{"id":1222,"date":"2023-07-27T05:49:03","date_gmt":"2023-07-27T05:49:03","guid":{"rendered":"https:\/\/statorials.org\/pt\/distribuicao-amostral-em-r\/"},"modified":"2023-07-27T05:49:03","modified_gmt":"2023-07-27T05:49:03","slug":"distribuicao-amostral-em-r","status":"publish","type":"post","link":"https:\/\/statorials.org\/pt\/distribuicao-amostral-em-r\/","title":{"rendered":"Como calcular distribui\u00e7\u00f5es amostrais em r"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">Uma <a href=\"https:\/\/statorials.org\/pt\/distribuicao-amostral-1\/\" target=\"_blank\" rel=\"noopener noreferrer\">distribui\u00e7\u00e3o amostral<\/a> \u00e9 uma distribui\u00e7\u00e3o de probabilidade de uma determinada <a href=\"https:\/\/statorials.org\/pt\/estatisticas-vs-parametro\/\" target=\"_blank\" rel=\"noopener noreferrer\">estat\u00edstica<\/a> baseada em muitas amostras aleat\u00f3rias de uma \u00fanica popula\u00e7\u00e3o.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Este tutorial explica como fazer o seguinte com distribui\u00e7\u00f5es de amostragem em R:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Gere uma distribui\u00e7\u00e3o amostral.<\/span><\/li>\n<li> <span style=\"color: #000000;\">Visualize a distribui\u00e7\u00e3o amostral.<\/span><\/li>\n<li> <span style=\"color: #000000;\">Calcule a m\u00e9dia e o desvio padr\u00e3o da distribui\u00e7\u00e3o amostral.<\/span><\/li>\n<li> <span style=\"color: #000000;\">Calcule as probabilidades relativas \u00e0 distribui\u00e7\u00e3o amostral.<\/span><\/li>\n<\/ul>\n<h3> <span style=\"color: #000000;\"><strong>Gere uma distribui\u00e7\u00e3o amostral em R<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">O c\u00f3digo a seguir mostra como gerar uma distribui\u00e7\u00e3o amostral em R:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <span style=\"color: #000000;\"><strong><span style=\"color: #008080;\">#make this example reproducible\n<\/span>set.seed(0)\n\n<span style=\"color: #008080;\">#define number of samples\n<\/span>n = 10000\n\n<span style=\"color: #008080;\">#create empty vector of length n\n<\/span>sample_means = <span style=\"color: #3366ff;\">rep<\/span> (NA, n)\n\n<span style=\"color: #008080;\">#fill empty vector with means\n<\/span><span style=\"color: #008000;\">for<\/span> (i <span style=\"color: #008000;\">in<\/span> 1:n){\n  sample_means[i] = <span style=\"color: #3366ff;\">mean<\/span> ( <span style=\"color: #3366ff;\">rnorm<\/span> (20, mean=5.3, sd=9))\n}\n\n<span style=\"color: #008080;\">#view first six sample means\n<\/span>head(sample_means)\n\n[1] 5.283992 6.304845 4.259583 3.915274 7.756386 4.532656\n<\/strong><\/span><\/pre>\n<p> <span style=\"color: #000000;\">Neste exemplo, usamos a fun\u00e7\u00e3o <a href=\"https:\/\/statorials.org\/pt\/dnorm-pnorm-rnorm-qnorm-em-r\/\" target=\"_blank\" rel=\"noopener noreferrer\">rnorm()<\/a> para calcular a m\u00e9dia de 10.000 amostras em que cada tamanho de amostra era 20 e foi gerado a partir de uma distribui\u00e7\u00e3o normal com m\u00e9dia de 5,3 e desvio padr\u00e3o de 9.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Podemos ver que a primeira amostra teve m\u00e9dia de 5,283992, a segunda amostra teve m\u00e9dia de 6,304845 e assim por diante.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Visualize a distribui\u00e7\u00e3o amostral<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">O c\u00f3digo a seguir mostra como criar um histograma simples para visualizar a distribui\u00e7\u00e3o da amostragem:<\/span> <\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <span style=\"color: #000000;\"><strong><span style=\"color: #008080;\">#create histogram to visualize the sampling distribution<\/span>\nhist(sample_means, main = \"\", xlab = \" <span style=\"color: #008000;\">Sample Means<\/span> \", col = \" <span style=\"color: #008000;\">steelblue<\/span> \")\n<\/strong><\/span><\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-12122 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/echantillonnagemoyenne1.png\" alt=\"Distribui\u00e7\u00e3o de amostragem no histograma R\" width=\"435\" height=\"407\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Pode-se observar que a distribui\u00e7\u00e3o amostral tem formato de sino com pico pr\u00f3ximo ao valor 5.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Por\u00e9m, pelas caudas da distribui\u00e7\u00e3o podemos ver que algumas amostras tiveram m\u00e9dias maiores que 10 e outras tiveram m\u00e9dias menores que 0.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Encontre a m\u00e9dia e o desvio padr\u00e3o<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">O c\u00f3digo a seguir mostra como calcular a m\u00e9dia e o desvio padr\u00e3o da distribui\u00e7\u00e3o amostral:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <span style=\"color: #000000;\"><strong><span style=\"color: #008080;\">#mean of sampling distribution<\/span>\nmean(sample_means)\n\n[1] 5.287195\n\n<span style=\"color: #008080;\">#standard deviation of sampling distribution\n<\/span>sd(sample_means)\n\n[1] 2.00224<\/strong><\/span><\/pre>\n<p> <span style=\"color: #000000;\">Teoricamente, a m\u00e9dia da distribui\u00e7\u00e3o amostral deveria ser 5,3. Podemos ver que a m\u00e9dia amostral real neste exemplo \u00e9 <strong>5,287195<\/strong> , que \u00e9 pr\u00f3xima de 5,3.<\/span><\/p>\n<p> <span style=\"color: #000000;\">E teoricamente, o desvio padr\u00e3o da distribui\u00e7\u00e3o amostral deveria ser igual a s\/\u221an, que seria 9 \/ \u221a20 = 2,012. Podemos ver que o desvio padr\u00e3o real da distribui\u00e7\u00e3o amostral \u00e9 <strong>2,00224<\/strong> , que \u00e9 pr\u00f3ximo de 2,012.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Calcule as probabilidades<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">O c\u00f3digo a seguir mostra como calcular a probabilidade de obter um determinado valor para uma m\u00e9dia amostral, dada uma m\u00e9dia populacional, o desvio padr\u00e3o populacional e o tamanho da amostra.<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <span style=\"color: #000000;\"><strong><span style=\"color: #008080;\">#calculate probability that sample mean is less than or equal to 6<\/span>\nsum(sample_means &lt;= 6) \/ length(sample_means)\n<\/strong><\/span><\/pre>\n<p> <span style=\"color: #000000;\">Neste exemplo espec\u00edfico, encontramos a probabilidade de a m\u00e9dia da amostra ser menor ou igual a 6, dado que a m\u00e9dia da popula\u00e7\u00e3o \u00e9 5,3, o desvio padr\u00e3o da popula\u00e7\u00e3o \u00e9 9 e o tamanho da amostra de 20 \u00e9 <strong>0,6417<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Isso est\u00e1 muito pr\u00f3ximo da probabilidade calculada pela <a href=\"https:\/\/statorials.org\/pt\/calculadora-de-distribuicao-de-amostragem\/\" target=\"_blank\" rel=\"noopener noreferrer\">Calculadora de Distribui\u00e7\u00e3o de Amostragem<\/a> :<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-12123 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/echantillonnagemoyenne2.png\" alt=\"C\u00e1lculo da distribui\u00e7\u00e3o amostral\" width=\"358\" height=\"550\" srcset=\"\" sizes=\"auto, \"><\/p>\n<h3> <span style=\"color: #000000;\"><strong>O c\u00f3digo completo<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">O c\u00f3digo R completo usado neste exemplo \u00e9 mostrado abaixo:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <span style=\"color: #000000;\"><strong><span style=\"color: #008080;\">#make this example reproducible\n<\/span>set.seed(0)\n\n<span style=\"color: #008080;\">#define number of samples\n<\/span>n = 10000\n\n<span style=\"color: #008080;\">#create empty vector of length n\n<\/span>sample_means = <span style=\"color: #3366ff;\">rep<\/span> (NA, n)\n\n<span style=\"color: #008080;\">#fill empty vector with means\n<\/span><span style=\"color: #008000;\">for<\/span> (i <span style=\"color: #008000;\">in<\/span> 1:n){\n  sample_means[i] = <span style=\"color: #3366ff;\">mean<\/span> ( <span style=\"color: #3366ff;\">rnorm<\/span> (20, mean=5.3, sd=9))\n}\n\n<span style=\"color: #008080;\">#view first six sample means\n<\/span>head(sample_means)\n\n<span style=\"color: #008080;\">#create histogram to visualize the sampling distribution\n<\/span>hist(sample_means, main = \"\", xlab = \" <span style=\"color: #008000;\">Sample Means<\/span> \", col = \" <span style=\"color: #008000;\">steelblue<\/span> \")\n\n<span style=\"color: #008080;\">#mean of sampling distribution\n<\/span>mean(sample_means)\n\n<span style=\"color: #008080;\">#standard deviation of sampling distribution\n<\/span>sd(sample_means)\n\n<span style=\"color: #008080;\">#calculate probability that sample mean is less than or equal to 6<\/span>\nsum(sample_means &lt;= 6) \/ length(sample_means)\n<\/strong><\/span><\/pre>\n<h3> <span style=\"color: #000000;\"><strong>Recursos adicionais<\/strong><\/span><\/h3>\n<p> <a href=\"https:\/\/statorials.org\/pt\/distribuicao-amostral-1\/\" target=\"_blank\" rel=\"noopener noreferrer\">Uma introdu\u00e7\u00e3o \u00e0s distribui\u00e7\u00f5es de amostragem<\/a><br \/> <a href=\"https:\/\/statorials.org\/pt\/calculadora-de-distribuicao-de-amostragem\/\" target=\"_blank\" rel=\"noopener noreferrer\">Calculadora de distribui\u00e7\u00e3o de amostragem<\/a><br \/> <a href=\"https:\/\/statorials.org\/pt\/teorema-do-limite-central\/\" target=\"_blank\" rel=\"noopener noreferrer\">Uma introdu\u00e7\u00e3o ao teorema do limite central<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Uma distribui\u00e7\u00e3o amostral \u00e9 uma distribui\u00e7\u00e3o de probabilidade de uma determinada estat\u00edstica baseada em muitas amostras aleat\u00f3rias de uma \u00fanica popula\u00e7\u00e3o. Este tutorial explica como fazer o seguinte com distribui\u00e7\u00f5es de amostragem em R: Gere uma distribui\u00e7\u00e3o amostral. Visualize a distribui\u00e7\u00e3o amostral. Calcule a m\u00e9dia e o desvio padr\u00e3o da distribui\u00e7\u00e3o amostral. Calcule as probabilidades [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[],"class_list":["post-1222","post","type-post","status-publish","format-standard","hentry","category-guia"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Como calcular distribui\u00e7\u00f5es amostrais em R<\/title>\n<meta name=\"description\" content=\"Este tutorial explica como calcular e visualizar distribui\u00e7\u00f5es de amostragem em R para um determinado conjunto de par\u00e2metros.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/statorials.org\/pt\/distribuicao-amostral-em-r\/\" \/>\n<meta property=\"og:locale\" content=\"pt_PT\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Como calcular distribui\u00e7\u00f5es amostrais em R\" \/>\n<meta property=\"og:description\" content=\"Este tutorial explica como calcular e visualizar distribui\u00e7\u00f5es de amostragem em R para um determinado conjunto de par\u00e2metros.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pt\/distribuicao-amostral-em-r\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-27T05:49:03+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/echantillonnagemoyenne1.png\" \/>\n<meta name=\"author\" content=\"Dr. benjamim anderson\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Escrito por\" \/>\n\t<meta name=\"twitter:data1\" content=\"Dr. benjamim anderson\" \/>\n\t<meta name=\"twitter:label2\" content=\"Tempo estimado de leitura\" \/>\n\t<meta name=\"twitter:data2\" content=\"3 minutos\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/pt\/distribuicao-amostral-em-r\/\",\"url\":\"https:\/\/statorials.org\/pt\/distribuicao-amostral-em-r\/\",\"name\":\"Como calcular distribui\u00e7\u00f5es amostrais em R\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pt\/#website\"},\"datePublished\":\"2023-07-27T05:49:03+00:00\",\"dateModified\":\"2023-07-27T05:49:03+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/pt\/#\/schema\/person\/e08f98e8db95e0aa9c310e1b27c9c666\"},\"description\":\"Este tutorial explica como calcular e visualizar distribui\u00e7\u00f5es de amostragem em R para um determinado conjunto de par\u00e2metros.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pt\/distribuicao-amostral-em-r\/#breadcrumb\"},\"inLanguage\":\"pt-PT\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pt\/distribuicao-amostral-em-r\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pt\/distribuicao-amostral-em-r\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Lar\",\"item\":\"https:\/\/statorials.org\/pt\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Como calcular distribui\u00e7\u00f5es amostrais em r\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/statorials.org\/pt\/#website\",\"url\":\"https:\/\/statorials.org\/pt\/\",\"name\":\"Statorials\",\"description\":\"O seu guia para a literacia estat\u00edstica!\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/statorials.org\/pt\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"pt-PT\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/statorials.org\/pt\/#\/schema\/person\/e08f98e8db95e0aa9c310e1b27c9c666\",\"name\":\"Dr. benjamim anderson\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"pt-PT\",\"@id\":\"https:\/\/statorials.org\/pt\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/statorials.org\/pt\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"contentUrl\":\"https:\/\/statorials.org\/pt\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"caption\":\"Dr. benjamim anderson\"},\"description\":\"Ol\u00e1, sou Benjamin, um professor aposentado de estat\u00edstica que se tornou professor dedicado na Statorials. 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