Changes in test scores distribution for students of the fourth grade in Brazil: A relative distribution analysis for the years 1997 to 2005
To assess the quality of school education, much of educational research is concerned with comparisons of test scores means or medians. In this paper, we shift this focus and explore test scores data by addressing some often neglected questions. In the case of Brazil, the mean of test scores in Math for students of the fourth grade has declined approximately 0,2 standard deviation in the late 1990s. But what about changes in the distribution of scores? It is unclear whether the decline was caused by deterioration in student performance in upper and/or lower tails of the distribution. To answer this question, we propose the use of the relative distribution method developed by Handcock and Morris (1999). The advantage of this methodology is that it compares two distributions of test scores data through a single distribution and synthesizes all the differences between them. Moreover, it is possible to decompose the total difference between two distributions in a level effect (changes in median) and shape effect (changes in shape of the distribution). We find 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 only specific to any quantile of distribution.
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- Weili Ding & Steven Lehrer, 2005. "Class Size and Student Achievement: Experimental Estimates of Who Benefits and Who Loses from Reductions," Working Papers 1046, Queen's University, Department of Economics.
- Woessmann, Ludger, 2004.
"How Equal Are Educational Opportunities? Family Background and Student Achievement in Europe and the United States,"
IZA Discussion Papers
1284, Institute for the Study of Labor (IZA).
- Ludger Woessmann, 2004. "How Equal Are Educational Opportunities? Family Background and Student Achievement in Europe and the United States," CESifo Working Paper Series 1162, CESifo Group Munich.
- Behrman, Jere R. & Khan, Shahrukh & Ross, David & Sabot, Richard, 1997. "School quality and cognitive achievement production: A case study for rural Pakistan," Economics of Education Review, Elsevier, vol. 16(2), pages 127-142, April.
- Peter Hall & Terence Tao, 2002. "Relative efficiencies of kernel and local likelihood density estimators," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 537-547.
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