<?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>S2007-09342024000200005</article-id>
<article-id pub-id-type="doi">10.29312/remexca.v15i2.3634</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Tratamientos anidados dentro de un arreglo en grupos de bloques completos balanceados]]></article-title>
<article-title xml:lang="en"><![CDATA[Treatments nested within a balanced complete block group arrangement]]></article-title>
</title-group>
<contrib-group>
<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 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[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[Rubí Arriaga]]></surname>
<given-names><![CDATA[Martín]]></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-group>
<aff id="Af1">
<institution><![CDATA[,Universidad Autónoma del Estado de México Centro de Investigación y Estudios Avanzados en Fitomejoramiento Facultad de Ciencias Agrícolas]]></institution>
<addr-line><![CDATA[Toluca Estado de México]]></addr-line>
<country>Mexico</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>03</month>
<year>2024</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>03</month>
<year>2024</year>
</pub-date>
<volume>15</volume>
<numero>2</numero>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S2007-09342024000200005&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S2007-09342024000200005&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S2007-09342024000200005&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen Cuando se diseña y analiza un experimento o una serie de ensayos en tiempo o espacio podría ser de gran relevancia realizar una subdivisión del número de tratamientos por medio de la formación de grupos en los que se considere alguna diferencia importante entre éstos y alguna similitud dentro de ellos. En este estudio se analizó el caso presentado por Gomez y Gomez (1984) con relación al rendimiento de grano registrado en 45 variedades de arroz, clasificadas en tres grupos, se presentó su modelo estadístico para un diseño experimental de bloques completos al azar, se incluyeron fórmulas complementarias para calcular las sumas de cuadrados con las metodologías de mínimos cuadrados y formas cuadráticas o matriciales y se propone el procedimiento para generar una salida si fuera aplicado InfoStat. Adicionalmente, son mencionadas otras formas para calcular grados de libertad si el área experimental es dividida en unidad principal y subunidad, así como los correspondientes al residual del modelo o error b, las cuales simplifican los cálculos manuales. Se homologaron las fórmulas para ambas metodologías partiendo del uso formal de la simbología utilizada en las notaciones suma y punto, con base en éstas últimas se presentan sus formas cuadráticas. Se discute la diferencia entre un análisis de varianza convencional y el que es considerado en este trabajo, con base en las sumas de cuadrados finalmente, se indica cómo aplicar la prueba de Tukey para la comparación de medias de variedades dentro de cada grupo si es utilizado InfoStat. También se recomienda el uso de una calculadora de matrices para solucionar cálculos cuando se utilizan formas cuadráticas, la cual se encuentra disponible gratuitamente en su sitio WEB.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract When designing and analyzing an experiment or a series of trials in time or space, it could be of great relevance to subdivide the number of treatments by forming groups in which some important difference between them and some similarity within them are considered. This study analyzed the case presented by Gomez and Gomez (1984) regarding the grain yield recorded in 45 rice varieties, classified into three groups; their statistical model for an experimental design of randomized complete blocks was presented, complementary formulas were included to calculate the sums of squares with the methodologies of least squares and quadratic or matrix forms, and the procedure to generate an output if InfoStat were applied is proposed. In addition, other ways are mentioned to calculate degrees of freedom if the experimental area is divided into main unit and subunit, and those corresponding to the model residual or error b, which simplify manual calculations. The formulas for both methodologies were standardized based on the formal use of the symbology used in the sum and point notations; their quadratic forms are presented based on the latter. The difference between a conventional analysis of variance and the one considered in this paper, based on the sums of squares, is discussed. Finally, it is indicated how to apply Tukey&#8217;s test for the comparison of means of varieties within each group if InfoStat is used. It is also recommended to use a matrix calculator to solve calculations when using quadratic forms, which is freely available on their website.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[diseño de bloques completos al azar]]></kwd>
<kwd lng="es"><![CDATA[formas cuadráticas]]></kwd>
<kwd lng="es"><![CDATA[InfoStat]]></kwd>
<kwd lng="es"><![CDATA[mínimos cuadrados]]></kwd>
<kwd lng="en"><![CDATA[InfoStat]]></kwd>
<kwd lng="en"><![CDATA[least squares]]></kwd>
<kwd lng="en"><![CDATA[quadratic forms]]></kwd>
<kwd lng="en"><![CDATA[randomized complete block design]]></kwd>
</kwd-group>
</article-meta>
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