# Re-Defining, Analyzing and Predicting Persistence Using Student Events in Online Learning +
## 3 Materials and Methods
### Variables and Measures  
This section presents the variables used in the study and how they are measured. First, persistence in described. In this case, two definitions are used in the paper:  
* Global persistence: It is a binary variable to indicate whether or not a student has activity in the course and/or completes it. It is directly related with the term dropout, as students who do not complete the course (i.e., they are not persistent in a global sense) can count as a dropout. As dropout can be measured in many different ways and its definition may be sometimes difficult because some students can be inactive for a period and then continue the course [29], two measures are considered and discussed throughout the paper. * Definition related to activity: Students are persistent at the global level if they engage with the course (i.e., by watching a video and/or attempting an exercise) at least once every fortnight. In other words, they are not persistent when they do not interact with the course for two consecutive weeks. As there can be periods where students do not necessarily need to interact (e.g., public holidays and/or periods where the instructor wants to focus in other activities different from the SPOCs), weeks where less than 10% of students interact are not considered towards the calculation of global persistence. * Definition related to completion: Students are persistent at the global level when they complete most of the exercises, regardless when they complete them. In this case, 75% of activities need to be completed to be persistent at the global level, although this threshold could be adaptable in other contexts. In this case, it can be reasonable as it is used in other well-known platforms, such as MiriadaX ([[https://miriadax.net/en/faq?faqI=8635212](https://miriadax.net/en/faq?faqI=8635212)]([https://miriadax.net/en/faq?faqI=8635212](https://miriadax.net/en/faq?faqI=8635212))), which requires completing 75% (and passing, which is not required here) of modules to get certification of participation. This definition differs the former (definition related to activity) because this definition focuses on students' completion of activities (regardless the period), while the former focuses on accessing the SPOC (regardless activities are done or not). * Local persistence: It is a continuous variable that measures to what extent students continue attempting an exercise until getting the correct answer once they have answered it incorrectly. It is considered as \"local\" because it is focused on the atomic unit of an exercise, while global persistence focuses on the whole course. Section 4 provides more details about the computation of this variable. For computing this variable, all interactions with exercises are needed to know the outcome (correct/incorrect) for each attempt and students' actions after incorrect attempts. However, lack of details about course context are an important limitation because some contexts do not allow computing local persistence (e.g., students cannot show persistence if only one attempt is allowed in the exercise). In order to alleviate this limitation, the following filtering criterion was applied: exercises that were only attempted once or twice by all students are removed. Note that if one exercise is not excluded, there might be students (but not all) who got it right at first or second attempt. This rule serve to: (1) eliminate true/false exercise (or exercises with only two possible options), (2) eliminate easy exercises that are always solved correctly with few attempts (they are not useful to show local persistence), and (3) eliminate exercises where only 1-2 attempts are allowed (e.g., a typical policy is allowing one attempt for summative exercises). With these filtering, all exercises had a format and maximum number of attempts that allowed students showing local persistence. Using this criterion, 656 out of 3002 exercises (from 28 SPOCs) were included.