{"id":1228,"date":"2023-07-27T05:20:12","date_gmt":"2023-07-27T05:20:12","guid":{"rendered":"https:\/\/statorials.org\/pt\/intervalo-de-confianca-em-r\/"},"modified":"2023-07-27T05:20:12","modified_gmt":"2023-07-27T05:20:12","slug":"intervalo-de-confianca-em-r","status":"publish","type":"post","link":"https:\/\/statorials.org\/pt\/intervalo-de-confianca-em-r\/","title":{"rendered":"Como encontrar intervalos de confian\u00e7a em r (com exemplos)"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">Um <a href=\"https:\/\/statorials.org\/pt\/intervalos-de-confianca\/\" target=\"_blank\" rel=\"noopener noreferrer\">intervalo de confian\u00e7a<\/a> \u00e9 um intervalo de valores que provavelmente cont\u00e9m um <a href=\"https:\/\/statorials.org\/pt\/estatisticas-vs-parametro\/\" target=\"_blank\" rel=\"noopener noreferrer\">par\u00e2metro populacional<\/a> com um certo n\u00edvel de confian\u00e7a.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00c9 calculado de acordo com a seguinte f\u00f3rmula geral:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Intervalo de confian\u00e7a<\/strong> = (estimativa pontual) +\/- (valor cr\u00edtico)* (erro padr\u00e3o)<\/span><\/p>\n<p> <span style=\"color: #000000;\">Esta f\u00f3rmula cria um intervalo com um limite inferior e um limite superior, que provavelmente cont\u00e9m um par\u00e2metro populacional com algum n\u00edvel de confian\u00e7a:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Intervalo de confian\u00e7a<\/strong> = [limite inferior, limite superior]<\/span><\/p>\n<p> <span style=\"color: #000000;\">Este tutorial explica como calcular os seguintes intervalos de confian\u00e7a em R:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1.<\/strong> Intervalo de confian\u00e7a para uma m\u00e9dia<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>2.<\/strong> Intervalo de confian\u00e7a para diferen\u00e7a de m\u00e9dias<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>3.<\/strong> Intervalo de confian\u00e7a para uma propor\u00e7\u00e3o<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>4.<\/strong> Intervalo de confian\u00e7a para diferen\u00e7a de propor\u00e7\u00f5es<\/span><\/p>\n<p> <span style=\"color: #000000;\">Vamos!<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Exemplo 1: Intervalo de confian\u00e7a para uma m\u00e9dia<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Usamos a seguinte f\u00f3rmula para calcular um <a href=\"https:\/\/statorials.org\/pt\/intervalo-de-confianca-medio\/\" target=\"_blank\" rel=\"noopener noreferrer\">intervalo de confian\u00e7a para uma m\u00e9dia<\/a> :<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Intervalo de confian\u00e7a = <span style=\"text-decoration: overline;\">x<\/span> +\/- t <sub>n-1, 1-\u03b1\/2<\/sub> *(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> o valor t-cr\u00edtico<\/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;\"><strong>Exemplo:<\/strong> Suponha que coletamos uma amostra aleat\u00f3ria de tartarugas com as seguintes informa\u00e7\u00f5es:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Tamanho da amostra <strong>n = 25<\/strong><\/span><\/li>\n<li> <span style=\"color: #000000;\">Peso m\u00e9dio da amostra <strong><span style=\"text-decoration: overline;\">x<\/span> = 300<\/strong><\/span><\/li>\n<li> <span style=\"color: #000000;\">Desvio padr\u00e3o amostral <strong>s = 18,5<\/strong><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">O c\u00f3digo a seguir mostra como calcular um intervalo de confian\u00e7a de 95% para o peso m\u00e9dio real da popula\u00e7\u00e3o de tartarugas:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#input sample size, sample mean, and sample standard deviation\n<\/span>n &lt;- 25\nxbar &lt;- 300 \ns &lt;- 18.5\n\n<span style=\"color: #008080;\">#calculate margin of error\n<\/span>margin &lt;- qt(0.975,df=n-1)*s\/sqrt(n)\n\n<span style=\"color: #008080;\">#calculate lower and upper bounds of confidence interval\n<\/span>low &lt;- xbar - margin\nlow\n\n[1] 292.3636\n\nhigh &lt;- xbar + margin\nhigh\n\n[1] 307.6364\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">O intervalo de confian\u00e7a de 95% para o verdadeiro peso m\u00e9dio da popula\u00e7\u00e3o de tartarugas \u00e9 <strong>[292,36, 307,64]<\/strong> .<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Exemplo 2: Intervalo de confian\u00e7a para diferen\u00e7a de m\u00e9dias<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Usamos a seguinte f\u00f3rmula para calcular um intervalo de confian\u00e7a para uma <a href=\"https:\/\/statorials.org\/pt\/diferenca-de-intervalo-de-confianca-entre-medias\/\" target=\"_blank\" rel=\"noopener noreferrer\">diferen\u00e7a nas m\u00e9dias populacionais<\/a> :<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Intervalo de confian\u00e7a<\/strong> = ( <span style=\"text-decoration: overline;\">x<\/span> <sub>1<\/sub> \u2013 <span style=\"text-decoration: overline;\">x<\/span> <sub>2<\/sub> ) +\/- t*\u221a((s <sub>p<\/sub> <sup>2<\/sup> \/n <sub>1<\/sub> ) + (s <sub>p<\/sub> <sup>2<\/sup> \/n <sub>2<\/sub> ))<\/span><\/p>\n<p> <span style=\"color: #000000;\">Ouro:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><span style=\"text-decoration: overline;\">x<\/span> <sub>1<\/sub> , <span style=\"text-decoration: overline;\">x<\/span> <sub>2<\/sub> : m\u00e9dia da amostra 1, m\u00e9dia da amostra 2<\/span><\/li>\n<li> <span style=\"color: #000000;\">t: o valor t-cr\u00edtico baseado no n\u00edvel de confian\u00e7a e (n <sub>1<\/sub> + n <sub>2<\/sub> -2) graus de liberdade<\/span><\/li>\n<li> <span style=\"color: #000000;\">s <sub>p<\/sub> <sup>2<\/sup> : vari\u00e2ncia combinada, calculada como ((n <sub>1<\/sub> -1)s <sub>1<\/sub> <sup>2<\/sup> + (n <sub>2<\/sub> -1)s <sub>2<\/sub> <sup>2<\/sup> ) \/ (n <sub>1<\/sub> +n <sub>2<\/sub> -2)<\/span><\/li>\n<li> <span style=\"color: #000000;\">t: o valor t-cr\u00edtico<\/span><\/li>\n<li> <span style=\"color: #000000;\">n <sub>1<\/sub> , n <sub>2<\/sub> : tamanho da amostra 1, tamanho da amostra 2<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><strong>Exemplo:<\/strong> Suponha que queiramos estimar a diferen\u00e7a no peso m\u00e9dio entre duas esp\u00e9cies diferentes de tartarugas. Portanto, coletamos uma amostra aleat\u00f3ria de 15 tartarugas de cada popula\u00e7\u00e3o. Aqui est\u00e3o os dados resumidos para cada amostra:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Amostra 1:<\/strong><\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><span style=\"text-decoration: overline;\">x1<\/span> = <sub>310<\/sub><\/span><\/li>\n<li> <span style=\"color: #000000;\">s <sub>1<\/sub> = 18,5<\/span><\/li>\n<li> <span style=\"color: #000000;\">n <sub>1<\/sub> = 15<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><strong>Amostra 2:<\/strong><\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><span style=\"text-decoration: overline;\">x2<\/span> <sub>=<\/sub> 300<\/span><\/li>\n<li> <span style=\"color: #000000;\"><sub>s2<\/sub> = 16,4<\/span><\/li>\n<li> <span style=\"color: #000000;\"><sub>n2<\/sub> = 15<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">O c\u00f3digo a seguir mostra como calcular um intervalo de confian\u00e7a de 95% para a verdadeira diferen\u00e7a nas m\u00e9dias populacionais:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#input sample size, sample mean, and sample standard deviation\n<\/span>n1 &lt;- 15\nxbar1 &lt;- 310 \ns1 &lt;- 18.5\n\nn2 &lt;- 15\nxbar2 &lt;- 300\ns2 &lt;- 16.4\n\n<span style=\"color: #008080;\">#calculate pooled variance\n<span style=\"color: #000000;\">sp = ((n1-1)*s1^2 + (n2-1)*s2^2) \/ (n1+n2-2)<\/span>\n\n#calculate margin of error\n<\/span>margin &lt;- qt(0.975,df=n1+n2-1)*sqrt(sp\/n1 + sp\/n2)\n\n<span style=\"color: #008080;\">#calculate lower and upper bounds of confidence interval\n<\/span>low &lt;- (xbar1-xbar2) - margin\nlow\n\n[1] -3.055445\n\nhigh &lt;- (xbar1-xbar2) + margin\nhigh\n\n[1] 23.05544\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">O intervalo de confian\u00e7a de 95% para a verdadeira diferen\u00e7a entre as m\u00e9dias da popula\u00e7\u00e3o \u00e9 <strong>[-3,06, 23,06]<\/strong> .<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Exemplo 3: Intervalo de confian\u00e7a para uma propor\u00e7\u00e3o<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Usamos a seguinte f\u00f3rmula para calcular um <a href=\"https:\/\/statorials.org\/pt\/proporcao-do-intervalo-de-confianca\/\" target=\"_blank\" rel=\"noopener noreferrer\">intervalo de confian\u00e7a para uma propor\u00e7\u00e3o<\/a> :<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Intervalo de confian\u00e7a = p<\/strong> <strong>+\/- z*(\u221a <span style=\"text-decoration: overline;\">p(1-p) \/ n<\/span> )<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Ouro:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>p:<\/strong> propor\u00e7\u00e3o da amostra<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>z:<\/strong> o valor z escolhido<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>n:<\/strong> tamanho da amostra<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><strong>Exemplo:<\/strong> Suponha que queiramos estimar a propor\u00e7\u00e3o de residentes num condado que s\u00e3o a favor de uma determinada lei. Selecionamos uma amostra aleat\u00f3ria de 100 residentes e perguntamos qual \u00e9 a sua posi\u00e7\u00e3o em rela\u00e7\u00e3o \u00e0 lei. Aqui est\u00e3o os resultados:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Tamanho da amostra <strong>n = 100<\/strong><\/span><\/li>\n<li> <span style=\"color: #000000;\">Propor\u00e7\u00e3o a favor da lei <strong>p = 0,56<\/strong><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">O c\u00f3digo a seguir mostra como calcular um intervalo de confian\u00e7a de 95% para a verdadeira propor\u00e7\u00e3o de residentes em todo o condado que s\u00e3o a favor da lei:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#input sample size and sample proportion\n<\/span>n &lt;- 100\np &lt;- .56<span style=\"color: #008080;\">\n\n#calculate margin of error\n<\/span>margin &lt;- qnorm(0.975)*sqrt(p*(1-p)\/n)\n\n<span style=\"color: #008080;\">#calculate lower and upper bounds of confidence interval\n<\/span>low &lt;- p - margin\nlow\n\n[1] 0.4627099\n\nhigh &lt;- p + margin\nhigh\n\n[1] 0.6572901\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">O intervalo de confian\u00e7a de 95% para a verdadeira propor\u00e7\u00e3o de residentes em todo o condado que s\u00e3o a favor da lei \u00e9 <strong>[0,463, 0,657]<\/strong> .<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Exemplo 4: Intervalo de confian\u00e7a para diferen\u00e7a de propor\u00e7\u00f5es<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Usamos a seguinte f\u00f3rmula para calcular um <a href=\"https:\/\/statorials.org\/pt\/intervalo-de-confianca-diferenca-de-proporcoes\/\" target=\"_blank\" rel=\"noopener noreferrer\">intervalo de confian\u00e7a para uma diferen\u00e7a em propor\u00e7\u00f5es<\/a> :<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Intervalo de confian\u00e7a = (p <sub>1<\/sub> \u2013p <sub>2<\/sub> ) +\/- z*\u221a(p <sub>1<\/sub> (1-p <sub>1<\/sub> )\/n <sub>1<\/sub> + p <sub>2<\/sub> (1-p <sub>2<\/sub> )\/n <sub>2<\/sub> )<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Ouro:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">p <sub>1<\/sub> , p <sub>2<\/sub> : propor\u00e7\u00e3o da amostra 1, propor\u00e7\u00e3o da amostra 2<\/span><\/li>\n<li> <span style=\"color: #000000;\">z: o valor cr\u00edtico z com base no n\u00edvel de confian\u00e7a<\/span><\/li>\n<li> <span style=\"color: #000000;\">n <sub>1<\/sub> , n <sub>2<\/sub> : tamanho da amostra 1, tamanho da amostra 2<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><strong>Exemplo:<\/strong> Suponha que queremos estimar a diferen\u00e7a entre a propor\u00e7\u00e3o de residentes que apoiam uma determinada lei no condado A e a propor\u00e7\u00e3o que apoia a lei no condado B. Aqui est\u00e3o os dados resumidos para cada amostra:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Amostra 1:<\/strong><\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">n <sub>1<\/sub> = 100<\/span><\/li>\n<li> <span style=\"color: #000000;\">p <sub>1<\/sub> = 0,62 (ou seja, 62 habitantes em cada 100 apoiam a lei)<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><strong>Amostra 2:<\/strong><\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><sub>n2<\/sub> = 100<\/span><\/li>\n<li> <span style=\"color: #000000;\">p <sub>2<\/sub> = 0,46 (ou seja, 46 habitantes em cada 100 apoiam a lei)<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">O c\u00f3digo a seguir mostra como calcular um intervalo de confian\u00e7a de 95% para a verdadeira diferen\u00e7a na propor\u00e7\u00e3o de residentes que apoiam a lei entre condados:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#input sample sizes and sample proportions\n<\/span>n1 &lt;- 100\np1 &lt;- .62\n\nn2 &lt;- 100\np2 &lt;- .46<span style=\"color: #008080;\">\n\n#calculate margin of error\n<\/span>margin &lt;- qnorm(0.975)*sqrt(p1*(1-p1)\/n1 + p2*(1-p2)\/n2)\n\n<span style=\"color: #008080;\">#calculate lower and upper bounds of confidence interval\n<\/span>low &lt;- (p1-p2) - margin\nlow\n\n[1] 0.02364509\n\n\nhigh &lt;- (p1-p2) + margin\nhigh\n\n[1] 0.2963549\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">O intervalo de confian\u00e7a de 95% para a verdadeira diferen\u00e7a na propor\u00e7\u00e3o de residentes que apoiam a lei entre condados \u00e9 <strong>[0,024, 0,296]<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\"><em>Voc\u00ea pode encontrar mais tutoriais de R <a href=\"https:\/\/statorials.org\/pt\/estatologia-explica-conceitos-de-forma-simples-e-direta-facilitamos-o-aprendizado-de-estatistica\/\" target=\"_blank\" rel=\"noopener noreferrer\">aqui<\/a> .<\/em><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Um intervalo de confian\u00e7a \u00e9 um intervalo de valores que provavelmente cont\u00e9m um par\u00e2metro populacional com um certo n\u00edvel de confian\u00e7a. \u00c9 calculado de acordo com a seguinte f\u00f3rmula geral: Intervalo de confian\u00e7a = (estimativa pontual) +\/- (valor cr\u00edtico)* (erro padr\u00e3o) Esta f\u00f3rmula cria um intervalo com um limite inferior e um limite superior, que [&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-1228","post","type-post","status-publish","format-standard","hentry","category-guia"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - 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