## 8 Academic Performance Clustering Analysis
### GPA Analysis  
The average GPA for each strategy cluster is shown in Figure 4. To compute the average GPA, we first calculate the average cumulative GPA for each student over their semesters, and then for each enrollment strategy group, we take the average over students' cumulative GPA in that group. Results show that the FES group has the highest average  
Figure 3: Average annually family income for different enrollment strategies, with 5 th, 25 th, 50 th, 75 th, and 95 th percentiles. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Ethnicity** & **FES** & **MES** & **PES** & **Other** & **Population Size** \\ \hline White & 43.0\% & 5.6\% & 23.0\% & 28.4\% & 40,139 \\ Hispanic & 38.9\% & 6.5\% & 26.4\% & 28.2\% & 1939 \\ Black & 41.6\% & 5.9\% & 26.3\% & 26.2\% & 9514 \\ Other race & 40.3\% & 6.1\% & 23.5\% & 30.1\% & 7424 \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Distribution of enrollment strategies by race/ethnicity for transfer students. GPA (2.97). The lowest GPA corresponds to the PES group (2.55), while the MES group's GPA (2.78) lies between PES and FES. Statistical hypothesis Games-Howell post hoc multiple comparison tests were conducted to assess if the average GPA for each group is statistically different from the average GPA of other groups. We use the Games-Howell test because it is non-parametric and does not assume homogeneity of variances (which is the underlying assumption for the ANOVA test). The test statistic \(p\)-values for all the hypothesis tests are 0, indicating that each group's average GPA is statistically different from the others (the sample size for FES, MES, and PES is 88,319, 6,363, and 28,504, respectively). The table in Figure 4 provides an effect size categorization and dissimilarity% metric, that is the percentage by which the distribution of each group differs from each other. The relationship between dissimilarity% and the commonly used Cohen's d metric for normal distributions is explained in Appendix A. Based on the table, the difference in GPA between FES and PES groups is more significant than the other pairs. Furthermore, the box and whiskers in Figure 4 indicate that student clusters that employ FES and MES have more consistent performance than the PES student cluster. These findings suggest that increased student engagement through full-time enrollment with the university is associated with higher academic performance. Therefore university policymakers may help students improve their academic performance by providing the necessary support and opportunities (e.g., financial aid, on-campus work) to students to better facilitate full-time enrollment. Figure 5 illustrates the average GPA for FES, MES, and PES groups separately for FTIC and transfer students. The average GPA for FTIC and transfer students is 2.99 and 2.75, respectively. For both FTIC and transfer students, FES groups have the highest average GPAs (3.03 for FTIC and 2.85 for transfer), followed by MES (2.75 for FTIC and 2.76 for transfer), and PES (2.42 for FTIC and 2.44 for transfer). Furthermore, PES students have a less consistent GPA (wider interquartile range) compared to FES and MES students for both groups. The effect size table in the figure shows that the mean GPA differences between different enrollment strategies for FTIC students (large) are larger than the difference for transfer students (medium). In fact, FTIC students' GPAs are more sensitive to enrollment strategy compared to transfer students' GPAs. Figure 4: Average GPA for different enrollment strategies, with 5 th, 25 th, 50 th, 75 th, and 95 th percentiles. Conducted KS2 tests show that for both FTIC and transfer students, the GPA distribution for FES, MES, and PES groups statistically differ from each other (for FTIC students, sample sizes for FES, MES, and PES groups are 39,414, 578, and 600, respectively. For transfer students, these sample sizes are 31,748, 4515, and 18,580, respectively). Furthermore, we compared the mean GPA of FTIC and transfer students with different enrollment strategies.