{"id":932,"date":"2023-07-28T06:40:51","date_gmt":"2023-07-28T06:40:51","guid":{"rendered":"https:\/\/statorials.org\/pt\/desvio-padrao-vs-erro-padrao\/"},"modified":"2023-07-28T06:40:51","modified_gmt":"2023-07-28T06:40:51","slug":"desvio-padrao-vs-erro-padrao","status":"publish","type":"post","link":"https:\/\/statorials.org\/pt\/desvio-padrao-vs-erro-padrao\/","title":{"rendered":"Desvio padr\u00e3o e erro padr\u00e3o: qual a diferen\u00e7a?"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">Dois termos que os alunos costumam confundir em estat\u00edstica s\u00e3o <strong>desvio padr\u00e3o<\/strong> e <strong>erro padr\u00e3o<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>O desvio padr\u00e3o<\/strong> mede a distribui\u00e7\u00e3o de valores em um conjunto de dados.<\/span><\/p>\n<p> <span style=\"color: #000000;\">O <strong>erro padr\u00e3o<\/strong> \u00e9 o desvio padr\u00e3o da m\u00e9dia de amostras repetidas de uma popula\u00e7\u00e3o.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Vejamos um exemplo para ilustrar claramente essa ideia.<\/span><\/p>\n<h2> <strong>Exemplo: desvio padr\u00e3o versus erro padr\u00e3o<\/strong><\/h2>\n<p> <span style=\"color: #000000;\">Suponha que medimos o peso de 10 tartarugas diferentes.<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-9896 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/standard_dev_vs_standard_error1.png\" alt=\"\" width=\"492\" height=\"122\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Para esta amostra de 10 tartarugas, podemos calcular a m\u00e9dia amostral e o desvio padr\u00e3o amostral:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-9899 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/standard_dev_vs_standard_error2-1.png\" alt=\"\" width=\"492\" height=\"129\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Suponha que o desvio padr\u00e3o seja 8,68. Isso nos d\u00e1 uma ideia da distribui\u00e7\u00e3o de peso dessas tartarugas.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Mas suponhamos que recolhamos outra <a href=\"https:\/\/statorials.org\/pt\/metodos-de-amostragem\/\" target=\"_blank\" rel=\"noopener noreferrer\">amostra aleat\u00f3ria simples<\/a> de 10 tartarugas e tamb\u00e9m fa\u00e7amos as suas medi\u00e7\u00f5es.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00c9 mais do que prov\u00e1vel que esta amostra de 10 tartarugas tenha uma m\u00e9dia e um desvio padr\u00e3o ligeiramente diferentes, embora venham da mesma popula\u00e7\u00e3o:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-9900 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/standard_dev_vs_standard_error3.png\" alt=\"\" width=\"498\" height=\"132\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Agora, se imaginarmos que pegamos amostras repetidas da mesma popula\u00e7\u00e3o e registramos a m\u00e9dia amostral e o desvio padr\u00e3o amostral para cada amostra:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-9901 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/standard_dev_vs_standard_error4.png\" alt=\"\" width=\"492\" height=\"144\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Agora imagine que plotamos cada uma das m\u00e9dias amostrais na mesma linha:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-9902 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/standard_dev_vs_standard_error5.png\" alt=\"\" width=\"480\" height=\"126\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\"><strong>O desvio padr\u00e3o dessas m\u00e9dias \u00e9 chamado de erro padr\u00e3o.<\/strong><\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-9903 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/standard_dev_vs_standard_error6.png\" alt=\"\" width=\"490\" height=\"117\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">A f\u00f3rmula para realmente calcular o erro padr\u00e3o \u00e9:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Erro padr\u00e3o = s\/ \u221a <span style=\"border-top: 1px solid black;\">n<\/span><\/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<h2> <span style=\"color: #000000;\"><strong>Qual \u00e9 o sentido de usar o erro padr\u00e3o?<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Quando calculamos a m\u00e9dia de uma determinada amostra, n\u00e3o estamos realmente procurando saber a m\u00e9dia dessa amostra espec\u00edfica, mas sim a m\u00e9dia da popula\u00e7\u00e3o maior da qual prov\u00e9m a amostra.<\/span><\/p>\n<p> <span style=\"color: #000000;\">No entanto, utilizamos amostras porque \u00e9 muito mais f\u00e1cil recolher dados para elas do que para uma popula\u00e7\u00e3o inteira.<\/span><\/p>\n<p> <span style=\"color: #000000;\">E, claro, a m\u00e9dia amostral varia de amostra para amostra, por isso utilizamos o <strong>erro padr\u00e3o da m\u00e9dia<\/strong> como forma de medir a precis\u00e3o da nossa estimativa da m\u00e9dia.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Voc\u00ea notar\u00e1 na f\u00f3rmula de c\u00e1lculo do erro padr\u00e3o que \u00e0 medida que o tamanho da amostra (n) aumenta, o erro padr\u00e3o diminui:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Erro padr\u00e3o = s\/ \u221a <span style=\"border-top: 1px solid black;\">n<\/span><\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Isto deve fazer sentido, porque amostras maiores reduzem a variabilidade e aumentam a probabilidade de a nossa m\u00e9dia amostral estar mais pr\u00f3xima da verdadeira m\u00e9dia populacional.<\/span><\/p>\n<h2> <strong><span style=\"color: #000000;\">Quando usar o desvio padr\u00e3o versus erro padr\u00e3o<\/span><\/strong><\/h2>\n<p> <span style=\"color: #000000;\">Se quisermos simplesmente medir a distribui\u00e7\u00e3o de valores em um conjunto de dados, podemos usar <strong>o desvio padr\u00e3o<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Contudo, se quisermos quantificar a incerteza em torno de uma estimativa da m\u00e9dia, podemos utilizar o <strong>erro padr\u00e3o da m\u00e9dia<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Dependendo do seu cen\u00e1rio espec\u00edfico e do que voc\u00ea est\u00e1 tentando realizar, voc\u00ea pode optar por usar o desvio padr\u00e3o ou o erro padr\u00e3o.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Dois termos que os alunos costumam confundir em estat\u00edstica s\u00e3o desvio padr\u00e3o e erro padr\u00e3o . O desvio padr\u00e3o mede a distribui\u00e7\u00e3o de valores em um conjunto de dados. O erro padr\u00e3o \u00e9 o desvio padr\u00e3o da m\u00e9dia de amostras repetidas de uma popula\u00e7\u00e3o. Vejamos um exemplo para ilustrar claramente essa ideia. Exemplo: desvio padr\u00e3o [&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-932","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>Desvio padr\u00e3o e erro padr\u00e3o: qual a diferen\u00e7a?<\/title>\n<meta name=\"description\" content=\"Uma explica\u00e7\u00e3o simples da diferen\u00e7a entre desvio padr\u00e3o 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\/desvio-padrao-vs-erro-padrao\/\" \/>\n<meta property=\"og:locale\" content=\"pt_PT\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Desvio padr\u00e3o e erro padr\u00e3o: qual a diferen\u00e7a?\" \/>\n<meta property=\"og:description\" content=\"Uma explica\u00e7\u00e3o simples da diferen\u00e7a entre desvio padr\u00e3o e erro padr\u00e3o, com um exemplo.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pt\/desvio-padrao-vs-erro-padrao\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-28T06:40:51+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/standard_dev_vs_standard_error1.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=\"2 minutos\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/pt\/desvio-padrao-vs-erro-padrao\/\",\"url\":\"https:\/\/statorials.org\/pt\/desvio-padrao-vs-erro-padrao\/\",\"name\":\"Desvio padr\u00e3o e erro padr\u00e3o: qual a diferen\u00e7a?\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pt\/#website\"},\"datePublished\":\"2023-07-28T06:40:51+00:00\",\"dateModified\":\"2023-07-28T06:40:51+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/pt\/#\/schema\/person\/e08f98e8db95e0aa9c310e1b27c9c666\"},\"description\":\"Uma explica\u00e7\u00e3o simples da diferen\u00e7a entre desvio padr\u00e3o e erro padr\u00e3o, com um exemplo.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pt\/desvio-padrao-vs-erro-padrao\/#breadcrumb\"},\"inLanguage\":\"pt-PT\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pt\/desvio-padrao-vs-erro-padrao\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pt\/desvio-padrao-vs-erro-padrao\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Lar\",\"item\":\"https:\/\/statorials.org\/pt\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Desvio padr\u00e3o e 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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