{"id":291,"date":"2022-07-07T09:59:54","date_gmt":"2022-07-07T00:59:54","guid":{"rendered":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/pooled-standard-deviation-for-sample-size-calculation\/"},"modified":"2025-04-26T07:34:50","modified_gmt":"2025-04-25T22:34:50","slug":"pooled-standard-deviation-for-sample-size-calculation","status":"publish","type":"post","link":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/pooled-standard-deviation-for-sample-size-calculation\/","title":{"rendered":"\u5fc5\u8981\u306a\u30b5\u30f3\u30d7\u30eb\u6570\u8a08\u7b97\u306e\u305f\u3081\u306e 2 \u7fa4\u5171\u901a\u306e\u6a19\u6e96\u504f\u5dee\u306e\u6c42\u3081\u65b9"},"content":{"rendered":"\n<p>2\u7fa4\u306e\u5e73\u5747\u5024\u6bd4\u8f03\u3001\u3044\u308f\u3086\u308b\uff54\u691c\u5b9a\u306e\u305f\u3081\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\u306e\u969b\u306e\uff12\u7fa4\u5171\u901a\u306e\u6a19\u6e96\u504f\u5dee\u306e\u6c42\u3081\u65b9\u3002<\/p>\n\n\n\n<p>\uff12\u7fa4\u5171\u901a\u306e\u6a19\u6e96\u504f\u5dee\u3068\u306f\u3001\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u3067\u91cd\u307f\u4ed8\u3051\u3057\u305f\u3001\u6a19\u6e96\u504f\u5dee\u306e\u91cd\u307f\u4ed8\u3051\u5e73\u5747\u306e\u3053\u3068\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<!--more-->\n\n\n\n<h2 class=\"wp-block-heading\" id=\"\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\u306e\u305f\u3081\u306e-2-\u7fa4\u5171\u901a\u306e\u6a19\u6e96\u504f\u5dee\u306e\u8a08\u7b97\u5f0f\">\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\u306e\u305f\u3081\u306e 2 \u7fa4\u5171\u901a\u306e\u6a19\u6e96\u504f\u5dee\u306e\u8a08\u7b97\u5f0f<\/h2>\n\n\n\n<p>\uff12\u7fa4\u5171\u901a\u306e\u6a19\u6e96\u504f\u5dee\u306e\u3082\u3068\u3068\u306a\u308b\u30012\u7fa4\u5171\u901a\u306e\u4e0d\u504f\u5206\u6563\u3068\u306f\u3001\u4ee5\u4e0b\u306e\u5f0f\u3067\u8a08\u7b97\u3067\u304d\u308b\u3002<\/p>\n\n\n\n<p>$$ s^2 = \\frac{(n_A &#8211; 1) S_A^2 + (n_B &#8211; 1) S_B^2}{(n_A &#8211; 1) + (n_B -1)} $$<\/p>\n\n\n\n\n\n\n\n<p>A\u3068B\u306f\u3001\u305d\u308c\u305e\u308c\u306e\u7fa4\u306e\u540d\u524d\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<p>$ n_A $, $ n_B $ \u306f\u3001\u305d\u308c\u305e\u308c\u306e\u7fa4\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<p>$ S_A^2 $, $ S_B^2 $ \u306f\u3001\u5404\u7fa4\u306e\u4e0d\u504f\u5206\u6563\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<p>\u8a08\u7b97\u3055\u308c\u305f $ s^2 $ \u306e\u5e73\u65b9\u6839\u3092\u8a08\u7b97\u3059\u308b\u3068\u3001\uff12\u7fa4\u5171\u901a\u306e\u6a19\u6e96\u504f\u5dee\u3068\u306a\u308b\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\u306e\u305f\u3081\u306e-2-\u7fa4\u5171\u901a\u306e\u6a19\u6e96\u504f\u5dee\u8a08\u7b97\u4f8b\">\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\u306e\u305f\u3081\u306e 2 \u7fa4\u5171\u901a\u306e\u6a19\u6e96\u504f\u5dee\u8a08\u7b97\u4f8b<\/h2>\n\n\n\n<p>\u5148\u884c\u7814\u7a76\u304b\u3089\u3001\u4ee5\u4e0b\u306e\u60c5\u5831\u304c\u5f97\u3089\u308c\u305f\u3068\u3059\u308b\u3002<\/p>\n\n\n\n<p>\u3053\u306e\u6642\u306e\uff12\u7fa4\u5171\u901a\u306e\u6a19\u6e96\u504f\u5dee\u3092\u8a08\u7b97\u3057\u3066\u307f\u308b\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A\u7fa4\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u304c16\u4f8b\u3001B\u7fa4\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u304c21\u4f8b<\/li>\n\n\n\n<li>A\u7fa4\u306e\u6a19\u6e96\u504f\u5dee\u304c6.5\u3001B\u7fa4\u306e\u6a19\u6e96\u504f\u5dee\u304c5.2<\/li>\n<\/ul>\n\n\n\n<p>\u3053\u306e\u3068\u304d\u307e\u305a\u4e21\u7fa4\u306e\u4e0d\u504f\u5206\u6563\u3092\u8a08\u7b97\u3059\u308b\u3068\u3001\u305d\u308c\u305e\u308c42.25\u300127.04\u3068\u8a08\u7b97\u3055\u308c\u308b\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code><span class=\"synStatement\">&gt;<\/span> sd <span class=\"synStatement\">&lt;-<\/span> <span class=\"synIdentifier\">c<\/span><span class=\"synSpecial\">(<\/span><span class=\"synConstant\">6.5<\/span><span class=\"synSpecial\">,<\/span> <span class=\"synConstant\">5.2<\/span><span class=\"synSpecial\">)<\/span>\n<span class=\"synStatement\">&gt;<\/span> sd<span class=\"synStatement\">^<\/span><span class=\"synConstant\">2<\/span>\n<span class=\"synSpecial\">&#91;<\/span><span class=\"synConstant\">1<\/span><span class=\"synSpecial\">]<\/span> <span class=\"synConstant\">42.25<\/span> <span class=\"synConstant\">27.04<\/span>\n<\/code><\/pre>\n\n\n\n<p>\u4e0a\u8a18\u306e\u5f0f\u306b\u4ee3\u5165\u3057\u3066\u30012\u7fa4\u5171\u901a\u306e\u4e0d\u504f\u5206\u6563\u3092\u8a08\u7b97\u3059\u308b\u3002<\/p>\n\n\n\n<p>\u307e\u305a\u5206\u5b50\u3092\u8a08\u7b97\u3057\u3066\u307f\u308b\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code><span class=\"synStatement\">&gt;<\/span> <span class=\"synSpecial\">(<\/span><span class=\"synConstant\">16<\/span><span class=\"synStatement\">-<\/span><span class=\"synConstant\">1<\/span><span class=\"synSpecial\">)<\/span><span class=\"synStatement\">*<\/span><span class=\"synConstant\">42.25<\/span> <span class=\"synStatement\">+<\/span> <span class=\"synSpecial\">(<\/span><span class=\"synConstant\">21<\/span><span class=\"synStatement\">-<\/span><span class=\"synConstant\">1<\/span><span class=\"synSpecial\">)<\/span><span class=\"synStatement\">*<\/span><span class=\"synConstant\">27.04<\/span>\n<span class=\"synSpecial\">&#91;<\/span><span class=\"synConstant\">1<\/span><span class=\"synSpecial\">]<\/span> <span class=\"synConstant\">1174.55<\/span>\n<\/code><\/pre>\n\n\n\n<p>\u5206\u6bcd\u306f\u300116-1+21-1 = 35\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code><span class=\"synStatement\">&gt;<\/span> <span class=\"synSpecial\">(<\/span><span class=\"synConstant\">16<\/span><span class=\"synStatement\">-<\/span><span class=\"synConstant\">1<\/span><span class=\"synSpecial\">)<\/span><span class=\"synStatement\">+<\/span><span class=\"synSpecial\">(<\/span><span class=\"synConstant\">21<\/span><span class=\"synStatement\">-<\/span><span class=\"synConstant\">1<\/span><span class=\"synSpecial\">)<\/span>\n<span class=\"synSpecial\">&#91;<\/span><span class=\"synConstant\">1<\/span><span class=\"synSpecial\">]<\/span> <span class=\"synConstant\">35<\/span>\n<\/code><\/pre>\n\n\n\n<p>\u5206\u5b50\u00f7\u5206\u6bcd\u3067\u30012 \u7fa4\u5171\u901a\u306e\u4e0d\u504f\u5206\u6563\u304c\u8a08\u7b97\u3067\u304d\u308b\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code><span class=\"synStatement\">&gt;<\/span> <span class=\"synConstant\">1174.55<\/span><span class=\"synStatement\">\/<\/span><span class=\"synConstant\">35<\/span>\n<span class=\"synSpecial\">&#91;<\/span><span class=\"synConstant\">1<\/span><span class=\"synSpecial\">]<\/span> <span class=\"synConstant\">33.55857<\/span>\n<\/code><\/pre>\n\n\n\n<p>2 \u7fa4\u5171\u901a\u306e\u4e0d\u504f\u5206\u6563\u306e\u5e73\u65b9\u6839\u304c\u30012 \u7fa4\u5171\u901a\u306e\u6a19\u6e96\u504f\u5dee\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code><span class=\"synStatement\">&gt;<\/span> <span class=\"synIdentifier\">sqrt<\/span><span class=\"synSpecial\">(<\/span><span class=\"synConstant\">33.55857<\/span><span class=\"synSpecial\">)<\/span>\n<span class=\"synSpecial\">&#91;<\/span><span class=\"synConstant\">1<\/span><span class=\"synSpecial\">]<\/span> <span class=\"synConstant\">5.792976<\/span>\n<\/code><\/pre>\n\n\n\n<p>\u3053\u306e\u5834\u5408\u3001\u5c0f\u6570\u70b9\u4ee5\u4e0b\u4e8c\u6841\u304f\u3089\u3044\u3067\u30015.79 \u304c2\u7fa4\u5171\u901a\u306e\u6a19\u6e96\u504f\u5dee\u306e\u63a8\u5b9a\u5024\u3068\u3044\u3046\u3053\u3068\u3067\u3088\u3044\u3060\u308d\u3046\u3002<\/p>\n\n\n\n<p>\u3082\u3068\u3082\u3068\u304c\u5c0f\u6570\u70b9\u4ee5\u4e0b\u4e00\u6841\u3060\u3063\u305f\u306e\u3067\u3001\u4e8c\u6841\u3067\u5341\u5206\u3060\u3002<\/p>\n\n\n\n<div id=\"biost-4187377765\" 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\" 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data-id=\"https:\/\/amzn.to\/430SYlf\">EZR\u3067\u3084\u3055\u3057\u304f\u5b66\u3076\u7d71\u8a08\u5b66 \u6539\u8a023\u7248 \u301cEBM\u306e\u5b9f\u8df5\u304b\u3089\u81e8\u5e8a\u7814\u7a76\u307e\u3067\u301c<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>2\u7fa4\u306e\u5e73\u5747\u5024\u6bd4\u8f03\u3001\u3044\u308f\u3086\u308b\uff54\u691c\u5b9a\u306e\u305f\u3081\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\u306e\u969b\u306e\uff12\u7fa4\u5171\u901a\u306e\u6a19\u6e96\u504f\u5dee\u306e\u6c42\u3081\u65b9\u3002 \uff12\u7fa4\u5171\u901a\u306e\u6a19\u6e96\u504f\u5dee\u3068\u306f\u3001\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u3067\u91cd\u307f\u4ed8\u3051\u3057\u305f\u3001\u6a19\u6e96\u504f\u5dee\u306e\u91cd\u307f\u4ed8\u3051\u5e73\u5747\u306e\u3053\u3068\u3067\u3042\u308b\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":[5,35,16],"tags":[],"class_list":["post-291","post","type-post","status-publish","format-standard","hentry","category-r","category-t-","category-16"],"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\/291","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=291"}],"version-history":[{"count":3,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts\/291\/revisions"}],"predecessor-version":[{"id":3581,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts\/291\/revisions\/3581"}],"wp:attachment":[{"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/media?parent=291"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/categories?post=291"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/tags?post=291"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}