Resumo

DELGADO, VICTOR MAIA SENNA. THE THEIL-T INDEX AND THE KL DIVERGENCE: A SUPPLEMENTARY REPLY TO PROF. R. HOFFMANN. Est. Aval. Educ. [online]. 2025, vol.36, e12362.  Epub 22-Dez-2025. ISSN 1984-932X.  https://doi.org/10.18222/eae.v36.12362.

The note responds to Professor R. Hoffmann’s criticism of the use of the Kullback-Leibler (KL) divergence to measure educational inequalities. It is shown that the method of relative densities is more general than the measure of divergence in question. Hoffmann’s examples are questioned because they use uniform distributions for comparison and for not considering the Item Response Theory (IRT) construction method. It is argued that a good reference for the proficiency scale represents a desired educational goal. It is proven mathematically, in the Appendix, that the Theil-T index is actually a special case of the KL divergence. This demonstrates that KL is not an inadequate measure, but rather a more general and flexible tool for analyzing educational inequalities.

Palavras-chave : EDUCATIONAL INDICATORS; EDUCATIONAL INEQUALITIES; EDUCATIONAL EVALUATION; LEARNING ASSESSMENT..

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