Investigating the statistical distribution of learning coverage in MOOCs

Learners participating in Massive Open Online Courses (MOOC) have a wide range of backgrounds and motivations. Many MOOC learners enroll in the courses to take a brief look; only a few go through the entire content, and even fewer are able to eventually obtain a certificate. We discovered this phenomenon after having examined 92 courses on both xuetangX and edX platforms. More specifically, we found that the learning coverage in many courses-one of the metrics used to estimate the learners' active engagement with the online courses-observes a Zipf distribution. We apply the maximum likelihood estimation method to fit the Zipf's law and test our hypothesis using a chi-square test. In the xuetangX dataset, the learning coverage in 53 of 76 courses fits Zipf's law, but in all of 16 courses on the edX platform, the learning coverage rejects the Zipf's law. The result from our study is expected to bring insight to the unique learning behavior on MOOC.