New considerations on how to measure proficiency inequality
DOI:
https://doi.org/10.18222/eae.v37.12573Keywords:
Educational Assessment, Educational Inequalities, Kullback–Leibler DivergenceAbstract
I will discuss some of the issues addressed in Soares and Ernica’s (2025) response to my critique (Hoffmann, 2025) of the use of the Kullback-Leibler divergence in assessing proficiency in educational tests. First, I seek to clarify that Theil’s measures of inequality are not special cases of the Kullback–Leibler divergence. I then acknowledge the importance of distinguishing inequality of opportunity in achieving adequate proficiency levels, while emphasizing that it is valid and relevant to consider this inequality as a component of total inequality. I also recognize that the analysis of relative distributions can be a very useful methodology; however, in the final section I argue that the simplest and clearest approach is to use traditional measures of central tendency, dispersion, inequality, and asymmetry.
Downloads
References
Alves, D. B. (2025). Índices de desigualdades educacionais: Um estudo para o Brasil [Tese de doutorado, Universidade de São Paulo]. Biblioteca Digital de Teses e Dissertações da USP. https://www.teses.usp.br/teses/disponiveis/11/11132/tde-16092025-112834/pt-br.php
Ernica, M., Rodrigues, E. C., & Soares, J. F. (2025). Desigualdades educacionais no Brasil contemporâneo: Definição, medida e resultados. Dados, 68(1), Artigo e20220109. https://doi.org/10.1590/dados.2025.68.1.345 DOI: https://doi.org/10.1590/dados.2025.68.1.345
Handcock, M. S., & Morris, M. (1999). Relative distribution methods in the social sciences. Springer.
Hoffmann, R. (2025). Sobre como medir diferenças de resultados no ensino. Estudos em Avaliação Educacional, 36, Artigo e10663. https://doi.org/10.18222/eae.v36.10663 DOI: https://doi.org/10.18222/eae.v36.10663
Hoffmann, R., Botassio, D. C., & Jesus, J. G. de. (2019). Distribuição de renda: Medidas de desigualdade, pobreza, concentração, segregação e polarização (2ª ed.). Edusp.
Hoffmann, R., & Kassouf, A. L. (2025). Measuring and mismeasuring income polarization. Social Indicators Research, 177, 787-807. https://doi.org/10.1007/s11205-025-03535-8 DOI: https://doi.org/10.1007/s11205-025-03535-8
Soares, J. F., & Delgado, V. M. S. (2016). Medida das desigualdades de aprendizado entre estudantes de ensino fundamental. Estudos em Avaliação Educacional, 27(66), 754-780. https://doi.org/10.18222/eae.v27i66.4101 DOI: https://doi.org/10.18222/eae.v27i66.4101
Soares, J. F., & Ernica, M. (2025). O conceito rege o método: Uma resposta a Hoffmann. Estudos em Avaliação Educacional, 36, Debate e12270. https://doi.org/10.18222/eae.v36.12270 DOI: https://doi.org/10.18222/eae.v36.12270
Theil, H. (1967). Economics and information theory. North-Holland; Rand McNally.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2026 Rodolfo Hoffmann
This work is licensed under a Creative Commons Attribution 4.0 International License.
a. Authors retain the copyright and grant the journal the right to first publication.
b. All works are licensed under the Creative Commons Attribution License, which allows the sharing of the paper with acknowledgment of authorship.
Until 2024, Estudos em Avaliação Educacional adopted the Creative Commons Attribution-NonCommercial (CC BY-NC) license for its publications. For texts published from 2025 onwards, the journal will adopt the Creative Commons Attribution (CC BY) license, in line with the principles of Open Science.
