# Re-Defining, Analyzing and Predicting Persistence Using Student Events in Online Learning +
## 5 Results
### Analysis of the Evolution of Local Persistence over Time
In order to alleviate the issue of different students interacting each week in the computation of weekly local persistence, we took the students who had engaged in all the periods during the semester to analyze the evolution of their local persistence over time. The analysis showed that not many students engaged with the SPOC at least once a month, as only 115 students from only two SPOCs (about 14% of students taking SPOCs in the first semester), B and D, did so. In the rest of the SPOCs,  
Figure 3: **(a: top-left)** Evolution of the local persistence in the first semester using all the courses, **(b: top-right)** evolution of the local persistence in the first semester for each course, where each course is a different line, **(c: bottom-left)** number of students engaging with exercises in each week of the semester for each course, **(d: bottom-right)** number of exercises students have attempted in each week of the course. Note: Actual names of the courses are omitted for confidentiality reasons. nobody engaged at least once in all months. In fact, out of the 901 students taking SPOCs in the first semester, only 334 engaged with the SPOC at least once in two months and 212 in three out of the four months of the course (September-December, both included). Considering the 115 students who interacted in all months (from courses B and D), Figure 4 shows the evolution of local persistence over months. Results show that even when the students are the same, there are significant changes in local persistence. Moreover, evolution of local persistence over time in course B is totally opposite from course D (which contains most of the 115 students taking either course B or D). These results have two implications: 1) students' local persistence may evolve over the time, and 2) students' local persistence can be highly course dependent (i.e., changes in the contents, materials, etc. can affect local persistence). Taking these findings into account, instructors should think about the best design for their courses to ensure that all activities are challenging and engaging enough so that students feel motivated to do their best to get the correct answers. Relationship between Local Persistence and Global Persistence, Students' Performance and Engagement with Videos  
Many researchers have analyzed which variables affect dropout [6] and they have proposed predictive models to forecast which learners will drop out the course (e.g., [PERSON] et al. [42]). This fact is particularly relevant because of the high dropout rates usually reported in the courses, or even in the academic programs [43]. The first part of the analysis in this subsection aims to discover if there is a relationship between local persistence and dropout (i.e., global persistence). In this case, dropout is analyzed following the definition of global persistence related to completion (a student has dropped out and s/he is not persistent at the global level if s/he has not completed at least 75% of the exercises of the SPOC). This way, the analysis serves to analyze the relationship between local and global persistence. For this analysis, only the first semester of the academic year 2018/2019 is considered. In order to analyze the relationship between local and global persistence/dropout, a boxplot was made using these two variables (see Figure 5). This figure shows that local persistence of students who do not drop out the course is similar to those who drop out. The mean of local persistence for both groups is 0.71 and 0.68, respectively. The difference of local persistence, evaluated through the Mann-Whitney test, was not statistically significant (\(p\)-value = 0.25). This implies that local and global persistence are not necessarily related, and local persistence does not mean completion.