{"id":408,"date":"2020-04-23T21:22:47","date_gmt":"2020-04-23T12:22:47","guid":{"rendered":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/clopper-peason-confidence-interval-in-r\/"},"modified":"2024-12-29T18:09:11","modified_gmt":"2024-12-29T09:09:11","slug":"clopper-peason-confidence-interval-in-r","status":"publish","type":"post","link":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/clopper-peason-confidence-interval-in-r\/","title":{"rendered":"R \u3067 \u30af\u30ed\u30c3\u30d1\u30fc\u30d4\u30a2\u30bd\u30f3\u306e\u5272\u5408\u306e\u4fe1\u983c\u533a\u9593\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5"},"content":{"rendered":"\n<p>\u6b63\u898f\u5206\u5e03\u8fd1\u4f3c\u3092\u7528\u3044\u305f\u4fe1\u983c\u533a\u9593\u3068Clopper-Pearson \u4fe1\u983c\u533a\u9593\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5\u3002<\/p>\n\n\n\n<!--more-->\n\n\n\n<h2 class=\"wp-block-heading\" id=\"\u5272\u5408\u306e\u533a\u9593\u63a8\u5b9a\u6b63\u898f\u5206\u5e03\u8fd1\u4f3c\u3092\u7528\u3044\u305f\u7c21\u6613\u7684\u306a\u65b9\u6cd5\">\u5272\u5408\u306e\u533a\u9593\u63a8\u5b9a\uff08\u6b63\u898f\u5206\u5e03\u8fd1\u4f3c\u3092\u7528\u3044\u305f\u7c21\u6613\u7684\u306a\u65b9\u6cd5\uff09<\/h2>\n\n\n\n<p>\u5272\u5408\u306e\u5206\u6563\u306f\u3001\u5272\u5408\u3092p\u3001\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u3092n\u3068\u3059\u308b\u3068\u3001<\/p>\n\n\n\n<p>$$ \\frac{p (1 &#8211; p)}{n} $$<\/p>\n\n\n\n\n\n\n\n<p>\u3067\u8a08\u7b97\u3067\u304d\u308b\u3002<\/p>\n\n\n\n<p>\u6a19\u6e96\u8aa4\u5dee\u306f\u305d\u306e\u5e73\u65b9\u6839\u3067\u3001<\/p>\n\n\n\n<p>$$ \\sqrt{\\frac{p (1 &#8211; p)}{n}} $$<\/p>\n\n\n\n\n\n\n\n<p>\u3067\u8a08\u7b97\u3067\u304d\u308b\u3002<\/p>\n\n\n\n<p>\u5272\u5408\u306e\u533a\u9593\u63a8\u5b9a\u306f\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3067\u304d\u308b\u3002<\/p>\n\n\n\n<p>$$ p \\pm Z_{\\alpha\/2} \\sqrt{\\frac{p (1 &#8211; p)}{n}} $$<\/p>\n\n\n\n\n\n\n\n<p>95%\u4fe1\u983c\u533a\u9593\u3092\u8a08\u7b97\u3059\u308b\u30b9\u30af\u30ea\u30d7\u30c8\u306b\u3059\u308b\u3068\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308b\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>conf.int &lt;- function (p, n, sig.level=0.05){\n  res &lt;- c(-1, 1)*qnorm(sig.level\/2, lower.tail=F)*sqrt((p*(1-p)\/n))+p\n  print(round(c(p=p, conf.int=res),3))\n}\n<\/code><\/pre>\n\n\n\n<p>\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba100\u3067\u30010.95\u306e95%\u4fe1\u983c\u533a\u9593\u3092\u8a08\u7b97\u3059\u308b\u3068\u30010.907\u304b\u30890.993\u3068\u8a08\u7b97\u3055\u308c\u308b\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>&gt; conf.int(p=0.95,n=100)\n        p conf.int1 conf.int2 \n    0.950     0.907     0.993 <\/code><\/pre>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"Clopper-Pearson\u4fe1\u983c\u533a\u9593\u6b63\u78ba\u306a\u65b9\u6cd5\">Clopper-Pearson\u4fe1\u983c\u533a\u9593\uff08\u6b63\u78ba\u306a\u65b9\u6cd5\uff09<\/h2>\n\n\n\n<p>Clopper-Pearson\u6cd5\u306f\u3001F\u5206\u5e03\u3092\u4f7f\u3063\u305f\u65b9\u6cd5\u3067\u3001\u3088\u308a\u6b63\u78ba\u306a\u65b9\u6cd5\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<p>\u7d71\u8a08\u30bd\u30d5\u30c8R\u306e\u30b9\u30af\u30ea\u30d7\u30c8\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308b\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>clopper.pearson &lt;- function (x, n, sig.level=0.05){\n  LL &lt;- x\/(x+(n-x+1)*qf(sig.level\/2, lower.tail=F, 2*(n-x+1), 2*x))\n  UL &lt;- (x+1)*qf(sig.level\/2, lower.tail=F, 2*(x+1),2*(n-x))\/((n-x)+(x+1)*qf(sig.level\/2, lower.tail=F, 2*(x+1),2*(n-x)))\n  print(round(c(p=x\/n, \"lower limit\"=LL, \"upper limit\"=UL),3))\n}\n<\/code><\/pre>\n\n\n\n<p>0.95\u306e95%\u4fe1\u983c\u533a\u9593\u306f\u30010.887\u304b\u30890.984\u3068\u8a08\u7b97\u3055\u308c\u305f\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>&gt; clopper.pearson(x=95,n=100)\n          p lower limit upper limit \n      0.950       0.887       0.984 <\/code><\/pre>\n\n\n\n<div id=\"biost-3711425370\" class=\"biost- biost-entity-placement\"><p style=\"text-align: center;\"><span style=\"font-size: 20px;\"><strong><a href=\"https:\/\/best-biostatistics.com\/kmhl\">\uff1e\uff1e\u3082\u3046\u7d71\u8a08\u3067\u60a9\u3080\u306e\u306f\u7d42\u308f\u308a\u306b\u3057\u307e\u305b\u3093\u304b\uff1f\u00a0<\/a><\/strong><\/span><\/p>\r\n<a href=\"https:\/\/best-biostatistics.com\/kmhl\"><img class=\"aligncenter wp-image-2794 size-full\" src=\"https:\/\/best-biostatistics.com\/wp\/wp-content\/uploads\/2023\/11\/bn_r_03.png\" alt=\"\" width=\"500\" height=\"327\" \/><\/a>\r\n<p style=\"text-align: center;\"><span style=\"color: #ff0000; font-size: 20px;\"><strong><span class=\"marker2\">\u21911\u4e07\u4eba\u4ee5\u4e0a\u306e\u533b\u7642\u5f93\u4e8b\u8005\u304c\u8cfc\u8aad\u4e2d<\/span><\/strong><\/span><\/p><\/div><h2 class=\"wp-block-heading\" id=\"\u5272\u5408\u306e\u4fe1\u983c\u533a\u9593\u30a8\u30af\u30bb\u30eb\u8a08\u7b97\u6a5f\">\u5272\u5408\u306e\u4fe1\u983c\u533a\u9593\u30a8\u30af\u30bb\u30eb\u8a08\u7b97\u6a5f<\/h2>\n\n\n\n<p>\u30a8\u30af\u30bb\u30eb\u30d5\u30a1\u30a4\u30eb\u3092\u4f5c\u6210\u3057\u305f\u3002<\/p>\n\n\n\n<p>\u826f\u3051\u308c\u3070\u3069\u3046\u305e\u3002<\/p>\n\n\n\n<p><a href=\"https:\/\/happyhappygk.base.ec\/items\/34122108\">\u5272\u5408\u306e\u4fe1\u983c\u533a\u9593\u8a08\u7b97\u6a5f\u3010\u30a8\u30af\u30bb\u30eb\u8a08\u7b97\u6a5f\u3011 | TKER SHOP<\/a><\/p>\n\n\n\n<p>\u4f7f\u3044\u65b9\u52d5\u753b\u3092\u4f5c\u6210\u3057\u305f\u3002<\/p>\n\n\n\n<p>\u3053\u3061\u3089\u3082\u3088\u3051\u308c\u3070\u3002<\/p>\n\n\n\n<p><iframe width=\"560\" height=\"315\" src=\"https:\/\/www.youtube.com\/embed\/A_1wiwOKhik?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen=\"allowfullscreen\" title=\"\u5272\u5408\u306e\u4fe1\u983c\u533a\u9593\u30a8\u30af\u30bb\u30eb\u8a08\u7b97\u6a5f\"><\/iframe><cite class=\"hatena-citation\"><a href=\"https:\/\/youtu.be\/A_1wiwOKhik\">youtu.be<\/a><\/cite><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u5272\u5408\u306e\u4fe1\u983c\u533a\u9593\u8a08\u7b97\u30a2\u30d7\u30ea<\/h2>\n\n\n\n<p>\u30c7\u30b9\u30af\u30c8\u30c3\u30d7\u30a2\u30d7\u30ea\u306f\u3053\u3061\u3089\u2193<\/p>\n\n\n\n<p><a href=\"https:\/\/happyhappygk.base.ec\/items\/96256224\" data-type=\"link\" data-id=\"https:\/\/happyhappygk.base.ec\/items\/96256224\">\u5272\u5408\u306e\u4fe1\u983c\u533a\u9593\u8a08\u7b97\u30a2\u30d7\u30ea\u3010Win \u7248\u3011<\/a><\/p>\n\n\n\n<p><a href=\"https:\/\/happyhappygk.base.ec\/items\/96582179\" data-type=\"link\" data-id=\"https:\/\/happyhappygk.base.ec\/items\/96582179\">\u5272\u5408\u306e\u4fe1\u983c\u533a\u9593\u8a08\u7b97\u30a2\u30d7\u30ea\u3010Mac \u7248\u3011<\/a><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"\u307e\u3068\u3081\">\u307e\u3068\u3081<\/h2>\n\n\n\n<p>\u5272\u5408\u306e\u4fe1\u983c\u533a\u9593\u3092\u6c42\u3081\u308b\u65b9\u6cd5\u3068\u3057\u3066\u3001\u6b63\u898f\u8fd1\u4f3c\u3092\u7528\u3044\u305f\u7c21\u6613\u7684\u306a\u65b9\u6cd5\u3068\u6b63\u78ba\u65b9\u6cd5Clopper-Pearson\u6cd5\u3092\u6bd4\u8f03\u3057\u3066\u307f\u305f\u3002<\/p>\n\n\n\n<p>\u4f7f\u3044\u5206\u3051\u306f\u8003\u3048\u305a\u306b\u3001\u3044\u3064\u3082\u6b63\u78ba\u306a\u65b9\u6cd5\u304c\u826f\u3044\u3068\u601d\u3046\u3002<\/p>\n\n\n\n<p>\u53c2\u8003\u306b\u306a\u308c\u3070\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"\u53c2\u8003\u30a6\u30a7\u30d6\u30b5\u30a4\u30c8\">\u53c2\u8003\u30b5\u30a4\u30c8<\/h2>\n\n\n\n<figure class=\"wp-block-embed is-type-wp-embed is-provider-web wp-block-embed-web\"><div class=\"wp-block-embed__wrapper\">\nhttps:\/\/bellcurve.jp\/statistics\/course\/14835.html\n<\/div><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">\u53c2\u8003\u6587\u732e<\/h2>\n\n\n\n<p><a href=\"https:\/\/academic.oup.com\/biomet\/article-abstract\/26\/4\/404\/291538?redirectedFrom=fulltext&amp;login=false\" data-type=\"link\" data-id=\"https:\/\/academic.oup.com\/biomet\/article-abstract\/26\/4\/404\/291538?redirectedFrom=fulltext&amp;login=false\">THE USE OF CONFIDENCE OR FIDUCIAL LIMITS ILLUSTRATED IN THE CASE OF THE BINOMIAL<\/a><\/p>\n\n\n\n<p><a href=\"https:\/\/www.tandfonline.com\/doi\/abs\/10.1080\/00031305.1998.10480550\" data-type=\"link\" data-id=\"https:\/\/www.tandfonline.com\/doi\/abs\/10.1080\/00031305.1998.10480550\">Approximate is Better than \u201cExact\u201d for Interval Estimation of Binomial Proportions<\/a><\/p>\n\n\n\n<p><a href=\"https:\/\/en.wikipedia.org\/wiki\/Binomial_proportion_confidence_interval#Clopper%E2%80%93Pearson_interval\" data-type=\"link\" data-id=\"https:\/\/en.wikipedia.org\/wiki\/Binomial_proportion_confidence_interval#Clopper%E2%80%93Pearson_interval\">Clopper\u2013Pearson interval<\/a><\/p>\n\n\n\n\n","protected":false},"excerpt":{"rendered":"<p>\u6b63\u898f\u5206\u5e03\u8fd1\u4f3c\u3092\u7528\u3044\u305f\u4fe1\u983c\u533a\u9593\u3068Clopper-Pearson \u4fe1\u983c\u533a\u9593\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5\u3002<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"swell_btn_cv_data":"","_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[5,30,9],"tags":[],"class_list":["post-408","post","type-post","status-publish","format-standard","hentry","category-r","category-30","category-9"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts\/408","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/comments?post=408"}],"version-history":[{"count":5,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts\/408\/revisions"}],"predecessor-version":[{"id":3369,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts\/408\/revisions\/3369"}],"wp:attachment":[{"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/media?parent=408"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/categories?post=408"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/tags?post=408"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}