Universality, correlations, and rankings in the Brazilian universities national admission examinations

We analyze the scores obtained by students who have taken the ENEM examination, The Brazilian High School National Examination which is used in the admission process at Brazilian universities. The average high schools scores from different disciplines are compared through the Pearson correlation coefficient. The results show a very large correlation between the performance in the different school subjects. Even though the students' scores in the ENEM form a Gaussian due to the standardization, we show that the high schools' scores form a bimodal distribution that cannot be used to evaluate and compare students performance over time. We also show that this high schools distribution reflects the correlation between school performance and the economic level (based on the average family income) of the students. The ENEM scores are compared with a Brazilian non standardized exam, the entrance examination from the Universidade Federal do Rio Grande do Sul. The analysis of the performance of the same individuals in both tests shows that the two tests not only select different abilities, but also lead to the admission of different sets of individuals. Our results indicate that standardized tests might be an interesting tool to compare performance of individuals over the years, but not of institutions.