## 4 Experimental Evaluations
### Methods and Results
The results indicate that there are clear differences in the mean performances of the students from the two groups on the post-test (\(p\) = 0.000 \(<\) 0.05). Specifically, \(p\)-value \(<\) 0.05 is considered statistically significant. The results of the study point out that after controlling for initial quantitative ability, the differences are statistically significantly different in the post-test scores for the two groups of the study. Therefore, it can be concluded that students from GroupB gave more correct answers than students from GroupA and that students from GroupB learned better than the students from GroupA. The results show that the boost of the performance of the students from GroupA was approximately 37.7% while the performance of the students from GroupB was 46%. After the completion of the experiment that lasted five weeks, the students from the two groups were asked to fill in two questionnaires, which were the System Usability Scale (SUS) questionnaire [32] and a Likert-scale questionnaire. The purpose of these two instruments was to assess learners' opinions about the virtual environment, the embodied pedagogical agents, and their overall learning experience. The first questionnaire that students were asked to fill in was a five-point Likert scale questionnaire that asked students to express their agreement with a set of statements. In total, there were 10 questions based on the Likert scale (1: Not at all, 5: Very much), and the results of which are illustrated in Table 3. The second questionnaire that students were asked to fill in was the System Usability Scale (SUS) that was used for assessing the usability of the environment. The SUS questionnaire was employed for its short length and ease to answer. The ten questions were organized into two groups (positive and negative) and participants were asked to rate them on a five-point scale ranging from strongly disagree to strongly agree. The final score of the SUS is a number from 0 to 100 and it can be easily interpreted. SUS is, in general, a robust way to evaluate the usability of a system, even when there is a limited sample size available. An overall SUS score over 85 indicates that the system is highly usable, a score from 70 to 85 shows that the system is good to excellent, a score from 50 to 70 indicates that the system needs improvements while a score below 50 indicates that the system is unacceptable [33]. Regarding the reliability of the questionnaires and in order to derive secure conclusions from the questionnaire data, [PERSON]'s alpha [34] was calculated. The Cronbach's alpha metric was calculated to be 0.78 and 0.80 thus, pointing out a high reliability score. Hence, strong and secure conclusions can be drawn. In the following tables, the results of the questionnaires of the two groups are illustrated. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Levene’s Test for**} & \multicolumn{3}{c}{**t-Test for Mean**} & \\  & \multicolumn{3}{c}{**Equality of Variances**} & & & & & & & \\ \cline{3-8}
**Equality of Variance** & & & & & & & & **95\% Confidence** \\ \cline{3-8}  & \multirow{2}{*}{F} & \multirow{2}{*}{**Sig.**} & \multirow{2}{*}{**t**} & \multirow{2}{*}{**df**} & \multirow{2}{*}{**Sig.(2-Tailed)**} & \multirow{2}{*}{**MD**} & **Interval of the Difference** \\  & & & & & & & **Lower, Upper** \\ \hline \multirow{2}{*}{Pre-Test} & Equal & 8.514 & 0.004 & \(-\)1.759 & 142 & 0.081 & \(-\)0.174 & \(-\)0.368, 0.021 \\ \cline{2-8}  & Unequal & & & \(-\)1.759 & 138.231 & 0.081 & \(-\)0.174 & \(-\)0.368, 0.021 \\ \hline \multirow{2}{*}{Post-Test} & Equal & \multirow{2}{*}{14.969} & \multirow{2}{*}{0.000} & \(-\)9.214 & 142 & 0.000 & \(-\)1.340 & \(-\)1.627, \(-\)1.052 \\ \cline{2-8}  & Unequal & & & \(-\)9.214 & 132.377 & 0.000 & \(-\)1.340 & \(-\)1.628, \(-\)1.052 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Analyses of pre-test and post-test. The answers of the two groups show that students from GroupB, who studied in the second scenario, had a better learning experience.