<?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>0120-1751</journal-id>
<journal-title><![CDATA[Revista Colombiana de Estadística]]></journal-title>
<abbrev-journal-title><![CDATA[Rev.Colomb.Estad.]]></abbrev-journal-title>
<issn>0120-1751</issn>
<publisher>
<publisher-name><![CDATA[Departamento de Estadística - Universidad Nacional de Colombia.]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0120-17512008000200006</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Intervalos de confianza e intervalos de credibilidad para una proporción]]></article-title>
<article-title xml:lang="en"><![CDATA[Confidence Intervals and Credibility Intervals for a Proportion]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[CEPEDA-CUERVO]]></surname>
<given-names><![CDATA[EDILBERTO]]></given-names>
</name>
<xref ref-type="aff" rid="A01"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[AGUILAR]]></surname>
<given-names><![CDATA[WILSON]]></given-names>
</name>
<xref ref-type="aff" rid="A02"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[CERVANTES]]></surname>
<given-names><![CDATA[VÍCTOR]]></given-names>
</name>
<xref ref-type="aff" rid="A03"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[CORRALES]]></surname>
<given-names><![CDATA[MARTHA]]></given-names>
</name>
<xref ref-type="aff" rid="A04"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[DÍAZ]]></surname>
<given-names><![CDATA[IVÁN]]></given-names>
</name>
<xref ref-type="aff" rid="A05"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[RODRÍGUEZ]]></surname>
<given-names><![CDATA[DIANA]]></given-names>
</name>
<xref ref-type="aff" rid="A06"/>
</contrib>
</contrib-group>
<aff id="A01">
<institution><![CDATA[,Universidad Nacional de Colombia Facultad de Ciencias Departamento de Estadística]]></institution>
<addr-line><![CDATA[Bogotá ]]></addr-line>
<country>Colombia</country>
</aff>
<aff id="A02">
<institution><![CDATA[,Universidad Nacional de Colombia Facultad de Ciencias Departamento de Estadística]]></institution>
<addr-line><![CDATA[Bogotá ]]></addr-line>
<country>Colombia</country>
</aff>
<aff id="A03">
<institution><![CDATA[,Universidad Nacional de Colombia Facultad de Ciencias Departamento de Estadística]]></institution>
<addr-line><![CDATA[Bogotá ]]></addr-line>
<country>Colombia</country>
</aff>
<aff id="A04">
<institution><![CDATA[,Universidad Nacional de Colombia Facultad de Ciencias Departamento de Estadística]]></institution>
<addr-line><![CDATA[Bogotá ]]></addr-line>
<country>Colombia</country>
</aff>
<aff id="A05">
<institution><![CDATA[,Universidad Nacional de Colombia Facultad de Ciencias Departamento de Estadística]]></institution>
<addr-line><![CDATA[Bogotá ]]></addr-line>
<country>Colombia</country>
</aff>
<aff id="A06">
<institution><![CDATA[,Universidad Nacional de Colombia Facultad de Ciencias Departamento de Estadística]]></institution>
<addr-line><![CDATA[Bogotá ]]></addr-line>
<country>Colombia</country>
</aff>
<pub-date pub-type="pub">
<day>15</day>
<month>12</month>
<year>2008</year>
</pub-date>
<pub-date pub-type="epub">
<day>15</day>
<month>12</month>
<year>2008</year>
</pub-date>
<volume>31</volume>
<numero>2</numero>
<fpage>211</fpage>
<lpage>228</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0120-17512008000200006&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0120-17512008000200006&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0120-17512008000200006&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[En este artículo se evalúa y se compara el comportamiento de diferentes metodologías empleadas para la obtención de intervalos de confianza de credibilidad, analizando sus probabilidades de cobertura estimada, su longitud esperada y la varianza de su longitud. Definidos estos tres conceptos, la comparación entre los intervalos considerados se desarrolla mediante procesos computacionales utilizando el paquete estadístico R. En este proceso, además de la verificación de conclusiones conocidas, como el mal comportamiento del intervalo de Wald y la sobrecobertura del intervalo exacto, se determinan, entre otros aspectos, características de los intervalos relacionadas con la variabilidad de su longitud.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Different methodologies for obtaining confidence and credibility intervals for a proportion are studied in this paper. Expected coverage, length and length variance of the interval are defined and used as a means for comparing the intervals produced by each methodology presented. These indicators were calculated using the statistical package R, used to characterize each interval; furthermore, some known properties, such as Wald intervals proportion undercoverage and Exact intervals overcoverage are verified in this study.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[proporciones]]></kwd>
<kwd lng="es"><![CDATA[intervalos de confianza]]></kwd>
<kwd lng="es"><![CDATA[métodos bayesianos]]></kwd>
<kwd lng="es"><![CDATA[intervalos de credibilidad]]></kwd>
<kwd lng="es"><![CDATA[cobertura]]></kwd>
<kwd lng="en"><![CDATA[Proportions]]></kwd>
<kwd lng="en"><![CDATA[Confidence intervals]]></kwd>
<kwd lng="en"><![CDATA[Bayesian methods]]></kwd>
<kwd lng="en"><![CDATA[Credibility interval]]></kwd>
<kwd lng="en"><![CDATA[Coverage]]></kwd>
</kwd-group>
</article-meta>
</front><body><![CDATA[  <font size="2" face="verdana">      <p> <b> <font size="4">     <center> Intervalos de confianza e intervalos de credibilidad para una proporci&oacute;n </center> </font> </b> </p>      <p> <b> <font size="3">     <center> Confidence Intervals and Credibility Intervals for a Proportion </center> </font> </b> </p>      <p>     <center> EDILBERTO CEPEDA-CUERVO<sup>1</sup>,  WILSON AGUILAR<sup>2</sup>,  V&Iacute;CTOR CERVANTES<sup>3</sup>,  MARTHA CORRALES<sup>4</sup>,  IV&Aacute;N D&Iacute;AZ<sup>5</sup>,  DIANA RODR&Iacute;GUEZ<sup>6</sup> </center> </p>      <p> <sup>1</sup>Universidad Nacional de Colombia, Facultad de Ciencias, Departamento de Estad&iacute;stica, Bogot&aacute;, Colombia. Profesor asociado. Email: <a href="mailto:ecepedac@unal.edu.co">ecepedac@unal.edu.co</a>     <br>  <sup>2</sup>Universidad Nacional de Colombia, Facultad de Ciencias, Departamento de Estad&iacute;stica, Bogot&aacute;, Colombia. Estudiante de maestr&iacute;a. Email: <a href="mailto:weaguilarl@unal.edu.co">weaguilarl@unal.edu.co</a>     <br>  <sup>3</sup>Universidad Nacional de Colombia, Facultad de Ciencias, Departamento de Estad&iacute;stica, Bogot&aacute;, Colombia. Estudiante de maestr&iacute;a. Email: <a href="mailto:vhcervantesb@unal.edu.co">vhcervantesb@unal.edu.co</a>     ]]></body>
<body><![CDATA[<br>  <sup>4</sup>Universidad Nacional de Colombia, Facultad de Ciencias, Departamento de Estad&iacute;stica, Bogot&aacute;, Colombia. Estudiante de maestr&iacute;a. Email: <a href="mailto:mlcorralesb@unal.edu.co">mlcorralesb@unal.edu.co</a>     <br>  <sup>5</sup>Universidad Nacional de Colombia, Facultad de Ciencias, Departamento de Estad&iacute;stica, Bogot&aacute;, Colombia. Estudiante de maestr&iacute;a. Email: <a href="mailto:ildiazm@unal.edu.co">ildiazm@unal.edu.co</a>     <br>  <sup>6</sup>Universidad Nacional de Colombia, Facultad de Ciencias, Departamento de Estad&iacute;stica, Bogot&aacute;, Colombia. Estudiante de maestr&iacute;a. Email: <a href="mailto:dprodriguezc@unal.edu.co">dprodriguezc@unal.edu.co</a>     <br> </p>  <hr size="1">      <p> <b>     <center> Resumen </center> </b> </p>      <p> En este art&iacute;culo se eval&uacute;a y se compara el comportamiento de diferentes metodolog&iacute;as empleadas para la obtenci&oacute;n de intervalos de confianza de credibilidad, analizando sus probabilidades de cobertura estimada, su longitud esperada y la varianza de su longitud. Definidos estos tres conceptos, la comparaci&oacute;n entre los intervalos considerados se desarrolla mediante procesos computacionales utilizando el paquete estad&iacute;stico <i>R</i>. En este proceso, adem&aacute;s de la verificaci&oacute;n de conclusiones conocidas, como el mal comportamiento del intervalo de Wald y la sobrecobertura del intervalo exacto, se determinan, entre otros aspectos, caracter&iacute;sticas de los intervalos relacionadas con la variabilidad de su longitud. </p>      <p> <b> Palabras clave: </b> proporciones, intervalos de confianza, m&eacute;todos bayesianos, intervalos de credibilidad, cobertura. </p>  <hr size="1">      <p> <b>     <center> Abstract </center> </b> </p>      ]]></body>
<body><![CDATA[<p> Different methodologies for obtaining confidence and credibility intervals for a proportion are studied in this paper. Expected coverage, length and length variance of the interval are defined and used as a means for comparing the intervals produced by each methodology presented. These indicators were calculated using the statistical package <i>R</i>, used to characterize each interval; furthermore, some known properties, such as Wald intervals proportion undercoverage and Exact intervals overcoverage are verified in this study. </p>      <p> <b> Key words: </b> Proportions, Confidence intervals, Bayesian methods, Credibility interval, Coverage. </p>  <hr size="1">      <p> Texto completo disponible en <a href="pdf/rce/v31n2/v31n2a06.pdf">PDF</a> </p>  <hr size="1">      <p> <b> <font size="3"> Referencias </font> </b> </p>       <!-- ref --><p> 1. Agresti, A. & Caffo, B. (2000), `Simple and Effective Confidence Intervals for Proportion and Differences of Proportions Result from Adding Two Successes and Two Failures´, <i>The American Statistician</i> <b>54</b>, 280-288. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000027&pid=S0120-1751200800020000600001&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p> 2. Agresti, A. & Coull, B. (1998), `Approximate is Better than Exact for Interval Estimation of Binomial Proportions´, <i>The American Statistician</i> <b>52</b>, 119-126. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000028&pid=S0120-1751200800020000600002&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p> 3. Agresti, A. & Min, Y. (2001), `On Small-Sample Confidence Intervals for Parameters in Discrete Distribution´, <i>Biometrics</i> <b>57</b>, 963-971. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000029&pid=S0120-1751200800020000600003&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p> 4. Bernardo, J. M. & Smith, A. F. M. (2000), <i>Bayesian Theory</i>, John Wiley & Sons, Ltd., Chichester, England. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000030&pid=S0120-1751200800020000600004&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p> 5. Brown, L., Cai, D. & DasGupta, A. (2001), `Interval Estimation for a Binomial Proportion´, <i>Statistical Science</i> <b>16</b>, 101-133. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000031&pid=S0120-1751200800020000600005&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p> 6. Brown, L., Cai, D. & DasGupta, A. (2002), `Confidence Intervals for a Binomial Proportion and Asymptotic Expansions´, <i>The Annals of Statistics</i> <b>30</b>, 160-201. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000032&pid=S0120-1751200800020000600006&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p> 7. Canavos, G. (1988), <i>Probabilidad y Estad&iacute;stica: Aplicaciones y m&eacute;todos</i>, McGraw Hill, M&eacute;xico D. F., M&eacute;xico. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000033&pid=S0120-1751200800020000600007&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p> 8. Correa, J. & Sierra, E. (2003), `Intervalos de confianza para la comparaci&oacute;n de dos proporciones´, <i>Revista Colombiana de Estadistica</i> <b>26</b>, 61-75. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000034&pid=S0120-1751200800020000600008&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p> 9. Henderson, M. & Meyer, M. (2001), `Exploring the Confidence Interval for a Binomial Parameter in a First Course in Statistical Computing´, <i>The American Statistician</i> <b>55</b>, 337-344. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000035&pid=S0120-1751200800020000600009&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p> 10. Migon, H. & Gamerman, D. (1999), <i>Statistical Inference: An Integrated Aproach</i>, Oxford University Press Inc., Madison Avenue, United States. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000036&pid=S0120-1751200800020000600010&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p> 11. Newcombe, R. & Merino, C. (2006), `Intervalos de confianza para las estimaciones de proporciones y las diferencias entre ellas´, <i>Interdisciplinaria</i> <b>23</b>, 141-154. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000037&pid=S0120-1751200800020000600011&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p> 12. R Development Core Team, (2007), <i>R: A Language and Environment for Statistical Computing</i>, R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0. *<a href="http://www.R-project.org" target="_blank">http://www.R-project.org</a> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000038&pid=S0120-1751200800020000600012&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p> 13. Wasserman, L. (1991), An Inferential Interpretation of Default Priors, Dept. Statistics, Carnegie Mellon Univ.. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000039&pid=S0120-1751200800020000600013&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><center> <b>&#91;Recibido en enero de 2008. Aceptado en septiembre de 2008&#93;</b> </center> <hr size="1">      <p> Este art&iacute;culo se puede citar en <i>LaTeX</i> utilizando la siguiente referencia bibliogr&aacute;fica de <i>BibTeX</i>: </p> <code><font size="2">@ARTICLE{RCEv31n2a06,    <br>  &nbsp;&nbsp;&nbsp; AUTHOR &nbsp;= {Cepeda-Cuervo, Edilberto and Aguilar, Wilson and Cervantes, V&iacute;ctor and Corrales, Martha and D&iacute;az, Iv&aacute;n and Rodr&iacute;guez, Diana},    ]]></body>
<body><![CDATA[<br>  &nbsp;&nbsp;&nbsp; TITLE &nbsp; = {{Intervalos de confianza e intervalos de credibilidad para una proporci&oacute;n}},    <br>  &nbsp;&nbsp;&nbsp; JOURNAL = {Revista Colombiana de Estad&iacute;stica},    <br> &nbsp;&nbsp;&nbsp; YEAR &nbsp;&nbsp; = {2008},    <br> &nbsp;&nbsp;&nbsp; volume &nbsp;= {31},    <br> &nbsp;&nbsp;&nbsp; number &nbsp;= {2},    <br> &nbsp;&nbsp;&nbsp; pages &nbsp; = {211-228}    <br> }</font></code>  <hr size="1"> </font>      ]]></body><back>
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