School grades and students' achievement: how to identify grading standards and measure their effects

A new procedure to identify grading practice is proposed. In our approach, grading practice are given in terms of a categorical variable whilst usually in the literature, coefficients of the regression line which models school grades as a function of students' achievement, are taken as indicators of grading standards. The new procedure, which is essentially nonparametric, allows to identity clearly a variety of grading practices and their effect on students' performance. It also shows that ordering grading standards is not possible: hence the usual approach based on regression coefficients is unlikely to be satisfactory. The new methodology is easy to implement and widely applicable. As an example, we consider data from a survey on Italian lower secondary school students. The evidence, which essentially confirms the generic result given in the literature, suggests that higher grading standards improve students' achievement but in our case, grading standards are easily interpretable.