# Re-Defining, Analyzing and Predicting Persistence Using Student Events in Online Learning +
## 5 Results
### Analysis of the Evolution of Local Persistence over Time
A possible reason is because local persistence is only measured with the attempted exercises, and students may try to complete the exercises they attempt (even using brute force if necessary) but they may stop using the SPOC at some  
Figure 4: **(a: left)** Evolution of the local persistence of students who engage all months for all courses together and **(b: right)** for each individual course. point. Another possible reason is that exercises might not be discriminative enough in terms of local persistence because if they have few options to select, students can get the answers by using brute force. Other reasons may be due to the course context, as context can affect local persistence (as seen in Section 5.2, and it matches with [PERSON] et al. [26]). However, further research should be done to delve into the possible reasons. After analyzing the relationship between local persistence and dropout, the relationship between the average grade (considering only attempted exercises and all the attempts) and local persistence is presented. Moreover, an analysis of the relationship between the percentage of completed videos and local persistence is presented to discover whether persistent students at the local level also complete the videos or not. In order to analyze these variables, plots were made to relate local persistence and the variables (see Figure 6). Figure 5: Boxplot with the relationship between local persistence and dropout. Figure 6: Relationship between local persistence and (**a: left**) average grade, (**b: right**) % of completed videos. Figure 6a illustrates that the average grade has clear positive relationship with local persistence as the average grade tends to be higher when local persistence is higher. In fact, the Pearson correlation coefficient is 0.55 (\(p\)-value \(<\ 10^{-3}\), 95% confidence interval between 0.53 and 0.58), which is a moderate correlation, according to [PERSON] and [PERSON] (2018). While average grade fluctuates more for students with low local persistence, i.e., there can be students with low local persistence with high grades and more variance is presented, students with high local persistence usually achieve good grades. Nevertheless, there are some cases of students with high local persistence but low grades. As the average grade is only computed with attempted exercises, this means that students had a very poor performance on exercises where the number of attempts is limited (which are excluded in the calculation of local persistence but not to compute the average grade). This implies that there may be cases where students can be persistent at the local level by using brute force to solve the exercises, but they are not actually learning, and grade may also not reflect learning. Thus, local persistence does not necessarily mean learning, although it means perseverance. However, the trend is that the average grade is more positive as local persistence increases. This suggests that while local persistence is not crucial for success, it can be beneficial for the student and having good local persistence can lead to high performance, provided that the student reflects on the questions and do not guess the answers to the exercises by brute force. In the latter case, persistence may not have effect on learning unless the student eventually understands why the solution is the option s/he eventually guessed. In order to analyze this issue, further work could be done. For example, a pre-test and post-test can be added to analyze how learning gains are related to persistence, and how possible patterns of using brute force to solve exercises are related to more or less increase in knowledge. In contrast, when analyzing the relationship between local persistence and percentage of completed videos, Figure 6b show that there is no relationship between both variables, and the correlation is almost 0 (\(p\)-value = 0.42, 95% confidence interval between \(-\)0.05 and 0.02), which implies there is no association between the variables.