## 5 Results and Analysis Using Learning Analytics Techniques
### Clustering
#### 5.2.1 MI Clustering  
In Figure 4a,b, the populations of the four MI clusters and their corresponding average grades are presented, in the pie chart and the bar diagram, respectively. Table 3 also presents these values, along with the average grades and their standard deviations. The  
Figure 3: PCA Biplot diagrams and Correlation of dimensions of (**a**) MI and (**b**) SRLAS dimensions.  
populations of the four MI clusters and their corresponding average grades are presented, in the pie chart and the bar diagram, respectively. Table 2 also presents these values, along with the standard deviation of the average grades.  
From Table 3, it is observed that the average grades for Clusters 1, 2, and 3 are similar but relatively different from that of Cluster 4. Therefore, paired one-tail \(t\)-tests between the clusters were performed to validate these results. It was found that there was no statistical difference among the average grades of Clusters 1, 2, and 3. On the other hand, Cluster 4 was compared with the union of Clusters 1, 2, and 3. The following hypotheses were used:  
\[H_{o}:\mu_{1\cup 2\cup 3}=\mu_{4}\]  
\[H_{a}:\mu_{1\cup 2\cup 3}>\mu_{4}\]  
It was observed that the average grade for Clusters 1, 2, and 3 is statistically higher than the average grade for Cluster 4 with a \(p\)-value = 0.0580 (Table 4).  
To investigate the possible differences among MI clusters in more detail, a bar-plot in a 1-5 scale, with the average values obtained for each MI dimension, was constructed (Figure 5a). Cluster 3, consisting of 34 students and having a slightly higher average grade, presents the smaller values of all MI dimensions, as compared with the other clusters. To emphasize the differences among clusters and to facilitate the analysis of the data, in Figure 5b, a normalized radar is formed by setting the differen  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **Cluster 1 \(\cup\) 2 \(\cup\) 3** & **Cluster 4** \\ \hline \(N\) & 530 & 88 \\ \hline Average final grade & 76.5 & 74.1 \\ \hline Std. Dev. & 12.9 & 15.2 \\ \hline \(p\)-value & 0.0580 \\ \hline \hline \end{tabular}
\end{table}
Table 4: \(p\)-values for one-tail \(t\)-tests’ comparisons among clusters’ average grades (MI dimensions).  
Figure 4: (a) MI clusters’ sizes; (b) MI clusters’ average grades.  
and minimum values of the sample equal to 1 and interpolating the remaining values of the sample.  
As previously mentioned above, it is seen that Cluster 3 (red line in Figure 5) has the lowest values for all MI dimensions, despite exhibiting (slightly) the highest average grade. Cluster 1 shows the highest value for almost all dimensions, while Clusters 2 and 3 present intermediate values. The results indicate that Cluster 4, composed of 88 students with the lowest average grade, presents a very high value of the intrapersonal dimension but a relatively low value of the interpersonal dimension. These results suggest that MI dimensions alone are not useful enough to categorically explain the differences between students' grades.  
Consequently, in this study, the information derived from MI is complemented with that provided by SRLAS to determine the combination of dimensions that could better explain the academic performance of undergraduate engineering students.