A Comparison of Classical Non-Parametric and Bayesian Non-parametric Approaches in Grade Comparisons in a Tertiary Institution
Shola Olamuyiwa
*
Department of Mathematical Sciences, Dennis Osadebay University, Asaba, Nigeria.
Chrysogonus Chinagorom Nwaigwe
Department of Statistics, Federal University of Technology, Owerri and Department of Mathematical Sciences, Dennis Osadebay University, Asaba, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
In educational research, comparison of the performances of students in the courses/subjects they offered may be done in order to compare the methods in which they were taught, understand the influence of knowledge of one course on another or to compare the cognitive knowledge of students in different disciplines. The purpose is often to understand how best the performances of the students can be improved upon. In this study, using a sample size of two hundred (200) students in each faculty, two statistical methods, the Mann Whitney U test and the Bayesian non-parametric (BNP) Mann Whitney U test were employed to investigate if there exist a significant statistical difference in performances (recorded as grades) of students in two faculties of a university. While the classical test yielded no statistically significant difference (p = 0.229), the Bayesian analysis provided moderate evidence favoring the null hypothesis with a Bayes’ factor (BF₁₀ = 0.284), though posterior estimates suggested a slight performance edge for Computing students. These findings underscore the ability of the Bayesian method to yield more informative conclusions and hence its use in educational research, especially when classical results are inconclusive.
Keywords: Non-parametric statistics, bayesian inference, Mann-whitney U test, students performances, comparison