## 8 Academic Performance Clustering Analysis
### DFW Rate Analysis  
As another indicator of students' performance we compare the DFW rate for students with different enrollment strategies. The DFW rate is defined as the number of courses with D, F, and W grades over the total number of courses taken by a student. Appendix B shows an example of computing the DFW rate. Whisker plots for DFW rates separated by FTIC and transfer students are provided in Figure 8. As expected, for both FTIC and transfer students, the PES group is the most likely to get DFW grades, followed by MES and FES, respectively. Games-Howell post hoc multiple comparison tests were conducted to see if the average DFW rates of each group differ from other groups. For both FTIC and transfer students, the \(p\)-values of the tests for all possible pairs between FES, MES, and FES is 0, which means the difference is statistically significant (For FTIC students, the sample  
\begin{table}
\begin{tabular}{l l c c} \hline \hline
**Pairs** & **Semester** & **Dissimilarity**\% & **Effect Size** \\ \hline \multirow{2}{*}{FES vs. MES} & Full-time & 19\% & Medium \\  & Part-time & 5\% & Small \\ \hline \multirow{2}{*}{FES vs. PES} & Full-time & 36\% & Very Large \\  & Part-time & 17\% & Medium \\ \hline \multirow{2}{*}{MES vs. PES} & Full-time & 22\% & Large \\  & Part-time & 15\% & Medium \\ \hline \hline \end{tabular}
\end{table}
Table 13: Effect size and distribution dissimilarity percentage between full-time and part-time semester GPA for FTIC students with different enrollment strategies.  
\begin{table}
\begin{tabular}{l l c c} \hline \hline
**Pairs** & **Semester** & **Dissimilarity**\% & **Effect Size** \\ \hline \multirow{2}{*}{FES vs. MES} & Full-time & 10\% & Medium \\  & Part-time & 6\% & Small \\ \hline \multirow{2}{*}{FES vs. PES} & Full-time & 9\% & Small \\  & Part-time & 14\% & Medium \\ \hline \multirow{2}{*}{MES vs. PES} & Full-time & 6\% & Small \\  & Part-time & 11\% & Medium \\ \hline \hline \end{tabular}
\end{table}
Table 14: Effect size and distribution dissimilarity percentage between full-time and part-time semester GPA for transfer students with different enrollment strategies.  
size of FES, MES, and PES groups is 39,371, 578, and 596, respectively, and for transfer students, the values are 31,721, 4515, and 18,521, respectively).  
Furthermore, effect size results in the figure show that the mean DFW rate for FTIC students is more sensitive to enrollment strategy than transfer students' DFW rates. When comparing FTIC and transfer students in terms of the DFW rate, we find that for the FES group, FTIC students have a lower average DFW rate compared to transfer students, and the difference is statistically significant. However, for MES and PES groups, there is no significant difference in the mean DFW rate. To get a better idea of the grade distribution, Figure 9 represents DFW rates broken to D, F, and W for FTIC and transfer students separately. Based on the figure, following a similar pattern as for the DFW rates, FES students have the lowest rates of D, F, and W grades when compared to MES and PES students. Moreover, among students who are not in an overall good standing (having DFW grades), those adopting PES show more intention to drop the course (38% FTIC and 54% transfer) compared to MES (35% FTIC and 38% transfer) and FES (29% FTIC and 36% transfer).  
Figure 8: Average DFW rate for FTIC and transfer students with different enrollment strategies, with 5 th, 25 th, 50 th, 75 th, and 95 th percentiles.  
Figure 9: Average D, F, and W rate for FTIC and transfer students with different enrollment strategies.  
Key Finding 7: FTIC and Transfer Students: PES students have a higher DFW rate compared to MES and FES groups. As before, the academic performance of FTIC students, as measured by DFW rate, appears more sensitivity to enrollment strategy, then that of transfer students.