{"id":864,"date":"2023-07-28T12:11:13","date_gmt":"2023-07-28T12:11:13","guid":{"rendered":"https:\/\/statorials.org\/pt\/intervalos-de-confianca-python\/"},"modified":"2023-07-28T12:11:13","modified_gmt":"2023-07-28T12:11:13","slug":"intervalos-de-confianca-python","status":"publish","type":"post","link":"https:\/\/statorials.org\/pt\/intervalos-de-confianca-python\/","title":{"rendered":"Como calcular intervalos de confian\u00e7a em python"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">Um <strong>intervalo de confian\u00e7a para uma m\u00e9dia<\/strong> \u00e9 um intervalo de valores que provavelmente cont\u00e9m uma m\u00e9dia populacional com um certo n\u00edvel de confian\u00e7a.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00c9 calculado da seguinte forma:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Intervalo de confian\u00e7a =<\/strong> <strong><span style=\"text-decoration: overline;\">x<\/span> +\/- t*(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\u00e9dia amostral<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>t:<\/strong> valor t que corresponde ao 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;\">Este tutorial explica como calcular intervalos de confian\u00e7a em Python.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Intervalos de confian\u00e7a usando a distribui\u00e7\u00e3o t<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Se estivermos trabalhando com uma amostra pequena (n &lt;30), podemos usar a <a href=\"https:\/\/docs.scipy.org\/doc\/scipy\/reference\/generated\/scipy.stats.t.html\" target=\"_blank\" rel=\"noopener\">fun\u00e7\u00e3o t.interval()<\/a> da biblioteca scipy.stats para calcular um intervalo de confian\u00e7a para uma m\u00e9dia populacional.<\/span><\/p>\n<p> <span style=\"color: #000000;\">O exemplo a seguir mostra como calcular um intervalo de confian\u00e7a para a altura m\u00e9dia real da popula\u00e7\u00e3o (em polegadas) de uma determinada esp\u00e9cie de planta, usando uma amostra de 15 plantas:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #107d3f;\">import<\/span> numpy <span style=\"color: #107d3f;\">as<\/span> np\n<span style=\"color: #107d3f;\">import<\/span> scipy.stats <span style=\"color: #107d3f;\">as<\/span> st\n\n<span style=\"color: #008080;\">#define sample data<\/span>\ndata = [12, 12, 13, 13, 15, 16, 17, 22, 23, 25, 26, 27, 28, 28, 29]\n\n<span style=\"color: #008080;\">#create 95% confidence interval for population mean weight\n<\/span>st.t.interval(alpha=0.95, df=len(data)-1, loc=np.mean(data), scale=st.sem(data)) \n\n(16.758, 24.042)<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">O intervalo de confian\u00e7a de 95% para o verdadeiro tamanho m\u00e9dio da popula\u00e7\u00e3o \u00e9 <strong>(16,758, 24,042)<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Voc\u00ea notar\u00e1 que quanto maior o n\u00edvel de confian\u00e7a, maior ser\u00e1 o intervalo de confian\u00e7a. Por exemplo, veja como calcular um IC de 99% para exatamente os mesmos dados:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#create 99% confidence interval for same sample\n<\/span>st.t.interval(alpha= <span style=\"color: #008000;\">0.99<\/span> , df=len(data)-1, loc=np.mean(data), scale=st.sem(data)) \n\n(15.348, 25.455)<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">O intervalo de confian\u00e7a de 99% para o verdadeiro tamanho m\u00e9dio da popula\u00e7\u00e3o \u00e9 <strong>(15,348, 25,455)<\/strong> . Observe que esse intervalo \u00e9 maior que o intervalo de confian\u00e7a anterior de 95%.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Intervalos de confian\u00e7a usando a distribui\u00e7\u00e3o normal<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Se estivermos trabalhando com amostras maiores (n\u226530), podemos assumir que a distribui\u00e7\u00e3o amostral da m\u00e9dia amostral \u00e9 normalmente distribu\u00edda (gra\u00e7as ao <a href=\"https:\/\/statorials.org\/pt\/teorema-do-limite-central\/\" target=\"_blank\" rel=\"noopener\">teorema do limite central<\/a> ) e podemos, em vez disso, usar a <a href=\"https:\/\/docs.scipy.org\/doc\/scipy\/reference\/generated\/scipy.stats.norm.html\" target=\"_blank\" rel=\"noopener\">fun\u00e7\u00e3o norma. interval()<\/a> da biblioteca scipy .stats.<\/span><\/p>\n<p> <span style=\"color: #000000;\">O exemplo a seguir mostra como calcular um intervalo de confian\u00e7a para a altura m\u00e9dia real da popula\u00e7\u00e3o (em polegadas) de uma determinada esp\u00e9cie de planta, usando uma amostra de 50 plantas:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #107d3f;\">import<\/span> numpy <span style=\"color: #107d3f;\">as<\/span> np\n<span style=\"color: #107d3f;\">import<\/span> scipy.stats <span style=\"color: #107d3f;\">as<\/span> st\n\n<span style=\"color: #008080;\">#define sample data<\/span>\nnp.random.seed(0)\ndata = np.random.randint(10, 30, 50)\n\n<span style=\"color: #008080;\">#create 95% confidence interval for population mean weight\n<\/span>st.norm.interval(alpha=0.95, loc=np.mean(data), scale=st.sem(data))\n\n(17.40, 21.08)<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">O intervalo de confian\u00e7a de 95% para o verdadeiro tamanho m\u00e9dio da popula\u00e7\u00e3o \u00e9 <strong>(17,40, 21,08)<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">E tal como acontece com a distribui\u00e7\u00e3o t, n\u00edveis de confian\u00e7a mais elevados levam a intervalos de confian\u00e7a mais amplos. Por exemplo, veja como calcular um IC de 99% para exatamente os mesmos dados:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#create 99% confidence interval for same sample\n<\/span>st.norm.interval(alpha= <span style=\"color: #008000;\">0.99<\/span> , loc=np.mean(data), scale=st.sem(data))\n\n(16.82, 21.66)<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">O intervalo de confian\u00e7a de 95% para o verdadeiro tamanho m\u00e9dio da popula\u00e7\u00e3o \u00e9 <strong>(17,82, 21,66)<\/strong> .<\/span><\/p>\n<h3> <strong><span style=\"color: #000000;\">Como interpretar intervalos de confian\u00e7a<\/span><\/strong><\/h3>\n<p> <span style=\"color: #000000;\">Suponha que nosso intervalo de confian\u00e7a de 95% para a altura m\u00e9dia real de uma esp\u00e9cie de planta seja:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Intervalo de confian\u00e7a de 95% = (16,758, 24,042)<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">A forma de interpretar este intervalo de confian\u00e7a \u00e9 a seguinte:<\/span><\/p>\n<blockquote data-slot-rendered-dynamic=\"true\">\n<p> <span style=\"color: #000000;\">H\u00e1 95% de chance de que o intervalo de confian\u00e7a de [16,758, 24,042] contenha a verdadeira altura m\u00e9dia das plantas da popula\u00e7\u00e3o.<\/span><\/p>\n<\/blockquote>\n<p> <span style=\"color: #000000;\">Outra maneira de dizer a mesma coisa \u00e9 que h\u00e1 apenas 5% de probabilidade de que a verdadeira m\u00e9dia da popula\u00e7\u00e3o esteja fora do intervalo de confian\u00e7a de 95%. Ou seja, h\u00e1 apenas 5% de chance de que a altura m\u00e9dia real da planta seja inferior a 16,758 polegadas ou superior a 24,042 polegadas.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Um intervalo de confian\u00e7a para uma m\u00e9dia \u00e9 um intervalo de valores que provavelmente cont\u00e9m uma m\u00e9dia populacional com um certo n\u00edvel de confian\u00e7a. \u00c9 calculado da seguinte forma: Intervalo de confian\u00e7a = x +\/- t*(s\/\u221an) Ouro: x : m\u00e9dia amostral t: valor t que corresponde ao n\u00edvel de confian\u00e7a s: desvio padr\u00e3o da amostra [&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-864","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 intervalos de confian\u00e7a em Python - Estatologia<\/title>\n<meta name=\"description\" content=\"Uma explica\u00e7\u00e3o simples sobre como calcular intervalos de confian\u00e7a em Python.\" \/>\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\/intervalos-de-confianca-python\/\" \/>\n<meta property=\"og:locale\" content=\"pt_PT\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Como calcular intervalos de confian\u00e7a em Python - Estatologia\" \/>\n<meta property=\"og:description\" content=\"Uma explica\u00e7\u00e3o simples sobre como calcular intervalos de confian\u00e7a em Python.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pt\/intervalos-de-confianca-python\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-28T12:11:13+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=\"3 minutos\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/pt\/intervalos-de-confianca-python\/\",\"url\":\"https:\/\/statorials.org\/pt\/intervalos-de-confianca-python\/\",\"name\":\"Como calcular intervalos de confian\u00e7a em Python - Estatologia\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pt\/#website\"},\"datePublished\":\"2023-07-28T12:11:13+00:00\",\"dateModified\":\"2023-07-28T12:11:13+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/pt\/#\/schema\/person\/e08f98e8db95e0aa9c310e1b27c9c666\"},\"description\":\"Uma explica\u00e7\u00e3o simples sobre como calcular intervalos de confian\u00e7a em Python.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pt\/intervalos-de-confianca-python\/#breadcrumb\"},\"inLanguage\":\"pt-PT\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pt\/intervalos-de-confianca-python\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pt\/intervalos-de-confianca-python\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Lar\",\"item\":\"https:\/\/statorials.org\/pt\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Como calcular intervalos de confian\u00e7a em python\"}]},{\"@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. Com vasta experi\u00eancia e conhecimento na \u00e1rea de estat\u00edstica, estou empenhado em compartilhar meu conhecimento para capacitar os alunos por meio de Statorials. Saber mais\",\"sameAs\":[\"https:\/\/statorials.org\/pt\"]}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Como calcular intervalos de confian\u00e7a em Python - Estatologia","description":"Uma explica\u00e7\u00e3o simples sobre como calcular intervalos de confian\u00e7a em Python.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/statorials.org\/pt\/intervalos-de-confianca-python\/","og_locale":"pt_PT","og_type":"article","og_title":"Como calcular intervalos de confian\u00e7a em Python - Estatologia","og_description":"Uma explica\u00e7\u00e3o simples sobre como calcular intervalos de confian\u00e7a em Python.","og_url":"https:\/\/statorials.org\/pt\/intervalos-de-confianca-python\/","og_site_name":"Statorials","article_published_time":"2023-07-28T12:11:13+00:00","author":"Dr. benjamim anderson","twitter_card":"summary_large_image","twitter_misc":{"Escrito por":"Dr. benjamim anderson","Tempo estimado de leitura":"3 minutos"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/statorials.org\/pt\/intervalos-de-confianca-python\/","url":"https:\/\/statorials.org\/pt\/intervalos-de-confianca-python\/","name":"Como calcular intervalos de confian\u00e7a em Python - Estatologia","isPartOf":{"@id":"https:\/\/statorials.org\/pt\/#website"},"datePublished":"2023-07-28T12:11:13+00:00","dateModified":"2023-07-28T12:11:13+00:00","author":{"@id":"https:\/\/statorials.org\/pt\/#\/schema\/person\/e08f98e8db95e0aa9c310e1b27c9c666"},"description":"Uma explica\u00e7\u00e3o simples sobre como calcular intervalos de confian\u00e7a em Python.","breadcrumb":{"@id":"https:\/\/statorials.org\/pt\/intervalos-de-confianca-python\/#breadcrumb"},"inLanguage":"pt-PT","potentialAction":[{"@type":"ReadAction","target":["https:\/\/statorials.org\/pt\/intervalos-de-confianca-python\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/statorials.org\/pt\/intervalos-de-confianca-python\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Lar","item":"https:\/\/statorials.org\/pt\/"},{"@type":"ListItem","position":2,"name":"Como calcular intervalos de confian\u00e7a em python"}]},{"@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. Com vasta experi\u00eancia e conhecimento na \u00e1rea de estat\u00edstica, estou empenhado em compartilhar meu conhecimento para capacitar os alunos por meio de Statorials. Saber mais","sameAs":["https:\/\/statorials.org\/pt"]}]}},"yoast_meta":{"yoast_wpseo_title":"","yoast_wpseo_metadesc":"","yoast_wpseo_canonical":""},"_links":{"self":[{"href":"https:\/\/statorials.org\/pt\/wp-json\/wp\/v2\/posts\/864","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/statorials.org\/pt\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/statorials.org\/pt\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/statorials.org\/pt\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/statorials.org\/pt\/wp-json\/wp\/v2\/comments?post=864"}],"version-history":[{"count":0,"href":"https:\/\/statorials.org\/pt\/wp-json\/wp\/v2\/posts\/864\/revisions"}],"wp:attachment":[{"href":"https:\/\/statorials.org\/pt\/wp-json\/wp\/v2\/media?parent=864"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/statorials.org\/pt\/wp-json\/wp\/v2\/categories?post=864"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/statorials.org\/pt\/wp-json\/wp\/v2\/tags?post=864"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}