# 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 \(t\)-test is conducted for multiple groups of results to compare \(\text{BBA}_{\text{LHS}}\) and \(\text{BBA}_{\text{CO}}\) in terms of the population's diversity and quality in different generations. The population's diversity is measured using standard deviation, which is greater for more diverse populations. Moreover, the population's quality is measured by the average quality of its solutions and the relative errors as shown in the following subsections. Figure 7: Diversity of solutions in (**a**) first generation, (**b**) generation 20, (**c**) generation 50, (**d**) generation 80 and (**e**) generation 100, using \(\text{BBA}_{\text{LHS}}\) (left) and \(\text{BBA}_{\text{CO}}\) (right) for WebKB dataset. Figure 8: Convergence behavior of the population using BBA\({}_{\text{LHS}}\) and BBA\({}_{\text{CO}}\) for Reuters dataset. Figure 10: Convergence behavior of 5 solutions using BBA\({}_{\text{CO}}\) for Reuters dataset. Figure 9: Convergence behavior of the population using BBA\({}_{\text{LHS}}\) and BBA\({}_{\text{CO}}\) for WebKB dataset. The quality dispersion of the solutions in the population is measured on the basis of the standard deviation (SD), which is higher for more diverse distributions and lower for less diverse distributions. SD is calculated as in the equation below. Consequently, the SD of the population in certain generations (1, 20, 50, 80, 100) is calculated and recorded for 32 different runs in BBA\({}_{\text{LHS}}\) and BBA\({}_{\text{CO}}\) for each dataset. Table 3 shows the results of the \(t\)-test which is conducted between the results obtained using BBA\({}_{\text{LHS}}\) and BBA\({}_{\text{CO}}\) to investigate whether or not they are statistically different:  
\[SD=\sqrt{\frac{\sum_{i=1}^{n}\left(fitness_{i}-\overline{fitness}\right)^{2}} {n}}\]  
where SD stands for standard deviation; \(n\) is the population size; \(fitness_{i}\) is the fitness of solution \(i\); \(\overline{fitness}\) is the average fitness of the initial population. Table 3 shows that the SD of the population in the selected generations for both datasets using BBA\({}_{\text{CO}}\) is significantly higher than the SD when BBA\({}_{\text{LHS}}\) is used. Additionally, it could be stated that when using the \(t\)-test, the first group of results is significantly higher than the second group of results when \(t\)_State_ is greater than \(t\)_Critical two-tail_. On the other hand, if \(t\)_State_ is less than \(-t\)_Critical two-tail_, this means that the results in the second group are significantly higher than the results in the first group. Meanwhile, if \(t\)_State_ is within the interval [\(-t\)_Critical two-tail_, \(t\)_Critical two-tail_], the difference is not considered to be significant. The results in Table 3 show that \(t\)_State_ is higher than \(t\)_Critical two-tail_ in all the selected generations. The value of \(t\)_State_ is higher than \(t\)_Critical two-tail_ in all generations. The results of the \(t\)-test indicate that the population diversity which is expressed by standard deviation, is higher in BBA\({}_{\text{CO}}\) during the search process. This reveals the ability of BBA\({}_{\text{CO}}\) to control the population's diversity during the search process. In order to measure the population quality, the average quality of the solutions will be used. This measure was utilized by the authors of [73] to measure the population quality. It is defined as the average quality of solutions in the population, as given in the following equation:  
\[population\ quality\ (\%)=\left(1-\frac{\overline{fitness}-best_{known}}{ best_{known}}\right)\]  
Figure 11: Convergence behavior of 5 solutions using BBA\({}_{\text{CO}}\) for WebKB dataset. where \(\widehat{fitness}\) is the average quality (i.e., dependency value; fitness) of solutions in the population; \(\mathit{best}_{known}\) is the best-known quality that the solution could reach.