Statistical Analysis of Educational Data Using Copula Functions: The Case of 2018 PISA

In this study, using 2018 PISA data, the dependency structures between mathematics, science, and reading scores were analysed with elliptic and archimedean copula functions according to the factors of gender and educational level at home. PISA is an international assessment that measures the education levels of students in science, mathematics, and reading and aims to compare education levels among countries. Copula functions are statistical tools that allow flexible modeling of dependency relationships between variables and provide the most appropriate way of obtaining multivariate distributions. In this study, firstly, models were constructed for data pairs consisting of PISA maths, reading, and science scores according to home education level and gender factors. Then, the copula models that best explain these structures were determined by goodness-of-fit tests, and the copula parameters for the selected models were estimated. Finally, joint and conditional probabilities were calculated for these score pairs in order to evaluate the effect of reading scores on maths and science courses. The study emphasizes the potential use of copula models in educational research and provides new findings on the impact of gender and home education level on PISA performances.