## 5 Results and Analysis Using Learning Analytics Techniques
### Clustering
#### 5.2.2 SRLAS Clustering  
A similar clustering analysis for the SRLAS dimensions was performed, where four clusters were also determined after an analysis of the results derived from different number of clusters. Figure 6a,b present the populations of the four clusters formed based on the SRLAS dimensions and their corresponding average grades using pie chart and bar diagrams, respectively. These values are also included in Table 5 along with the average final grades and their standard deviations.  
Figure 5: Comparison of MI clusters: (**a**) bar diagram; (**b**) normalized radar.  
Figure 6: (**a**) SRLAS clusters’ sizes; (**b**) SRLAS clusters’ average final grades.  
It was found that the average grade for Cluster 1 is higher than those for Clusters 2, 3, and 4. Similar to the MI dimensions, one-tail \(t\)-tests between clusters were performed to determine whether the differences in the average final grades are statistically different. The study observed no statistically significant differences among Clusters 2, 3, and 4. Therefore, we opted to compare the average grade for Cluster 1 with those for Clusters 2, 3, and 4 combined (Table 6). The following hypotheses were used:  
\[H_{o}:\mu_{2\cup 3,\mathcal{U}} =\mu_{1}\] \[H_{a}:\mu_{2\cup 3,\mathcal{U}} <\mu_{1}\]  
Table 6 conclusively indicates that the difference between the average grades for Cluster 1 and the union of Clusters 2, 3, and 4 is statistically significant with a very small \(p\)-value (less than \(1\times 10^{-4}\))  
To study the difference among clusters in more detail, a bar-plot in a 1-5 scale was constructed, with the average values obtained for each of the SRLAS dimensions (Figure 7a), similarly to how it was done for the MI dimensions. The corresponding radar diagram, emphasizing the differences among the clusters' dimensions, is presented in Figure 7b.  
As can be seen in Figure 7b, Cluster 1, which has the best academic performance, is the cluster with the lowest anxiety values and the lowest need for extrinsic motivation.  
It is important to mention that, although the MI and SRLAS constructs were combined in preliminary analyses, this integration is not recommended due to the information overload produced by the 16 dimensions involved. No additional benefits were obtained, so it was decided to study these two constructs separately in this work.  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **Cluster 1** & **Cluster 2**\(\cup\) 3 \(\cup\) 4 \\ \hline \(N\) & 156 & 462 \\ \hline Average final grade & 81.3 & 74.4 \\ \hline Std. Dev. & 11.4 & 13.5 \\ \hline \(p\)-value & 0.0000 \\ \hline \hline \end{tabular}
\end{table}
Table 6: \(p\)-values for one-tail \(t\)-tests comparisons among clusters’ average grades (SRLAS).  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Cluster 1** & **Cluster 2** & **Cluster 3** & **Cluster 4** \\ \hline \(N\) & 156 & 261 & 174 & 27 \\ \hline Average final grade & 81.3 & 75.6 & 72.7 & 74.4 \\ \hline Std. Dev. & 11.4 & 13.5 & 13.5 & 12.3 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Size, Average Final Grade, and Standard Deviation of clusters formed with SRLAS dimensions.  
Figure 7: Comparing SRLAS clusters: (**a**) bar diagram; (**b**) normalized radar.