Bayesian modeling of university first-year students' grades after placement test

University first-year students grades are naturally correlated with the scores obtained at placement tests. Often this characteristic leads the university grades in the first exams to be asymmetrically distributed. Motivated by the analysis of grades of the basic Statistics examination of first-year students, we discuss informative priors for the shape parameter of the skew-normal model, a class of distribution which account for several degree of asymmetry. Our proposed prior leads to closed-form full-conditional posterior distributions, particularly useful in Markov Chain Monte Carlo simulation. A Gibbs sampling algorithm is discussed for the joint vector of parameters and the method is applied to a real data set from the School of Economics, University of Padua, Italy. Our analysis reveals that the correlation between the placement test and the grades of first-year students leads to a measurable positive skewness of the distribution of the university grades.