{"id":933,"date":"2023-07-28T06:38:23","date_gmt":"2023-07-28T06:38:23","guid":{"rendered":"https:\/\/statorials.org\/pt\/margem-de-erro-vs-erro-padrao-qual-e-a-diferenca\/"},"modified":"2023-07-28T06:38:23","modified_gmt":"2023-07-28T06:38:23","slug":"margem-de-erro-vs-erro-padrao-qual-e-a-diferenca","status":"publish","type":"post","link":"https:\/\/statorials.org\/pt\/margem-de-erro-vs-erro-padrao-qual-e-a-diferenca\/","title":{"rendered":"Margem de erro versus erro padr\u00e3o: qual a diferen\u00e7a?"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">Dois termos que os estudantes muitas vezes confundem em estat\u00edstica s\u00e3o <strong>erro padr\u00e3o<\/strong> e <strong>margem de erro<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">O <strong>erro padr\u00e3o<\/strong> mede a precis\u00e3o de uma estimativa da m\u00e9dia populacional. \u00c9 calculado da seguinte forma:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Erro padr\u00e3o = s \/ \u221an<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Ouro:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>s:<\/strong> desvio padr\u00e3o da amostra<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>n:<\/strong> tamanho da amostra<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">A <strong>margem de erro<\/strong> mede a metade de um <a href=\"https:\/\/statorials.org\/pt\/intervalo-de-confianca-medio\/\" target=\"_blank\" rel=\"noopener noreferrer\">intervalo de confian\u00e7a para uma m\u00e9dia populacional<\/a> . \u00c9 calculado da seguinte forma:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Margem de erro = z*(s\/\u221an)<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Ouro:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>z:<\/strong> valor Z que corresponde a um determinado n\u00edvel de confian\u00e7a<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>s:<\/strong> desvio padr\u00e3o da amostra<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>n:<\/strong> tamanho da amostra<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Vejamos um exemplo para ilustrar essa ideia.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Exemplo: margem de erro comparada ao erro padr\u00e3o<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Suponha que coletamos uma amostra aleat\u00f3ria de tartarugas com as seguintes informa\u00e7\u00f5es:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Tamanho da amostra <strong>n = 25<\/strong><\/span><\/li>\n<li> <span style=\"color: #000000;\">Peso m\u00e9dio da amostra <strong>x = 300<\/strong><\/span><\/li>\n<li> <span style=\"color: #000000;\">Desvio padr\u00e3o amostral <strong>s = 18,5<\/strong><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Agora suponhamos que queremos criar um intervalo de confian\u00e7a de 95% para o verdadeiro peso m\u00e9dio da popula\u00e7\u00e3o de tartarugas. A f\u00f3rmula para calcular esse intervalo de confian\u00e7a \u00e9 a seguinte:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Intervalo de confian\u00e7a = <span style=\"text-decoration: overline;\">x<\/span> +\/- z*(s\/\u221an)<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Ouro:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong><span style=\"text-decoration: overline;\">x<\/span> :<\/strong> m\u00e9dias amostrais<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>s:<\/strong> desvio padr\u00e3o da amostra<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>n:<\/strong> tamanho da amostra<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>z:<\/strong> valor Z que corresponde a um determinado n\u00edvel de confian\u00e7a<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">O valor z usado depende do n\u00edvel de confian\u00e7a escolhido. A tabela a seguir mostra o valor z que corresponde \u00e0s op\u00e7\u00f5es de n\u00edvel de confian\u00e7a mais comuns:<\/span><\/p>\n<table>\n<tbody>\n<tr>\n<th> <span style=\"color: #000000;\"><strong>Um n\u00edvel de confian\u00e7a<\/strong><\/span><\/th>\n<th> <span style=\"color: #000000;\"><strong>valor z<\/strong><\/span><\/th>\n<\/tr>\n<tr>\n<td> <span style=\"color: #000000;\">0,90<\/span><\/td>\n<td> <span style=\"color: #000000;\">1.645<\/span><\/td>\n<\/tr>\n<tr>\n<td> <span style=\"color: #000000;\">0,95<\/span><\/td>\n<td> <span style=\"color: #000000;\">1,96<\/span><\/td>\n<\/tr>\n<tr>\n<td> <span style=\"color: #000000;\">0,99<\/span><\/td>\n<td> <span style=\"color: #000000;\">2,58<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p> <span style=\"color: #000000;\">Observe que n\u00edveis de confian\u00e7a mais elevados correspondem a valores z maiores, o que leva a intervalos de confian\u00e7a mais amplos. Isto significa que, por exemplo, um intervalo de confian\u00e7a de 99% ser\u00e1 maior do que um intervalo de confian\u00e7a de 95% para o mesmo conjunto de dados.<\/span><\/p>\n<p> <span style=\"color: #000000;\">O <strong>erro padr\u00e3o<\/strong> seria calculado da seguinte forma:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <span style=\"color: #000000;\"><strong>Standard error<\/strong> = s\/\u221an = 18.5\/\u221a25 = <strong>3.7<\/strong><\/span><\/pre>\n<p> <span style=\"color: #000000;\">A <strong>margem de erro<\/strong> seria calculada da seguinte forma<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <span style=\"color: #000000;\"><strong>Margin of error<\/strong> = z*(s\/\u221an) = 1.96*(18.5\/\u221a25) = <strong>7.25<\/strong><\/span><\/pre>\n<p> <span style=\"color: #000000;\">E o intervalo de confian\u00e7a de 95% seria calculado da seguinte forma:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <span style=\"color: #000000;\"><strong>95% Confidence Interval<\/strong> = <span style=\"text-decoration: overline;\">x<\/span> +\/- z*(s\/\u221an) = 300 +\/- 1.96*(18.5\/\u221a25) = <strong>[292.75, 307.25]<\/strong><\/span><\/pre>\n<p> <span style=\"color: #000000;\"><span style=\"color: #000000;\">Observe que a largura de todo o intervalo de confian\u00e7a \u00e9 307,25 \u2013 292,75 = <strong>14,5<\/strong> .<\/span><\/span><\/p>\n<p> <span style=\"color: #000000;\"><span style=\"color: #000000;\">Observe que a margem de erro \u00e9 igual \u00e0 metade dessa largura: 14,5 \/ 2 = <strong>7,25<\/strong> .<\/span><\/span><\/p>\n<p> <span style=\"color: #000000;\">Observe tamb\u00e9m que a margem de erro ser\u00e1 sempre maior que o erro padr\u00e3o simplesmente porque a margem de erro \u00e9 igual ao erro padr\u00e3o vezes um valor cr\u00edtico de Z. No exemplo anterior, multiplicamos o erro padr\u00e3o por 1,96 para obter a margem de erro.<\/span><\/p>\n<h3> <strong><span style=\"color: #000000;\">Recursos<\/span> <span style=\"color: #000000;\">Adicionais<\/span><\/strong><\/h3>\n<p> <a href=\"https:\/\/statorials.org\/pt\/intervalos-de-confianca\/\" target=\"_blank\" rel=\"noopener noreferrer\">O que s\u00e3o intervalos de confian\u00e7a?<\/a><br \/> <a href=\"https:\/\/statorials.org\/pt\/desvio-padrao-vs-erro-padrao\/\" target=\"_blank\" rel=\"noopener noreferrer\">Desvio padr\u00e3o e erro padr\u00e3o: qual a diferen\u00e7a?<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Dois termos que os estudantes muitas vezes confundem em estat\u00edstica s\u00e3o erro padr\u00e3o e margem de erro . O erro padr\u00e3o mede a precis\u00e3o de uma estimativa da m\u00e9dia populacional. \u00c9 calculado da seguinte forma: Erro padr\u00e3o = s \/ \u221an Ouro: s: desvio padr\u00e3o da amostra n: tamanho da amostra A margem de erro [&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-933","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>Margem de erro versus erro padr\u00e3o: qual a diferen\u00e7a?<\/title>\n<meta name=\"description\" content=\"Uma explica\u00e7\u00e3o simples da diferen\u00e7a entre margem de erro e erro padr\u00e3o, com um exemplo.\" \/>\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\/margem-de-erro-vs-erro-padrao-qual-e-a-diferenca\/\" \/>\n<meta property=\"og:locale\" content=\"pt_PT\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Margem de erro versus erro padr\u00e3o: qual a diferen\u00e7a?\" \/>\n<meta property=\"og:description\" content=\"Uma explica\u00e7\u00e3o simples da diferen\u00e7a entre margem de erro e erro padr\u00e3o, com um exemplo.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pt\/margem-de-erro-vs-erro-padrao-qual-e-a-diferenca\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-28T06:38:23+00:00\" \/>\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=\"2 minutos\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/pt\/margem-de-erro-vs-erro-padrao-qual-e-a-diferenca\/\",\"url\":\"https:\/\/statorials.org\/pt\/margem-de-erro-vs-erro-padrao-qual-e-a-diferenca\/\",\"name\":\"Margem de erro versus erro padr\u00e3o: qual a diferen\u00e7a?\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pt\/#website\"},\"datePublished\":\"2023-07-28T06:38:23+00:00\",\"dateModified\":\"2023-07-28T06:38:23+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/pt\/#\/schema\/person\/e08f98e8db95e0aa9c310e1b27c9c666\"},\"description\":\"Uma explica\u00e7\u00e3o simples da diferen\u00e7a entre margem de erro e erro padr\u00e3o, com um exemplo.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pt\/margem-de-erro-vs-erro-padrao-qual-e-a-diferenca\/#breadcrumb\"},\"inLanguage\":\"pt-PT\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pt\/margem-de-erro-vs-erro-padrao-qual-e-a-diferenca\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pt\/margem-de-erro-vs-erro-padrao-qual-e-a-diferenca\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Lar\",\"item\":\"https:\/\/statorials.org\/pt\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Margem de erro versus erro padr\u00e3o: qual a diferen\u00e7a?\"}]},{\"@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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