{"id":771,"date":"2023-07-28T19:45:12","date_gmt":"2023-07-28T19:45:12","guid":{"rendered":"https:\/\/statorials.org\/pt\/one-way-anova-a-la-main\/"},"modified":"2023-07-28T19:45:12","modified_gmt":"2023-07-28T19:45:12","slug":"one-way-anova-a-la-main","status":"publish","type":"post","link":"https:\/\/statorials.org\/pt\/one-way-anova-a-la-main\/","title":{"rendered":"Como realizar manualmente uma anova unidirecional"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">Uma <a href=\"https:\/\/statorials.org\/pt\/uma-maneira-anova\/\" target=\"_blank\" rel=\"noopener\">ANOVA unidirecional<\/a> (\u201can\u00e1lise de vari\u00e2ncia\u201d) compara as m\u00e9dias de tr\u00eas ou mais grupos independentes para determinar se existe uma diferen\u00e7a estatisticamente significativa entre as m\u00e9dias da popula\u00e7\u00e3o correspondente.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Este tutorial explica como realizar manualmente uma ANOVA unidirecional.<\/span><\/p>\n<h3> <strong><span style=\"color: #000000;\">Exemplo: ANOVA unilateral manual<\/span><\/strong><\/h3>\n<p> <span style=\"color: #000000;\">Suponha que queiramos saber se tr\u00eas programas diferentes de prepara\u00e7\u00e3o para testes levam ou n\u00e3o a pontua\u00e7\u00f5es m\u00e9dias diferentes em um determinado exame. Para testar isso, recrutamos 30 estudantes para participar de um estudo e os dividimos em tr\u00eas grupos.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Os alunos de cada grupo s\u00e3o designados aleatoriamente para usar um dos tr\u00eas programas de prepara\u00e7\u00e3o para testes nas tr\u00eas semanas seguintes para se prepararem para um exame. No final das tr\u00eas semanas, todos os alunos fazem o mesmo exame.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Os resultados dos exames para cada grupo s\u00e3o mostrados abaixo:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-8258 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/aller-simple2.png\" sizes=\"auto, \" srcset=\"\" alt=\"Exemplo de dados ANOVA unilaterais\" width=\"237\" height=\"246\"><\/p>\n<p> <span style=\"color: #000000;\">Siga as etapas a seguir para realizar manualmente uma ANOVA unidirecional para determinar se a pontua\u00e7\u00e3o m\u00e9dia do exame \u00e9 diferente entre os tr\u00eas grupos:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Etapa 1: Calcule a m\u00e9dia do grupo e a m\u00e9dia geral.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Primeiro, calcularemos a m\u00e9dia dos tr\u00eas grupos, bem como a m\u00e9dia geral:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-8434 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/anovamain1-1.png\" alt=\"\" width=\"300\" height=\"257\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\"><strong>Etapa 2: Calcule o SSR.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">A seguir, calcularemos a regress\u00e3o da soma dos quadrados (SSR) usando a seguinte f\u00f3rmula:<\/span><\/p>\n<p> <span style=\"color: #000000;\">n\u03a3(X <sub>j<\/sub> \u2013 <span style=\"text-decoration: overline;\">X<\/span> ..) <sup>2<\/sup><\/span><\/p>\n<p> <span style=\"color: #000000;\">Ouro:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>n<\/strong> : o tamanho da amostra do grupo j<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>\u03a3<\/strong> : um s\u00edmbolo grego que significa \u201csoma\u201d<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>X <sub>j<\/sub><\/strong> : a m\u00e9dia do grupo j<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong><span style=\"text-decoration: overline;\">X<\/span> ..<\/strong> : a m\u00e9dia geral<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Em nosso exemplo, calculamos que SSR = 10(83,4-85,8) <sup>2<\/sup> + 10(89,3-85,8) <sup>2<\/sup> + 10(84,7-85,8) <sup>2<\/sup> = <strong>192,2<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Etapa 3: Calcule o SES.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">A seguir, calcularemos a soma do erro quadr\u00e1tico (SSE) usando a seguinte f\u00f3rmula:<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u03a3(X <sub>ij<\/sub> \u2013 <span style=\"text-decoration: overline;\">X<\/span> <sub>j<\/sub> ) <sup>2<\/sup><\/span><\/p>\n<p> <span style=\"color: #000000;\">Ouro:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>\u03a3<\/strong> : um s\u00edmbolo grego que significa \u201csoma\u201d<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>X <sub>ij<\/sub><\/strong> : a <sup>i-\u00e9sima<\/sup> observa\u00e7\u00e3o do grupo j<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong><span style=\"text-decoration: overline;\">X<\/span> <sub>j<\/sub><\/strong> : a m\u00e9dia do grupo j<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Em nosso exemplo, calculamos o SSE da seguinte forma:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Grupo 1:<\/strong> (85-83,4) <sup>2<\/sup> + (86-83,4) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (88-83,4) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (75-83,4) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (78-83,4) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (94-83,4) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (98-83,4) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (79-83,4) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (71-83,4) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (80-83,4) <sup>2<\/sup> = <strong>640,4<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Grupo 2:<\/strong> (91-89,3) <sup>2<\/sup> + (92-89,3) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (93-89,3) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (85-89,3) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (87-89,3) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (84-89,3) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (82-89,3) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (88-89,3) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (95-89,3) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (96-89,3) <sup>2<\/sup> = <strong>208,1<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Grupo 3:<\/strong> (79-84,7) <sup>2<\/sup> + (78-84,7) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (88-84,7) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (94-84,7) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (92-84,7) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (85-84,7) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (83-84,7) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (85-84,7) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (82-84,7) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (81-84,7) <sup>2<\/sup> = <strong>252,1<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>ESS:<\/strong> 640,4 + 208,1 + 252,1 = <strong>1.100,6<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Etapa 4: Calcule o SST.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">A seguir, calcularemos a soma total dos quadrados (SST) usando a seguinte f\u00f3rmula:<\/span><\/p>\n<p> <span style=\"color: #000000;\">SST = SSR + SSE<\/span><\/p>\n<p> <span style=\"color: #000000;\">Em nosso exemplo, SST = 192,2 + 1100,6 = <strong>1292,8<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Etapa 5: preencha a tabela ANOVA.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Agora que temos SSR, SSE e SST, podemos preencher a tabela ANOVA:<\/span><\/p>\n<table>\n<tbody>\n<tr>\n<th style=\"text-align: center;\"> <span style=\"color: #000000;\"><strong>Fonte<\/strong><\/span><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">Soma dos quadrados (SS)<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">df<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">Quadrados m\u00e9dios (MS)<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">F<\/span><\/strong><\/th>\n<\/tr>\n<tr>\n<td> <span style=\"color: #000000;\"><strong>Tratamento<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">192,2<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">2<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">96,1<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">2.358<\/span><\/td>\n<\/tr>\n<tr>\n<td> <span style=\"color: #000000;\"><strong>Erro<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">1100,6<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">27<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">40,8<\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td> <span style=\"color: #000000;\"><strong>Total<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">1292,8<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">29<\/span><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p> <span style=\"color: #000000;\">Aqui est\u00e1 como calculamos os diferentes n\u00fameros na tabela:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>tratamento df:<\/strong> k-1 = 3-1 = 2<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>erro df:<\/strong> nk = 30-3 = 27<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>total de gl:<\/strong> n-1 = 30-1 = 29<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>Tratamento SEP:<\/strong> tratamento SST \/ df = 192,2 \/ 2 = 96,1<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>Erro MS:<\/strong> erro SSE \/ df = 1100,6 \/ 27 = 40,8<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>F:<\/strong> Processamento MS \/ erro MS = 96,1 \/ 40,8 = 2,358<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><em><strong>Nota:<\/strong> n = n\u00famero total de observa\u00e7\u00f5es, k = n\u00famero de grupos<\/em><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Etapa 6: interprete os resultados.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">A estat\u00edstica do teste F para esta ANOVA unidirecional \u00e9 <strong>2,358<\/strong> . Para determinar se este \u00e9 um resultado estatisticamente significativo, precisamos compar\u00e1-lo com o valor cr\u00edtico de F encontrado na <a href=\"https:\/\/statorials.org\/pt\/tabela-de-distribuicao-f\/\" target=\"_blank\" rel=\"noopener\">tabela de distribui\u00e7\u00e3o F<\/a> com os seguintes valores:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">\u03b1 (n\u00edvel de signific\u00e2ncia) = 0,05<\/span><\/li>\n<li> <span style=\"color: #000000;\">DF1 (graus de liberdade do numerador) = tratamento df = 2<\/span><\/li>\n<li> <span style=\"color: #000000;\">DF2 (graus de liberdade do denominador) = erro df = 27<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Descobrimos que o valor cr\u00edtico de F \u00e9 <strong>3,3541<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Como a estat\u00edstica do teste F na tabela ANOVA \u00e9 menor que o valor cr\u00edtico F na tabela de distribui\u00e7\u00e3o F, n\u00e3o conseguimos rejeitar a hip\u00f3tese nula. Isto significa que n\u00e3o temos evid\u00eancias suficientes para afirmar que existe uma diferen\u00e7a estatisticamente significativa entre as notas m\u00e9dias dos exames dos tr\u00eas grupos.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Recurso b\u00f4nus:<\/strong> Use esta <a href=\"https:\/\/statorials.org\/pt\/calculadora-danova-unidirecional\/\" target=\"_blank\" rel=\"noopener\">calculadora ANOVA unidirecional<\/a> para realizar automaticamente uma ANOVA unidirecional para at\u00e9 cinco amostras.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Uma ANOVA unidirecional (\u201can\u00e1lise de vari\u00e2ncia\u201d) compara as m\u00e9dias de tr\u00eas ou mais grupos independentes para determinar se existe uma diferen\u00e7a estatisticamente significativa entre as m\u00e9dias da popula\u00e7\u00e3o correspondente. Este tutorial explica como realizar manualmente uma ANOVA unidirecional. Exemplo: ANOVA unilateral manual Suponha que queiramos saber se tr\u00eas programas diferentes de prepara\u00e7\u00e3o para testes levam [&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-771","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 realizar ANOVA unidirecional manualmente - Statorials<\/title>\n<meta name=\"description\" content=\"Uma explica\u00e7\u00e3o simples sobre como realizar manualmente uma ANOVA unidirecional.\" \/>\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\/one-way-anova-a-la-main\/\" \/>\n<meta property=\"og:locale\" content=\"pt_PT\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Como realizar ANOVA unidirecional manualmente - Statorials\" \/>\n<meta property=\"og:description\" content=\"Uma explica\u00e7\u00e3o simples sobre como realizar manualmente uma ANOVA unidirecional.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pt\/one-way-anova-a-la-main\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-28T19:45:12+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/aller-simple2.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\/one-way-anova-a-la-main\/\",\"url\":\"https:\/\/statorials.org\/pt\/one-way-anova-a-la-main\/\",\"name\":\"Como realizar ANOVA unidirecional manualmente - Statorials\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pt\/#website\"},\"datePublished\":\"2023-07-28T19:45:12+00:00\",\"dateModified\":\"2023-07-28T19:45:12+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/pt\/#\/schema\/person\/e08f98e8db95e0aa9c310e1b27c9c666\"},\"description\":\"Uma explica\u00e7\u00e3o simples sobre como realizar manualmente uma ANOVA unidirecional.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pt\/one-way-anova-a-la-main\/#breadcrumb\"},\"inLanguage\":\"pt-PT\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pt\/one-way-anova-a-la-main\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pt\/one-way-anova-a-la-main\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Lar\",\"item\":\"https:\/\/statorials.org\/pt\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Como realizar manualmente uma anova unidirecional\"}]},{\"@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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