Analysis of Grade Distribution across the University of Copenhagen using Compositional Data Regression

Specialeforsvar: Dongdong Yang

Titel: Analysis of Grade Distribution across the University of Copenhagen using Compositional Data Regression

Abstract: University is a place for research and learning. Many courses and exams are conducted every year to ensure the quality of education and learning outcomes. Course examination results and their proportions are a common concern for university lecturers, students, and administrators. In this project, the statistics of exam grades are studied. In the Danish education system, grades 2, 4, 7, 10, and 12 are given to the students who pass the exams. The number of students passing exams with different grades can be modeled using a multinomial distribution. The parameters 𝜃 of this distribution can then be modeled as a Dirichlet distribution, and the data can be preprocessed using the Bayesian analysis method. Due to the fact that 𝜃 is 5-dimensional compositional data, the data can be converted into 4- dimensional linear space data using the Aitchison geometry method. Finally, linear mixed models can be established to analyze the contribution of several interesting factors to the grade distribution, such as course size, semester (exam year and term), department, season, corona, etc. Furthermore, Python and R scripts are implemented to scrape data from the KU website, solve and analyze the linear mixed models, and generate diagrams to illustrate the modeling and analysis results.

Vejleder: Bo Markussen
censor:   Anders Stockmarr, DTU