<?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>1900-2386</journal-id>
<journal-title><![CDATA[Psychologia. Avances de la Disciplina]]></journal-title>
<abbrev-journal-title><![CDATA[Psychol. av. discip.]]></abbrev-journal-title>
<issn>1900-2386</issn>
<publisher>
<publisher-name><![CDATA[Universidad San Buenaventura]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S1900-23862022000200063</article-id>
<article-id pub-id-type="doi">10.21500/19002386.5642</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Una medida de variación para datos cualitativos con cualquier tipo de distribución]]></article-title>
<article-title xml:lang="en"><![CDATA[A measure of variation for qualitative data with any type of distribution]]></article-title>
<article-title xml:lang="pt"><![CDATA[Uma medida de variação para dados qualitativos com qualquer tipo de distribuição]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Rubia]]></surname>
<given-names><![CDATA[José Moral de la]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad Autónoma de Nuevo León Facultad de Psicología ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Mexico</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>2022</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>2022</year>
</pub-date>
<volume>16</volume>
<numero>2</numero>
<fpage>63</fpage>
<lpage>76</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S1900-23862022000200063&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S1900-23862022000200063&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S1900-23862022000200063&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen Existe muchas medidas de variación para datos nominales, pero son poco conocidas cuando este tipo de datos son comunes en ciencias sociales y de la salud. Entre estas medidas, destacan el índice de variación cualitativa (IVC) de Gibbs y Poston, la razón de variación (RV) de Freeman, la razón de variación de la moda (RVMod) de Wilcox, la entropía relativa (ERel) de Shannon y la desviación estándar desde la moda (DEM) de Kvalseth. El objetivo del artículo es proponer una modificación de la razón de variación que supere la limitación a distribuciones unimodales de las fórmulas de Freeman y Wilcox; asimismo, describir el patrón de comportamiento de los seis índices. Al nuevo índice se denomina razón de variación universal (RVU), ya que es válido para cualquier tipo de distribución con datos cualitativos. Se observa que RV, RVU, RVMod y DEM se aproximan rápidamente a 0 cuando hay una moda muy definida con proximidad a la distribución de una variable aleatoria constante. Por el contrario, ERel y ICV se aproximan rápidamente a 1 cuando hay múltiples modas o proximidad a una distribución uniforme con una moda única. Se concluye que, entre las seis medidas, DEM y RVU son las mejores.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract There are many measures of variation for nominal data, but they are little known, when this type of data is common in health and social science research. Among these measures, the Gibbs-Poston&#8217;s qualitative variation index (QVI), the Freeman&#8217;s variation ratio (VR), the Wilcox&#8217;s variation ratio from the mode (VRMod), the Shannon&#8217;s relative entropy (ERel), and the Kvalseth&#8217;s standard deviation from the mode (SDM) stand out. The objective of this article is to propose a modification of the variation ratio that overcomes the limitation to unimodal distributions of Freeman and Wilcox formulas; also describe the behavior pattern of the six indices. This new index is named the universal variation ratio (UVR), since it is valid for any type of distribution with qualitative data. It is observed that RV, UVR, RVMod and DEM quickly approach 0 when there is a very defined mode with proximity to the distribution of a constant random variable. On the contrary, ERel and QVI quickly approach 1 when there are multiple modes or proximity to a uniform distribution with a unique mode. It is concluded that, among six indices, SDM and UVR are the best measures.]]></p></abstract>
<abstract abstract-type="short" xml:lang="pt"><p><![CDATA[Resumo Existem muitas medidas de variação para dados nominais, mas são pouco conhecidas, quando este tipo de dados é comum em pesquisas em saúde e ciências sociais. Entre essas medidas, o índice de variação qualitativa de Gibbs-Poston (IVQ), a razão de variação de Freeman (VR), a razão de variação da moda de Wilcox (RVMod), a entropia relativa de Shannon (ERel) e o desvio padrão da moda de Kvalseth (DPM) se destacam. O objetivo deste artigo é propor uma modificação da razão de variação que supere a limitação a distribuições unimodais das fórmulas de Freeman e Wilcox; também descreve o padrão de comportamento dos seis índices. Esse novo índice é denominado razão de variação universal (RVU), pois é válido para qualquer tipo de distribuição com dados qualitativos. Observa-se que RV, RVU, RVMod e DPM rapidamente se aproximam de 0 quando existe um modo muito definido com proximidade da distribuição de uma variável aleatória constante. Pelo contrário, ERel e IVQ rapidamente se aproximam de 1 quando há vários modos ou proximidade de uma distribuição uniforme com uma moda única. Conclui-se que, entre seis índices, DPM e RVU são as melhores medidas.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[variación cualitativa]]></kwd>
<kwd lng="es"><![CDATA[escala de medición nominal]]></kwd>
<kwd lng="es"><![CDATA[variable cualitativa]]></kwd>
<kwd lng="es"><![CDATA[medidas de variabilidad]]></kwd>
<kwd lng="es"><![CDATA[estadística descriptiva]]></kwd>
<kwd lng="en"><![CDATA[qualitative variation]]></kwd>
<kwd lng="en"><![CDATA[nominal scale of measurement]]></kwd>
<kwd lng="en"><![CDATA[qualitative variable]]></kwd>
<kwd lng="en"><![CDATA[variability measures]]></kwd>
<kwd lng="en"><![CDATA[descriptive statistics.]]></kwd>
<kwd lng="pt"><![CDATA[variação qualitativa]]></kwd>
<kwd lng="pt"><![CDATA[escala nominal de medida]]></kwd>
<kwd lng="pt"><![CDATA[variável qualitativa]]></kwd>
<kwd lng="pt"><![CDATA[medidas de variabilidade]]></kwd>
<kwd lng="pt"><![CDATA[estatística descritiva]]></kwd>
</kwd-group>
</article-meta>
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