{"id":59199,"date":"2023-08-16T21:38:45","date_gmt":"2023-08-16T19:38:45","guid":{"rendered":"https:\/\/www.carolinacampalans.com\/glossary\/estadistica\/"},"modified":"2023-08-16T21:38:45","modified_gmt":"2023-08-16T19:38:45","slug":"estadistica","status":"publish","type":"glosario","link":"https:\/\/www.carolinacampalans.com\/?glosario=estadistica","title":{"rendered":"estad\u00edstica"},"content":{"rendered":"<div class=\"ttr_start\"><\/div><div class=\"fusion-fullwidth fullwidth-box fusion-builder-row-1 fusion-flex-container nonhundred-percent-fullwidth non-hundred-percent-height-scrolling\" style=\"--awb-border-radius-top-left:0px;--awb-border-radius-top-right:0px;--awb-border-radius-bottom-right:0px;--awb-border-radius-bottom-left:0px;--awb-flex-wrap:wrap;\" ><div class=\"fusion-builder-row fusion-row fusion-flex-align-items-flex-start fusion-flex-content-wrap\" style=\"max-width:1248px;margin-left: calc(-4% \/ 2 );margin-right: calc(-4% \/ 2 );\"><div class=\"fusion-layout-column fusion_builder_column fusion-builder-column-0 fusion_builder_column_1_1 1_1 fusion-flex-column\" style=\"--awb-bg-size:cover;--awb-width-large:100%;--awb-margin-top-large:0px;--awb-spacing-right-large:1.92%;--awb-margin-bottom-large:20px;--awb-spacing-left-large:1.92%;--awb-width-medium:100%;--awb-order-medium:0;--awb-spacing-right-medium:1.92%;--awb-spacing-left-medium:1.92%;--awb-width-small:100%;--awb-order-small:0;--awb-spacing-right-small:1.92%;--awb-spacing-left-small:1.92%;\"><div class=\"fusion-column-wrapper fusion-column-has-shadow fusion-flex-justify-content-flex-start fusion-content-layout-column\"><div class=\"fusion-text fusion-text-1\"><p>Una ciencia formal que estudia conjuntos de datos num\u00e9ricos para obtener inferencias basadas en las leyes de la probabilidad.<\/p>\n<\/div><div class=\"fusion-text fusion-text-2\">\n<\/div><\/div><\/div><\/div><\/div><div class=\"fusion-fullwidth fullwidth-box fusion-builder-row-2 fusion-flex-container nonhundred-percent-fullwidth non-hundred-percent-height-scrolling\" style=\"--awb-border-radius-top-left:0px;--awb-border-radius-top-right:0px;--awb-border-radius-bottom-right:0px;--awb-border-radius-bottom-left:0px;--awb-flex-wrap:wrap;\" ><div class=\"fusion-builder-row fusion-row fusion-flex-align-items-flex-start fusion-flex-content-wrap\" style=\"max-width:1248px;margin-left: calc(-4% \/ 2 );margin-right: calc(-4% \/ 2 );\"><div class=\"fusion-layout-column fusion_builder_column fusion-builder-column-1 fusion_builder_column_1_1 1_1 fusion-flex-column\" style=\"--awb-bg-size:cover;--awb-width-large:100%;--awb-margin-top-large:0px;--awb-spacing-right-large:1.92%;--awb-margin-bottom-large:20px;--awb-spacing-left-large:1.92%;--awb-width-medium:100%;--awb-order-medium:0;--awb-spacing-right-medium:1.92%;--awb-spacing-left-medium:1.92%;--awb-width-small:100%;--awb-order-small:0;--awb-spacing-right-small:1.92%;--awb-spacing-left-small:1.92%;\"><div class=\"fusion-column-wrapper fusion-column-has-shadow fusion-flex-justify-content-flex-start fusion-content-layout-column\"><div class=\"fusion-title title fusion-title-1 fusion-sep-none fusion-title-text fusion-title-size-two\"><h2 class=\"fusion-title-heading title-heading-left fusion-responsive-typography-calculated\" style=\"margin:0;--fontSize:36;line-height:1.5;\">Descripci\u00f3n<\/h2><\/div><div class=\"fusion-text fusion-text-3\"><p data-path-to-node=\"0\">Podemos entender la estad\u00edstica como la rama de las matem\u00e1ticas que se encarga de recolectar, organizar, analizar e interpretar datos para extraer conclusiones v\u00e1lidas y tomar decisiones informadas bajo condiciones de incertidumbre.<\/p>\n<\/div><div class=\"fusion-text fusion-text-4\"><h3><span class=\"ez-toc-section\" id=\"Procedimientos\"><\/span>Procedimientos<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Los tres pasos t\u00edpicos del an\u00e1lisis estad\u00edstico son:<\/p>\n<ol>\n<li>recolecci\u00f3n de datos<\/li>\n<li>descripci\u00f3n y visualizaci\u00f3n de datos<\/li>\n<li>obtenci\u00f3n de conclusiones<\/li>\n<\/ol>\n<\/div><\/div><\/div><div class=\"fusion-layout-column fusion_builder_column fusion-builder-column-2 fusion_builder_column_1_1 1_1 fusion-flex-column\" style=\"--awb-bg-size:cover;--awb-width-large:100%;--awb-margin-top-large:0px;--awb-spacing-right-large:1.92%;--awb-margin-bottom-large:20px;--awb-spacing-left-large:1.92%;--awb-width-medium:100%;--awb-order-medium:0;--awb-spacing-right-medium:1.92%;--awb-spacing-left-medium:1.92%;--awb-width-small:100%;--awb-order-small:0;--awb-spacing-right-small:1.92%;--awb-spacing-left-small:1.92%;\"><div class=\"fusion-column-wrapper fusion-column-has-shadow fusion-flex-justify-content-flex-start fusion-content-layout-column\"><div class=\"fusion-title title fusion-title-2 fusion-sep-none fusion-title-text fusion-title-size-three\"><h3 class=\"fusion-title-heading title-heading-left fusion-responsive-typography-calculated\" style=\"margin:0;--fontSize:24;--minFontSize:24;line-height:1.5;\">Enfoques<\/h3><\/div><div class=\"fusion-text fusion-text-5\"><p data-path-to-node=\"0\">La transici\u00f3n de la estad\u00edstica de una herramienta de registro a una ciencia de decisi\u00f3n se bas\u00f3 en un intenso debate intelectual entre dos escuelas de pensamiento. Lo que hoy estudiamos en los libros de texto como un sistema unificado es, en realidad, un \u00abh\u00edbrido\u00bb de dos visiones enfrentadas.<\/p>\n<\/div><div class=\"fusion-text fusion-text-6\"><h4 data-path-to-node=\"4\"><span class=\"ez-toc-section\" id=\"El_enfoque_inductivo\"><\/span>El enfoque inductivo<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p data-path-to-node=\"4\">Para Ronald Fisher, el objetivo de la estad\u00edstica era la inferencia: descubrir si los datos de un experimento aportaban evidencia suficiente para rechazar una idea.<\/p>\n<p data-path-to-node=\"5,0,0\">Fisher introdujo la idea de que debemos trabajar bajo la suposici\u00f3n de que \u00abno hay efecto\u00bb (por ejemplo, que una medicina no funciona); es lo que se conoce como hip\u00f3tesis nula (H0). Su gran invento fue el valor p (<i>p-value<\/i>), empleado para evaluar la probabilidad de obtener los resultados observados si la <span class=\"math-inline\" data-math=\"H_0\" data-index-in-node=\"101\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">H<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> fuera cierta; si el <em><span class=\"math-inline\" data-math=\"p\" data-index-in-node=\"125\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">p<\/span><\/span><\/span><\/span><\/span>-value<\/em> es muy bajo (t\u00edpicamente <span class=\"math-inline\" data-math=\"&lt; 0.05\" data-index-in-node=\"158\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mrel\">&lt;<\/span><\/span><span class=\"base\"><span class=\"mord\">0.05<\/span><\/span><\/span><\/span><\/span>), Fisher dec\u00eda que el resultado era \u00absignificativo\u00bb.<\/p>\n<p data-path-to-node=\"5,2,0\">Para \u00e9l, la estad\u00edstica era una herramienta para los investigadores individuales que buscaban la verdad en sus laboratorios.<\/p>\n<\/div><div class=\"fusion-text fusion-text-7\"><h4 data-path-to-node=\"8\"><span class=\"ez-toc-section\" id=\"El_enfoque_deductivo\"><\/span>El enfoque deductivo<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p data-path-to-node=\"8\">Jerzy Neyman y Egon Pearson criticaron a Fisher por ser poco riguroso. Ellos no buscaban \u00abla verdad\u00bb, sino establecer reglas de comportamiento para minimizar errores a largo plazo.<\/p>\n<p data-path-to-node=\"9,0,0\"><b data-path-to-node=\"9,0,0\" data-index-in-node=\"0\"><\/b>Neyman y Pearson introdujeron la distinci\u00f3n de dos errores que hoy es est\u00e1ndar:<\/p>\n<ul>\n<li data-path-to-node=\"9,0,1,0,0\"><b data-path-to-node=\"9,0,1,0,0\" data-index-in-node=\"0\">Error tipo I (<span class=\"math-inline\" data-math=\"alpha\" data-index-in-node=\"14\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">\u03b1<\/span><\/span><\/span><\/span><\/span>):<\/b> Rechazar la <span class=\"math-inline\" data-math=\"H_0\" data-index-in-node=\"35\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">H<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> cuando es verdadera (un falso positivo).<\/li>\n<li data-path-to-node=\"9,0,1,0,0\"><b data-path-to-node=\"9,0,1,1,0\" data-index-in-node=\"0\">Error tipo II (<span class=\"math-inline\" data-math=\"beta\" data-index-in-node=\"15\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">\u03b2<\/span><\/span><\/span><\/span><\/span>):<\/b> No rechazar la <span class=\"math-inline\" data-math=\"H_0\" data-index-in-node=\"38\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">H<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> cuando es falsa (un falso negativo).<\/li>\n<\/ul>\n<p data-path-to-node=\"9,1,0\">A diferencia de Fisher, ellos consideraban que no podemos rechazar una idea sin tener otra alternativa contra la cual comparar; es decir, debemos contar con una hip\u00f3tesis alternativa (H1). En su planteamiento, el <i>poder estad\u00edstico<\/i> es un concepto clave para determinar el tama\u00f1o que debe tener una muestra para que permita detectar un efecto real.<\/p>\n<\/div><div class=\"fusion-text fusion-text-8\"><h4 data-path-to-node=\"12\"><span class=\"ez-toc-section\" id=\"La_sintesis\"><\/span>La s\u00edntesis<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p data-path-to-node=\"12\">Lo que usamos hoy en d\u00eda en las ciencias modernas es una mezcla de ambos enfoques, a menudo llamada NHST (<em>null hypothesis significance testing<\/em>).<\/p>\n<div class=\"horizontal-scroll-wrapper\">\n<div class=\"table-block-component\">\n<div class=\"table-block has-export-button\">\n<div class=\"table-content not-end-of-paragraph\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div><\/div><\/div><div class=\"fusion-layout-column fusion_builder_column fusion-builder-column-3 fusion_builder_column_1_1 1_1 fusion-flex-column\" style=\"--awb-bg-size:cover;--awb-width-large:100%;--awb-margin-top-large:0px;--awb-spacing-right-large:1.92%;--awb-margin-bottom-large:20px;--awb-spacing-left-large:1.92%;--awb-width-medium:100%;--awb-order-medium:0;--awb-spacing-right-medium:1.92%;--awb-spacing-left-medium:1.92%;--awb-width-small:100%;--awb-order-small:0;--awb-spacing-right-small:1.92%;--awb-spacing-left-small:1.92%;\"><div class=\"fusion-column-wrapper fusion-column-has-shadow fusion-flex-justify-content-flex-start fusion-content-layout-column\"><div class=\"fusion-title title fusion-title-3 fusion-sep-none fusion-title-text fusion-title-size-three\"><h3 class=\"fusion-title-heading title-heading-left fusion-responsive-typography-calculated\" style=\"margin:0;--fontSize:24;--minFontSize:24;line-height:1.5;\">Evoluci\u00f3n hist\u00f3rica<\/h3><\/div><div class=\"fusion-text fusion-text-9\"><h4><span class=\"ez-toc-section\" id=\"El_salto_a_la_inferencia_finales_del_s_XIX\"><\/span>El salto a la inferencia (finales del s. XIX)<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p data-path-to-node=\"4\">La estad\u00edstica moderna nace cuando dejamos de \u00abdescribir lo que pas\u00f3\u00bb y empezamos a \u00abestimar lo que no vemos\u00bb.<\/p>\n<p data-path-to-node=\"5,0,0\"><b data-path-to-node=\"5,0,0\" data-index-in-node=\"0\">Francis Galton y la regresi\u00f3n<\/b><\/p>\n<p data-path-to-node=\"5,0,0\">Primo de Darwin, Galton quer\u00eda medir la herencia. Al estudiar la altura de padres e hijos, descubri\u00f3 que los extremos tienden a volver al promedio. Invent\u00f3 el concepto de regresi\u00f3n y correlaci\u00f3n, las herramientas b\u00e1sicas para entender relaciones entre variables hoy en d\u00eda.<\/p>\n<p data-path-to-node=\"5,1,0\"><b data-path-to-node=\"5,1,0\" data-index-in-node=\"0\">Karl Pearson<\/b><\/p>\n<p data-path-to-node=\"5,1,0\">Fue quien sistematiz\u00f3 la disciplina. Cre\u00f3 el Laboratorio Biom\u00e9trico en Londres y desarroll\u00f3 la prueba de chi-cuadrado (<span class=\"math-inline\" data-math=\"chi^2\" data-index-in-node=\"133\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">\u03c7<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>), que permite saber si los datos observados se ajustan a una teor\u00eda o son fruto del azar.<\/p>\n<\/div><div class=\"fusion-text fusion-text-10\"><h4><span class=\"ez-toc-section\" id=\"La_revolucion_de_las_muestras_pequenas_1900-1920\"><\/span>La revoluci\u00f3n de las muestras peque\u00f1as (1900-1920)<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p data-path-to-node=\"8\">Antes de este punto, se cre\u00eda que para que la estad\u00edstica fuera v\u00e1lida hac\u00edan falta miles de datos.<\/p>\n<p data-path-to-node=\"9,0,0\"><b data-path-to-node=\"9,0,0\" data-index-in-node=\"0\">William Sealy Gosset (\u00abStudent\u00bb)<\/b><\/p>\n<p data-path-to-node=\"9,0,0\">Trabajaba para la cervecera Guinness. Como no pod\u00eda desperdiciar miles de barriles para hacer pruebas de calidad, desarroll\u00f3 la distribuci\u00f3n t de Student. Esto permiti\u00f3 hacer inferencias v\u00e1lidas con muestras muy peque\u00f1as (de 10 o 20 unidades), algo vital para la medicina y la industria moderna.<\/p>\n<\/div><div class=\"fusion-text fusion-text-11\"><h4><span class=\"ez-toc-section\" id=\"La_%C2%ABedad_de_oro%C2%BB_y_el_diseno_experimental_1920-1950\"><\/span>La \u00abedad de oro\u00bb y el dise\u00f1o experimental (1920-1950)<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p data-path-to-node=\"12\">En este periodo, la estad\u00edstica se convierte en el lenguaje universal de la ciencia gracias a una figura dominante.<\/p>\n<p data-path-to-node=\"13,0,0\"><b data-path-to-node=\"13,0,0\" data-index-in-node=\"0\">Ronald A. Fisher<\/b><\/p>\n<p data-path-to-node=\"13,0,0\">Es considerado el arquitecto de la estad\u00edstica moderna. En su libro <i data-path-to-node=\"13,0,0\" data-index-in-node=\"86\">Statistical Methods for Research Workers<\/i>, introdujo:<\/p>\n<ul>\n<li data-path-to-node=\"13,0,1,0,0\"><b data-path-to-node=\"13,0,1,0,0\" data-index-in-node=\"0\">El an\u00e1lisis de varianza (ANOVA):<\/b> Para comparar m\u00faltiples grupos a la vez.<\/li>\n<li data-path-to-node=\"13,0,1,0,0\"><b data-path-to-node=\"13,0,1,1,0\" data-index-in-node=\"0\">La aleatorizaci\u00f3n:<\/b> La idea de que, en un experimento (como probar un f\u00e1rmaco), los sujetos deben asignarse al azar para evitar sesgos.<\/li>\n<li data-path-to-node=\"13,0,1,0,0\"><b data-path-to-node=\"13,0,1,2,0\" data-index-in-node=\"0\">El valor p (<span class=\"math-inline\" data-math=\"p\" data-index-in-node=\"12\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">p<\/span><\/span><\/span><\/span><\/span>-value):<\/b> La medida est\u00e1ndar para decidir si un resultado cient\u00edfico es \u00absignificativo\u00bb.<\/li>\n<li style=\"list-style-type: none;\"><\/li>\n<\/ul>\n<\/div><div class=\"fusion-text fusion-text-12\"><h4><span class=\"ez-toc-section\" id=\"La_consolidacion_matematica_y_el_teorema_del_limite_central\"><\/span>La consolidaci\u00f3n matem\u00e1tica y el teorema del l\u00edmite central<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p data-path-to-node=\"16\">Durante mediados del siglo XX, matem\u00e1ticos como <b data-path-to-node=\"16\" data-index-in-node=\"48\">Jerzy Neyman<\/b> o\u00a0<b data-path-to-node=\"16\" data-index-in-node=\"63\">Egon Pearson<\/b> (hijo de Karl) refinaron las teor\u00edas de Fisher, creando el sistema de contraste de hip\u00f3tesis: la idea de la hip\u00f3tesis nula (<span class=\"math-inline\" data-math=\"H_0\" data-index-in-node=\"260\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">H<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>) frente a la hip\u00f3tesis alternativa (<span class=\"math-inline\" data-math=\"H_1\" data-index-in-node=\"300\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">H<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>).<\/p>\n<\/div><div class=\"fusion-text fusion-text-13\"><h4><span class=\"ez-toc-section\" id=\"La_era_informatica_y_bayesiana_1970-actualidad\"><\/span>La era inform\u00e1tica y bayesiana (1970-actualidad)<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p data-path-to-node=\"19\">La estad\u00edstica moderna dio un \u00faltimo giro radical con la potencia de c\u00e1lculo.<\/p>\n<p data-path-to-node=\"20,0,0\"><b data-path-to-node=\"20,0,0\" data-index-in-node=\"0\">Bradley Efron y el bootstrap<\/b><\/p>\n<p data-path-to-node=\"20,0,0\">En 1979 introdujo m\u00e9todos de \u00abremuestreo\u00bb que permiten hacer estad\u00edstica compleja mediante simulaciones por ordenador, sin necesidad de f\u00f3rmulas matem\u00e1ticas te\u00f3ricas pesadas.<\/p>\n<p data-path-to-node=\"20,1,0\"><b data-path-to-node=\"20,1,0\" data-index-in-node=\"0\">El resurgimiento bayesiano<\/b><\/p>\n<p data-path-to-node=\"20,1,0\">Aunque Thomas Bayes vivi\u00f3 en el s. XVIII, su enfoque (que permite actualizar probabilidades a medida que llega nueva informaci\u00f3n) solo se volvi\u00f3 pr\u00e1ctico con los ordenadores modernos. Es la base de los filtros de <em>spam<\/em> y los algoritmos de inteligencia artificial.<\/p>\n<\/div><\/div><\/div><\/div><\/div><div class=\"fusion-fullwidth fullwidth-box fusion-builder-row-3 fusion-flex-container nonhundred-percent-fullwidth non-hundred-percent-height-scrolling\" style=\"--awb-border-radius-top-left:0px;--awb-border-radius-top-right:0px;--awb-border-radius-bottom-right:0px;--awb-border-radius-bottom-left:0px;--awb-padding-top:20px;--awb-flex-wrap:wrap;\" ><div class=\"fusion-builder-row fusion-row fusion-flex-align-items-flex-start fusion-flex-content-wrap\" style=\"max-width:1248px;margin-left: calc(-4% \/ 2 );margin-right: calc(-4% \/ 2 );\"><div class=\"fusion-layout-column fusion_builder_column fusion-builder-column-4 fusion_builder_column_1_1 1_1 fusion-flex-column\" style=\"--awb-bg-size:cover;--awb-width-large:100%;--awb-margin-top-large:0px;--awb-spacing-right-large:1.92%;--awb-margin-bottom-large:20px;--awb-spacing-left-large:1.92%;--awb-width-medium:100%;--awb-order-medium:0;--awb-spacing-right-medium:1.92%;--awb-spacing-left-medium:1.92%;--awb-width-small:100%;--awb-order-small:0;--awb-spacing-right-small:1.92%;--awb-spacing-left-small:1.92%;\"><div class=\"fusion-column-wrapper fusion-column-has-shadow fusion-flex-justify-content-flex-start fusion-content-layout-column\"><div class=\"fusion-title title fusion-title-4 fusion-sep-none fusion-title-text fusion-title-size-two\"><h2 class=\"fusion-title-heading title-heading-left fusion-responsive-typography-calculated\" style=\"margin:0;--fontSize:36;line-height:1.5;\">Tipos<\/h2><\/div><\/div><\/div><div class=\"fusion-layout-column fusion_builder_column fusion-builder-column-5 fusion_builder_column_1_1 1_1 fusion-flex-column\" style=\"--awb-bg-size:cover;--awb-width-large:100%;--awb-margin-top-large:0px;--awb-spacing-right-large:1.92%;--awb-margin-bottom-large:20px;--awb-spacing-left-large:1.92%;--awb-width-medium:100%;--awb-order-medium:0;--awb-spacing-right-medium:1.92%;--awb-spacing-left-medium:1.92%;--awb-width-small:100%;--awb-order-small:0;--awb-spacing-right-small:1.92%;--awb-spacing-left-small:1.92%;\"><div class=\"fusion-column-wrapper fusion-column-has-shadow fusion-flex-justify-content-flex-start fusion-content-layout-column\"><div class=\"fusion-title title fusion-title-5 fusion-sep-none fusion-title-text fusion-title-size-three\"><h3 class=\"fusion-title-heading title-heading-left fusion-responsive-typography-calculated\" style=\"margin:0;--fontSize:24;--minFontSize:24;line-height:1.5;\">Estad\u00edstica descriptiva<\/h3><\/div><div class=\"fusion-text fusion-text-14\"><p>Rama de la estad\u00edstica cuyo objetivo es estructurar un conjunto de datos para revelar c\u00f3mo se comporta la muestra estad\u00edstica en un momento determinado.<\/p>\n<blockquote>\n<p>La estad\u00edstica descriptiva se dedica b\u00e1sicamente a la recogida, resumen y caracterizaci\u00f3n de los datos que se obtienen cuando se observa un determinado fen\u00f3meno de masa, aportando un conjunto de indicadores que sintetizan o resumen lo m\u00e1s relevante en relaci\u00f3n a dicho fen\u00f3meno.<span id='easy-footnote-1-59199' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/www.carolinacampalans.com\/?glosario=estadistica#easy-footnote-bottom-1-59199' title='F. Garc\u00eda Ordaz, J.J. Garc\u00eda del Hoyo y M.D. Gonz\u00e1lez Gal\u00e1n, &lt;em&gt;Estad\u00edstica y m\u00e9todos cuantitativos I&lt;\/em&gt;. Huelva, Universidad de Huelva, 2021, p. 20.'><sup>1<\/sup><\/a><\/span><\/p><\/blockquote>\n<p>La principal diferencia respecto a la estad\u00edstica inferencial es que se enfoca en el tiempo presente.<\/p>\n<\/div><\/div><\/div><div class=\"fusion-layout-column fusion_builder_column fusion-builder-column-6 fusion_builder_column_1_1 1_1 fusion-flex-column\" style=\"--awb-bg-size:cover;--awb-width-large:100%;--awb-margin-top-large:0px;--awb-spacing-right-large:1.92%;--awb-margin-bottom-large:20px;--awb-spacing-left-large:1.92%;--awb-width-medium:100%;--awb-order-medium:0;--awb-spacing-right-medium:1.92%;--awb-spacing-left-medium:1.92%;--awb-width-small:100%;--awb-order-small:0;--awb-spacing-right-small:1.92%;--awb-spacing-left-small:1.92%;\"><div class=\"fusion-column-wrapper fusion-column-has-shadow fusion-flex-justify-content-flex-start fusion-content-layout-column\"><div class=\"fusion-title title fusion-title-6 fusion-sep-none fusion-title-text fusion-title-size-three\"><h3 class=\"fusion-title-heading title-heading-left fusion-responsive-typography-calculated\" style=\"margin:0;--fontSize:24;--minFontSize:24;line-height:1.5;\">Estad\u00edstica inferencial<\/h3><\/div><div class=\"fusion-text fusion-text-15\"><p>Modalidad de la disciplina estad\u00edstica que utiliza el c\u00e1lculo de probabilidades para realizar estimaciones sobre el posible comportamiento futuro de un fen\u00f3meno.<\/p>\n<blockquote>\n<p>Es la rama de la estad\u00edstica que, apoy\u00e1ndose en la teor\u00eda de la probabilidad y a partir del estudio descriptivo previo de datos muestrales, efect\u00faa estimaciones, predicciones y otras generalizaciones sobre un conjunto mayor de datos (la poblaci\u00f3n de partida). Su fin es, pues, estimar las caracter\u00edsticas de la poblaci\u00f3n a partir de la informaci\u00f3n que proporciona una muestra.<span id='easy-footnote-2-59199' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/www.carolinacampalans.com\/?glosario=estadistica#easy-footnote-bottom-2-59199' title='Carlos Gamero Bur\u00f3n, &lt;em&gt;Elementos de Estad\u00edstica Descriptiva y de Teor\u00eda de la Probabilidad&lt;\/em&gt;. M\u00e1laga, UMA Editorial, 2023, p. 23.'><sup>2<\/sup><\/a><\/span><\/p><\/blockquote>\n<p>A diferencia de la estad\u00edstica descriptiva, su foco est\u00e1 puesto en el futuro y por eso se la conoce\u00a0tambi\u00e9n \u00a0como estad\u00edstica inductiva.<\/p>\n<blockquote>\n<p>La inferencia estad\u00edstica pretende llegar a conclusiones acerca del comportamiento del fen\u00f3meno objeto de estudio, pero en un sentido amplio. En la mayor\u00eda de los casos, dicho fen\u00f3meno no podr\u00e1 observarse de forma exhaustiva, por lo que tendremos que observarlo de forma parcial a trav\u00e9s de una muestra. Aqu\u00ed es cuando aparece la inferencia estad\u00edstica, pues pretender\u00e1 extraer conclusiones sobre la poblaci\u00f3n a partir de dicha observaci\u00f3n parcial o muestral.<span id='easy-footnote-3-59199' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/www.carolinacampalans.com\/?glosario=estadistica#easy-footnote-bottom-3-59199' title='F. Garc\u00eda Ordaz, J.J. Garc\u00eda del Hoyo y M.D. Gonz\u00e1lez Gal\u00e1n, &lt;em&gt;Estad\u00edstica y M\u00e9todos Cuantitativos I.&lt;\/em&gt; Huelva, Universidad de Huelva, 2021, p. 20.'><sup>3<\/sup><\/a><\/span><\/p><\/blockquote>\n<p>Las principales modalidades de estad\u00edstica inferencial son la prueba de hip\u00f3tesis y la estimaci\u00f3n estad\u00edstica.<\/p>\n<\/div><\/div><\/div><\/div><\/div><div class=\"fusion-fullwidth fullwidth-box fusion-builder-row-4 fusion-flex-container nonhundred-percent-fullwidth non-hundred-percent-height-scrolling\" style=\"--awb-border-radius-top-left:0px;--awb-border-radius-top-right:0px;--awb-border-radius-bottom-right:0px;--awb-border-radius-bottom-left:0px;--awb-padding-top:20px;--awb-flex-wrap:wrap;\" ><div class=\"fusion-builder-row fusion-row fusion-flex-align-items-flex-start fusion-flex-content-wrap\" style=\"max-width:1248px;margin-left: calc(-4% \/ 2 );margin-right: calc(-4% \/ 2 );\"><div class=\"fusion-layout-column fusion_builder_column fusion-builder-column-7 fusion_builder_column_1_1 1_1 fusion-flex-column\" style=\"--awb-bg-size:cover;--awb-width-large:100%;--awb-margin-top-large:0px;--awb-spacing-right-large:1.92%;--awb-margin-bottom-large:20px;--awb-spacing-left-large:1.92%;--awb-width-medium:100%;--awb-order-medium:0;--awb-spacing-right-medium:1.92%;--awb-spacing-left-medium:1.92%;--awb-width-small:100%;--awb-order-small:0;--awb-spacing-right-small:1.92%;--awb-spacing-left-small:1.92%;\"><div class=\"fusion-column-wrapper fusion-column-has-shadow fusion-flex-justify-content-flex-start fusion-content-layout-column\"><div class=\"fusion-title title fusion-title-7 fusion-sep-none fusion-title-text fusion-title-size-two\"><h2 class=\"fusion-title-heading title-heading-left fusion-responsive-typography-calculated\" style=\"margin:0;--fontSize:36;line-height:1.5;\">Conceptos relacionados<\/h2><\/div><div class=\"accordian fusion-accordian\" style=\"--awb-border-size:1px;--awb-icon-size:15px;--awb-content-font-size:20px;--awb-icon-alignment:left;--awb-hover-color:#f9f9f9;--awb-border-color:#cccccc;--awb-background-color:#ffffff;--awb-divider-color:#000000;--awb-divider-hover-color:#000000;--awb-icon-color:#ffffff;--awb-title-color:#af7baf;--awb-content-color:#747474;--awb-icon-box-color:#333333;--awb-toggle-hover-accent-color:#9b00af;--awb-title-font-family:&quot;Roboto Condensed&quot;;--awb-title-font-weight:regular;--awb-title-font-style:normal;--awb-title-font-size:20px;--awb-content-font-family:&quot;Open Sans&quot;;--awb-content-font-style:normal;--awb-content-font-weight:400;\"><div class=\"panel-group fusion-toggle-icon-boxed\" id=\"accordion-59199-1\"><div class=\"fusion-panel panel-default panel-8f26523edb5bc0a72 fusion-toggle-has-divider\" style=\"--awb-title-color:#af7baf;\"><div class=\"panel-heading\"><h3 class=\"panel-title toggle\" id=\"toggle_8f26523edb5bc0a72\"><a aria-expanded=\"false\" aria-controls=\"8f26523edb5bc0a72\" role=\"button\" data-toggle=\"collapse\" data-parent=\"#accordion-59199-1\" data-target=\"#8f26523edb5bc0a72\" href=\"#8f26523edb5bc0a72\"><span class=\"fusion-toggle-icon-wrapper\" aria-hidden=\"true\"><i class=\"fa-fusion-box active-icon awb-icon-minus\" aria-hidden=\"true\"><\/i><i class=\"fa-fusion-box inactive-icon awb-icon-plus\" aria-hidden=\"true\"><\/i><\/span><span class=\"fusion-toggle-heading\">Dispersi\u00f3n estad\u00edstica<\/span><\/a><\/h3><\/div><div id=\"8f26523edb5bc0a72\" class=\"panel-collapse collapse \" aria-labelledby=\"toggle_8f26523edb5bc0a72\"><div class=\"panel-body toggle-content fusion-clearfix\">\n<p>La dispersi\u00f3n estad\u00edstica corresponde al grado en que una distribuci\u00f3n de datos num\u00e9ricos se aleja o se acerca a un estad\u00edstico central como podr\u00eda ser, por ejemplo, la media aritm\u00e9tica.<\/p>\n<p>Existen diversas medidas de dispersi\u00f3n; las m\u00e1s habituales son:<\/p>\n<ul>\n<li>rango de dispersi\u00f3n<\/li>\n<li>cuartiles y percentiles<\/li>\n<li>rango intercuartil<\/li>\n<li>desviaci\u00f3n est\u00e1ndar<\/li>\n<\/ul>\n<\/div><\/div><\/div><div class=\"fusion-panel panel-default panel-145866f3659c8ecbf fusion-toggle-has-divider\" style=\"--awb-title-color:#af7baf;\"><div class=\"panel-heading\"><h3 class=\"panel-title toggle\" id=\"toggle_145866f3659c8ecbf\"><a aria-expanded=\"false\" aria-controls=\"145866f3659c8ecbf\" role=\"button\" data-toggle=\"collapse\" data-parent=\"#accordion-59199-1\" data-target=\"#145866f3659c8ecbf\" href=\"#145866f3659c8ecbf\"><span class=\"fusion-toggle-icon-wrapper\" aria-hidden=\"true\"><i class=\"fa-fusion-box active-icon awb-icon-minus\" aria-hidden=\"true\"><\/i><i class=\"fa-fusion-box inactive-icon awb-icon-plus\" aria-hidden=\"true\"><\/i><\/span><span class=\"fusion-toggle-heading\">Estad\u00edstico<\/span><\/a><\/h3><\/div><div id=\"145866f3659c8ecbf\" class=\"panel-collapse collapse \" aria-labelledby=\"toggle_145866f3659c8ecbf\"><div class=\"panel-body toggle-content fusion-clearfix\">\n<p>Hablamos de <em>estad\u00edstico<\/em> para referirnos a un valor num\u00e9rico calculado sobre la base de una muestra estad\u00edstica y que resume los valores que dicha muestra toma en cierto atributo.<\/p>\n<p>Se diferencia del par\u00e1metro poblacional, ya que \u00e9ste se calcula sobre la poblaci\u00f3n estad\u00edstica.<\/p>\n<\/div><\/div><\/div><div class=\"fusion-panel panel-default panel-86127f5364c57cc11 fusion-toggle-has-divider\" style=\"--awb-title-color:#af7baf;\"><div class=\"panel-heading\"><h3 class=\"panel-title toggle\" id=\"toggle_86127f5364c57cc11\"><a aria-expanded=\"false\" aria-controls=\"86127f5364c57cc11\" role=\"button\" data-toggle=\"collapse\" data-parent=\"#accordion-59199-1\" data-target=\"#86127f5364c57cc11\" href=\"#86127f5364c57cc11\"><span class=\"fusion-toggle-icon-wrapper\" aria-hidden=\"true\"><i class=\"fa-fusion-box active-icon awb-icon-minus\" aria-hidden=\"true\"><\/i><i class=\"fa-fusion-box inactive-icon awb-icon-plus\" aria-hidden=\"true\"><\/i><\/span><span class=\"fusion-toggle-heading\">Estandarizaci\u00f3n<\/span><\/a><\/h3><\/div><div id=\"86127f5364c57cc11\" class=\"panel-collapse collapse \" aria-labelledby=\"toggle_86127f5364c57cc11\"><div class=\"panel-body toggle-content fusion-clearfix\">\n<p>Un proceso mediante el cual se transforman los datos de una variable estad\u00edstica para que tengan ciertas caracter\u00edsticas, t\u00edpicamente una media igual a 0 y una desviaci\u00f3n est\u00e1ndar igual a 1. Esta transformaci\u00f3n es \u00fatil para comparar variables que originalmente tienen diferentes unidades de medida o escalas. Al estandarizar las variables, se facilita la comparaci\u00f3n y se eliminan los efectos de las unidades de medida.<\/p>\n<p>El proceso de estandarizaci\u00f3n estad\u00edstica implica la transformaci\u00f3n de cada valor de la variable en su valor est\u00e1ndar (valor z o score z).<\/p>\n<\/div><\/div><\/div><div class=\"fusion-panel panel-default panel-a162613b7d2d6799a fusion-toggle-has-divider\" style=\"--awb-title-color:#af7baf;\"><div class=\"panel-heading\"><h3 class=\"panel-title toggle\" id=\"toggle_a162613b7d2d6799a\"><a aria-expanded=\"false\" aria-controls=\"a162613b7d2d6799a\" role=\"button\" data-toggle=\"collapse\" data-parent=\"#accordion-59199-1\" data-target=\"#a162613b7d2d6799a\" href=\"#a162613b7d2d6799a\"><span class=\"fusion-toggle-icon-wrapper\" aria-hidden=\"true\"><i class=\"fa-fusion-box active-icon awb-icon-minus\" aria-hidden=\"true\"><\/i><i class=\"fa-fusion-box inactive-icon awb-icon-plus\" aria-hidden=\"true\"><\/i><\/span><span class=\"fusion-toggle-heading\">Explotaci\u00f3n<\/span><\/a><\/h3><\/div><div id=\"a162613b7d2d6799a\" class=\"panel-collapse collapse \" aria-labelledby=\"toggle_a162613b7d2d6799a\"><div class=\"panel-body toggle-content fusion-clearfix\">\n<p>La explotaci\u00f3n estad\u00edstica es el proceso de recopilaci\u00f3n, an\u00e1lisis y utilizaci\u00f3n de la informaci\u00f3n estad\u00edstica para obtener conclusiones y tomar decisiones basadas en datos.<\/p>\n<\/div><\/div><\/div><div class=\"fusion-panel panel-default panel-82683ac1cd9d2c88b fusion-toggle-has-divider\" style=\"--awb-title-color:#af7baf;\"><div class=\"panel-heading\"><h3 class=\"panel-title toggle\" id=\"toggle_82683ac1cd9d2c88b\"><a aria-expanded=\"false\" aria-controls=\"82683ac1cd9d2c88b\" role=\"button\" data-toggle=\"collapse\" data-parent=\"#accordion-59199-1\" data-target=\"#82683ac1cd9d2c88b\" href=\"#82683ac1cd9d2c88b\"><span class=\"fusion-toggle-icon-wrapper\" aria-hidden=\"true\"><i class=\"fa-fusion-box active-icon awb-icon-minus\" aria-hidden=\"true\"><\/i><i class=\"fa-fusion-box inactive-icon awb-icon-plus\" aria-hidden=\"true\"><\/i><\/span><span class=\"fusion-toggle-heading\">Muestra<\/span><\/a><\/h3><\/div><div id=\"82683ac1cd9d2c88b\" class=\"panel-collapse collapse \" aria-labelledby=\"toggle_82683ac1cd9d2c88b\"><div class=\"panel-body toggle-content fusion-clearfix\">\n<p>Una muestra estad\u00edstica es aquella parte de la poblaci\u00f3n estad\u00edstica sobre la cual se aplica el an\u00e1lisis para as\u00ed obtener conclusiones extensibles al resto de dicha poblaci\u00f3n.<\/p>\n<\/div><\/div><\/div><div class=\"fusion-panel panel-default panel-a8d607a5befb89ff2 fusion-toggle-has-divider\" style=\"--awb-title-color:#af7baf;\"><div class=\"panel-heading\"><h3 class=\"panel-title toggle\" id=\"toggle_a8d607a5befb89ff2\"><a aria-expanded=\"false\" aria-controls=\"a8d607a5befb89ff2\" role=\"button\" data-toggle=\"collapse\" data-parent=\"#accordion-59199-1\" data-target=\"#a8d607a5befb89ff2\" href=\"#a8d607a5befb89ff2\"><span class=\"fusion-toggle-icon-wrapper\" aria-hidden=\"true\"><i class=\"fa-fusion-box active-icon awb-icon-minus\" aria-hidden=\"true\"><\/i><i class=\"fa-fusion-box inactive-icon awb-icon-plus\" aria-hidden=\"true\"><\/i><\/span><span class=\"fusion-toggle-heading\">Poblaci\u00f3n<\/span><\/a><\/h3><\/div><div id=\"a8d607a5befb89ff2\" class=\"panel-collapse collapse \" aria-labelledby=\"toggle_a8d607a5befb89ff2\"><div class=\"panel-body toggle-content fusion-clearfix\">\n<p>La poblaci\u00f3n es el grupo de sujetos, elementos o datos sobre los que se quiere obtener una informaci\u00f3n estad\u00edstica.<\/p>\n<\/div><\/div><\/div><div class=\"fusion-panel panel-default panel-1a9584c6a76ec9f38 fusion-toggle-has-divider\" style=\"--awb-title-color:#af7baf;\"><div class=\"panel-heading\"><h3 class=\"panel-title toggle\" id=\"toggle_1a9584c6a76ec9f38\"><a aria-expanded=\"false\" aria-controls=\"1a9584c6a76ec9f38\" role=\"button\" data-toggle=\"collapse\" data-parent=\"#accordion-59199-1\" data-target=\"#1a9584c6a76ec9f38\" href=\"#1a9584c6a76ec9f38\"><span class=\"fusion-toggle-icon-wrapper\" aria-hidden=\"true\"><i class=\"fa-fusion-box active-icon awb-icon-minus\" aria-hidden=\"true\"><\/i><i class=\"fa-fusion-box inactive-icon awb-icon-plus\" aria-hidden=\"true\"><\/i><\/span><span class=\"fusion-toggle-heading\">Rango<\/span><\/a><\/h3><\/div><div id=\"1a9584c6a76ec9f38\" class=\"panel-collapse collapse \" aria-labelledby=\"toggle_1a9584c6a76ec9f38\"><div class=\"panel-body toggle-content fusion-clearfix\">\n<p>El rango estad\u00edstico es una medida de la dispersi\u00f3n de los datos. Representa la diferencia entre el menor valor y el mayor valor de un conjunto de datos num\u00e9ricos.<\/p>\n<\/div><\/div><\/div><div class=\"fusion-panel panel-default panel-8c2bbfc5724c3d23a fusion-toggle-has-divider\" style=\"--awb-title-color:#af7baf;\"><div class=\"panel-heading\"><h3 class=\"panel-title toggle\" id=\"toggle_8c2bbfc5724c3d23a\"><a aria-expanded=\"false\" aria-controls=\"8c2bbfc5724c3d23a\" role=\"button\" data-toggle=\"collapse\" data-parent=\"#accordion-59199-1\" data-target=\"#8c2bbfc5724c3d23a\" href=\"#8c2bbfc5724c3d23a\"><span class=\"fusion-toggle-icon-wrapper\" aria-hidden=\"true\"><i class=\"fa-fusion-box active-icon awb-icon-minus\" aria-hidden=\"true\"><\/i><i class=\"fa-fusion-box inactive-icon awb-icon-plus\" aria-hidden=\"true\"><\/i><\/span><span class=\"fusion-toggle-heading\">S\u00edmbolo estad\u00edstico<\/span><\/a><\/h3><\/div><div id=\"8c2bbfc5724c3d23a\" class=\"panel-collapse collapse \" aria-labelledby=\"toggle_8c2bbfc5724c3d23a\"><div class=\"panel-body toggle-content fusion-clearfix\">\n<p>Un s\u00edmbolo estad\u00edstico es un s\u00edmbolo matem\u00e1tico que se utiliza para representar un proceso de c\u00e1lculo estad\u00edstico.<\/p>\n<p>Ejemplos:<\/p>\n<ul>\n<li>\u03bc media poblacional)<\/li>\n<li>X\u0305 (media muestral)<\/li>\n<li>\u03c3 (desviaci\u00f3n est\u00e1ndar; tambi\u00e9n se representa con la letra s)<\/li>\n<li>\u03a3 (operador de sumatoria)<\/li>\n<li>x (variable cuyo valor desconocemos y queremos calcular<\/li>\n<li>i (\u00edndice; identifica cada observaci\u00f3n de la variable x)<\/li>\n<li>n (n\u00famero de observaciones)<\/li>\n<\/ul>\n<\/div><\/div><\/div><div class=\"fusion-panel panel-default panel-e3fa2f6126aa057b9 fusion-toggle-has-divider\" style=\"--awb-title-color:#af7baf;\"><div class=\"panel-heading\"><h3 class=\"panel-title toggle\" id=\"toggle_e3fa2f6126aa057b9\"><a aria-expanded=\"false\" aria-controls=\"e3fa2f6126aa057b9\" role=\"button\" data-toggle=\"collapse\" data-parent=\"#accordion-59199-1\" data-target=\"#e3fa2f6126aa057b9\" href=\"#e3fa2f6126aa057b9\"><span class=\"fusion-toggle-icon-wrapper\" aria-hidden=\"true\"><i class=\"fa-fusion-box active-icon awb-icon-minus\" aria-hidden=\"true\"><\/i><i class=\"fa-fusion-box inactive-icon awb-icon-plus\" aria-hidden=\"true\"><\/i><\/span><span class=\"fusion-toggle-heading\">Variable<\/span><\/a><\/h3><\/div><div id=\"e3fa2f6126aa057b9\" class=\"panel-collapse collapse \" aria-labelledby=\"toggle_e3fa2f6126aa057b9\"><div class=\"panel-body toggle-content fusion-clearfix\">\n<p>Una variable es una caracter\u00edstica de una muestra estad\u00edstica o de una poblaci\u00f3n estad\u00edstica susceptible de fluctuaci\u00f3n, cuya variaci\u00f3n puede adoptar diversos valores observables y medibles. Cuando diferentes variables se relacionan entre s\u00ed, pueden formar parte de una hip\u00f3tesis o una teor\u00eda.<\/p>\n<p>Existen diversos tipos de variables:<\/p>\n<ul>\n<li><strong>variable cuantitativa, <\/strong>que a su vez puede ser una\n<ul>\n<li>variable continua<\/li>\n<li>variable discreta<\/li>\n<\/ul>\n<\/li>\n<li><strong>variable cualitativa<\/strong>, con los subtipos de\n<ul>\n<li>variable ordinal<\/li>\n<li>variable nominal<\/li>\n<\/ul>\n<\/li>\n<li><strong>variable independiente<\/strong><\/li>\n<li><strong>variable dependiente<\/strong><\/li>\n<li><strong>variable cardinal<\/strong><\/li>\n<li><strong>variable dicot\u00f3mica<\/strong><\/li>\n<li><strong>variable categ\u00f3rica<\/strong><\/li>\n<\/ul>\n<\/div><\/div><\/div><\/div><\/div><\/div><\/div><\/div><\/div><div class=\"fusion-fullwidth fullwidth-box fusion-builder-row-5 fusion-flex-container nonhundred-percent-fullwidth non-hundred-percent-height-scrolling\" style=\"--awb-border-radius-top-left:0px;--awb-border-radius-top-right:0px;--awb-border-radius-bottom-right:0px;--awb-border-radius-bottom-left:0px;--awb-padding-top:20px;--awb-flex-wrap:wrap;\" ><div class=\"fusion-builder-row fusion-row fusion-flex-align-items-flex-start fusion-flex-content-wrap\" style=\"max-width:1248px;margin-left: calc(-4% \/ 2 );margin-right: calc(-4% \/ 2 );\"><div class=\"fusion-layout-column fusion_builder_column fusion-builder-column-8 fusion_builder_column_1_1 1_1 fusion-flex-column\" style=\"--awb-bg-size:cover;--awb-width-large:100%;--awb-margin-top-large:0px;--awb-spacing-right-large:1.92%;--awb-margin-bottom-large:20px;--awb-spacing-left-large:1.92%;--awb-width-medium:100%;--awb-order-medium:0;--awb-spacing-right-medium:1.92%;--awb-spacing-left-medium:1.92%;--awb-width-small:100%;--awb-order-small:0;--awb-spacing-right-small:1.92%;--awb-spacing-left-small:1.92%;\"><div class=\"fusion-column-wrapper fusion-column-has-shadow fusion-flex-justify-content-flex-start fusion-content-layout-column\"><div class=\"fusion-title title fusion-title-8 fusion-sep-none fusion-title-text fusion-title-size-two\"><h2 class=\"fusion-title-heading title-heading-left fusion-responsive-typography-calculated\" style=\"margin:0;--fontSize:36;line-height:1.5;\">Ejemplos<\/h2><\/div><div class=\"accordian fusion-accordian\" style=\"--awb-border-size:1px;--awb-icon-size:15px;--awb-content-font-size:20px;--awb-icon-alignment:left;--awb-hover-color:#f9f9f9;--awb-border-color:#cccccc;--awb-background-color:#ffffff;--awb-divider-color:#000000;--awb-divider-hover-color:#000000;--awb-icon-color:#ffffff;--awb-title-color:#af7baf;--awb-content-color:#747474;--awb-icon-box-color:#333333;--awb-toggle-hover-accent-color:#9b00af;--awb-title-font-family:&quot;Roboto Condensed&quot;;--awb-title-font-weight:regular;--awb-title-font-style:normal;--awb-title-font-size:20px;--awb-content-font-family:&quot;Open Sans&quot;;--awb-content-font-style:normal;--awb-content-font-weight:400;\"><div class=\"panel-group fusion-toggle-icon-boxed\" id=\"accordion-59199-2\"><div class=\"fusion-panel panel-default panel-0ce68f97e223b8471 fusion-toggle-has-divider\" style=\"--awb-title-color:#af7baf;\"><div class=\"panel-heading\"><h3 class=\"panel-title toggle\" id=\"toggle_0ce68f97e223b8471\"><a aria-expanded=\"false\" aria-controls=\"0ce68f97e223b8471\" role=\"button\" data-toggle=\"collapse\" data-parent=\"#accordion-59199-2\" data-target=\"#0ce68f97e223b8471\" href=\"#0ce68f97e223b8471\"><span class=\"fusion-toggle-icon-wrapper\" aria-hidden=\"true\"><i class=\"fa-fusion-box active-icon awb-icon-minus\" aria-hidden=\"true\"><\/i><i class=\"fa-fusion-box inactive-icon awb-icon-plus\" aria-hidden=\"true\"><\/i><\/span><span class=\"fusion-toggle-heading\">Estudio de mercado<\/span><\/a><\/h3><\/div><div id=\"0ce68f97e223b8471\" class=\"panel-collapse collapse \" aria-labelledby=\"toggle_0ce68f97e223b8471\"><div class=\"panel-body toggle-content fusion-clearfix\">\n<p data-path-to-node=\"0\">Imaginemos que una empresa tecnol\u00f3gica quiere lanzar un <b data-path-to-node=\"0\" data-index-in-node=\"108\">nuevo modelo de auriculares con cancelaci\u00f3n de ruido<\/b> en Espa\u00f1a y necesita decidir el precio \u00f3ptimo. Para conseguirlo, la estad\u00edstica descriptiva y la inferencial trabajar\u00e1n en conjunto.<\/p>\n<h4 data-path-to-node=\"3\"><span class=\"ez-toc-section\" id=\"Fase_descriptiva_Entender_la_muestra\"><\/span>Fase descriptiva: Entender la muestra<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p data-path-to-node=\"4\">La empresa realiza una encuesta a 1000 potenciales compradores. En esta etapa, el objetivo es resumir la informaci\u00f3n recolectada de forma clara.<\/p>\n<ul data-path-to-node=\"5\">\n<li>\n<p data-path-to-node=\"5,0,0\"><b data-path-to-node=\"5,0,0\" data-index-in-node=\"0\">Medidas de tendencia central:<\/b> Se calcula que el precio medio que los encuestados est\u00e1n dispuestos a pagar es de 150\u20ac.<\/p>\n<\/li>\n<li>\n<p data-path-to-node=\"5,1,0\"><b data-path-to-node=\"5,1,0\" data-index-in-node=\"0\">Distribuci\u00f3n de frecuencias:<\/b> Se crea un histograma para estudiar si la mayor\u00eda de la gente se concentra en los 150\u20ac o si hay grupos separados (por ejemplo, unos que quieren lujo a 300\u20ac y otros, ahorro a 50\u20ac).<\/p>\n<\/li>\n<li>\n<p data-path-to-node=\"5,2,0\"><b data-path-to-node=\"5,2,0\" data-index-in-node=\"0\">Visualizaci\u00f3n:<\/b> Se utilizan diagramas de caja (<i data-path-to-node=\"5,2,0\" data-index-in-node=\"46\">boxplot<\/i>) para identificar valores at\u00edpicos (personas que dicen que pagar\u00edan 2000\u20ac, lo cual podr\u00eda sesgar el promedio).<\/p>\n<\/li>\n<\/ul>\n<h4 data-path-to-node=\"7\"><span class=\"ez-toc-section\" id=\"Fase_inferencial_Saltar_a_la_poblacion\"><\/span>Fase inferencial: Saltar a la poblaci\u00f3n<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p data-path-to-node=\"8\">La empresa no solo quiere saber que piensan esas 1000 personas encuestadas, sino que pensar\u00e1n <span data-path-to-node=\"8\" data-index-in-node=\"86\">millones<\/span> de posibles clientes en todo el pa\u00eds.<\/p>\n<ul data-path-to-node=\"9\">\n<li>\n<p data-path-to-node=\"9,0,0\"><b data-path-to-node=\"9,0,0\" data-index-in-node=\"0\">Intervalos de confianza:<\/b> El an\u00e1lisis estad\u00edstico no dir\u00e1 \u00abel precio es 150\u20ac\u00bb. Dir\u00e1: <i data-path-to-node=\"9,0,0\" data-index-in-node=\"75\">\u00abTenemos un 95% de confianza en que el precio que el mercado aceptar\u00e1 est\u00e1 entre 145\u20ac y 155\u20ac\u00bb<\/i>.<\/p>\n<\/li>\n<li>\n<p data-path-to-node=\"9,1,0\"><b data-path-to-node=\"9,1,0\" data-index-in-node=\"0\">Contraste de hip\u00f3tesis:<\/b><\/p>\n<ul data-path-to-node=\"9,1,1\">\n<li>\n<p data-path-to-node=\"9,1,1,0,0\"><b data-path-to-node=\"9,1,1,0,0\" data-index-in-node=\"0\">Hip\u00f3tesis nula (<span class=\"math-inline\" data-math=\"H_0\" data-index-in-node=\"16\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">H<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>):<\/b> \u00abEl nuevo dise\u00f1o no aumenta la intenci\u00f3n de compra respecto al modelo anterior\u00bb.<\/p>\n<\/li>\n<li>\n<p data-path-to-node=\"9,1,1,1,0\"><b data-path-to-node=\"9,1,1,1,0\" data-index-in-node=\"0\">Valor p:<\/b> Si tras mostrar el dise\u00f1o el valor <span class=\"math-inline\" data-math=\"p\" data-index-in-node=\"44\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">p<\/span><\/span><\/span><\/span><\/span> es <span data-path-to-node=\"9,1,1,1,0\" data-index-in-node=\"49\">0.02<\/span>, la empresa rechaza la <span class=\"math-inline\" data-math=\"H_0\" data-index-in-node=\"77\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">H<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>. Hay evidencia estad\u00edstica de que el nuevo dise\u00f1o s\u00ed atrae m\u00e1s clientes.<\/p>\n<\/li>\n<\/ul>\n<\/li>\n<li>\n<p data-path-to-node=\"9,2,0\"><b data-path-to-node=\"9,2,0\" data-index-in-node=\"0\">Segmentaci\u00f3n (ANOVA):<\/b> Se utiliza el an\u00e1lisis de varianza para ver si hay diferencias significativas entre grupos (por ejemplo, si los j\u00f3venes de 20 a\u00f1os est\u00e1n dispuestos a pagar significativamente mas que las personas mayores de 50).<\/p>\n<\/li>\n<\/ul>\n<h4 data-path-to-node=\"11\"><span class=\"ez-toc-section\" id=\"La_toma_de_decision\"><\/span>La toma de decisi\u00f3n<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p data-path-to-node=\"12\">Finalmente, la estad\u00edstica permite pasar del dato a la acci\u00f3n:<\/p>\n<ol start=\"1\" data-path-to-node=\"13\">\n<li>\n<p data-path-to-node=\"13,0,0\"><b data-path-to-node=\"13,0,0\" data-index-in-node=\"0\">Si el error tipo I (<span class=\"math-inline\" data-math=\"alpha\" data-index-in-node=\"20\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">\u03b1<\/span><\/span><\/span><\/span><\/span>) es bajo:<\/b> La empresa lanza el producto, confiando en que la preferencia detectada es real y no fruto del azar.<\/p>\n<\/li>\n<li>\n<p data-path-to-node=\"13,1,0\"><b data-path-to-node=\"13,1,0\" data-index-in-node=\"0\">Si la correlaci\u00f3n es alta:<\/b> Si se observa que a mayor duraci\u00f3n de bater\u00eda, mayor es el precio aceptado, la empresa invertir\u00e1 mas en ingenier\u00eda de bater\u00edas que en est\u00e9tica.<\/p>\n<\/li>\n<\/ol>\n<\/div><\/div><\/div><div class=\"fusion-panel panel-default panel-6a26ed6ed13c1efdc fusion-toggle-has-divider\" style=\"--awb-title-color:#af7baf;\"><div class=\"panel-heading\"><h3 class=\"panel-title toggle\" id=\"toggle_6a26ed6ed13c1efdc\"><a aria-expanded=\"false\" aria-controls=\"6a26ed6ed13c1efdc\" role=\"button\" data-toggle=\"collapse\" data-parent=\"#accordion-59199-2\" data-target=\"#6a26ed6ed13c1efdc\" href=\"#6a26ed6ed13c1efdc\"><span class=\"fusion-toggle-icon-wrapper\" aria-hidden=\"true\"><i class=\"fa-fusion-box active-icon awb-icon-minus\" aria-hidden=\"true\"><\/i><i class=\"fa-fusion-box inactive-icon awb-icon-plus\" aria-hidden=\"true\"><\/i><\/span><span class=\"fusion-toggle-heading\">Ensayo cl\u00ednico<\/span><\/a><\/h3><\/div><div id=\"6a26ed6ed13c1efdc\" class=\"panel-collapse collapse \" aria-labelledby=\"toggle_6a26ed6ed13c1efdc\"><div class=\"panel-body toggle-content fusion-clearfix\">\n<p data-path-to-node=\"0\">En un ensayo cl\u00ednico para una vacuna, la estad\u00edstica ayuda a obtener evidencia de eficacia y seguridad.<\/p>\n<h4 data-path-to-node=\"3\"><span class=\"ez-toc-section\" id=\"Fase_descriptiva_Los_datos_brutos_del_ensayo\"><\/span>Fase descriptiva: Los datos brutos del ensayo<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p data-path-to-node=\"4\">Imaginemos un ensayo con 40000 voluntarios. Se dividen en dos grupos: 20000 reciben la vacuna y 20000 reciben un placebo.<\/p>\n<ul data-path-to-node=\"5\">\n<li>\n<p data-path-to-node=\"5,0,0\"><b data-path-to-node=\"5,0,0\" data-index-in-node=\"0\">Tabulaci\u00f3n de eventos:<\/b> Se registran cuantos contagios ocurren en cada grupo. Por ejemplo: 10 contagios en el grupo vacunado y 190 en el grupo placebo.<\/p>\n<\/li>\n<li>\n<p data-path-to-node=\"5,1,0\"><b data-path-to-node=\"5,1,0\" data-index-in-node=\"0\">Proporciones y porcentajes:<\/b> Se describe la tasa de incidencia. Aqu\u00ed se calcula la e<span data-path-to-node=\"5,1,0\" data-index-in-node=\"82\">ficacia relativa<\/span>:<\/p>\n<\/li>\n<\/ul>\n<div data-path-to-node=\"5,1,1\">\n<div class=\"math-block\" style=\"text-align: center;\" data-math=\"text{Eficacia} = left(1 - frac{text{Tasa en vacunados}}{text{Tasa en placebo}}right) times 100\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord text\"><span class=\"mord\">Eficacia<\/span><\/span><span class=\"mrel\">=[<\/span><\/span><span class=\"base\"><span class=\"minner\"><span class=\"mord\">1<\/span><span class=\"mbin\">\u2212(<\/span><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"\"><span class=\"mord text\">Tasa en vacunados\/Tasa en placebo<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\"><span class=\"delimsizing size3\">)]<\/span><\/span><\/span><span class=\"mbin\">\u00d7<\/span><\/span><span class=\"base\"><span class=\"mord\">100<\/span><\/span><\/span><\/span><\/span><\/div>\n<div data-math=\"text{Eficacia} = left(1 - frac{text{Tasa en vacunados}}{text{Tasa en placebo}}right) times 100\">\n<ul data-path-to-node=\"5\">\n<li>\n<p data-path-to-node=\"5,2,0\"><b data-path-to-node=\"5,2,0\" data-index-in-node=\"0\">Seguridad:<\/b> Se describen los efectos secundarios (fiebre, dolor de brazo) usando medidas de frecuencia para ver qu\u00e9 es com\u00fan y qu\u00e9 es raro.<\/p>\n<\/li>\n<\/ul>\n<h4 data-path-to-node=\"7\"><span class=\"ez-toc-section\" id=\"Fase_inferencial_El_rigor_cientifico\"><\/span>Fase inferencial: El rigor cient\u00edfico<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p data-path-to-node=\"8\">Aqu\u00ed es donde entran los personajes que mencionamos antes (<span data-path-to-node=\"8\" data-index-in-node=\"59\">Fisher, Gosset, Neyman-Pearson<\/span>) para asegurar que los resultados no sean una coincidencia.<\/p>\n<ul data-path-to-node=\"9\">\n<li>\n<p data-path-to-node=\"9,0,0\"><b data-path-to-node=\"9,0,0\" data-index-in-node=\"0\">El papel del valor p (<span class=\"math-inline\" data-math=\"p\" data-index-in-node=\"22\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">p<\/span><\/span><\/span><\/span><\/span>-value):<\/b> El equipo estad\u00edstico calcula la probabilidad de que esa diferencia de contagios (10 vs 190) haya ocurrido por simple azar. Si el <span class=\"math-inline\" data-math=\"p &lt; 0.0001\" data-index-in-node=\"171\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">p<\/span><span class=\"mrel\">&lt;<\/span><\/span><span class=\"base\"><span class=\"mord\">0.0001<\/span><\/span><\/span><\/span><\/span>, se concluye que la vacuna funciona.<\/p>\n<\/li>\n<li>\n<p data-path-to-node=\"9,1,0\"><b data-path-to-node=\"9,1,0\" data-index-in-node=\"0\">Intervalos de confianza:<\/b> No basta con determinar \u00ab95% de eficacia\u00bb; la estad\u00edstica moderna exige un rango. Se dir\u00e1: <i data-path-to-node=\"9,1,0\" data-index-in-node=\"111\">\u00abLa eficacia es del 95%, con un intervalo de confianza al 95% de [92%, 97%]\u00bb<\/i>. Si el l\u00edmite inferior es muy bajo, la vacuna no se aprueba.<\/p>\n<\/li>\n<li>\n<p data-path-to-node=\"9,2,0\"><b data-path-to-node=\"9,2,0\" data-index-in-node=\"0\">An\u00e1lisis de supervivencia (curvas de Kaplan-Meier):<\/b> Se utiliza para visualizar el tiempo que tardan los participantes en contagiarse. Si la curva del grupo vacunado se mantiene \u00abplana\u00bb mientras la del placebo cae r\u00e1pidamente, la evidencia visual de protecci\u00f3n es clara.<\/p>\n<\/li>\n<\/ul>\n<h4 data-path-to-node=\"11\"><span class=\"ez-toc-section\" id=\"El_control_del_error_Neyman-Pearson\"><\/span>El control del error (Neyman-Pearson)<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p data-path-to-node=\"12\">En medicina, los errores tienen consecuencias cr\u00edticas:<\/p>\n<ul data-path-to-node=\"13\">\n<li>\n<p data-path-to-node=\"13,0,0\"><b data-path-to-node=\"13,0,0\" data-index-in-node=\"0\">Error tipo I (<span class=\"math-inline\" data-math=\"alpha\" data-index-in-node=\"14\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">\u03b1<\/span><\/span><\/span><\/span><\/span>):<\/b> Aprobar una vacuna que <span data-path-to-node=\"13,0,0\" data-index-in-node=\"46\">no funciona<\/span>. Es el error m\u00e1s protegido; se suele fijar un nivel de exigencia muy alto (usualmente 0.05 o menos).<\/p>\n<\/li>\n<li>\n<p data-path-to-node=\"13,1,0\"><b data-path-to-node=\"13,1,0\" data-index-in-node=\"0\">Error tipo II (<span class=\"math-inline\" data-math=\"beta\" data-index-in-node=\"15\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">\u03b2<\/span><\/span><\/span><\/span><\/span>):<\/b> Rechazar una vacuna que <span data-path-to-node=\"13,1,0\" data-index-in-node=\"47\">s\u00ed funciona<\/span>. Esto ser\u00eda una tragedia de salud p\u00fablica, por lo que el estudio debe tener suficiente p<span data-path-to-node=\"13,1,0\" data-index-in-node=\"146\">oder estad\u00edstico<\/span> (una muestra grande) para no descartar una buena soluci\u00f3n por falta de datos.<\/p>\n<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div><\/div><\/div><div class=\"fusion-panel panel-default panel-30e677f64fb7594fe fusion-toggle-has-divider\" style=\"--awb-title-color:#af7baf;\"><div class=\"panel-heading\"><h3 class=\"panel-title toggle\" id=\"toggle_30e677f64fb7594fe\"><a aria-expanded=\"false\" aria-controls=\"30e677f64fb7594fe\" role=\"button\" data-toggle=\"collapse\" data-parent=\"#accordion-59199-2\" data-target=\"#30e677f64fb7594fe\" href=\"#30e677f64fb7594fe\"><span class=\"fusion-toggle-icon-wrapper\" aria-hidden=\"true\"><i class=\"fa-fusion-box active-icon awb-icon-minus\" aria-hidden=\"true\"><\/i><i class=\"fa-fusion-box inactive-icon awb-icon-plus\" aria-hidden=\"true\"><\/i><\/span><span class=\"fusion-toggle-heading\">Intenci\u00f3n de voto<\/span><\/a><\/h3><\/div><div id=\"30e677f64fb7594fe\" class=\"panel-collapse collapse \" aria-labelledby=\"toggle_30e677f64fb7594fe\"><div class=\"panel-body toggle-content fusion-clearfix\">\n<p data-path-to-node=\"0\">En la pol\u00edtica moderna, la estad\u00edstica no solo mide la opini\u00f3n, sino que intenta predecir el comportamiento humano en una de las situaciones de mayor incertidumbre: la urna de votaci\u00f3n.<\/p>\n<p data-path-to-node=\"1\">Imaginemos un escenario donde un pa\u00eds se prepara para elegir a su siguiente gobierno entre dos candidatos principales: Candidato A y Candidato B.<\/p>\n<h4 data-path-to-node=\"3\"><span class=\"ez-toc-section\" id=\"Fase_descriptiva_La_fotografia_del_momento\"><\/span>Fase descriptiva: La fotograf\u00eda del momento<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p data-path-to-node=\"4\">Se realiza una encuesta telef\u00f3nica y presencial a 2500 ciudadanos seleccionados de forma representativa.<\/p>\n<ul data-path-to-node=\"5\">\n<li>\n<p data-path-to-node=\"5,0,0\"><b data-path-to-node=\"5,0,0\" data-index-in-node=\"0\">Frecuencias relativas:<\/b> Se calcula el porcentaje directo de respuestas. Por ejemplo: 42% para el Candidato A, 38% para el Candidato B y 20% de indecisos\/blanco.<\/p>\n<\/li>\n<li>\n<p data-path-to-node=\"5,1,0\"><b data-path-to-node=\"5,1,0\" data-index-in-node=\"0\">Cruce de variables (tablas de contingencia):<\/b> Se analiza c\u00f3mo votan diferentes sectores. \u00bfEl Candidato A es m\u00e1s fuerte en zonas urbanas o rurales? \u00bfQu\u00e9 porcentaje de mujeres apoya al Candidato B?<\/p>\n<\/li>\n<li>\n<p data-path-to-node=\"5,2,0\"><b data-path-to-node=\"5,2,0\" data-index-in-node=\"0\">Medidas de dispersi\u00f3n:<\/b> Se observa si el voto est\u00e1 concentrado geogr\u00e1ficamente o si es uniforme en todo el pa\u00eds.<\/p>\n<\/li>\n<\/ul>\n<h4 data-path-to-node=\"7\"><span class=\"ez-toc-section\" id=\"Fase_inferencial_Del_sondeo_a_la_urna\"><\/span>Fase inferencial: Del sondeo a la urna<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p data-path-to-node=\"8\">Aqu\u00ed es donde los encuestadores intentan predecir qu\u00e9 pasar\u00e1 con los <span data-path-to-node=\"8\" data-index-in-node=\"69\">millones<\/span> de votantes reales a partir de la observaci\u00f3n de los 2500 encuestados.<\/p>\n<ul data-path-to-node=\"9\">\n<li>\n<p data-path-to-node=\"9,0,0\"><b data-path-to-node=\"9,0,0\" data-index-in-node=\"0\">Margen de error e intervalos de confianza:<\/b> Ning\u00fan an\u00e1lisis estad\u00edstico serio dir\u00eda \u00abEl Candidato A tiene el 42%\u00bb. Dir\u00e1: <i data-path-to-node=\"9,0,0\" data-index-in-node=\"110\">\u00abEl Candidato A tiene un 42% con un margen de error de \u00b12%\u00bb<\/i>. Esto significa que el apoyo real probablemente est\u00e9 entre el 40% y el 44%.<\/p>\n<\/li>\n<li>\n<p data-path-to-node=\"9,1,0\"><b data-path-to-node=\"9,1,0\" data-index-in-node=\"0\">El problema del sesgo y la \u00abcocina\u00bb (ajustes):<\/b> Aqu\u00ed se aplican modelos para corregir el <span data-path-to-node=\"9,1,0\" data-index-in-node=\"88\">sesgo de no respuesta<\/span><b data-path-to-node=\"9,1,0\" data-index-in-node=\"88\"> <\/b>(gente que no coge el tel\u00e9fono) o el <span data-path-to-node=\"9,1,0\" data-index-in-node=\"147\">voto oculto<\/span> (gente que miente sobre su voto por presi\u00f3n social). Se usan registros hist\u00f3ricos para \u00abpesar\u00bb la muestra.<\/p>\n<\/li>\n<li>\n<p data-path-to-node=\"9,2,0\"><b data-path-to-node=\"9,2,0\" data-index-in-node=\"0\">Nivel de significancia (<span class=\"math-inline\" data-math=\"p\" data-index-in-node=\"24\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">p<\/span><\/span><\/span><\/span><\/span>-value):<\/b> Si la diferencia entre candidatos es muy estrecha (ej. 41% vs 40%), se calcula si esa diferencia es estad\u00edsticamente significativa o si es tan peque\u00f1a que cae dentro del \u00abruido\u00bb del azar.<\/p>\n<\/li>\n<\/ul>\n<h4 data-path-to-node=\"11\"><span class=\"ez-toc-section\" id=\"El_control_del_error_y_la_prediccion_Neyman-Pearson\"><\/span>El control del error y la predicci\u00f3n (Neyman-Pearson)<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p data-path-to-node=\"12\">En pol\u00edtica, los errores de predicci\u00f3n tienen un alto coste reputacional para las encuestadoras.<\/p>\n<ul data-path-to-node=\"13\">\n<li>\n<p data-path-to-node=\"13,0,0\"><b data-path-to-node=\"13,0,0\" data-index-in-node=\"0\">Error tipo I (falso positivo):<\/b> Predecir que un candidato ganar\u00e1 cuando en realidad perder\u00e1. Esto ocurri\u00f3 en casos famosos como el Brexit o las elecciones de EEUU en 2016, donde los modelos infravaloraron ciertos segmentos de la poblaci\u00f3n.<\/p>\n<\/li>\n<li>\n<p data-path-to-node=\"13,1,0\"><b data-path-to-node=\"13,1,0\" data-index-in-node=\"0\">Poder estad\u00edstico:<\/b> Para detectar una victoria ajustada (por ejemplo, por 0.5 puntos), se necesita una muestra mucho m\u00e1s grande y refinada que para una victoria por goleada.<\/p>\n<\/li>\n<li>\n<p data-path-to-node=\"13,2,0\"><b data-path-to-node=\"13,2,0\" data-index-in-node=\"0\">Simulaciones de Montecarlo:<\/b> Los an\u00e1lisis estad\u00edsticos modernos corren miles de \u00abelecciones virtuales\u00bb en ordenador, variando ligeramente los datos para ver en cu\u00e1ntos de esos escenarios gana cada candidato. Es lo que vemos en medios especializados para dar una \u00abprobabilidad de victoria\u00bb.<\/p>\n<\/li>\n<\/ul>\n<\/div><\/div><\/div><div class=\"fusion-panel panel-default panel-0ae3c1a470f7ee994 fusion-toggle-has-divider\" style=\"--awb-title-color:#af7baf;\"><div class=\"panel-heading\"><h3 class=\"panel-title toggle\" id=\"toggle_0ae3c1a470f7ee994\"><a aria-expanded=\"false\" aria-controls=\"0ae3c1a470f7ee994\" role=\"button\" data-toggle=\"collapse\" data-parent=\"#accordion-59199-2\" data-target=\"#0ae3c1a470f7ee994\" href=\"#0ae3c1a470f7ee994\"><span class=\"fusion-toggle-icon-wrapper\" aria-hidden=\"true\"><i class=\"fa-fusion-box active-icon awb-icon-minus\" aria-hidden=\"true\"><\/i><i class=\"fa-fusion-box inactive-icon awb-icon-plus\" aria-hidden=\"true\"><\/i><\/span><span class=\"fusion-toggle-heading\">IA y reconocimiento biom\u00e9trico<\/span><\/a><\/h3><\/div><div id=\"0ae3c1a470f7ee994\" class=\"panel-collapse collapse \" aria-labelledby=\"toggle_0ae3c1a470f7ee994\"><div class=\"panel-body toggle-content fusion-clearfix\">\n<p data-path-to-node=\"0\">Para la IA, mi cara o mi voz no son im\u00e1genes o sonidos, sino una monta\u00f1a de datos estad\u00edsticos. El reconocimiento biom\u00e9trico (como el FaceID o los asistentes de voz) es, en esencia, una aplicaci\u00f3n masiva de los conceptos de Pearson, Fisher y Neyman-Pearson llevados a la era de la inform\u00e1tica.<\/p>\n<p data-path-to-node=\"1\">As\u00ed es como mi tel\u00e9fono inteligente usa la estad\u00edstica moderna para saber qui\u00e9n soy.<\/p>\n<h4 data-path-to-node=\"3\"><span class=\"ez-toc-section\" id=\"Fase_descriptiva_La_creacion_de_la_firma_digital\"><\/span>Fase descriptiva: La creaci\u00f3n de la firma digital<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p data-path-to-node=\"4\">Cuando configuro por primera vez mi cara o mi voz, el dispositivo no guarda una foto o un audio; realiza una descripci\u00f3n estad\u00edstica de mis rasgos.<\/p>\n<ul data-path-to-node=\"5\">\n<li>\n<p data-path-to-node=\"5,0,0\"><b data-path-to-node=\"5,0,0\" data-index-in-node=\"0\">Extracci\u00f3n de atributos <em>(landmarks):<\/em><\/b> El sistema identifica puntos clave (la distancia entre mis ojos, la curvatura de mis labios o la frecuencia de mi voz).<\/p>\n<\/li>\n<li>\n<p data-path-to-node=\"5,1,0\"><b data-path-to-node=\"5,1,0\" data-index-in-node=\"0\">Normalizaci\u00f3n:<\/b> La estad\u00edstica descriptiva se usa para \u00ablimpiar\u00bb los datos. Si el escaneo lo hago con poca luz o con ruido de fondo, el sistema ajusta la media y la varianza de la se\u00f1al para que los datos sean comparables en cualquier situaci\u00f3n.<\/p>\n<\/li>\n<li>\n<p data-path-to-node=\"5,2,0\"><b data-path-to-node=\"5,2,0\" data-index-in-node=\"0\">Vectores de caracter\u00edsticas <em>(embeddings):<\/em><\/b> Mis rasgos se convierten en una lista de n\u00fameros (un vector). Si la distancia entre mis ojos es <em><span class=\"math-inline\" data-math=\"x\" data-index-in-node=\"138\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span><\/span><\/em> y el ancho de mi nariz es\u00a0<em><span class=\"math-inline\" data-math=\"y\" data-index-in-node=\"166\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">y<\/span><\/span><\/span><\/span><\/span><\/em>, mi cara es un punto en un mapa de miles de dimensiones.<\/p>\n<\/li>\n<\/ul>\n<h4 data-path-to-node=\"7\"><span class=\"ez-toc-section\" id=\"Fase_inferencial_El_desafio_de_la_identidad\"><\/span>Fase inferencial: El desaf\u00edo de la identidad<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p data-path-to-node=\"8\">Cada vez que intento desbloquear el tel\u00e9fono, el sistema realiza una inferencia estad\u00edstica en milisegundos. El tel\u00e9fono se pregunta: <i data-path-to-node=\"8\" data-index-in-node=\"135\">\u00abBas\u00e1ndome en esta muestra de datos actual, \u00bfqu\u00e9 probabilidad hay de que este rostro sea el de la due\u00f1a del tel\u00e9fono?\u00bb<\/i>.<\/p>\n<ul data-path-to-node=\"9\">\n<li>\n<p data-path-to-node=\"9,0,0\"><b data-path-to-node=\"9,0,0\" data-index-in-node=\"0\">Similitud de coseno y distancia euclidiana:<\/b> El sistema mide cuan cerca est\u00e1 el \u00abpunto\u00bb de mi cara actual del \u00abpunto\u00bb que guard\u00f3 en la memoria. No busca una coincidencia exacta (eso ser\u00eda imposible, pues siempre cambiamos de luz o \u00e1ngulo), sino una proximidad estad\u00edstica.<\/p>\n<\/li>\n<li>\n<p data-path-to-node=\"9,1,0\"><b data-path-to-node=\"9,1,0\" data-index-in-node=\"0\">Modelos probabil\u00edsticos:<\/b> Se utilizan algoritmos como la regresi\u00f3n log\u00edstica o las redes neuronales para asignar una probabilidad. Si la probabilidad de que sea yo es del 99.2%, el tel\u00e9fono se desbloquea.<\/p>\n<\/li>\n<li>\n<p data-path-to-node=\"9,2,0\"><b data-path-to-node=\"9,2,0\" data-index-in-node=\"0\">Clasificaci\u00f3n bayesiana:<\/b> El sistema utiliza informaci\u00f3n previa para mejorar la decisi\u00f3n. Si el tel\u00e9fono se acaba de desbloquear con mi c\u00f3digo, la \u00abprobabilidad previa\u00bb de que la cara que tiene delante sea la m\u00eda aumenta.<\/p>\n<\/li>\n<\/ul>\n<h4 data-path-to-node=\"11\"><span class=\"ez-toc-section\" id=\"El_control_del_error_Neyman-Pearson_en_el_bolsillo\"><\/span>El control del error (Neyman-Pearson en el bolsillo)<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p data-path-to-node=\"12\">Aqu\u00ed es donde la teor\u00eda de los dos errores se vuelve cr\u00edtica para la seguridad.<\/p>\n<ul data-path-to-node=\"13\">\n<li>\n<p data-path-to-node=\"13,0,0\"><b data-path-to-node=\"13,0,0\" data-index-in-node=\"0\">Falso positivo (error tipo I):<\/b> El tel\u00e9fono se desbloquea con la cara de un extra\u00f1o. En IA, esto se llama <i>f<span data-path-to-node=\"13,0,0\" data-index-in-node=\"105\">alse acceptance rate<\/span><\/i> (FAR). Para evitarlo, los ingenieros ajustan el \u00abumbral de decisi\u00f3n\u00bb de forma muy estricta (usando un nivel de significancia <span class=\"math-inline\" data-math=\"alpha\" data-index-in-node=\"252\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">\u03b1<\/span><\/span><\/span><\/span><\/span> extremadamente peque\u00f1o).<\/p>\n<\/li>\n<li>\n<p data-path-to-node=\"13,1,0\"><b data-path-to-node=\"13,1,0\" data-index-in-node=\"0\">Falso negativo (error tipo II):<\/b> El tel\u00e9fono no me reconoce (porque llevo gafas o acabo de despertar, por ejemplo). Esto es un caso de <i>f<span data-path-to-node=\"13,1,0\" data-index-in-node=\"120\">alse rejection rate<\/span><\/i> (FRR).<\/p>\n<\/li>\n<\/ul>\n<\/div><\/div><\/div><div class=\"fusion-panel panel-default panel-c5dae31d0f1b81d51 fusion-toggle-has-divider\" style=\"--awb-title-color:#af7baf;\"><div class=\"panel-heading\"><h3 class=\"panel-title toggle\" id=\"toggle_c5dae31d0f1b81d51\"><a aria-expanded=\"false\" aria-controls=\"c5dae31d0f1b81d51\" role=\"button\" data-toggle=\"collapse\" data-parent=\"#accordion-59199-2\" data-target=\"#c5dae31d0f1b81d51\" href=\"#c5dae31d0f1b81d51\"><span class=\"fusion-toggle-icon-wrapper\" aria-hidden=\"true\"><i class=\"fa-fusion-box active-icon awb-icon-minus\" aria-hidden=\"true\"><\/i><i class=\"fa-fusion-box inactive-icon awb-icon-plus\" aria-hidden=\"true\"><\/i><\/span><span class=\"fusion-toggle-heading\">Anuncios en redes sociales<\/span><\/a><\/h3><\/div><div id=\"c5dae31d0f1b81d51\" class=\"panel-collapse collapse \" aria-labelledby=\"toggle_c5dae31d0f1b81d51\"><div class=\"panel-body toggle-content fusion-clearfix\">\n<p data-path-to-node=\"0\"><span class=\"citation-17 citation-end-17\">En el mundo de las redes sociales, la publicidad es un experimento estad\u00edstico masivo que ocurre en tiempo real.<\/span> Algoritmos inspirados en las teor\u00edas de Fisher y Pearson deciden qu\u00e9 anuncio mostrarte con base en la probabilidad de que hagas clic.<\/p>\n<p data-path-to-node=\"1\">Usemos el ejemplo de una marca de <b data-path-to-node=\"1\" data-index-in-node=\"34\">zapatillas deportivas sostenibles<\/b> que quiere anunciarse en Instagram.<\/p>\n<h4 data-path-to-node=\"3\"><span class=\"ez-toc-section\" id=\"Fase_descriptiva_Perfilado_y_segmentacion\"><\/span>Fase descriptiva: Perfilado y segmentaci\u00f3n<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p data-path-to-node=\"4\">Antes de mostrar el anuncio, la plataforma organiza los datos de miles de millones de usuarios para crear perfiles.<\/p>\n<ul data-path-to-node=\"5\">\n<li>\n<p data-path-to-node=\"5,0,0\"><b data-path-to-node=\"5,0,0\" data-index-in-node=\"0\">Agrupamiento (<i>clustering<\/i>):<\/b> El sistema utiliza estad\u00edstica descriptiva para agrupar usuarios. Si has dado \u00ablike\u00bb a fotos de naturaleza, sigues a marcas veganas y vives en ciudades grandes, te asigna al cl\u00faster de \u00abinter\u00e9s en sostenibilidad\u00bb.<\/p>\n<\/li>\n<li>\n<p data-path-to-node=\"5,1,0\"><b data-path-to-node=\"5,1,0\" data-index-in-node=\"0\">An\u00e1lisis de correlaci\u00f3n:<\/b> Los analistas observan qu\u00e9 variables est\u00e1n relacionadas. Por ejemplo, descubren que hay una <span data-path-to-node=\"5,1,0\" data-index-in-node=\"117\">fuerte correlaci\u00f3n positiva<\/span> entre los usuarios que escuchan podcasts de ecolog\u00eda y quienes compran calzado de marca.<\/p>\n<\/li>\n<li>\n<p data-path-to-node=\"5,2,0\"><b data-path-to-node=\"5,2,0\" data-index-in-node=\"0\">M\u00e9tricas de resumen:<\/b> La marca revisa sus campa\u00f1as anteriores: el <span data-path-to-node=\"5,2,0\" data-index-in-node=\"65\">CTR promedio<\/span>\u00a0fue del 1.5% y el gasto medio por cliente fue de 80\u20ac.<\/p>\n<\/li>\n<\/ul>\n<h4 data-path-to-node=\"7\"><span class=\"ez-toc-section\" id=\"Fase_inferencial_El_test_AB\"><\/span>Fase inferencial: El test A\/B<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p data-path-to-node=\"8\">Aqu\u00ed es donde aplicamos directamente el d<span data-path-to-node=\"8\" data-index-in-node=\"40\">ise\u00f1o de experimentos de Ronald Fisher<\/span>. La marca no sabe qu\u00e9 anuncio funcionar\u00e1 mejor, as\u00ed que hace un experimento aleatorizado.<\/p>\n<ul data-path-to-node=\"9\">\n<li>\n<p data-path-to-node=\"9,0,0\"><b data-path-to-node=\"9,0,0\" data-index-in-node=\"0\">Configuraci\u00f3n del experimento:<\/b> Se crean dos versiones del anuncio:<\/p>\n<ul data-path-to-node=\"9,0,1\">\n<li>\n<p data-path-to-node=\"9,0,1,0,0\"><b data-path-to-node=\"9,0,1,0,0\" data-index-in-node=\"0\">Anuncio A:<\/b> Enfocado en el dise\u00f1o y la moda.<\/p>\n<\/li>\n<li>\n<p data-path-to-node=\"9,0,1,1,0\"><b data-path-to-node=\"9,0,1,1,0\" data-index-in-node=\"0\">Anuncio B:<\/b> Enfocado en el impacto ecol\u00f3gico y materiales reciclados.<\/p>\n<\/li>\n<\/ul>\n<\/li>\n<li>\n<p data-path-to-node=\"9,1,0\"><b data-path-to-node=\"9,1,0\" data-index-in-node=\"0\">Inferencia en tiempo real:<\/b> El algoritmo muestra el Anuncio A a 5000 personas y el Anuncio B a otras 5000 de forma aleatoria.<\/p>\n<\/li>\n<li>\n<p data-path-to-node=\"9,2,0\"><b data-path-to-node=\"9,2,0\" data-index-in-node=\"0\">Contraste de hip\u00f3tesis:<\/b> <b data-path-to-node=\"9,2,0\" data-index-in-node=\"26\"><\/b><\/p>\n<ul data-path-to-node=\"9\">\n<li>\n<p data-path-to-node=\"9,2,0\"><b data-path-to-node=\"9,2,0\" data-index-in-node=\"26\">Hip\u00f3tesis nula (H0):<\/b> No hay diferencia de rendimiento entre ambos anuncios.<\/p>\n<\/li>\n<li>\n<p data-path-to-node=\"9,2,1,0,0\"><b data-path-to-node=\"9,2,1,0,0\" data-index-in-node=\"0\">Valor p:<\/b> Si el Anuncio B genera un 4% de clics y el A solo un 1%, el sistema calcula el valor p. Si <span class=\"math-inline\" data-math=\"p &lt; 0.01\" data-index-in-node=\"100\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">p<\/span><span class=\"mrel\">&lt;<\/span><\/span><span class=\"base\"><span class=\"mord\">0.01<\/span><\/span><\/span><\/span><\/span>, el algoritmo infiere que la diferencia no es casualidad y que el enfoque ecol\u00f3gico es realmente m\u00e1s efectivo para ese p\u00fablico.<\/p>\n<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h4 data-path-to-node=\"11\"><span class=\"ez-toc-section\" id=\"El_control_del_error_y_la_optimizacion_Neyman-Pearson\"><\/span>El control del error y la optimizaci\u00f3n (Neyman-Pearson)<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p data-path-to-node=\"12\">En publicidad digital, el coste de los errores se mide en dinero desperdiciado.<\/p>\n<ul data-path-to-node=\"13\">\n<li>\n<p data-path-to-node=\"13,0,0\"><b data-path-to-node=\"13,0,0\" data-index-in-node=\"0\">Error tipo I (falso positivo):<\/b> El sistema cree que un anuncio es ganador por simple azar y gasta todo el presupuesto en \u00e9l, cuando en realidad no atrae ventas reales.<\/p>\n<\/li>\n<li>\n<p data-path-to-node=\"13,1,0\"><b data-path-to-node=\"13,1,0\" data-index-in-node=\"0\">Modelos de atribuci\u00f3n (bayesianos):<\/b> Las plataformas modernas usan estad\u00edstica bayesiana para actualizar constantemente la probabilidad de \u00e9xito. Si un usuario hace clic pero no compra, el sistema \u00abaprende\u00bb y ajusta la probabilidad de mostrar ese anuncio a perfiles similares.<\/p>\n<\/li>\n<li>\n<p data-path-to-node=\"13,2,0\"><b data-path-to-node=\"13,2,0\" data-index-in-node=\"0\">Poder estad\u00edstico:<\/b> Para que la marca est\u00e9 segura de que el Anuncio B es mejor, necesita que la muestra sea lo suficientemente grande. Si solo lo muestra a 10 personas, el poder estad\u00edstico es bajo y cualquier conclusi\u00f3n ser\u00eda arriesgada.<\/p>\n<\/li>\n<\/ul>\n<\/div><\/div><\/div><\/div><\/div><\/div><\/div><\/div><\/div><div class=\"fusion-fullwidth fullwidth-box fusion-builder-row-6 fusion-flex-container nonhundred-percent-fullwidth non-hundred-percent-height-scrolling\" style=\"--awb-border-radius-top-left:0px;--awb-border-radius-top-right:0px;--awb-border-radius-bottom-right:0px;--awb-border-radius-bottom-left:0px;--awb-padding-top:20px;--awb-flex-wrap:wrap;\" ><div class=\"fusion-builder-row fusion-row fusion-flex-align-items-flex-start fusion-flex-content-wrap\" style=\"max-width:1248px;margin-left: calc(-4% \/ 2 );margin-right: calc(-4% \/ 2 );\"><div class=\"fusion-layout-column fusion_builder_column fusion-builder-column-9 fusion_builder_column_1_1 1_1 fusion-flex-column\" style=\"--awb-bg-size:cover;--awb-width-large:100%;--awb-margin-top-large:0px;--awb-spacing-right-large:1.92%;--awb-margin-bottom-large:20px;--awb-spacing-left-large:1.92%;--awb-width-medium:100%;--awb-order-medium:0;--awb-spacing-right-medium:1.92%;--awb-spacing-left-medium:1.92%;--awb-width-small:100%;--awb-order-small:0;--awb-spacing-right-small:1.92%;--awb-spacing-left-small:1.92%;\"><div class=\"fusion-column-wrapper fusion-column-has-shadow fusion-flex-justify-content-flex-start fusion-content-layout-column\"><div class=\"fusion-title title fusion-title-9 fusion-sep-none fusion-title-text fusion-title-size-two\"><h2 class=\"fusion-title-heading title-heading-left fusion-responsive-typography-calculated\" style=\"margin:0;--fontSize:36;line-height:1.5;\">Bibliograf\u00eda recomendada<\/h2><\/div><div class=\"fusion-text fusion-text-16\"><p style=\"font-weight: 400;\">Gamero Buron, C. (2023). <em>Estad\u00edstica I: Elementos de estad\u00edstica descriptiva y de teor\u00eda de la probabil\u00eddad<\/em>. UMA Editorial.<\/p>\n<p style=\"font-weight: 400;\">Garcia Ordaz, F., Garc\u00eda del Hoyo, J. J. y Gonz\u00e1lez Gal\u00e1n, M. D. (2020). <em>Estad\u00edstica y m\u00e9todos cuantitativos I<\/em>. Universidad de Huelva.<\/p>\n<\/div><\/div><\/div><div class=\"fusion-layout-column fusion_builder_column fusion-builder-column-10 fusion_builder_column_1_1 1_1 fusion-flex-column\" style=\"--awb-bg-size:cover;--awb-width-large:100%;--awb-margin-top-large:0px;--awb-spacing-right-large:1.92%;--awb-margin-bottom-large:20px;--awb-spacing-left-large:1.92%;--awb-width-medium:100%;--awb-order-medium:0;--awb-spacing-right-medium:1.92%;--awb-spacing-left-medium:1.92%;--awb-width-small:100%;--awb-order-small:0;--awb-spacing-right-small:1.92%;--awb-spacing-left-small:1.92%;\"><div class=\"fusion-column-wrapper fusion-column-has-shadow fusion-flex-justify-content-flex-start fusion-content-layout-column\"><div class=\"fusion-title title fusion-title-10 fusion-sep-none fusion-title-text fusion-title-size-two\"><h2 class=\"fusion-title-heading title-heading-left fusion-responsive-typography-calculated\" style=\"margin:0;--fontSize:36;line-height:1.5;\">Recursos en l\u00ednea<\/h2><\/div><div class=\"fusion-title title fusion-title-11 fusion-sep-none fusion-title-text fusion-title-size-three\"><h3 class=\"fusion-title-heading title-heading-left fusion-responsive-typography-calculated\" style=\"margin:0;--fontSize:24;--minFontSize:24;line-height:1.5;\">Fuentes de datos<\/h3><\/div><div class=\"fusion-content-boxes content-boxes columns row fusion-columns-1 fusion-columns-total-7 fusion-content-boxes-1 content-boxes-icon-with-title content-left\" style=\"--awb-hover-accent-color:#000000;--awb-circle-hover-accent-color:transparent;--awb-item-margin-bottom:40px;\" data-animationOffset=\"top-into-view\"><div style=\"--awb-backgroundcolor:#ffffff;\" class=\"fusion-column content-box-column content-box-column content-box-column-1 col-lg-12 col-md-12 col-sm-12 fusion-content-box-hover content-box-column-last-in-row\"><div class=\"col content-box-wrapper content-wrapper-background link-area-link-icon link-type-button-bar icon-hover-animation-fade\" data-animationOffset=\"top-into-view\"><div class=\"heading heading-with-icon icon-left\"><a class=\"heading-link\" style=\"float:left;\" href=\"https:\/\/ec.europa.eu\/eurostat\/web\/main\/data\" target=\"_blank\" rel=\"noopener noreferrer\"><div class=\"icon\"><i style=\"background-color:transparent;border-color:transparent;height:auto;width: 21px;line-height:normal;font-size:21px;\" aria-hidden=\"true\" class=\"fontawesome-icon fa-external-link-alt fas circle-no\"><\/i><\/div><h4 class=\"content-box-heading fusion-responsive-typography-calculated\" style=\"--h4_typography-font-size:20px;--fontSize:20;line-height:1.5;\">Eurostat Data<\/h4><\/a><\/div><div class=\"fusion-clearfix\"><\/div><div class=\"content-container\">\n<p>Portal de datos de la Uni\u00f3n Europea.<\/p>\n<\/div><div class=\"fusion-clearfix\"><\/div><a class=\" fusion-read-more fusion-button-bar\" style=\"float:left;\" href=\"https:\/\/ec.europa.eu\/eurostat\/web\/main\/data\" target=\"_blank\" rel=\"noopener noreferrer\">ed.europa.eu\/eurostat<\/a><div class=\"fusion-clearfix\"><\/div><\/div><\/div><div style=\"--awb-backgroundcolor:#ffffff;\" class=\"fusion-column content-box-column content-box-column content-box-column-2 col-lg-12 col-md-12 col-sm-12 fusion-content-box-hover content-box-column-last-in-row\"><div class=\"col content-box-wrapper content-wrapper-background link-area-link-icon link-type-button-bar icon-hover-animation-fade\" data-animationOffset=\"top-into-view\"><div class=\"heading heading-with-icon icon-left\"><a class=\"heading-link\" style=\"float:left;\" href=\"https:\/\/www.idescat.cat\/?lang=es\" target=\"_blank\" rel=\"noopener noreferrer\"><div class=\"icon\"><i style=\"background-color:transparent;border-color:transparent;height:auto;width: 21px;line-height:normal;font-size:21px;\" aria-hidden=\"true\" class=\"fontawesome-icon fa-external-link-alt fas circle-no\"><\/i><\/div><h4 class=\"content-box-heading fusion-responsive-typography-calculated\" style=\"--h4_typography-font-size:20px;--fontSize:20;line-height:1.5;\">Idescat<\/h4><\/a><\/div><div class=\"fusion-clearfix\"><\/div><div class=\"content-container\">\n<p>Estad\u00edstica oficial de Catalunya.<\/p>\n<\/div><div class=\"fusion-clearfix\"><\/div><a class=\" fusion-read-more fusion-button-bar\" style=\"float:left;\" href=\"https:\/\/www.idescat.cat\/?lang=es\" target=\"_blank\" rel=\"noopener noreferrer\">Idescat.cat<\/a><div class=\"fusion-clearfix\"><\/div><\/div><\/div><div style=\"--awb-backgroundcolor:#ffffff;\" class=\"fusion-column content-box-column content-box-column content-box-column-3 col-lg-12 col-md-12 col-sm-12 fusion-content-box-hover content-box-column-last-in-row\"><div class=\"col content-box-wrapper content-wrapper-background link-area-link-icon link-type-button-bar icon-hover-animation-fade\" data-animationOffset=\"top-into-view\"><div class=\"heading heading-with-icon icon-left\"><a class=\"heading-link\" style=\"float:left;\" href=\"https:\/\/www.imf.org\/en\/data\" target=\"_blank\" rel=\"noopener noreferrer\"><div class=\"icon\"><i style=\"background-color:transparent;border-color:transparent;height:auto;width: 21px;line-height:normal;font-size:21px;\" aria-hidden=\"true\" class=\"fontawesome-icon fa-external-link-alt fas circle-no\"><\/i><\/div><h4 class=\"content-box-heading fusion-responsive-typography-calculated\" style=\"--h4_typography-font-size:20px;--fontSize:20;line-height:1.5;\">IMF Data<\/h4><\/a><\/div><div class=\"fusion-clearfix\"><\/div><div class=\"content-container\">\n<p>Portal de datos del FMI.<\/p>\n<\/div><div class=\"fusion-clearfix\"><\/div><a class=\" fusion-read-more fusion-button-bar\" style=\"float:left;\" href=\"https:\/\/www.imf.org\/en\/data\" target=\"_blank\" rel=\"noopener noreferrer\">IMF.org<\/a><div class=\"fusion-clearfix\"><\/div><\/div><\/div><div style=\"--awb-backgroundcolor:#ffffff;\" class=\"fusion-column content-box-column content-box-column content-box-column-4 col-lg-12 col-md-12 col-sm-12 fusion-content-box-hover content-box-column-last-in-row\"><div class=\"col content-box-wrapper content-wrapper-background link-area-link-icon link-type-button-bar icon-hover-animation-fade\" data-animationOffset=\"top-into-view\"><div class=\"heading heading-with-icon icon-left\"><a class=\"heading-link\" style=\"float:left;\" href=\"https:\/\/www.ine.gob.cl\/\" target=\"_blank\" rel=\"noopener noreferrer\"><div class=\"icon\"><i style=\"background-color:transparent;border-color:transparent;height:auto;width: 21px;line-height:normal;font-size:21px;\" aria-hidden=\"true\" class=\"fontawesome-icon fa-external-link-alt fas circle-no\"><\/i><\/div><h4 class=\"content-box-heading fusion-responsive-typography-calculated\" style=\"--h4_typography-font-size:20px;--fontSize:20;line-height:1.5;\">INE Chile<\/h4><\/a><\/div><div class=\"fusion-clearfix\"><\/div><div class=\"content-container\">\n<p>Instituto Nacional de Estad\u00edsticas de Chile.<\/p>\n<\/div><div class=\"fusion-clearfix\"><\/div><a class=\" fusion-read-more fusion-button-bar\" style=\"float:left;\" href=\"https:\/\/www.ine.gob.cl\/\" target=\"_blank\" rel=\"noopener noreferrer\">INE.gob.cl<\/a><div class=\"fusion-clearfix\"><\/div><\/div><\/div><div style=\"--awb-backgroundcolor:#ffffff;\" class=\"fusion-column content-box-column content-box-column content-box-column-5 col-lg-12 col-md-12 col-sm-12 fusion-content-box-hover content-box-column-last-in-row\"><div class=\"col content-box-wrapper content-wrapper-background link-area-link-icon link-type-button-bar icon-hover-animation-fade\" data-animationOffset=\"top-into-view\"><div class=\"heading heading-with-icon icon-left\"><a class=\"heading-link\" style=\"float:left;\" href=\"https:\/\/www.ine.es\/\" target=\"_blank\" rel=\"noopener noreferrer\"><div class=\"icon\"><i style=\"background-color:transparent;border-color:transparent;height:auto;width: 21px;line-height:normal;font-size:21px;\" aria-hidden=\"true\" class=\"fontawesome-icon fa-external-link-alt fas circle-no\"><\/i><\/div><h4 class=\"content-box-heading fusion-responsive-typography-calculated\" style=\"--h4_typography-font-size:20px;--fontSize:20;line-height:1.5;\">INE Espa\u00f1a<\/h4><\/a><\/div><div class=\"fusion-clearfix\"><\/div><div class=\"content-container\">\n<p>Instituto Nacional de Estad\u00edstica de Espa\u00f1a.<\/p>\n<\/div><div class=\"fusion-clearfix\"><\/div><a class=\" fusion-read-more fusion-button-bar\" style=\"float:left;\" href=\"https:\/\/www.ine.es\/\" target=\"_blank\" rel=\"noopener noreferrer\">INE.es<\/a><div class=\"fusion-clearfix\"><\/div><\/div><\/div><div style=\"--awb-backgroundcolor:#ffffff;\" class=\"fusion-column content-box-column content-box-column content-box-column-6 col-lg-12 col-md-12 col-sm-12 fusion-content-box-hover content-box-column-last-in-row\"><div class=\"col content-box-wrapper content-wrapper-background link-area-link-icon link-type-button-bar icon-hover-animation-fade\" data-animationOffset=\"top-into-view\"><div class=\"heading heading-with-icon icon-left\"><a class=\"heading-link\" style=\"float:left;\" href=\"https:\/\/www.oecd.org\/en.html\" target=\"_blank\" rel=\"noopener noreferrer\"><div class=\"icon\"><i style=\"background-color:transparent;border-color:transparent;height:auto;width: 21px;line-height:normal;font-size:21px;\" aria-hidden=\"true\" class=\"fontawesome-icon fa-external-link-alt fas circle-no\"><\/i><\/div><h4 class=\"content-box-heading fusion-responsive-typography-calculated\" style=\"--h4_typography-font-size:20px;--fontSize:20;line-height:1.5;\">OECD Data<\/h4><\/a><\/div><div class=\"fusion-clearfix\"><\/div><div class=\"content-container\">\n<p>Estad\u00edsticas de la OCDE.<\/p>\n<\/div><div class=\"fusion-clearfix\"><\/div><a class=\" fusion-read-more fusion-button-bar\" style=\"float:left;\" href=\"https:\/\/www.oecd.org\/en.html\" target=\"_blank\" rel=\"noopener noreferrer\">OECD.org<\/a><div class=\"fusion-clearfix\"><\/div><\/div><\/div><div style=\"--awb-backgroundcolor:#ffffff;\" class=\"fusion-column content-box-column content-box-column content-box-column-7 col-lg-12 col-md-12 col-sm-12 fusion-content-box-hover content-box-column-last content-box-column-last-in-row\"><div class=\"col content-box-wrapper content-wrapper-background link-area-link-icon link-type-button-bar icon-hover-animation-fade\" data-animationOffset=\"top-into-view\"><div class=\"heading heading-with-icon icon-left\"><a class=\"heading-link\" style=\"float:left;\" href=\"https:\/\/unstats.un.org\/UNSDWebsite\/\" target=\"_blank\" rel=\"noopener noreferrer\"><div class=\"icon\"><i style=\"background-color:transparent;border-color:transparent;height:auto;width: 21px;line-height:normal;font-size:21px;\" aria-hidden=\"true\" class=\"fontawesome-icon fa-external-link-alt fas circle-no\"><\/i><\/div><h4 class=\"content-box-heading fusion-responsive-typography-calculated\" style=\"--h4_typography-font-size:20px;--fontSize:20;line-height:1.5;\">UNSTATS<\/h4><\/a><\/div><div class=\"fusion-clearfix\"><\/div><div class=\"content-container\">\n<p>Departamento de estad\u00edstica de las Naciones Unidas.<\/p>\n<\/div><div class=\"fusion-clearfix\"><\/div><a class=\" fusion-read-more fusion-button-bar\" style=\"float:left;\" href=\"https:\/\/unstats.un.org\/UNSDWebsite\/\" target=\"_blank\" rel=\"noopener noreferrer\">Unstats.un.org<\/a><div class=\"fusion-clearfix\"><\/div><\/div><\/div><div class=\"fusion-clearfix\"><\/div><\/div><\/div><\/div><\/div><\/div><div class=\"fusion-fullwidth fullwidth-box fusion-builder-row-7 fusion-flex-container nonhundred-percent-fullwidth non-hundred-percent-height-scrolling\" style=\"--awb-border-radius-top-left:0px;--awb-border-radius-top-right:0px;--awb-border-radius-bottom-right:0px;--awb-border-radius-bottom-left:0px;--awb-flex-wrap:wrap;\" ><div class=\"fusion-builder-row fusion-row fusion-flex-align-items-flex-start fusion-flex-content-wrap\" style=\"max-width:1248px;margin-left: calc(-4% \/ 2 );margin-right: calc(-4% \/ 2 );\"><div class=\"fusion-layout-column fusion_builder_column fusion-builder-column-11 fusion_builder_column_1_1 1_1 fusion-flex-column\" style=\"--awb-bg-size:cover;--awb-width-large:100%;--awb-margin-top-large:0px;--awb-spacing-right-large:1.92%;--awb-margin-bottom-large:20px;--awb-spacing-left-large:1.92%;--awb-width-medium:100%;--awb-order-medium:0;--awb-spacing-right-medium:1.92%;--awb-spacing-left-medium:1.92%;--awb-width-small:100%;--awb-order-small:0;--awb-spacing-right-small:1.92%;--awb-spacing-left-small:1.92%;\"><div class=\"fusion-column-wrapper fusion-column-has-shadow fusion-flex-justify-content-flex-start fusion-content-layout-column\"><div class=\"fusion-title title fusion-title-12 fusion-sep-none fusion-title-text fusion-title-size-two\"><h2 class=\"fusion-title-heading title-heading-left fusion-responsive-typography-calculated\" style=\"margin:0;--fontSize:36;line-height:1.5;\">Enlaces<\/h2><\/div><\/div><\/div><div class=\"fusion-layout-column fusion_builder_column fusion-builder-column-12 fusion_builder_column_1_3 1_3 fusion-flex-column\" style=\"--awb-bg-size:cover;--awb-width-large:33.333333333333%;--awb-margin-top-large:0px;--awb-spacing-right-large:5.76%;--awb-margin-bottom-large:20px;--awb-spacing-left-large:5.76%;--awb-width-medium:100%;--awb-order-medium:0;--awb-spacing-right-medium:1.92%;--awb-spacing-left-medium:1.92%;--awb-width-small:100%;--awb-order-small:0;--awb-spacing-right-small:1.92%;--awb-spacing-left-small:1.92%;\"><div class=\"fusion-column-wrapper fusion-column-has-shadow fusion-flex-justify-content-flex-start fusion-content-layout-column\"><div ><a class=\"fusion-button button-flat fusion-button-default-size button-default fusion-button-default button-1 fusion-button-span-yes fusion-button-default-type\" target=\"_blank\" rel=\"noopener noreferrer\" href=\"https:\/\/es.wikipedia.org\/wiki\/Ronald_Fisher\"><i class=\"fa-wikipedia-w fab awb-button__icon awb-button__icon--default button-icon-left\" aria-hidden=\"true\"><\/i><span class=\"fusion-button-text awb-button__text awb-button__text--default\">Ronald Fisher<\/span><\/a><\/div><\/div><\/div><div class=\"fusion-layout-column fusion_builder_column fusion-builder-column-13 fusion_builder_column_1_3 1_3 fusion-flex-column\" style=\"--awb-bg-size:cover;--awb-width-large:33.333333333333%;--awb-margin-top-large:0px;--awb-spacing-right-large:5.76%;--awb-margin-bottom-large:20px;--awb-spacing-left-large:5.76%;--awb-width-medium:100%;--awb-order-medium:0;--awb-spacing-right-medium:1.92%;--awb-spacing-left-medium:1.92%;--awb-width-small:100%;--awb-order-small:0;--awb-spacing-right-small:1.92%;--awb-spacing-left-small:1.92%;\"><div class=\"fusion-column-wrapper fusion-column-has-shadow fusion-flex-justify-content-flex-start fusion-content-layout-column\"><div ><a class=\"fusion-button button-flat fusion-button-default-size button-default fusion-button-default button-2 fusion-button-span-yes fusion-button-default-type\" target=\"_blank\" rel=\"noopener noreferrer\" href=\"https:\/\/es.wikipedia.org\/wiki\/Jerzy_Neyman\"><i class=\"fa-wikipedia-w fab awb-button__icon awb-button__icon--default button-icon-left\" aria-hidden=\"true\"><\/i><span class=\"fusion-button-text awb-button__text awb-button__text--default\">Jerzy Neyman<\/span><\/a><\/div><\/div><\/div><div class=\"fusion-layout-column fusion_builder_column fusion-builder-column-14 fusion_builder_column_1_3 1_3 fusion-flex-column\" style=\"--awb-bg-size:cover;--awb-width-large:33.333333333333%;--awb-margin-top-large:0px;--awb-spacing-right-large:5.76%;--awb-margin-bottom-large:20px;--awb-spacing-left-large:5.76%;--awb-width-medium:100%;--awb-order-medium:0;--awb-spacing-right-medium:1.92%;--awb-spacing-left-medium:1.92%;--awb-width-small:100%;--awb-order-small:0;--awb-spacing-right-small:1.92%;--awb-spacing-left-small:1.92%;\"><div class=\"fusion-column-wrapper fusion-column-has-shadow fusion-flex-justify-content-flex-start fusion-content-layout-column\"><div ><a class=\"fusion-button button-flat fusion-button-default-size button-default fusion-button-default button-3 fusion-button-span-yes fusion-button-default-type\" target=\"_blank\" rel=\"noopener noreferrer\" href=\"https:\/\/es.wikipedia.org\/wiki\/Egon_Pearson\"><i class=\"fa-wikipedia-w fab awb-button__icon awb-button__icon--default button-icon-left\" aria-hidden=\"true\"><\/i><span class=\"fusion-button-text awb-button__text awb-button__text--default\">Egon Pearson<\/span><\/a><\/div><\/div><\/div><div class=\"fusion-layout-column fusion_builder_column fusion-builder-column-15 fusion_builder_column_1_3 1_3 fusion-flex-column\" style=\"--awb-bg-size:cover;--awb-width-large:33.333333333333%;--awb-margin-top-large:0px;--awb-spacing-right-large:5.76%;--awb-margin-bottom-large:20px;--awb-spacing-left-large:5.76%;--awb-width-medium:100%;--awb-order-medium:0;--awb-spacing-right-medium:1.92%;--awb-spacing-left-medium:1.92%;--awb-width-small:100%;--awb-order-small:0;--awb-spacing-right-small:1.92%;--awb-spacing-left-small:1.92%;\"><div class=\"fusion-column-wrapper fusion-column-has-shadow fusion-flex-justify-content-flex-start fusion-content-layout-column\"><div ><a class=\"fusion-button button-flat fusion-button-default-size button-default fusion-button-default button-4 fusion-button-span-yes fusion-button-default-type\" target=\"_blank\" rel=\"noopener noreferrer\" href=\"https:\/\/es.wikipedia.org\/wiki\/Francis_Galton\"><i class=\"fa-wikipedia-w fab awb-button__icon awb-button__icon--default button-icon-left\" aria-hidden=\"true\"><\/i><span class=\"fusion-button-text awb-button__text awb-button__text--default\">Francis Galton<\/span><\/a><\/div><\/div><\/div><div class=\"fusion-layout-column fusion_builder_column fusion-builder-column-16 fusion_builder_column_1_3 1_3 fusion-flex-column\" style=\"--awb-bg-size:cover;--awb-width-large:33.333333333333%;--awb-margin-top-large:0px;--awb-spacing-right-large:5.76%;--awb-margin-bottom-large:20px;--awb-spacing-left-large:5.76%;--awb-width-medium:100%;--awb-order-medium:0;--awb-spacing-right-medium:1.92%;--awb-spacing-left-medium:1.92%;--awb-width-small:100%;--awb-order-small:0;--awb-spacing-right-small:1.92%;--awb-spacing-left-small:1.92%;\"><div class=\"fusion-column-wrapper fusion-column-has-shadow fusion-flex-justify-content-flex-start fusion-content-layout-column\"><div ><a class=\"fusion-button button-flat fusion-button-default-size button-default fusion-button-default button-5 fusion-button-span-yes fusion-button-default-type\" target=\"_blank\" rel=\"noopener noreferrer\" href=\"https:\/\/es.wikipedia.org\/wiki\/Karl_Pearson\"><i class=\"fa-wikipedia-w fab awb-button__icon awb-button__icon--default button-icon-left\" aria-hidden=\"true\"><\/i><span class=\"fusion-button-text awb-button__text awb-button__text--default\">Karl Pearson<\/span><\/a><\/div><\/div><\/div><div class=\"fusion-layout-column fusion_builder_column fusion-builder-column-17 fusion_builder_column_1_3 1_3 fusion-flex-column\" style=\"--awb-bg-size:cover;--awb-width-large:33.333333333333%;--awb-margin-top-large:0px;--awb-spacing-right-large:5.76%;--awb-margin-bottom-large:20px;--awb-spacing-left-large:5.76%;--awb-width-medium:100%;--awb-order-medium:0;--awb-spacing-right-medium:1.92%;--awb-spacing-left-medium:1.92%;--awb-width-small:100%;--awb-order-small:0;--awb-spacing-right-small:1.92%;--awb-spacing-left-small:1.92%;\"><div class=\"fusion-column-wrapper fusion-column-has-shadow fusion-flex-justify-content-flex-start fusion-content-layout-column\"><div ><a class=\"fusion-button button-flat fusion-button-default-size button-default fusion-button-default button-6 fusion-button-span-yes fusion-button-default-type\" target=\"_blank\" rel=\"noopener noreferrer\" href=\"https:\/\/es.wikipedia.org\/wiki\/William_Sealy_Gosset\"><i class=\"fa-wikipedia-w fab awb-button__icon awb-button__icon--default button-icon-left\" aria-hidden=\"true\"><\/i><span class=\"fusion-button-text awb-button__text awb-button__text--default\">William Sealy Gosset<\/span><\/a><\/div><\/div><\/div><div class=\"fusion-layout-column fusion_builder_column fusion-builder-column-18 fusion_builder_column_1_3 1_3 fusion-flex-column\" style=\"--awb-bg-size:cover;--awb-width-large:33.333333333333%;--awb-margin-top-large:0px;--awb-spacing-right-large:5.76%;--awb-margin-bottom-large:20px;--awb-spacing-left-large:5.76%;--awb-width-medium:100%;--awb-order-medium:0;--awb-spacing-right-medium:1.92%;--awb-spacing-left-medium:1.92%;--awb-width-small:100%;--awb-order-small:0;--awb-spacing-right-small:1.92%;--awb-spacing-left-small:1.92%;\"><div class=\"fusion-column-wrapper fusion-column-has-shadow fusion-flex-justify-content-flex-start fusion-content-layout-column\"><div ><a class=\"fusion-button button-flat fusion-button-default-size button-default fusion-button-default button-7 fusion-button-span-yes fusion-button-default-type\" target=\"_blank\" rel=\"noopener noreferrer\" href=\"https:\/\/es.wikipedia.org\/wiki\/Bradley_Efron\"><i class=\"fa-wikipedia-w fab awb-button__icon awb-button__icon--default button-icon-left\" aria-hidden=\"true\"><\/i><span class=\"fusion-button-text awb-button__text awb-button__text--default\">Bradley Efron<\/span><\/a><\/div><\/div><\/div><div class=\"fusion-layout-column fusion_builder_column fusion-builder-column-19 fusion_builder_column_1_3 1_3 fusion-flex-column\" style=\"--awb-bg-size:cover;--awb-width-large:33.333333333333%;--awb-margin-top-large:0px;--awb-spacing-right-large:5.76%;--awb-margin-bottom-large:20px;--awb-spacing-left-large:5.76%;--awb-width-medium:100%;--awb-order-medium:0;--awb-spacing-right-medium:1.92%;--awb-spacing-left-medium:1.92%;--awb-width-small:100%;--awb-order-small:0;--awb-spacing-right-small:1.92%;--awb-spacing-left-small:1.92%;\"><div class=\"fusion-column-wrapper fusion-column-has-shadow fusion-flex-justify-content-flex-start fusion-content-layout-column\"><\/div><\/div><div class=\"fusion-layout-column fusion_builder_column fusion-builder-column-20 fusion_builder_column_1_3 1_3 fusion-flex-column\" style=\"--awb-bg-size:cover;--awb-width-large:33.333333333333%;--awb-margin-top-large:0px;--awb-spacing-right-large:5.76%;--awb-margin-bottom-large:20px;--awb-spacing-left-large:5.76%;--awb-width-medium:100%;--awb-order-medium:0;--awb-spacing-right-medium:1.92%;--awb-spacing-left-medium:1.92%;--awb-width-small:100%;--awb-order-small:0;--awb-spacing-right-small:1.92%;--awb-spacing-left-small:1.92%;\"><div class=\"fusion-column-wrapper fusion-column-has-shadow fusion-flex-justify-content-flex-start fusion-content-layout-column\"><div ><a class=\"fusion-button button-flat fusion-button-default-size button-default fusion-button-default button-8 fusion-button-span-yes fusion-button-default-type\" target=\"_blank\" rel=\"noopener noreferrer\" href=\"https:\/\/es.wikipedia.org\/wiki\/Thomas_Bayes\"><i class=\"fa-wikipedia-w fab awb-button__icon awb-button__icon--default button-icon-left\" aria-hidden=\"true\"><\/i><span class=\"fusion-button-text awb-button__text awb-button__text--default\">Thomas Bayes<\/span><\/a><\/div><\/div><\/div><\/div><\/div><div class=\"fusion-fullwidth fullwidth-box fusion-builder-row-8 fusion-flex-container has-pattern-background has-mask-background nonhundred-percent-fullwidth non-hundred-percent-height-scrolling\" style=\"--awb-border-radius-top-left:0px;--awb-border-radius-top-right:0px;--awb-border-radius-bottom-right:0px;--awb-border-radius-bottom-left:0px;--awb-flex-wrap:wrap;\" ><div class=\"fusion-builder-row fusion-row fusion-flex-align-items-flex-start fusion-flex-content-wrap\" style=\"max-width:1248px;margin-left: calc(-4% \/ 2 );margin-right: calc(-4% \/ 2 );\"><div class=\"fusion-layout-column fusion_builder_column fusion-builder-column-21 fusion_builder_column_1_1 1_1 fusion-flex-column\" style=\"--awb-bg-size:cover;--awb-width-large:100%;--awb-margin-top-large:0px;--awb-spacing-right-large:1.92%;--awb-margin-bottom-large:20px;--awb-spacing-left-large:1.92%;--awb-width-medium:100%;--awb-order-medium:0;--awb-spacing-right-medium:1.92%;--awb-spacing-left-medium:1.92%;--awb-width-small:100%;--awb-order-small:0;--awb-spacing-right-small:1.92%;--awb-spacing-left-small:1.92%;\"><div class=\"fusion-column-wrapper fusion-column-has-shadow fusion-flex-justify-content-flex-start fusion-content-layout-column\"><div class=\"fusion-separator fusion-full-width-sep\" style=\"align-self: center;margin-left: auto;margin-right: auto;margin-top:60px;width:100%;\"><div class=\"fusion-separator-border sep-single sep-dotted\" style=\"--awb-height:20px;--awb-amount:20px;border-color:#000000;border-top-width:1px;\"><\/div><\/div><\/div><\/div><\/div><\/div>\n<div class=\"ttr_end\"><\/div>","protected":false},"excerpt":{"rendered":"","protected":false},"template":"","meta":{"inline_featured_image":false,"_vp_format_video_url":"","_vp_image_focal_point":[]},"glosario_categoria":[7025],"glosario_tag":[7019,7104,7099,7100,6996],"class_list":["post-59199","glosario","type-glosario","status-publish","hentry","glosario_categoria-investigacion-analisis","glosario_tag-analisis-visualizacion-datos","glosario_tag-ciencia-de-datos","glosario_tag-estadistica","glosario_tag-metodos-cuantitativos","glosario_tag-opinion-publica"],"_links":{"self":[{"href":"https:\/\/www.carolinacampalans.com\/index.php?rest_route=\/wp\/v2\/glosario\/59199","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.carolinacampalans.com\/index.php?rest_route=\/wp\/v2\/glosario"}],"about":[{"href":"https:\/\/www.carolinacampalans.com\/index.php?rest_route=\/wp\/v2\/types\/glosario"}],"wp:attachment":[{"href":"https:\/\/www.carolinacampalans.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=59199"}],"wp:term":[{"taxonomy":"glosario_categoria","embeddable":true,"href":"https:\/\/www.carolinacampalans.com\/index.php?rest_route=%2Fwp%2Fv2%2Fglosario_categoria&post=59199"},{"taxonomy":"glosario_tag","embeddable":true,"href":"https:\/\/www.carolinacampalans.com\/index.php?rest_route=%2Fwp%2Fv2%2Fglosario_tag&post=59199"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}