<?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>S0103-68312026000100301</article-id>
<article-id pub-id-type="doi">10.18222/eae.v37.12573</article-id>
<title-group>
<article-title xml:lang="pt"><![CDATA[NOVAS CONSIDERAÇÕES SOBRE COMO MEDIR DESIGUALDADE DE PROFICIÊNCIAS]]></article-title>
<article-title xml:lang="es"><![CDATA[NUEVAS CONSIDERACIONES SOBRE CÓMO MEDIR LA DESIGUALDAD DE SUFICIENCIAS]]></article-title>
<article-title xml:lang="en"><![CDATA[NEW CONSIDERATIONS ON HOW TO MEASURE PROFICIENCY INEQUALITY]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[HOFFMANN]]></surname>
<given-names><![CDATA[RODOLFO]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidade de São Paulo  ]]></institution>
<addr-line><![CDATA[Piracicaba SP]]></addr-line>
<country>Brasil</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>00</month>
<year>2026</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>00</month>
<year>2026</year>
</pub-date>
<volume>37</volume>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://educa.fcc.org.br/scielo.php?script=sci_arttext&amp;pid=S0103-68312026000100301&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://educa.fcc.org.br/scielo.php?script=sci_abstract&amp;pid=S0103-68312026000100301&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://educa.fcc.org.br/scielo.php?script=sci_pdf&amp;pid=S0103-68312026000100301&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="pt"><p><![CDATA[RESUMO Vou discutir alguns dos temas abordados na resposta de Soares e Ernica (2025) à minha crí-tica (Hoffmann, 2025) do uso da divergência de Kullback-Leibler na avaliação de proficiências em testes educacionais. Primeiro procuro deixar claro que as medidas de desigualdade de Theil não são casos particulares da divergência de Kullback-Leibler. Depois reconheço a importância de distinguir a desigualdade de oportunidades na obtenção de proficiências adequadas, mas ressalto que é válido e relevante considerar essa desigualdade como uma parcela da desigualdade total. Reconheço, também, que a análise da distribuição relativa pode ser uma metodologia muito útil; porém, no último tópico, destaco que o mais simples e claro é usar medidas clássicas de tendência central, dispersão, desigualdade e assimetria.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[RESUMEN Voy a discutir algunos de los temas abordados en la respuesta de Soares y Ernica (2025) a mi crítica (Hoffmann, 2025) sobre el uso de la divergencia de Kullback-Leibler en la evaluación de suficiencias en pruebas educativas. En primer lugar busco dejar claro que las medidas de desigualdad de Theil no constituyen casos particulares de la divergencia de Kullback-Leibler. Posteriormente reconozco la importancia de distinguir la desigualdad de oportunidades en la consecución de suficiencias adecuadas; no obstante, subrayo que es válido y relevante considerar dicha desigualdad como un componente de la desigualdad total. Asimismo, reconozco que el análisis de la distribución relativa puede representar una metodología de gran utilidad, aunque en el último apartado enfatizo que lo más sencillo y claro consiste en emplear medidas clásicas de tendencia central, dispersión, desigualdad y asimetría.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[ABSTRACT I will discuss some of the issues addressed in Soares and Ernica&#8217;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&#8217;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.]]></p></abstract>
<kwd-group>
<kwd lng="pt"><![CDATA[AVALIAÇÃO EDUCACIONAL]]></kwd>
<kwd lng="pt"><![CDATA[DESIGUALDADES EDUCACIONAIS]]></kwd>
<kwd lng="pt"><![CDATA[DIVERGÊNCIA DE KULLBACK-LEIBLER.]]></kwd>
<kwd lng="es"><![CDATA[EVALUACIÓN EDUCATIVA]]></kwd>
<kwd lng="es"><![CDATA[DESIGUALDADES EDUCATIVAS]]></kwd>
<kwd lng="es"><![CDATA[DIVERGENCIA DE KULLBACK-LEIBLER.]]></kwd>
<kwd lng="en"><![CDATA[EDUCATIONAL ASSESSMENT]]></kwd>
<kwd lng="en"><![CDATA[EDUCATIONAL INEQUALITIES]]></kwd>
<kwd lng="en"><![CDATA[KULLBACK-LEIBLER DIVERGENCE.]]></kwd>
</kwd-group>
</article-meta>
</front><back>
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