A copula-based consistency analysis of education indicators

In this paper we investigate the consistency of quality indicators of the Brazilian public educational system. According to the newspaper Estado de São Paulo – Brazil, of January 18, 2017, only 7.3% of students in the third year of high school have an adequate level of mathematics, this shows the relevance of the evaluation and assessment of the Brazilian educational system. In this paper we explore the dependence between two indicators: (i) mean value between the proportions (in two subjects: Portuguese and Mathematics) of students under the basic level (SARESP classification) and (ii) rate of fails, during the years 2013, 2014 and 2015. (i) and (ii) are bases to define the educational quality of public schools for the population of young people, between 14 and 17 years old. This inspection is carried out through the Bayesian estimation of the parameters of the Asymmetric Cubic Sections (ACS) copula. We show that the dependence profile, year after year, behaves in a very unstable way, although during those years there were no substantial changes which justify such instability. Through the copula we compute conditional probabilities of tail events. We verify that an inversion occurred in the concordance/discordance between (i) and (ii). We compute the probability of (i) assuming high values, conditioned to a threshold in (ii). In 2013, as the threshold in (ii) increases the probability increases (concordance), in 2014 the threshold in (ii) is almost irrelevant to the probability and in 2015, as the threshold in (ii) increases the probability decreases (discordance). The inspection of the tail dependence allows to expose some kind of manipulation, in view of for instance, the maintenance of a global index índice de desenvolvimento da educação de São Paulo (IDESP) used to classify the educational institutions.