100} \\ \hline Mean & 73.98 & 71.16 & 74.27 & 72.79 \\ \(p\)-Value & 0.51 & 0.29 & 0.22 & 0.18 \\ \(t\) State & & 2.79 & & 2.82 \\ \(t\) Critical two-tail & & 2.00 & & 2.01 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The \(t\)-test of population quality in different generations using BBA\({}_{\text{CO}}\) and BBA\({}_{\text{LHS}}\). As shown in Table 6, the ARE of BBA\({}_{\text{CO}}\) population is significantly higher than that of BBA\({}_{\text{LHS}}\) at the beginning of the search process in both datasets. In later generations (i.e., generations 20 and 50), the ARE of the population of BBA\({}_{\text{CO}}\) keeps reducing but the difference with the other group (i.e., ARE of the population of BBA\({}_{\text{LHS}}\)) is not statistically significant, in the Reuters dataset. By the last quarter of the search process (i.e., generations 80 and 100), the ARE of the population of BBA\({}_{\text{CO}}\) became statistically lower than that of BBA\({}_{\text{LHS}}\), in the Reuters dataset. In the WebKB dataset, the ARE of BBA\({}_{\text{CO}}\) was significantly higher than that of BBA\({}_{\text{LHS}}\) within the first half of the search process. Later, the ARE of the BBA\({}_{\text{CO}}\) population keeps reducing, but the difference with the other group is not significant. The results of ARE are consistent with those of BRE, as the population in BBA\({}_{\text{CO}}\) improves slower than that of BBA\({}_{\text{LHS}}\) because of controlling diversity.