Application of the Beta-Binomial Distribution for Statistical Processing of Student Grades

Statistical processing of students' grades is used to solve various problems in managing the educational process. Traditional methods of mathematical statistics do not correspond to the properties of student grades. The paper proposes to adapt the IRT models for describing grades to improve the whole process. A model based on beta-binomial distribution is proposed, in which the parameters take into account the student's ability and the difficulty of getting a passing grade. The use of this probability distribution is justified by the ability to take into account the variation of grades. It is proposed to use two approaches to identify the parameters. The first approach is based on the use of numerical methods for finding parameters for solving a system of equations. The second one uses the Bayesian approach, which makes it possible to rather effectively refine the parameters when obtaining new estimates. Based on the results of processing an array of estimates, the adequacy of the model was confirmed by several statistical criteria.