## 5 Results  
Students' Academic Performance  
RQ1. Does the building of a student model using Bayesian networks based on fuzzy logic increase the performance of ITS in terms of student academic performance compared to using fuzzy logic and Bayesian networks separately? To answer this question, the following hypothesis was put forward:  
H1: there is a statistically significant difference between the three groups (A1, A2, and A3) on student academic performance, in favor of Group A3. Table 2 shows that group A3 had the highest mean value on student academic performance (M = 82.95, SD = 18.59) while group A2 had the lowest mean value on student academic performance (M = 69.77, SD = 22.81). In order to test hypothesis H1, the analysis of covariance (ANCOVA) was conducted to compare the students' academic performances in three different groups involved in the experiment. The independent variable was the type of the e-learning system (Groups A1, A2, and A3), and the dependent variable consisted of scores on student academic performance administered after the experiment was completed. The participants' scores on the pre-test administration of the basic knowledge test were used as the covariate in this analysis. Preliminary checks were conducted to ensure that there was no violation of the assumptions of linearity, homogeneity of variances, homogeneity of regression slopes, and reliable measurement of the covariate. [PERSON]'s test for equality of variances was used for homogeneity of group variances. The assumption that variances were homogeneous was met, as shown in Table 3.  
Table 4 illustrated that, after adjusting for pre-test scores, there was a significant difference between the three groups on the post-test scores of the students, F (2, 56) = 11.571, \(p\) < 0.001, partial eta squared = 0.292 (The F means ratio of two variances, df means the number of degrees of freedom; the number of values in the final calculation of a statistic that are free to vary, A \(p\)-value which means significance value, less than 0.05 is statistically significant, partial Eta squared which is a squared measure of association defined as the ratio of variance in an outcome variable explained by a predictor variable, after controlling for other predictors), indicated a large effect size [44]. Moreover, the results show that, there was a significant moderate effect of the pre-test scores on the post-test scores of the students (F = 27.074, \(p\) < 0.05), as indicated by a partial eta squared value of 33%. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Dependent Variable: Post-Test** & \\ \hline
**Group** & **Mean** & **Std. Deviation** & **N** \\ \hline A1 & 79.09 & 21.39 & 20 \\ A2 & 69.77 & 22.81 & 20 \\ A3 & 82.95 & 18.59 & 20 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Descriptive Statistics of groups A1, A2, and A3. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**F** & **df1** & **df2** & \(p\) \\ \hline
0.555 & 2 & 57 & 0.575 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: [PERSON]’s test for homogeneity of the group variances. H1 is confirmed and it can be concluded that the students who used FB-ITS (A3) to learn Excel yield significantly better academic performance than the students who studied with the ITS using the Bayesian network (A1) and fuzzy logic (A2). RQ2. Do the students who studied using FB-ITS have a higher academic performance than the students who studied using the traditional e-learning system? To answer this question, the following hypothesis was put forward:  
H2: There is a statistically significant difference between the two groups (A3 and B) in student academic performance in favor of Group A3. The descriptive statistics for Groups A3 (FB-ITS) and B (traditional e-learning system) are presented in Table 6. This table shows that Group A3 had a higher mean value in the student academic performance (M = 82.95, SD = 18.587) than Group B (M = 64.33, SD = 26.256).