Statistical approach on grading the student achievement via normal mixture modelling

Abstract

The purpose of this study is to compare results obtained from three methods of assigning letter grades to students’ achievement. The conventional and the most popular method to assign grades is the Straight Scale method (SS). Statistical approaches which used the Standard Deviation (GC) and conditional Bayesian methods are considered to assign the grades. In the conditional Bayesian model, we assume the data to follow the Normal Mixture distribution where the grades are distinctively separated by the parameters: means and proportions of the Normal Mixture distribution. The problem lies in estimating the posterior density of the parameters which is analytically intractable. A solution to this problem is using the Markov Chain Monte Carlo approach namely Gibbs sampler algorithm. The Straight Scale, Standard Deviation and Conditional Bayesian methods are applied to the examination raw scores of two sets of students. The performances of these methods are measured using the Neutral Class Loss, Lenient Class Loss and Coefficient of Determination. The results showed that Conditional Bayesian outperformed the Conventional Methods of assigning grades.