{"id":525,"date":"2023-07-29T15:03:25","date_gmt":"2023-07-29T15:03:25","guid":{"rendered":"https:\/\/statorials.org\/pt\/distribuicao-de-intervalo-de-confianca-f\/"},"modified":"2023-07-29T15:03:25","modified_gmt":"2023-07-29T15:03:25","slug":"distribuicao-de-intervalo-de-confianca-f","status":"publish","type":"post","link":"https:\/\/statorials.org\/pt\/distribuicao-de-intervalo-de-confianca-f\/","title":{"rendered":"Como criar um intervalo de confian\u00e7a usando a distribui\u00e7\u00e3o f"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">Para determinar se as vari\u00e2ncias de duas popula\u00e7\u00f5es s\u00e3o iguais, podemos calcular a raz\u00e3o de vari\u00e2ncia <strong>\u03c3 <sup>2<\/sup> <sub>1<\/sub> \/ \u03c3 <sup>2<\/sup> <sub>2<\/sub><\/strong> , onde \u03c3 <sup>2<\/sup> <sub>1<\/sub> \u00e9 a vari\u00e2ncia da popula\u00e7\u00e3o 1 e \u03c3 <sup>2<\/sup> <sub>2<\/sub> \u00e9 a vari\u00e2ncia da popula\u00e7\u00e3o 2.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Para estimar a verdadeira raz\u00e3o de vari\u00e2ncia populacional, geralmente pegamos uma <a href=\"https:\/\/statorials.org\/pt\/metodos-de-amostragem\/\" target=\"_blank\" rel=\"noopener\">amostra aleat\u00f3ria simples<\/a> de cada popula\u00e7\u00e3o e calculamos a raz\u00e3o de vari\u00e2ncia amostral, <strong>s <sub>1<\/sub> <sup>2<\/sup> \/ s <sub>2<\/sub> <sup>2<\/sup><\/strong> , onde s <sub>1<\/sub> <sup>2<\/sup> e s <sub>2<\/sub> <sup>2<\/sup> s\u00e3o as vari\u00e2ncias amostrais para a amostra 1 e a amostra . 2, respectivamente.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Este teste assume que s <sub>1<\/sub> <sup>2<\/sup> e s <sub>2<\/sub> <sup>2<\/sup> s\u00e3o calculados a partir de amostras independentes de tamanho n <sub>1<\/sub> e n <sub>2<\/sub> , ambas de popula\u00e7\u00f5es normalmente distribu\u00eddas.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Quanto mais longe este r\u00e1cio estiver de um, mais forte ser\u00e1 a evid\u00eancia de varia\u00e7\u00f5es desiguais dentro da popula\u00e7\u00e3o.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>O intervalo de confian\u00e7a (1-\u03b1)100%<\/strong> para \u03c3 <sup>2<\/sup> <sub>1<\/sub> \/ \u03c3 <sup>2<\/sup> <sub>2<\/sub> \u00e9 definido como:<\/span><\/p>\n<p style=\"text-align: center;\"> <span style=\"color: #000000;\">(s <sub>1<\/sub> <sup>2<\/sup> \/ s <sub>2<\/sub> <sup>2<\/sup> ) * F <sub>n <sub>1<\/sub> -1, n <sub>2<\/sub> -1, \u03b1\/2<\/sub> \u2264 \u03c3 <sup>2<\/sup> <sub>1<\/sub> \/ \u03c3 <sup>2<\/sup> <sub>2<\/sub> \u2264 (s <sub>1<\/sub> <sup>2<\/sup> \/ s <sub>2<\/sub> <sup>2<\/sup> ) * F <sub>n <sub>2<\/sub> -1, n <sub>1<\/sub> -1,<\/sub> <sub>\u03b1\/2<\/sub><\/span><\/p>\n<p> <span style=\"color: #000000;\">onde F <sub>n <sub>2<\/sub> -1, n <sub>1<\/sub> -1, \u03b1\/2<\/sub> e F <sub>n <sub>1<\/sub> -1, n <sub>2<\/sub> -1,<\/sub> <sub>\u03b1\/2<\/sub> <sub>&nbsp;<\/sub> s\u00e3o os valores cr\u00edticos da distribui\u00e7\u00e3o F para o n\u00edvel de signific\u00e2ncia \u03b1 escolhido.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Os exemplos a seguir ilustram como criar um intervalo de confian\u00e7a para \u03c3 <sup>2<\/sup> <sub>1<\/sub> \/ \u03c3 <sup>2<\/sup> <sub>2<\/sub> usando tr\u00eas m\u00e9todos diferentes:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Pela m\u00e3o<\/span><\/li>\n<li> <span style=\"color: #000000;\">Utilize o Microsoft Excel<\/span><\/li>\n<li> <span style=\"color: #000000;\">Uso de software estat\u00edstico <em>R<\/em><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Para cada um dos exemplos a seguir, usaremos as seguintes informa\u00e7\u00f5es:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>\u03b1<\/strong> = 0,05<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>n <sub>1<\/sub><\/strong> = 16<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong><sub>n2<\/sub><\/strong> = 11<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>s <sub>1<\/sub> <sup>2<\/sup><\/strong> =28,2<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>s <sub>2<\/sub> <sup>2<\/sup><\/strong> = 19,3<\/span><\/li>\n<\/ul>\n<h2> <span style=\"color: #000000;\"><strong>Criando manualmente um intervalo de confian\u00e7a<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Para calcular manualmente um intervalo de confian\u00e7a para <strong>\u03c3 <sup>2<\/sup> <sub>1<\/sub> \/ \u03c3 <sup>2<\/sup> <sub>2<\/sub><\/strong> , simplesmente inseriremos os n\u00fameros que temos na f\u00f3rmula do intervalo de confian\u00e7a:<\/span><\/p>\n<p style=\"text-align: center;\"> <span style=\"color: #000000;\">(s <sub>1<\/sub> <sup>2<\/sup> \/ s <sub>2<\/sub> <sup>2<\/sup> ) * F <sub>n1-1, n2-1,\u03b1\/2<\/sub> \u2264 \u03c3 <sup>2<\/sup> <sub>1<\/sub> \/ \u03c3 <sup>2<\/sup> <sub>2<\/sub> \u2264 (s <sub>1<\/sub> <sup>2<\/sup> \/ s <sub>2<\/sub> <sup>2<\/sup> ) * F <sub>n2-1, n1-1,<\/sub> <sub>\u03b1\/2<\/sub><\/span><\/p>\n<p> <span style=\"color: #000000;\">Os \u00fanicos n\u00fameros que faltam s\u00e3o os valores cr\u00edticos.<\/span> <span style=\"color: #000000;\">Felizmente, podemos localizar esses valores cr\u00edticos <a href=\"https:\/\/statorials.org\/pt\/tabela-de-distribuicao-f\/\" target=\"_blank\" rel=\"noopener\">na tabela de distribui\u00e7\u00e3o F<\/a> :<\/span><\/p>\n<p> <span style=\"color: #000000;\">F <sub>n2-1, n1-1, \u03b1\/2<\/sub> = F <sub>10, 15, 0,025<\/sub> = <strong>3,0602<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">F <sub>n1-1, n2-1,<\/sub> <sub>\u03b1\/2<\/sub> = 1\/ F <sub>15, 10, 0,025<\/sub> = 1 \/ 3,5217 = <strong>0,2839<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><em>(Clique para ampliar a tabela)<\/em><\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-489 size-full\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/f2.5.png\" alt=\"Tabela de distribui\u00e7\u00e3o F para alfa = 0,025.\" width=\"1361\" height=\"829\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Agora podemos inserir todos os n\u00fameros no intervalo da f\u00f3rmula de confian\u00e7a:<\/span><\/p>\n<p style=\"text-align: center;\"> <span style=\"color: #000000;\">(s <sub>1<\/sub> <sup>2<\/sup> \/ s <sub>2<\/sub> <sup>2<\/sup> ) * F <sub>n1-1, n2-1,\u03b1\/2<\/sub> \u2264 \u03c3 <sup>2<\/sup> <sub>1<\/sub> \/ \u03c3 <sup>2<\/sup> <sub>2<\/sub> \u2264 (s <sub>1<\/sub> <sup>2<\/sup> \/ s <sub>2<\/sub> <sup>2<\/sup> ) * F <sub>n2-1, n1-1,<\/sub> <sub>\u03b1\/2<\/sub><\/span><\/p>\n<p style=\"text-align: center;\"> <span style=\"color: #000000;\">(28,2 \/ 19,3) * (0,2839) \u2264 \u03c3 <sup>2<\/sup> <sub>1<\/sub> \/ \u03c3 <sup>2<\/sup> <sub>2<\/sub> \u2264 (28,2 \/ 19,3) * (3,0602)<\/span><\/p>\n<p style=\"text-align: center;\"> <span style=\"color: #000000;\">0,4148 \u2264 \u03c3 <sup>2<\/sup> <sub>1<\/sub> \/ \u03c3 <sup>2<\/sup> <sub>2<\/sub> \u2264 4,4714<\/span><\/p>\n<p> <span style=\"color: #000000;\">Assim, o intervalo de confian\u00e7a de 95% para a raz\u00e3o das vari\u00e2ncias populacionais \u00e9 <strong>(0,4148, 4,4714)<\/strong> .<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>Criando um intervalo de confian\u00e7a usando Excel<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">A imagem a seguir mostra como calcular um intervalo de confian\u00e7a de 95% para a raz\u00e3o de vari\u00e2ncia populacional no Excel. Os limites inferior e superior do intervalo de confian\u00e7a s\u00e3o apresentados na coluna E e a f\u00f3rmula utilizada para encontrar os limites inferior e superior \u00e9 apresentada na coluna F:<\/span><\/p>\n<p> <span style=\"color: #000000;\">Assim, o intervalo de confian\u00e7a de 95% para a raz\u00e3o das vari\u00e2ncias populacionais \u00e9 <strong>(0,4148, 4,4714)<\/strong> . Isso corresponde ao que obtivemos quando calculamos manualmente o intervalo de confian\u00e7a.<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>Criando um intervalo de confian\u00e7a usando R<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">O c\u00f3digo a seguir ilustra como calcular um intervalo de confian\u00e7a de 95% para a raz\u00e3o das varia\u00e7\u00f5es populacionais em R:<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#define significance level, sample sizes, and sample variances\n<\/span>alpha &lt;- .05\nn1 &lt;- 16\nn2 &lt;- 11\nvar1 &lt;- 28.2\nvar2 &lt;- 19.3\n\n<span style=\"color: #008080;\">#define F critical values\n<\/span>upper_crit &lt;- 1\/qf(alpha\/2, n1-1, n2-1)\nlower_crit &lt;- qf(alpha\/2, n2-1, n1-1)\n\n<span style=\"color: #008080;\">#find confidence interval\n<\/span>lower_bound &lt;- (var1\/var2) * lower_crit\nupper_bound &lt;- (var1\/var2) * upper_crit\n\n<span style=\"color: #008080;\">#output confidence interval\n<\/span>paste0(\"(\", lower_bound, \", \", upper_bound, \" )\")\n\n#[1] \"(0.414899337980266, 4.47137571035219 )\"\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Assim, o intervalo de confian\u00e7a de 95% para a raz\u00e3o das vari\u00e2ncias populacionais \u00e9 <strong>(0,4148, 4,4714)<\/strong> . Isso corresponde ao que obtivemos quando calculamos manualmente o intervalo de confian\u00e7a.<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>Recursos adicionais<\/strong><\/span><\/h2>\n<p> <strong><a href=\"https:\/\/statorials.org\/pt\/como-ler-a-tabela-de-distribuicao-f\/\" target=\"_blank\" rel=\"noopener\">Como ler o quadro de distribui\u00e7\u00e3o F<\/a><br \/> <a href=\"https:\/\/statorials.org\/pt\/estatologia-explica-conceitos-de-forma-simples-e-direta-facilitamos-o-aprendizado-de-estatistica\/\" target=\"_blank\" rel=\"noopener\">Como encontrar o valor cr\u00edtico F no Excel<\/a><\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Para determinar se as vari\u00e2ncias de duas popula\u00e7\u00f5es s\u00e3o iguais, podemos calcular a raz\u00e3o de vari\u00e2ncia \u03c3 2 1 \/ \u03c3 2 2 , onde \u03c3 2 1 \u00e9 a vari\u00e2ncia da popula\u00e7\u00e3o 1 e \u03c3 2 2 \u00e9 a vari\u00e2ncia da popula\u00e7\u00e3o 2. Para estimar a verdadeira raz\u00e3o de vari\u00e2ncia populacional, geralmente pegamos uma [&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-525","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 criar um intervalo de confian\u00e7a usando a distribui\u00e7\u00e3o F \u2013 Statorials<\/title>\n<meta name=\"description\" content=\"Este tutorial explica como usar a distribui\u00e7\u00e3o F para criar um intervalo de confian\u00e7a para a raz\u00e3o de duas vari\u00e2ncias.\" \/>\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-de-intervalo-de-confianca-f\/\" \/>\n<meta property=\"og:locale\" content=\"pt_PT\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Como criar um intervalo de confian\u00e7a usando a distribui\u00e7\u00e3o F \u2013 Statorials\" \/>\n<meta property=\"og:description\" content=\"Este tutorial explica como usar a distribui\u00e7\u00e3o F para criar um intervalo de confian\u00e7a para a raz\u00e3o de duas vari\u00e2ncias.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pt\/distribuicao-de-intervalo-de-confianca-f\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-29T15:03:25+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/f2.5.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-de-intervalo-de-confianca-f\/\",\"url\":\"https:\/\/statorials.org\/pt\/distribuicao-de-intervalo-de-confianca-f\/\",\"name\":\"Como criar um intervalo de confian\u00e7a usando a distribui\u00e7\u00e3o F \u2013 Statorials\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pt\/#website\"},\"datePublished\":\"2023-07-29T15:03:25+00:00\",\"dateModified\":\"2023-07-29T15:03:25+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/pt\/#\/schema\/person\/e08f98e8db95e0aa9c310e1b27c9c666\"},\"description\":\"Este tutorial explica como usar a distribui\u00e7\u00e3o F para criar um intervalo de confian\u00e7a para a raz\u00e3o de duas vari\u00e2ncias.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pt\/distribuicao-de-intervalo-de-confianca-f\/#breadcrumb\"},\"inLanguage\":\"pt-PT\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pt\/distribuicao-de-intervalo-de-confianca-f\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pt\/distribuicao-de-intervalo-de-confianca-f\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Lar\",\"item\":\"https:\/\/statorials.org\/pt\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Como criar um intervalo de confian\u00e7a usando a distribui\u00e7\u00e3o f\"}]},{\"@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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