Changes in test scores distribution for students of the fourth grade in Brazil: A relative distribution analysis for the years 1997–2005

In Brazil, the mean of math test scores for students of the fourth grade declined by approximately 0.2 standard deviation in the late 1990s. However, the potential changes in the distribution of scores have never been addressed. It is unclear if the decline was caused by deterioration in student performance levels at the upper and/or lower tails of the distribution. In an effort to address this issue, we propose the use of the relative distribution method developed by Handcock and Morris (1999). Our findings suggest that the decline of average-test scores is mainly caused by a worsening in the position of all students throughout the distribution of scores and is not specific to a unique quantile of the distribution. In addition, we find that changes in student composition, for the most part, explain the gap in the distribution of test scores during the first biennium of analysis (1997–1999).

► We examine changes in test scores distribution in Brazil for the years 1997–2005. ► We try to explain if the decline of average test scores was caused by deterioration in upper/lower tail of the distribution. ► We propose the use of the relative distribution method. ► We find that the negative evolution of the average test scores is mainly caused by a worsening of all students.