{"id":266,"date":"2023-08-03T09:00:18","date_gmt":"2023-08-03T09:00:18","guid":{"rendered":"https:\/\/statorials.org\/pt\/estatisticas-de-contraste\/"},"modified":"2023-08-03T09:00:18","modified_gmt":"2023-08-03T09:00:18","slug":"estatisticas-de-contraste","status":"publish","type":"post","link":"https:\/\/statorials.org\/pt\/estatisticas-de-contraste\/","title":{"rendered":"Estat\u00edsticas de contraste"},"content":{"rendered":"<p>Este artigo explica o que \u00e9 uma estat\u00edstica de contraste, quais s\u00e3o as f\u00f3rmulas mais comuns para estat\u00edsticas de contraste e mais, a rela\u00e7\u00e3o entre estat\u00edstica de contraste, regi\u00e3o de rejei\u00e7\u00e3o e regi\u00e3o de aceita\u00e7\u00e3o. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-el-estadistico-de-contraste\"><\/span> Qual \u00e9 a estat\u00edstica de contraste?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> A <strong>estat\u00edstica de contraste<\/strong> \u00e9 uma vari\u00e1vel com distribui\u00e7\u00e3o de probabilidade conhecida relacionada \u00e0 hip\u00f3tese do estudo. Especificamente, a estat\u00edstica de contraste \u00e9 usada em testes de hip\u00f3teses para rejeitar ou aceitar a hip\u00f3tese nula.<\/p>\n<p> Na verdade, a decis\u00e3o de rejeitar ou n\u00e3o a hip\u00f3tese nula de um teste de hip\u00f3tese \u00e9 baseada no valor da estat\u00edstica do teste. Se o valor da estat\u00edstica de teste cair na regi\u00e3o de rejei\u00e7\u00e3o, a hip\u00f3tese nula \u00e9 rejeitada. ao passo que se o valor da estat\u00edstica de teste estiver dentro da regi\u00e3o de aceita\u00e7\u00e3o, a hip\u00f3tese nula \u00e9 aceita. <\/p>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 20px; padding-left: 30px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Veja:<\/strong> <a href=\"https:\/\/statorials.org\/pt\/contraste-de-hipotese\/\">Teste de hip\u00f3teses (estat\u00edsticas)<\/a> <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formulas-de-estadisticos-de-contraste\"><\/span> F\u00f3rmulas de estat\u00edsticas de contraste<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Dependendo do tipo de teste de hip\u00f3tese, a distribui\u00e7\u00e3o da estat\u00edstica do teste \u00e9 diferente. A f\u00f3rmula para a estat\u00edstica de teste, portanto, tamb\u00e9m depende do tipo de teste de hip\u00f3tese. A seguir veremos como a estat\u00edstica de teste \u00e9 calculada dependendo do tipo de teste de hip\u00f3tese. <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"estadistico-de-contraste-para-la-media\"><\/span> Estat\u00edstica de contraste para m\u00e9dia<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> A <strong>f\u00f3rmula para a estat\u00edstica de teste de hip\u00f3tese para a m\u00e9dia com vari\u00e2ncia conhecida<\/strong> \u00e9:<\/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-fdf1817a07bfb8c1eda9a8d8ccd8c828_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle Z=\\frac{\\overline{x}-\\mu}{\\displaystyle \\frac{\\sigma}{\\sqrt{n}}} \" title=\"Rendered by QuickLaTeX.com\" height=\"57\" width=\"81\" style=\"vertical-align: -34px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\"> Ouro:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-0be116875001706f29a24434bd0d91c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Z\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 a estat\u00edstica do teste de hip\u00f3tese para a m\u00e9dia.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-a39858a792fb4fe9a3173e004701f2a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 a m\u00e9dia da amostra.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-05d9eae892416bd34247a25207f8b718_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\mu\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"11\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u00e9 o valor m\u00e9dio proposto.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-eaaf379fee5e67946f3fedf5631047b1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sigma\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 o desvio padr\u00e3o da popula\u00e7\u00e3o.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-ec4217f4fa5fcd92a9edceba0e708cf7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 o tamanho da amostra.<\/li>\n<\/ul>\n<p> Uma vez calculada a estat\u00edstica de contraste de hip\u00f3tese para a m\u00e9dia, o resultado deve ser interpretado para rejeitar ou rejeitar a hip\u00f3tese nula:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">Se o teste de hip\u00f3tese para a m\u00e9dia for bilateral, a hip\u00f3tese nula \u00e9 rejeitada se o valor absoluto da estat\u00edstica for maior que o valor cr\u00edtico Z <sub>\u03b1\/2<\/sub> .<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">Se o teste de hip\u00f3tese para a m\u00e9dia corresponder \u00e0 cauda direita, a hip\u00f3tese nula ser\u00e1 rejeitada se a estat\u00edstica for maior que o valor cr\u00edtico Z <sub>\u03b1<\/sub> .<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">Se o teste de hip\u00f3tese para a m\u00e9dia corresponder \u00e0 cauda esquerda, a hip\u00f3tese nula ser\u00e1 rejeitada se a estat\u00edstica for menor que o valor cr\u00edtico -Z <sub>\u03b1<\/sub> .<\/span><\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-0e2ccadfc369eb7543b8f86dfccc528e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{l}H_1: \\mu\\neq \\mu_0 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Si } |Z|>Z_{\\alpha\/2} \\text{ se rechaza } H_0\\\\[3ex]H_1: \\mu> \\mu_0 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Si } Z>Z_{\\alpha} \\text{ se rechaza } H_0\\\\[3ex]H_1: \\mu< \\mu_0 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Si } Z<-Z_{\\alpha} \\text{ se rechaza } H_0\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"108\" width=\"440\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Neste caso, os valores cr\u00edticos s\u00e3o obtidos na tabela de distribui\u00e7\u00e3o normal padronizada.<\/p>\n<p> Por outro lado, a <strong>f\u00f3rmula para a estat\u00edstica de teste de hip\u00f3tese para a m\u00e9dia com vari\u00e2ncia desconhecida<\/strong> \u00e9:<\/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-f8277d83b2d28325f25f5d118486200f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle t=\\frac{\\overline{x}-\\mu}{\\displaystyle \\frac{s}{\\sqrt{n}}} \" title=\"Rendered by QuickLaTeX.com\" height=\"57\" width=\"75\" style=\"vertical-align: -34px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\"> Ouro:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-fd9cb27edab3f0a8a249bc80cc9c6ee2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 a estat\u00edstica do teste de hip\u00f3tese para a m\u00e9dia, que \u00e9 definida pela distribui\u00e7\u00e3o t de Student.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-a39858a792fb4fe9a3173e004701f2a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 a m\u00e9dia da amostra.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-05d9eae892416bd34247a25207f8b718_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\mu\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"11\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u00e9 o valor m\u00e9dio proposto.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-1edc883862ceed1a21913f60358e31d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 o desvio padr\u00e3o da amostra.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-ec4217f4fa5fcd92a9edceba0e708cf7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 o tamanho da amostra.<\/li>\n<\/ul>\n<p> Como antes, o resultado calculado da estat\u00edstica de contraste deve ser interpretado com o valor cr\u00edtico para rejeitar ou n\u00e3o a hip\u00f3tese nula:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">Se o teste de hip\u00f3tese para a m\u00e9dia for bilateral, a hip\u00f3tese nula \u00e9 rejeitada se o valor absoluto da estat\u00edstica for maior que o valor cr\u00edtico t <sub>\u03b1\/2|n-1<\/sub> .<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">Se o teste de hip\u00f3tese para a m\u00e9dia corresponder \u00e0 cauda direita, a hip\u00f3tese nula ser\u00e1 rejeitada se a estat\u00edstica for maior que o valor cr\u00edtico t <sub>\u03b1|n-1<\/sub> .<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">Se o teste de hip\u00f3tese para a m\u00e9dia corresponder \u00e0 cauda esquerda, a hip\u00f3tese nula ser\u00e1 rejeitada se a estat\u00edstica for menor que o valor cr\u00edtico -t <sub>\u03b1|n-1<\/sub> .<\/span><\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-31fb206b75a47181c7c673f54ba28ee8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{l}H_1: \\mu\\neq \\mu_0 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Si } |t|>t_{\\alpha\/2|n-1} \\text{ se rechaza } H_0\\\\[3ex]H_1: \\mu> \\mu_0 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Si } t>t_{\\alpha|n-1} \\text{ se rechaza } H_0\\\\[3ex]H_1: \\mu< \\mu_0 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Si } t<-t_{\\alpha|n-1} \\text{ se rechaza } H_0\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"112\" width=\"457\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Quando a vari\u00e2ncia \u00e9 desconhecida, os valores cr\u00edticos do teste s\u00e3o obtidos na tabela de distribui\u00e7\u00e3o de Student. <\/p>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 20px; padding-left: 30px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Veja:<\/strong> <a href=\"https:\/\/statorials.org\/pt\/teste-de-hipotese-para-a-media\/\">Teste de hip\u00f3tese para a m\u00e9dia<\/a> <\/div>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"estadistico-de-contraste-para-la-proporcion\"><\/span> Estat\u00edstica de contraste para propor\u00e7\u00e3o<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> A <strong>f\u00f3rmula para a estat\u00edstica de teste de hip\u00f3tese para propor\u00e7\u00e3o<\/strong> \u00e9:<\/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-e2f5ad36dae72cd89279809ab3ea6d20_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle Z=\\frac{\\widehat{p}-p}{\\displaystyle\\sqrt{\\frac{p(1-p)}{n}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"67\" width=\"123\" style=\"vertical-align: -41px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\"> Ouro:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-0be116875001706f29a24434bd0d91c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Z\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 a estat\u00edstica do teste de hip\u00f3tese para a propor\u00e7\u00e3o.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-ecd29d136a62fc6b274e1181e064e20e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\widehat{p}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"12\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u00e9 a propor\u00e7\u00e3o da amostra.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-5faad0904f612a3fa5b27faafb8dc903_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"p\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u00e9 o valor da propor\u00e7\u00e3o proposta.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-ec4217f4fa5fcd92a9edceba0e708cf7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 o tamanho da amostra.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-661a2bbf8dccd197bcf450330420cbc1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\sqrt{\\frac{p(1-p)}{n}}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"84\" style=\"vertical-align: -13px;\"><\/p>\n<p> \u00e9 o desvio padr\u00e3o da propor\u00e7\u00e3o.<\/li>\n<\/ul>\n<p> Tenha em mente que n\u00e3o basta calcular a estat\u00edstica do teste de hip\u00f3tese para a propor\u00e7\u00e3o, mas o resultado deve ent\u00e3o ser interpretado:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">Se o teste de hip\u00f3tese para a propor\u00e7\u00e3o for bilateral, a hip\u00f3tese nula \u00e9 rejeitada se o valor absoluto da estat\u00edstica for maior que o valor cr\u00edtico Z <sub>\u03b1\/2<\/sub> .<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">Se o teste de hip\u00f3tese para a propor\u00e7\u00e3o corresponder \u00e0 cauda direita, a hip\u00f3tese nula \u00e9 rejeitada se a estat\u00edstica for maior que o valor cr\u00edtico Z <sub>\u03b1<\/sub> .<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">Se o teste de hip\u00f3tese para a propor\u00e7\u00e3o corresponder \u00e0 cauda esquerda, a hip\u00f3tese nula \u00e9 rejeitada se a estat\u00edstica for menor que o valor cr\u00edtico -Z <sub>\u03b1<\/sub> .<\/span><\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-7d5bd583532769e3014286e8ffd94c9f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{l}H_1: p\\neq p_0 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Si } |Z|>Z_{\\alpha\/2} \\text{ se rechaza } H_0\\\\[3ex]H_1: p> p_0 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Si } Z>Z_{\\alpha} \\text{ se rechaza } H_0\\\\[3ex]H_1: p< p_0 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Si } Z<-Z_{\\alpha} \\text{ se rechaza } H_0\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"108\" width=\"437\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Lembre-se de que os valores cr\u00edticos podem ser facilmente obtidos na tabela de distribui\u00e7\u00e3o normal padr\u00e3o. <\/p>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 20px; padding-left: 30px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Veja:<\/strong> <a href=\"https:\/\/statorials.org\/pt\/teste-de-hipotese-para-proporcao\/\">Teste de hip\u00f3tese para propor\u00e7\u00e3o<\/a> <\/div>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"estadistico-de-contraste-para-la-varianza\"><\/span> Estat\u00edstica de contraste para vari\u00e2ncia<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> A <strong>f\u00f3rmula para calcular a estat\u00edstica do teste de hip\u00f3tese para vari\u00e2ncia<\/strong> \u00e9:<\/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-3917636d4c911eeaad1a005195204d08_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\chi^2=\\cfrac{(n-1)s^2}{\\sigma^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"115\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\"> Ouro:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-984dc78529fc235b078a9f3b62d0f0c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\chi^2\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"18\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u00e9 a estat\u00edstica de teste de hip\u00f3tese para vari\u00e2ncia, que tem uma distribui\u00e7\u00e3o qui-quadrado.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-ec4217f4fa5fcd92a9edceba0e708cf7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 o tamanho da amostra.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-3ab572e85f9cb7cb6f495387f2a6ab0b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s^2\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"15\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 a vari\u00e2ncia da amostra.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-c6d52162ef1ec2e8130fb00687aca707_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sigma^2\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"18\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 a vari\u00e2ncia da popula\u00e7\u00e3o proposta.<\/li>\n<\/ul>\n<p> Para interpretar o resultado da estat\u00edstica, o valor obtido deve ser comparado com o valor cr\u00edtico do teste.<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">Se o teste de hip\u00f3tese de vari\u00e2ncia for bicaudal, a hip\u00f3tese nula ser\u00e1 rejeitada se a estat\u00edstica for maior que o valor cr\u00edtico.\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-7bd4ac2951fb286bf19797944cba6955_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\chi_{1-\\alpha\/2|n-1}^2\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"81\" style=\"vertical-align: -10px;\"><\/p>\n<p><\/span> ou se o valor cr\u00edtico for menor que<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-931a3f10ab51df1c9003e6cb593907c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\chi_{\\alpha\/2|n-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"63\" style=\"vertical-align: -8px;\"><\/p>\n<p> .<\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">Se o teste de hip\u00f3tese para a vari\u00e2ncia corresponder \u00e0 cauda direita, a hip\u00f3tese nula ser\u00e1 rejeitada se a estat\u00edstica for maior que o valor cr\u00edtico\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-243ef3cc114070613fd8bee8c61f8c13_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\chi_{1-\\alpha|n-1}^2\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"67\" style=\"vertical-align: -10px;\"><\/p>\n<p><\/span> .<\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">Se o teste de hip\u00f3tese para vari\u00e2ncia corresponder \u00e0 cauda esquerda, a hip\u00f3tese nula ser\u00e1 rejeitada se a estat\u00edstica for menor que o valor cr\u00edtico\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-0436c61e0bdff7a21f6e6ab296607c66_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\chi_{\\alpha|n-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"49\" style=\"vertical-align: -8px;\"><\/p>\n<p><\/span> .<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-ca46378c1a2ee04b5cc5bfa93002fe9c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{l}H_1: \\sigma^2\\neq \\sigma_0 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Si } \\chi^2>\\chi^2_{1-\\alpha\/2|n-1}\\text{ se rechaza } H_0\\\\[3ex]H_1: \\sigma^2\\neq \\sigma_0 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Si }\\chi^2<\\chi^2_{\\alpha\/2|n-1}\\text{ se rechaza } H_0 \\\\[3ex]H_1: \\sigma^2> \\sigma_0 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Si } \\chi^2>\\chi^2_{1-\\alpha|n-1}\\text{ se rechaza } H_0\\\\[3ex]H_1: \\sigma^2< \\sigma_0 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Si } \\chi^2<\\chi^2_{\\alpha|n-1}\\text{ se rechaza } H_0\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"160\" width=\"489\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Os valores cr\u00edticos do teste de hip\u00f3tese para vari\u00e2ncia s\u00e3o obtidos na tabela de distribui\u00e7\u00e3o qui-quadrado. Observe que os graus de liberdade da distribui\u00e7\u00e3o qui-quadrado s\u00e3o o tamanho da amostra menos 1. <\/p>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 20px; padding-left: 30px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Veja:<\/strong> <a href=\"https:\/\/statorials.org\/pt\/teste-de-hipotese-para-variancia\/\">Teste de hip\u00f3tese de vari\u00e2ncia<\/a> <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"estadistico-de-contraste-region-de-rechazo-y-region-de-aceptacion\"><\/span> Estat\u00edstica de contraste, regi\u00e3o de rejei\u00e7\u00e3o e regi\u00e3o de aceita\u00e7\u00e3o<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Num teste de hip\u00f3tese, a <strong>regi\u00e3o de rejei\u00e7\u00e3o<\/strong> \u00e9 a regi\u00e3o do gr\u00e1fico da distribui\u00e7\u00e3o da estat\u00edstica de teste que implica rejei\u00e7\u00e3o da hip\u00f3tese nula (e aceita\u00e7\u00e3o da hip\u00f3tese alternativa). Por outro lado, a <strong>regi\u00e3o de aceita\u00e7\u00e3o<\/strong> \u00e9 a regi\u00e3o do gr\u00e1fico de distribui\u00e7\u00e3o da estat\u00edstica de teste que implica aceita\u00e7\u00e3o da hip\u00f3tese nula (e rejei\u00e7\u00e3o da hip\u00f3tese alternativa).<\/p>\n<p> Assim, o valor da estat\u00edstica de contraste determina o resultado de um teste de hip\u00f3tese da seguinte maneira:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">Se a estat\u00edstica de teste estiver dentro da regi\u00e3o de rejei\u00e7\u00e3o, a hip\u00f3tese nula \u00e9 rejeitada e a hip\u00f3tese alternativa \u00e9 aceita.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">Se a estat\u00edstica de teste estiver dentro da regi\u00e3o de aceita\u00e7\u00e3o, a hip\u00f3tese nula \u00e9 aceita e a hip\u00f3tese alternativa \u00e9 rejeitada.<\/span><\/li>\n<\/ul>\n<p> Os valores que separam a regi\u00e3o de rejei\u00e7\u00e3o da regi\u00e3o de aceita\u00e7\u00e3o s\u00e3o chamados <strong>de valores cr\u00edticos<\/strong> . Portanto, precisamos calcular os valores cr\u00edticos para conhecer os limites da regi\u00e3o de rejei\u00e7\u00e3o e da regi\u00e3o de aceita\u00e7\u00e3o e, portanto, saber quando rejeitar e quando aceitar a hip\u00f3tese nula. <\/p>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 20px; padding-left: 30px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Veja:<\/strong> <a href=\"https:\/\/statorials.org\/pt\/valor-critico\/\">Valor cr\u00edtico<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Este artigo explica o que \u00e9 uma estat\u00edstica de contraste, quais s\u00e3o as f\u00f3rmulas mais comuns para estat\u00edsticas de contraste e mais, a rela\u00e7\u00e3o entre estat\u00edstica de contraste, regi\u00e3o de rejei\u00e7\u00e3o e regi\u00e3o de aceita\u00e7\u00e3o. Qual \u00e9 a estat\u00edstica de contraste? A estat\u00edstica de contraste \u00e9 uma vari\u00e1vel com distribui\u00e7\u00e3o de probabilidade conhecida relacionada \u00e0 [&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-266","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 Estat\u00edsticas de contraste<\/title>\n<meta name=\"description\" content=\"Aqui voc\u00ea descobrir\u00e1 o que s\u00e3o estat\u00edsticas de contraste e quais f\u00f3rmulas de estat\u00edsticas de contraste s\u00e3o mais utilizadas em testes de hip\u00f3teses.\" \/>\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\/estatisticas-de-contraste\/\" \/>\n<meta property=\"og:locale\" content=\"pt_PT\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u25b7 Estat\u00edsticas de contraste\" \/>\n<meta property=\"og:description\" content=\"Aqui voc\u00ea descobrir\u00e1 o que s\u00e3o estat\u00edsticas de contraste e quais f\u00f3rmulas de estat\u00edsticas de contraste s\u00e3o mais utilizadas em testes de hip\u00f3teses.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pt\/estatisticas-de-contraste\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-08-03T09:00:18+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-fdf1817a07bfb8c1eda9a8d8ccd8c828_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\/estatisticas-de-contraste\/\",\"url\":\"https:\/\/statorials.org\/pt\/estatisticas-de-contraste\/\",\"name\":\"\u25b7 Estat\u00edsticas de contraste\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pt\/#website\"},\"datePublished\":\"2023-08-03T09:00:18+00:00\",\"dateModified\":\"2023-08-03T09:00:18+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/pt\/#\/schema\/person\/e08f98e8db95e0aa9c310e1b27c9c666\"},\"description\":\"Aqui voc\u00ea descobrir\u00e1 o que s\u00e3o estat\u00edsticas de contraste e quais f\u00f3rmulas de estat\u00edsticas de contraste s\u00e3o mais utilizadas em testes de hip\u00f3teses.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pt\/estatisticas-de-contraste\/#breadcrumb\"},\"inLanguage\":\"pt-PT\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pt\/estatisticas-de-contraste\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pt\/estatisticas-de-contraste\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Lar\",\"item\":\"https:\/\/statorials.org\/pt\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Estat\u00edsticas de contraste\"}]},{\"@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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