<?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>2007-0934</journal-id>
<journal-title><![CDATA[Revista mexicana de ciencias agrícolas]]></journal-title>
<abbrev-journal-title><![CDATA[Rev. Mex. Cienc. Agríc]]></abbrev-journal-title>
<issn>2007-0934</issn>
<publisher>
<publisher-name><![CDATA[Instituto Nacional de Investigaciones Forestales, Agrícolas y Pecuarias]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S2007-09342025000600110</article-id>
<article-id pub-id-type="doi">10.29312/remexca.v16i6.3861</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Fórmulas para serie de experimentos en cuadro latino en arreglo de parcelas divididas]]></article-title>
<article-title xml:lang="en"><![CDATA[Formulas for series of experiments in a Latin square design in a split-plot arrangement]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Pérez-López]]></surname>
<given-names><![CDATA[Delfina de Jesús]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Balbuena-Melgarejo]]></surname>
<given-names><![CDATA[Artemio]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Hernández-Ávila]]></surname>
<given-names><![CDATA[Jesús]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Franco-Martínez]]></surname>
<given-names><![CDATA[J. Ramón Pascual]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Rodríguez-González]]></surname>
<given-names><![CDATA[José Antonio]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[González-Huerta]]></surname>
<given-names><![CDATA[Andrés]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad Autónoma del Estado de México Facultad de Ciencias Agrícolas-Campus Universitario &#8216;El Cerrillo Centro de Investigación y Estudios Avanzados en Fitomejoramiento]]></institution>
<addr-line><![CDATA[Toluca de Lerdo Estado de México]]></addr-line>
<country>Mexico</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad Autónoma del Estado de México Facultad de Ciencias Agrícolas Programa de Maestría en Ciencias Agropecuarias y Recursos Naturales]]></institution>
<addr-line><![CDATA[Toluca de Lerdo Estado de México]]></addr-line>
<country>Mexico</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>09</month>
<year>2025</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>09</month>
<year>2025</year>
</pub-date>
<volume>16</volume>
<numero>6</numero>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S2007-09342025000600110&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S2007-09342025000600110&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S2007-09342025000600110&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen Las series de experimentos en tiempo, en espacio o combinando ambos ambientes en arreglo de parcelas divididas o subdivididas en cuadro latino no han sido utilizadas frecuentemente. En esta investigación se construye un modelo estadístico y las fórmulas para obtener grados de libertad y suma de cuadrados usando formas cuadráticas o matriciales y mínimos cuadrados, cuando las componentes de tiempo y espacio están confundidas en ambientes, como un prerrequisito para extender su análisis con submuestreo balanceado. Con relación a la parcela principal se parte de la suposición de ausencia de interacción entre hileras, columnas y niveles del factor A y de hileras y columnas con los ambientes, esta restricción también aplica entre hileras y columnas o ambos, con los factores A, B y su interacción, pero también se indica cómo llegar a los mismos resultados introduciendo el principio de cruzamiento y anidamiento, particularmente si será aplicado algún paquete estadístico, adicionalmente se hace énfasis en las fórmulas para calcular directamente grados de libertad y suma de cuadrados para los errores a y b, así como para los correspondientes a parcelas principales y subparcelas.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract Series of experiments in time, space, or combining both environments in a split-plot or split-split-plot arrangement in a Latin square design have not been frequently used. In this research, a statistical model and formulas are constructed to obtain degrees of freedom and sum of squares using quadratic or matrix forms and least squares, when the components of time and space are confused in environments, as a prerequisite to extend their analysis with balanced subsampling. In relation to the main plot, it is assumed that there is no interaction between rows, columns and levels of factor A, and rows and columns with the environments; this restriction also applies between rows and columns or both, with factors A, B and their interaction, but it is also indicated how to reach the same results by introducing the principle of crossing and nesting, particularly if a statistical package will be applied; emphasis is also placed on the formulas to directly calculate degrees of freedom and sum of squares for errors a and b, as well as for those corresponding to main plots and subplots.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[años y localidades confundidos en ambientes]]></kwd>
<kwd lng="es"><![CDATA[modelo estadístico]]></kwd>
<kwd lng="es"><![CDATA[matrices.]]></kwd>
<kwd lng="en"><![CDATA[matrices]]></kwd>
<kwd lng="en"><![CDATA[statistical models]]></kwd>
<kwd lng="en"><![CDATA[years and localities confused in environments]]></kwd>
</kwd-group>
</article-meta>
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