Abstract
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.
Highlights
With information available almost constantly and coming from institutions, it is possible to regularly review processes that impact on the life of those institutions, as is the case of institutions related to health, safety and education, among others, so that reviewing processes is a healthy task
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 constant inspection of the educational system performance
In this paper we explore the dependence between two indicators: (i) mean between the proportions of students under the basic level (SARESP classification) and (ii) rate of fails, during the years 2013, 2014 and 2015
Summary
With information available almost constantly and coming from institutions, it is possible to regularly review processes that impact on the life of those institutions, as is the case of institutions related to health, safety and education, among others, so that reviewing processes is a healthy task. 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 constant inspection of the educational system performance. We perform the estimation of the parameters of the model, under a Bayesian perspective, year by year This procedure allows us to construct annual estimates of ProbðU > ujV > vÞ and annual estimates of the expected value EðU jV > vÞ where U are the ranks of X scaled to [0,1] and V are the ranks of Y scaled to [0,1]. The ACS family has already shown a good performance in applications in the area, see for example [2] and [3] It is compatible with our data which, as we shall see, shows very low correlation. We show our general conclusions in the Conclusion section, which is followed by the acknowledgments and the references
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