<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>0103-6831</journal-id>
<journal-title><![CDATA[Estudos em Avaliação Educacional]]></journal-title>
<abbrev-journal-title><![CDATA[Est. Aval. Educ.]]></abbrev-journal-title>
<issn>0103-6831</issn>
<publisher>
<publisher-name><![CDATA[Fundação Carlos Chagas]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0103-68312025000100402</article-id>
<article-id pub-id-type="doi">10.18222/eae.v36.12362</article-id>
<title-group>
<article-title xml:lang="pt"><![CDATA[O ÍNDICE THEIL-T E A DIVERGÊNCIA KL: UMA NOTA COMPLEMENTAR AO PROF. R. HOFFMANN]]></article-title>
<article-title xml:lang="es"><![CDATA[EL ÍNDICE THEIL-T Y LA DIVERGENCIA KL: UNA NOTA COMPLEMENTARIA AL PROF. R. HOFFMANN]]></article-title>
<article-title xml:lang="en"><![CDATA[THE THEIL-T INDEX AND THE KL DIVERGENCE: A SUPPLEMENTARY REPLY TO PROF. R. HOFFMANN]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[DELGADO]]></surname>
<given-names><![CDATA[VICTOR MAIA SENNA]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidade Federal de Ouro Preto  ]]></institution>
<addr-line><![CDATA[Mariana MG]]></addr-line>
<country>Brasil</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>00</month>
<year>2025</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>00</month>
<year>2025</year>
</pub-date>
<volume>36</volume>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://educa.fcc.org.br/scielo.php?script=sci_arttext&amp;pid=S0103-68312025000100402&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://educa.fcc.org.br/scielo.php?script=sci_abstract&amp;pid=S0103-68312025000100402&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://educa.fcc.org.br/scielo.php?script=sci_pdf&amp;pid=S0103-68312025000100402&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="pt"><p><![CDATA[RESUMO A nota responde às críticas do professor Rodolfo Hoffmann sobre o uso da divergência Kullback-Leibler (KL) para medir desigualdades educacionais. Mostra-se que o método de densidades relativas é mais geral que a medida de divergência em questão. Os exemplos de Hoffmann são questionados por usarem de comparações de distribuições uniformes e por não considerar o método de construção de Teoria da Resposta ao Item (TRI). Argumenta-se que uma boa referência para a escala de proficiência representa uma meta educacional desejada. Prova-se matematicamente, no Apêndice, que o índice de Theil-T é, na verdade, um caso especial da divergência KL. Isso demonstra que a KL não é uma medida inadequada, mas uma ferramenta mais geral e flexível para analisar desigualdades educacionais.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[RESUMEN La nota responde a la crítica del profesor Rodolfo Hoffmann sobre el uso de la divergencia Kullback-Leibler (KL) para medir las desigualdades educativas. Se muestra que el método de densidades relativas es más general que la medida de divergencia en cuestión. Los ejemplos de Hoffmann son cuestionados porque utilizan distribuciones uniformes para la comparación y por no considerar el método de construcción de la Teoría de la Respuesta al Ítem (TRI). Se argumenta que una buena referencia para la escala de aprendizaje representa un objetivo educativo deseado. Está demostrado matemáticamente, en el Apéndice, que el índice Theil-T es en realidad un caso especial de la divergencia KL. Esto demuestra que el KL no es una medida inadecuada, sino una herramienta más general y flexible para analizar las desigualdades educativas.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[ABSTRACT The note responds to Professor R. Hoffmann&#8217;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&#8217;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.]]></p></abstract>
<kwd-group>
<kwd lng="pt"><![CDATA[INDICADORES EDUCACIONAIS]]></kwd>
<kwd lng="pt"><![CDATA[DESIGUALDADES EDUCACIONAIS]]></kwd>
<kwd lng="pt"><![CDATA[AVALIAÇÃO DA EDUCAÇÃO]]></kwd>
<kwd lng="pt"><![CDATA[AVALIAÇÃO DA APRENDIZAGEM.]]></kwd>
<kwd lng="es"><![CDATA[INDICADORES EDUCATIVOS]]></kwd>
<kwd lng="es"><![CDATA[DESIGUALDADES EDUCATIVAS]]></kwd>
<kwd lng="es"><![CDATA[EVALUACIÓN DE LA EDUCACIÓN]]></kwd>
<kwd lng="es"><![CDATA[EVALUACIÓN DEL APRENDIZAJE.]]></kwd>
<kwd lng="en"><![CDATA[EDUCATIONAL INDICATORS]]></kwd>
<kwd lng="en"><![CDATA[EDUCATIONAL INEQUALITIES]]></kwd>
<kwd lng="en"><![CDATA[EDUCATIONAL EVALUATION]]></kwd>
<kwd lng="en"><![CDATA[LEARNING ASSESSMENT.]]></kwd>
</kwd-group>
</article-meta>
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