{"id":305,"date":"2023-08-02T18:50:10","date_gmt":"2023-08-02T18:50:10","guid":{"rendered":"https:\/\/statorials.org\/pt\/analise-de-variancia-anova\/"},"modified":"2023-08-02T18:50:10","modified_gmt":"2023-08-02T18:50:10","slug":"analise-de-variancia-anova","status":"publish","type":"post","link":"https:\/\/statorials.org\/pt\/analise-de-variancia-anova\/","title":{"rendered":"An\u00e1lise de vari\u00e2ncia (anova)"},"content":{"rendered":"<p>Este artigo explica o que \u00e9 an\u00e1lise de vari\u00e2ncia, tamb\u00e9m conhecida como ANOVA, em estat\u00edstica. Assim, voc\u00ea descobrir\u00e1 como fazer uma an\u00e1lise de vari\u00e2ncia, o que \u00e9 a tabela ANOVA e um exerc\u00edcio resolvido passo a passo. Al\u00e9m disso, mostra quais s\u00e3o os pressupostos pr\u00e9vios que devem ser respeitados para realizar uma an\u00e1lise de vari\u00e2ncia e, por fim, quais s\u00e3o as vantagens e desvantagens da an\u00e1lise ANOVA. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-el-analisis-de-la-varianza-anova\"><\/span> O que \u00e9 an\u00e1lise de vari\u00e2ncia (ANOVA)?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Em estat\u00edstica, <strong>a an\u00e1lise de vari\u00e2ncia<\/strong> , tamb\u00e9m chamada de <strong>ANOVA<\/strong> (An\u00e1lise de Vari\u00e2ncia), \u00e9 uma t\u00e9cnica que permite comparar as vari\u00e2ncias entre as m\u00e9dias de diferentes amostras.<\/p>\n<p> A an\u00e1lise de vari\u00e2ncia (ANOVA) \u00e9 usada para analisar se h\u00e1 diferen\u00e7a entre as m\u00e9dias de mais de duas popula\u00e7\u00f5es. Assim, a an\u00e1lise de vari\u00e2ncia permite determinar se as m\u00e9dias populacionais de dois ou mais grupos s\u00e3o diferentes, analisando a variabilidade entre as m\u00e9dias amostrais.<\/p>\n<p> A hip\u00f3tese nula da an\u00e1lise de vari\u00e2ncia \u00e9, portanto, que as m\u00e9dias de todos os grupos analisados s\u00e3o iguais. Enquanto a hip\u00f3tese alternativa sustenta que pelo menos uma das m\u00e9dias \u00e9 diferente.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-6918550a8ad2954432ea33e07c7b83d0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{cases}H_0: \\mu_1=\\mu_2=\\ldots=\\mu_k=\\mu\\\\[2ex]H_1: \\exists \\mu_i\\neq \\mu \\quad i=1,2,\\ldots, k\\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"232\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Assim, a an\u00e1lise de vari\u00e2ncia \u00e9 particularmente \u00fatil para comparar as m\u00e9dias de mais de dois grupos, pois com este tipo de an\u00e1lise \u00e9 poss\u00edvel estudar as m\u00e9dias de todos os grupos ao mesmo tempo, em vez de comparar as m\u00e9dias aos pares. A seguir veremos quais s\u00e3o as vantagens e desvantagens da an\u00e1lise de vari\u00e2ncia.<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"tabla-anova\"><\/span> Tabela ANOVA<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> A an\u00e1lise de vari\u00e2ncia est\u00e1 resumida em uma tabela chamada <strong>tabela ANOVA<\/strong> , cujas f\u00f3rmulas s\u00e3o as seguintes: <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/tableau-anova-formules-.png\" alt=\"an\u00e1lise de vari\u00e2ncia ou f\u00f3rmulas ANOVA\" class=\"wp-image-6387\" width=\"664\" height=\"397\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p style=\"margin-bottom:5px\"> Ouro:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-5f087375b50e0b49186779714206626b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n_i\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"16\" style=\"vertical-align: -3px;\"><\/p>\n<p> \u00e9 o tamanho da amostra i.<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-7354bae77b50b7d1faed3e8ea7a3511a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"N\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 o n\u00famero total de observa\u00e7\u00f5es.<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-d42bc2203d6f76ad01b27ac9acc0bee1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 o n\u00famero de grupos diferentes na an\u00e1lise de vari\u00e2ncia.<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-393bb0c333649c80fe6365339bc42b38_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y_{ij}\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"20\" style=\"vertical-align: -6px;\"><\/p>\n<p> \u00e9 o valor j do grupo i.<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-8effb66cfe7466ba329c455ccb9289f1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{y}_{i}\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"14\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u00e9 a m\u00e9dia do grupo i.<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-ed5becac4ccb36fec040f449ba9fa52d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{y}\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"10\" style=\"vertical-align: -4px;\"><\/p>\n<p> Esta \u00e9 a m\u00e9dia de todos os dados analisados. <\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-un-analisis-de-la-varianza-anova\"><\/span> Exemplo de An\u00e1lise de Vari\u00e2ncia (ANOVA)<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Para finalizar a compreens\u00e3o do conceito de ANOVA, vamos ver como fazer an\u00e1lise de vari\u00e2ncia resolvendo passo a passo um exemplo.<\/p>\n<ul>\n<li> \u00c9 realizado um estudo estat\u00edstico para comparar as notas obtidas por quatro alunos em tr\u00eas disciplinas diferentes (A, B e C). A tabela a seguir detalha as notas obtidas por cada aluno em uma prova com nota m\u00e1xima de 20. Fa\u00e7a uma an\u00e1lise de vari\u00e2ncia para comparar as notas obtidas por cada aluno em cada disciplina. <\/li>\n<\/ul>\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/table-anova-donnees.png\" alt=\"\" class=\"wp-image-6389\" width=\"471\" height=\"205\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> A hip\u00f3tese nula desta an\u00e1lise de vari\u00e2ncia \u00e9 que as m\u00e9dias das pontua\u00e7\u00f5es dos tr\u00eas sujeitos s\u00e3o iguais. Por outro lado, a hip\u00f3tese nula \u00e9 que algumas dessas m\u00e9dias s\u00e3o diferentes.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-d1587da405a54d6a2bae626989b04562_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{cases}H_0: \\mu_A=\\mu_B=\\mu_C=\\mu\\\\[2ex]H_1: \\exists \\mu_i\\neq \\mu \\quad i=A, B, C\\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"215\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Para realizar a an\u00e1lise de vari\u00e2ncia, a primeira coisa a fazer \u00e9 calcular a m\u00e9dia de cada sujeito e a m\u00e9dia total dos dados:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-792e2e662519db421d0c9c4d7f831282_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{y}_A=\\cfrac{14+12+14+10}{4}=12,5\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"239\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-ace3ea8d1e0ce91dafdf4b5458e9760a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{y}_B=\\cfrac{13+14+10+14}{4}=12,75\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"249\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-d2781ad166914d48b6d458fe8e326f7d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{y}_C=\\cfrac{19+17+16+19}{4}=17,75\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"249\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-26caf7f83546e9112594e6886e8dccae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{y}=\\cfrac{14+12+14+10+13+14+10+14+19+17+16+19}{12}=14,33\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"553\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Uma vez conhecido o valor das m\u00e9dias, calculamos as somas dos quadrados usando as f\u00f3rmulas de an\u00e1lise de vari\u00e2ncia (ANOVA) vistas acima: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-77b3fecdc3b577841da684cd80297288_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\displaystyle SS_F&amp;=\\sum_{i=1}^k n_i(\\overline{y}_i-\\overline{y})^2\\\\[2ex] SS_F&amp;= 4\\cdot (12,5-14,33)^2+4\\cdot (12,75-14,33)^2+4\\cdot (17,75-14,33)^2\\\\[2ex] SS_F&amp;=70,17\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"138\" width=\"546\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-aa02f1b826df45c26ead3537ecc4c7e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\displaystyle SS_E=&amp;\\sum_{i=1}^k\\sum_{j=1}^{n_i} (y_{ij}-\\overline{y}_i)^2\\\\[2ex] \\displaystyle SS_E=\\ &amp;(14-12,5)^2+(12-12,5)^2+(14-12,5)^2+(10-12,5)^2+\\\\&amp;+(13-12,75)^2+(14-12,75)^2+(10-12,75)^2+(14-12,75)^2+\\\\&amp;+(19-17,75)^2+(17-17,75)^2+(16-17,75)^2+(19-17,75)^2\\\\[2ex] SS_E=\\ &amp;28,50\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"198\" width=\"575\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-2eb66d1d37653749f38916c905108a3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\displaystyle SS_T=&amp;\\sum_{i=1}^k\\sum_{j=1}^{n_i} (y_{ij}-\\overline{y})^2\\\\[2ex] \\displaystyle SS_T= \\ &amp;(14-14,33)^2+(12-14,33)^2+(14-14,33)^2+(10-14,33)^2+\\\\&amp;+(13-14,33)^2+(14-14,33)^2+(10-14,33)^2+(14-14,33)^2+\\\\&amp;+(19-14,33)^2+(17-14,33)^2+(16-14,33)^2+(19-14,33)^2\\\\[2ex] SS_T= \\ &amp;98,67\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"198\" width=\"575\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Depois determinamos os graus de liberdade do fator, do erro e do total: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-481e16a2bd9b99bcd934aa0b6e3bdce7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"GL_F=k-1=3-1=2\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"196\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-6c71951c1e79cb2368b941b79387fe82_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"GL_E=N-k=12-3=9\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"213\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-c62813e7a06bfd423af43109bfb508d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"GL_F=N-1=12-1=11\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"220\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p> Calculamos agora os erros quadr\u00e1ticos m\u00e9dios dividindo as somas dos quadrados do fator e do erro pelos seus respectivos graus de liberdade:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-477d73197865e6166394e3d20732b237_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"MSE_F=\\cfrac{SS_F}{GL_F}=\\cfrac{70,17}{2}=35,08\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"255\" style=\"vertical-align: -15px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-a5b4e07b9ec4135498762b5dbc0f173e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"MSE_R=\\cfrac{SS_R}{GL_R}=\\cfrac{28,50}{9}=3,17\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"245\" style=\"vertical-align: -15px;\"><\/p>\n<\/p>\n<p> E por fim, calculamos o valor da estat\u00edstica F dividindo os dois erros calculados na etapa anterior:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-4a30a3a61861deb9f53bd1cfcdb0b664_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"F=\\cfrac{MSE_F}{MSE_R}=\\cfrac{35,09}{3,17}=11,08\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"231\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Resumindo, a tabela ANOVA para os dados de exemplo ficaria assim: <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/table-anova-exemple.png\" alt=\"exemplo de an\u00e1lise de vari\u00e2ncia (ANOVA)\" class=\"wp-image-6408\" width=\"726\" height=\"279\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> Depois de calculados todos os valores da tabela ANOVA, resta interpretar os resultados obtidos. Para isso, precisamos encontrar a probabilidade de obter um valor maior que a estat\u00edstica F em uma distribui\u00e7\u00e3o F de Snedecor com os graus de liberdade correspondentes, ou seja, precisamos determinar o valor p do teste:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-b706e5d710c3919d145399dc9d8efca5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P[F>11,08]=0,004&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;18&#8243; width=&#8221;172&#8243; style=&#8221;vertical-align: -5px;&#8221;><\/p>\n<\/p>\n<p> Portanto, se tomarmos um n\u00edvel de signific\u00e2ncia \u03b1=0,05 (o mais comum), devemos rejeitar a hip\u00f3tese nula e aceitar a hip\u00f3tese alternativa, uma vez que o valor p do teste \u00e9 inferior ao n\u00edvel de signific\u00e2ncia. Isto significa que pelo menos algumas das m\u00e9dias dos grupos estudados s\u00e3o diferentes de outras.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-df22e22716e8cfbb1ab37d5e3e74fc9d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"0,004 < 0,05 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black}\\ \\text{Se rechaza } H_0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"346\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> Deve-se notar que atualmente existem v\u00e1rios programas de computador que podem realizar an\u00e1lises de vari\u00e2ncia em apenas alguns segundos. No entanto, tamb\u00e9m \u00e9 importante conhecer a teoria por tr\u00e1s dos c\u00e1lculos. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"supuestos-del-analisis-de-la-varianza-anova\"><\/span> Premissas de An\u00e1lise de Vari\u00e2ncia (ANOVA)<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Para realizar uma an\u00e1lise de vari\u00e2ncia (ANOVA), as seguintes condi\u00e7\u00f5es devem ser atendidas:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Independ\u00eancia<\/strong> : os valores observados s\u00e3o independentes entre si. Uma forma de garantir a independ\u00eancia das observa\u00e7\u00f5es \u00e9 adicionar aleatoriedade ao processo de amostragem.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Homocedasticidade<\/strong> : deve haver homogeneidade nas vari\u00e2ncias, ou seja, a variabilidade dos res\u00edduos \u00e9 constante.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Normalidade<\/strong> : Os res\u00edduos devem ter distribui\u00e7\u00e3o normal, ou seja, devem seguir uma distribui\u00e7\u00e3o normal.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Continuidade<\/strong> : A vari\u00e1vel dependente deve ser cont\u00ednua.<\/span> <\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"tipos-de-analisis-de-la-varianza-anova\"><\/span> Tipos de An\u00e1lise de Vari\u00e2ncia (ANOVA)<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Existem tr\u00eas <strong>tipos de an\u00e1lise de vari\u00e2ncia (ANOVA)<\/strong> :<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>An\u00e1lise de vari\u00e2ncia unidirecional (ANOVA unidirecional)<\/strong> : Na an\u00e1lise de vari\u00e2ncia, existe apenas um fator, ou seja, existe apenas uma vari\u00e1vel independente.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>An\u00e1lise de vari\u00e2ncia bidirecional (ANOVA bidirecional)<\/strong> : A an\u00e1lise de vari\u00e2ncia possui dois fatores, portanto s\u00e3o analisadas duas vari\u00e1veis independentes e a intera\u00e7\u00e3o entre elas.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>An\u00e1lise Multivariada de Vari\u00e2ncia (MANOVA)<\/strong> : Na an\u00e1lise de vari\u00e2ncia, existe mais de uma vari\u00e1vel dependente. O objetivo \u00e9 determinar se as vari\u00e1veis independentes mudam de valor quando as vari\u00e1veis dependentes variam.<\/span> <\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ventajas-y-desventajas-del-analisis-de-la-varianza-anova\"><\/span> Vantagens e desvantagens da an\u00e1lise de vari\u00e2ncia (ANOVA)<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Por fim, veremos quando \u00e9 adequado utilizarmos a an\u00e1lise de vari\u00e2ncia e, tamb\u00e9m, quais os limites deste tipo de an\u00e1lise estat\u00edstica.<\/p>\n<p> A principal vantagem da an\u00e1lise de vari\u00e2ncia (ANOVA) \u00e9 que ela permite comparar mais de dois grupos ao mesmo tempo. Ao contr\u00e1rio do <a href=\"https:\/\/statorials.org\/pt\/teste-t-do-aluno\/\">teste t<\/a> , onde voc\u00ea s\u00f3 pode analisar a m\u00e9dia de uma ou duas amostras, a an\u00e1lise de vari\u00e2ncia \u00e9 usada para determinar se m\u00faltiplas popula\u00e7\u00f5es t\u00eam ou n\u00e3o a mesma m\u00e9dia.<\/p>\n<p> No entanto, a an\u00e1lise de vari\u00e2ncia n\u00e3o nos diz qual grupo de estudo tem uma m\u00e9dia diferente, apenas nos permite saber se existem m\u00e9dias significativamente diferentes ou se todas as m\u00e9dias s\u00e3o semelhantes.<\/p>\n<p> Da mesma forma, outra desvantagem da an\u00e1lise de vari\u00e2ncia \u00e9 que quatro pressupostos anteriores (ver acima) devem ser cumpridos para realizar a an\u00e1lise ANOVA, caso contr\u00e1rio as conclus\u00f5es tiradas podem estar erradas. Portanto, deve-se sempre verificar se o conjunto de dados estat\u00edsticos atende a estes quatro requisitos.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Este artigo explica o que \u00e9 an\u00e1lise de vari\u00e2ncia, tamb\u00e9m conhecida como ANOVA, em estat\u00edstica. Assim, voc\u00ea descobrir\u00e1 como fazer uma an\u00e1lise de vari\u00e2ncia, o que \u00e9 a tabela ANOVA e um exerc\u00edcio resolvido passo a passo. Al\u00e9m disso, mostra quais s\u00e3o os pressupostos pr\u00e9vios que devem ser respeitados para realizar uma an\u00e1lise de vari\u00e2ncia [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[14],"tags":[],"class_list":["post-305","post","type-post","status-publish","format-standard","hentry","category-estatisticas"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u25b7 An\u00e1lise de vari\u00e2ncia (ANOVA)<\/title>\n<meta name=\"description\" content=\"Aqui voc\u00ea encontrar\u00e1 o que \u00e9 an\u00e1lise de vari\u00e2ncia (ANOVA), como \u00e9 realizada, um exemplo concreto e tamb\u00e9m as vantagens e desvantagens da an\u00e1lise ANOVA.\" \/>\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\/analise-de-variancia-anova\/\" \/>\n<meta property=\"og:locale\" content=\"pt_PT\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u25b7 An\u00e1lise de vari\u00e2ncia (ANOVA)\" \/>\n<meta property=\"og:description\" content=\"Aqui voc\u00ea encontrar\u00e1 o que \u00e9 an\u00e1lise de vari\u00e2ncia (ANOVA), como \u00e9 realizada, um exemplo concreto e tamb\u00e9m as vantagens e desvantagens da an\u00e1lise ANOVA.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pt\/analise-de-variancia-anova\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-08-02T18:50:10+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-6918550a8ad2954432ea33e07c7b83d0_l3.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=\"6 minutos\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/pt\/analise-de-variancia-anova\/\",\"url\":\"https:\/\/statorials.org\/pt\/analise-de-variancia-anova\/\",\"name\":\"\u25b7 An\u00e1lise de vari\u00e2ncia (ANOVA)\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pt\/#website\"},\"datePublished\":\"2023-08-02T18:50:10+00:00\",\"dateModified\":\"2023-08-02T18:50:10+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/pt\/#\/schema\/person\/e08f98e8db95e0aa9c310e1b27c9c666\"},\"description\":\"Aqui voc\u00ea encontrar\u00e1 o que \u00e9 an\u00e1lise de vari\u00e2ncia (ANOVA), como \u00e9 realizada, um exemplo concreto e tamb\u00e9m as vantagens e desvantagens da an\u00e1lise ANOVA.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pt\/analise-de-variancia-anova\/#breadcrumb\"},\"inLanguage\":\"pt-PT\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pt\/analise-de-variancia-anova\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pt\/analise-de-variancia-anova\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Lar\",\"item\":\"https:\/\/statorials.org\/pt\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"An\u00e1lise de vari\u00e2ncia (anova)\"}]},{\"@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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