## 4 Experiments and Results
### Correlation Between Student Clusters and Performance  
We now examine whether a relationship exists between the clusters identified in the previous section and students' final grades. An ANOVA test confirmed this relationship, revealing statistical significance (\(p\)-value < 0.05). To further  
associated with allocating time and strategic focus on specific resources. Clusters that spent more time in simulations and workshops at higher \(\text{CWA}_{U}\) thresholds performed better than those that focused on other educative resources. * Small Clusters, High Performance: Smaller clusters, such as Cluster 3 at 20% and 40% and Cluster 2 at 60% and 80% \(\text{CWA}_{U}\) thresholds, respectively, consistently exhibited higher weighted averages and more time spent with evaluative resources like simulations and workshops, suggesting that smaller groups of students who focused their study efforts efficiently on evaluative resources were able to achieve better performance. Our findings emphasize the importance of strategic engagement and focused study habits in shaping academic success. Specific clusters consistently outperform others, primarily due to their effective use of educational resources. We conducted an analysis comparing the weighted average with the Linearity Score. As shown in Table 9, students with higher weighted averages tend to have lower linearity scores, suggesting that these students do not follow a strictly sequential or predetermined path when engaging with learning resources and assessments. Instead, they exhibit a more adaptive and exploratory approach, often revisiting previous materials, iterating on assessments, or engaging in self-regulated learning strategies to reinforce their understanding. Note that from Tables 7 and 9, and Figure 13, clusters 3 and 2 seem to have swapped; this was indeed the case: 12 of the 13 students in cluster 3 at \(\text{CWA}_{U}=40\%\) moved to cluster 2 and stayed there for \(\text{CWA}_{U}\in\{60\%,80\%\}\)  
This behavior aligns with self-regulated learning (SRL) principles, where students actively plan, monitor, and regulate their learning process to optimize their academic performance [33]. Rather than simply following a linear progression through course content, these students take strategic paths, reviewing previous topics, selectively repeating assessments to improve their grades, or navigating resources to best suit their individual learning needs. Research on SRL in online learning environments supports this finding. It highlights how high-performing students engage in metacognitive monitoring, set learning goals, and adjust their strategies based on feedback and performance data [34]. These insights suggest that self-learning practices, emphasizing reflection, revision, and iterative assessment, contribute significantly to students' academic success in non-linear, self-paced learning environments. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{\(\text{CWA}_{U}\)} & \multirow{2}{*}{**Cluster**} & \multicolumn{3}{c}{\(p\)-Value} \\ \cline{3-5}  & & **Cluster 1** & **Cluster 2** & **Cluster 3** \\ \hline \multirow{3}{*}{20\%} & Cluster 0 & **0.001** & 0.765 & 0.749 \\  & Cluster 1 & & **0.005** & **0.016** \\  & Cluster 2 & & & 0.531 \\ \hline \multirow{3}{*}{40\%} & Cluster 0 & 0.063 & **0.001** & 0.900 \\  & Cluster 1 & & **0.001** & 0.900 \\  & Cluster 2 & & & 0.116 \\ \hline \multirow{3}{*}{60\%} & Cluster 0 & **0.031** & 0.551 & **0.001** \\  & Cluster 1 & & 0.900 & **0.001** \\  & Cluster 2 & & & 0.143 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: \(p\)-values result for each cluster at different \(\text{CWA}_{U}\) thresholds. Bold values indicate significant clusters (\(p\leq 0.05\)). We analyzed students' active forum participation, including posting and responding to discussions.