Considerations on Prof. Delgado’s note

Abstract

In previous article I improperly used “grades” as a synonym for “proficiencies”. Certainly, the methodology of learning assessment has advanced significantly with Item Response Theory (IRT). The debate about the choice of appropriate measures refers to the comparison of proficiency distributions. Theil’s T is not a special case of the Kullback-Leibler divergence. I continue to advocate the use of basic measures of central tendency, dispersion, and inequality in comparing proficiency distributions. A measure of asymmetry could be added. Graphical representations can be enlightening. Other methods could be tried, but it makes no sense to advocate the use of the Kullback-Leibler divergence to replace means and variances or to avoid the use of common measures of inequality. To illustrate, microdata from Sistema de Avaliação da Educação Básica [Basic Education Assessment System] are analysed.