{"id":4485,"date":"2025-12-28T17:45:00","date_gmt":"2025-12-28T08:45:00","guid":{"rendered":"https:\/\/best-biostatistics.com\/toukei-er\/?p=4485"},"modified":"2025-12-28T17:45:03","modified_gmt":"2025-12-28T08:45:03","slug":"calculating-sample-sizes-for-unequal-groups-a-guide-for-means-proportions-and-survival-analysis","status":"publish","type":"post","link":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/calculating-sample-sizes-for-unequal-groups-a-guide-for-means-proportions-and-survival-analysis\/","title":{"rendered":"\u30a2\u30f3\u30d0\u30e9\u30f3\u30b9\u306a2\u7fa4\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\u30ac\u30a4\u30c9\uff1a\u5e73\u5747\u30fb\u5272\u5408\u30fb\u751f\u5b58\u7387\u306e\u30b1\u30fc\u30b9\u5225\u89e3\u8aac"},"content":{"rendered":"\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p>\u5b9f\u52d9\u3067\u7d71\u8a08\u3092\u6271\u3063\u3066\u3044\u308b\u3068\u3001\u300c\u6bd4\u8f03\u3057\u305f\u30442\u3064\u306e\u30b0\u30eb\u30fc\u30d7\u306e\u4eba\u6570\u304c\u3069\u3046\u3057\u3066\u3082\u540c\u3058\u306b\u306a\u3089\u306a\u3044\u300d\u3068\u3044\u3046\u5834\u9762\u306b\u983b\u7e41\u306b\u906d\u9047\u3059\u308b\u3002\u4f8b\u3048\u3070\u3001\u5e0c\u5c11\u75be\u60a3\u306e\u6cbb\u9a13\u3067\u300c\u65b0\u85ac\u7fa4\u300d\u306e\u60a3\u8005\u78ba\u4fdd\u304c\u96e3\u3057\u304b\u3063\u305f\u308a\u3001Web\u30de\u30fc\u30b1\u30c6\u30a3\u30f3\u30b0\u3067\u300c\u65b0\u30c7\u30b6\u30a4\u30f3\u300d\u3092\u30ea\u30b9\u30af\u56de\u907f\u306e\u305f\u3081\u306b\u4e00\u90e8\u306e\u30e6\u30fc\u30b6\u30fc\u306b\u306e\u307f\u5148\u884c\u516c\u958b\u3057\u305f\u308a\u3059\u308b\u5834\u5408\u3060\u3002<\/p>\n\n\n\n<p>\u30d0\u30e9\u30f3\u30b9\u306e\u53d6\u308c\u305f2\u7fa4\uff081:1\uff09\u306e\u8a08\u7b97\u306f\u30b7\u30f3\u30d7\u30eb\u3060\u304c\u3001\u30a2\u30f3\u30d0\u30e9\u30f3\u30b9\u306a\uff08\u4eba\u6570\u6bd4\u304c\u7570\u306a\u308b\uff09\u5834\u5408\u306f\u5c11\u3057\u8a08\u7b97\u306e\u30b3\u30c4\u304c\u5fc5\u8981\u3067\u3042\u308b\u3002\u3053\u306e\u8a18\u4e8b\u3067\u306f\u3001\u521d\u5fc3\u8005\u306b\u5411\u3051\u3066\u4e3b\u8981\u306a3\u3064\u306e\u30b1\u30fc\u30b9\uff08\u5e73\u5747\u3001\u5272\u5408\u3001\u751f\u5b58\u7387\uff09\u306b\u304a\u3051\u308b\u8a08\u7b97\u306e\u8003\u3048\u65b9\u3092\u89e3\u8aac\u3059\u308b\u3002<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<!--more-->\n\n\n\n<h2 class=\"wp-block-heading\">\u30a2\u30f3\u30d0\u30e9\u30f3\u30b9\u306a2\u7fa4\u306b\u304a\u3051\u308b\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\u306e\u57fa\u672c<\/h2>\n\n\n\n<p>\u307e\u305a\u524d\u63d0\u3068\u3057\u3066\u30012\u7fa4\u306e\u4eba\u6570\u6bd4\u3092 $1 : k$ \u3068\u7f6e\u304f\uff08$k$ \u306f\u300c\u5272\u308a\u4ed8\u3051\u6bd4\u300d\u3068\u547c\u3070\u308c\u308b\uff09\u3002<\/p>\n\n\n\n<p>1:1\u306e\u6642\u306b\u5fc5\u8981\u306a\u300c\u5404\u7fa4\u306e\u4eba\u6570\u300d\u3092 $n$ \u3068\u3057\u305f\u5834\u5408\u3001\u5408\u8a08\u4eba\u6570\u304c\u6700\u5c0f\u306b\u306a\u308b\u306e\u306f\u5f53\u7136 $k=1$\uff081:1\uff09\u306e\u6642\u3067\u3042\u308b\u3002\u30a2\u30f3\u30d0\u30e9\u30f3\u30b9\u306b\u306a\u308c\u3070\u306a\u308b\u307b\u3069\u3001\u540c\u3058\u691c\u51fa\u529b\uff08\u5dee\u3092\u898b\u3064\u3051\u308b\u529b\uff09\u3092\u7dad\u6301\u3059\u308b\u305f\u3081\u306b\u5fc5\u8981\u306a\u300c\u5408\u8a08\u4eba\u6570\u300d\u306f\u5897\u3048\u3066\u3044\u304f\u3002\u3053\u308c\u306f\u3001\u7d71\u8a08\u5b66\u7684\u306a\u300c\u52b9\u7387\u300d\u304c\u4f4e\u4e0b\u3059\u308b\u305f\u3081\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\u5e73\u5747\u5024\u306e\u5dee\u306e\u691c\u5b9a\uff1a\u30a2\u30f3\u30d0\u30e9\u30f3\u30b9\u306a\u5834\u5408\u306e\u8a08\u7b97\u65b9\u6cd5<\/h2>\n\n\n\n<p>\u8840\u5727\u3084\u58f2\u4e0a\u91d1\u984d\u306a\u3069\u3001\u6570\u5024\u306e\u5e73\u5747\u3092\u6bd4\u3079\u308b\u5834\u5408\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u8003\u3048\u65b9\uff1a<\/strong> 2\u7fa4\u306e\u5206\u6563\uff08\u30c7\u30fc\u30bf\u306e\u30d0\u30e9\u30c4\u30ad\uff09\u304c\u7b49\u3057\u3044\u3068\u4eee\u5b9a\u3059\u308b\u3068\u30011:1\u306e\u6642\u306b\u5fc5\u8981\u306a1\u7fa4\u3042\u305f\u308a\u306e\u4eba\u6570 $n$ \u306b\u5bfe\u3057\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8abf\u6574\u3059\u308b\u3002<\/li>\n\n\n\n<li><strong>\u8a08\u7b97\u306e\u30b3\u30c4\uff1a<\/strong>\n<ul class=\"wp-block-list\">\n<li><strong>\u30b0\u30eb\u30fc\u30d71\uff08\u4eba\u6570\u304c\u5c11\u306a\u3044\u65b9\uff09\uff1a<\/strong> $n_1 = \\frac{(k+1)n}{2k}$<\/li>\n\n\n\n<li><strong>\u30b0\u30eb\u30fc\u30d72\uff08\u4eba\u6570\u304c\u591a\u3044\u65b9\uff09\uff1a<\/strong> $n_2 = k \\times n_1$<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p>\u4f8b\u3048\u3070\u30011:2\u306b\u5206\u3051\u308b\u5834\u5408\uff08$k=2$\uff09\u30011:1\u306a\u3089\u5404\u7fa4100\u4eba\uff08\u8a08200\u4eba\uff09\u3067\u6e08\u3080\u3068\u3053\u308d\u3092\u30011:2\u3067\u306f\u300c75\u4eba\u3068150\u4eba\uff08\u8a08225\u4eba\uff09\u300d\u304c\u5fc5\u8981\u306b\u306a\u308b\u3002\u5408\u8a08\u4eba\u6570\u304c1\u5272\u5f37\u5897\u3048\u308b\u8a08\u7b97\u3060\u3002<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<div id=\"biost-2655482850\" 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\">\u5272\u5408\u306e\u5dee\u306e\u691c\u5b9a\uff1a\u30a2\u30f3\u30d0\u30e9\u30f3\u30b9\u306a\u5834\u5408\u306e\u8a08\u7b97\u65b9\u6cd5<\/h2>\n\n\n\n<p>\u30b3\u30f3\u30d0\u30fc\u30b8\u30e7\u30f3\u7387\u3084\u75c5\u6c17\u306e\u6cbb\u7652\u7387\u306a\u3069\u3001\u300cYes\u304bNo\u304b\u300d\u306e\u5272\u5408\u3092\u6bd4\u3079\u308b\u5834\u5408\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u8003\u3048\u65b9\uff1a<\/strong> \u57fa\u672c\u7684\u306b\u306f\u5e73\u5747\u5024\u306e\u8a08\u7b97\u3068\u540c\u69d8\u3060\u304c\u3001\u5272\u5408\u306e\u5834\u5408\u306f\u300c\u305d\u306e\u5272\u5408\u81ea\u4f53\uff0810%\u306a\u306e\u304b50%\u306a\u306e\u304b\uff09\u300d\u306b\u3088\u3063\u3066\u5fc5\u8981\u306a\u4eba\u6570\u304c\u5927\u304d\u304f\u5909\u52d5\u3059\u308b\u3002<\/li>\n\n\n\n<li><strong>\u8a08\u7b97\u306e\u30b3\u30c4\uff1a<\/strong> 1:1\u306e\u8a08\u7b97\u5f0f\u306b\u304a\u3051\u308b\u300c\u6a19\u6e96\u8aa4\u5dee\u300d\u306e\u90e8\u5206\u306b\u3001\u5272\u308a\u4ed8\u3051\u6bd4 $k$ \u3092\u53cd\u6620\u3055\u305b\u305f\u300c\u91cd\u307f\u4ed8\u304d\u5e73\u5747\u300d\u3092\u7d44\u307f\u8fbc\u3080\u3002\u591a\u304f\u306e\u7d71\u8a08\u30bd\u30d5\u30c8\uff08EZR\u3084SAS\u306a\u3069\uff09\u3067\u306f\u3001\u5358\u7d14\u306b\u300cAllocation ratio\u300d\u306e\u9805\u76ee\u306b $k$ \u306e\u5024\u3092\u5165\u529b\u3059\u308b\u3060\u3051\u3067\u7b97\u51fa\u53ef\u80fd\u3067\u3042\u308b\u3002<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\u751f\u5b58\u7387\u306e\u6bd4\uff08\u30cf\u30b6\u30fc\u30c9\u6bd4\uff09\u306e\u691c\u5b9a\uff1a\u30a2\u30f3\u30d0\u30e9\u30f3\u30b9\u306a\u5834\u5408\u306e\u8a08\u7b97\u65b9\u6cd5<\/h2>\n\n\n\n<p>\u751f\u5b58\u671f\u9593\u3084\u30a4\u30d9\u30f3\u30c8\u767a\u751f\u307e\u3067\u306e\u671f\u9593\u3092\u6bd4\u8f03\u3059\u308b\u5834\u5408\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u8003\u3048\u65b9\uff1a<\/strong> \u751f\u5b58\u6642\u9593\u89e3\u6790\uff08\u30ed\u30b0\u30e9\u30f3\u30af\u691c\u5b9a\u306a\u3069\uff09\u3067\u306f\u3001\u5fc5\u8981\u306a\u306e\u306f\u4eba\u6570\u305d\u306e\u3082\u306e\u3088\u308a\u3082\u3001<span class=\"swl-marker mark_orange\">\u300c\u4f55\u4ef6\u306e\u30a4\u30d9\u30f3\u30c8\uff08\u6b7b\u4ea1\u3084\u518d\u767a\u306a\u3069\uff09\u304c\u767a\u751f\u3059\u308b\u304b\u300d<\/span>\u3067\u3042\u308b\u3002<\/li>\n\n\n\n<li>\u8a08\u7b97\u306e\u30b3\u30c4\uff1a\u5168\u30a4\u30d9\u30f3\u30c8\u6570 $E$ \u3092\u6c42\u3081\u305f\u5f8c\u3001\u5404\u7fa4\u306e\u4eba\u6570\u3092 $n_1, n_2$ \u3068\u3059\u308b\u3068\u3001\u7d71\u8a08\u5b66\u7684\u306a\u5206\u6563\u52b9\u7387\u306f $\\frac{k}{(1+k)^2}$ \u306e\u6bd4\u7387\u3067\u5909\u5316\u3059\u308b\u3002<\/li>\n<\/ul>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>\u3010\u30b3\u30e9\u30e0\uff1a\u5206\u6563\u52b9\u7387\u3068\u306f\uff1f\u3011<\/p>\n\n\n\n<p>\u3053\u306e\u6570\u5f0f\u306f\u300c\u30c7\u30fc\u30bf\u306e\u5bc6\u5ea6\u306e\u6fc3\u3055\u300d\u3092\u8868\u3059\u30b9\u30b3\u30a2\u306e\u3088\u3046\u306a\u3082\u306e\u3060\u3002$k=1$\uff081:1\uff09\u306e\u6642\u3001\u3053\u306e\u5024\u306f\u6700\u5927\u5024\u306e $0.25$ \u3068\u306a\u308a\u3001\u6700\u3082\u52b9\u7387\u3088\u304f\u5dee\u3092\u691c\u51fa\u3067\u304d\u308b\u3002\u3057\u304b\u3057\u3001\u4f8b\u3048\u3070 1:4\uff08$k=4$\uff09\u306b\u3059\u308b\u3068\u5024\u306f $0.16$ \u307e\u3067\u4f4e\u4e0b\u3059\u308b\u3002<\/p>\n\n\n\n<p>\u7247\u65b9\u306e\u4eba\u6570\u3092\u3044\u304f\u3089\u5897\u3084\u3057\u3066\u3082\u3001\u3082\u3046\u7247\u65b9\u306e\u4eba\u6570\uff08\u30a4\u30d9\u30f3\u30c8\u6570\uff09\u304c\u5c11\u306a\u3044\u3068\u3001\u6bd4\u8f03\u306e\u7cbe\u5ea6\u306f\u4f4e\u3044\u65b9\u306b\u5f15\u304d\u305a\u3089\u308c\u3066\u3057\u307e\u3046\u3002\u305d\u306e\u305f\u3081\u3001\u30a2\u30f3\u30d0\u30e9\u30f3\u30b9\u306b\u306a\u308c\u3070\u306a\u308b\u307b\u3069\u3001\u5168\u4f53\u3067\u3088\u308a\u591a\u304f\u306e\u30a4\u30d9\u30f3\u30c8\u6570\u304c\u5fc5\u8981\u306b\u306a\u308b\u306e\u3067\u3042\u308b\u3002<\/p>\n<\/blockquote>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\u304a\u3059\u3059\u3081\u306f\u30d0\u30e9\u30f3\u30b9\u304c\u53d6\u308c\u305f2\u7fa4 \u2015 \u305d\u306e\u7406\u7531<\/h2>\n\n\n\n<p>\u5b9f\u52d9\u4e0a\u306e\u5236\u7d04\u304c\u306a\u3044\u9650\u308a\u3001\u7d71\u8a08\u5b66\u7684\u306b\u306f\u300c1:1\u300d\u304c\u6700\u3082\u63a8\u5968\u3055\u308c\u308b\u3002\u7406\u7531\u306f\u4e3b\u306b3\u3064\u3042\u308b\u3002<\/p>\n\n\n\n<ol start=\"1\" class=\"wp-block-list\">\n<li><strong>\u6700\u5c0f\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u3067\u6e08\u3080\uff1a<\/strong> 1:1\u304c\u6700\u3082\u52b9\u7387\u3088\u304f\u5dee\u3092\u691c\u51fa\u3067\u304d\u308b\u305f\u3081\u3001\u30b3\u30b9\u30c8\u3084\u6642\u9593\u3092\u6700\u5c0f\u9650\u306b\u6291\u3048\u3089\u308c\u308b\u3002<\/li>\n\n\n\n<li><strong>\u9811\u5065\u6027\uff08\u30ed\u30d0\u30b9\u30c8\u6027\uff09\uff1a<\/strong> \u300c\u7b49\u5206\u6563\u6027\uff08\u30d0\u30e9\u30c4\u30ad\u304c\u540c\u3058\u3067\u3042\u308b\u3053\u3068\uff09\u300d\u306e\u4eee\u5b9a\u304c\u5d29\u308c\u305f\u6642\u3001\u4eba\u6570\u304c\u4e0d\u5747\u8861\u3060\u3068\u691c\u5b9a\u7d50\u679c\u306e\u4fe1\u983c\u6027\u304c\u4f4e\u304f\u306a\u308a\u3084\u3059\u3044\u3002<\/li>\n\n\n\n<li><strong>\u89e3\u91c8\u304c\u30b7\u30f3\u30d7\u30eb\uff1a<\/strong> \u7b2c\u4e09\u8005\u304c\u898b\u305f\u969b\u306b\u3082\u300c\u516c\u5e73\u306a\u6bd4\u8f03\u300d\u3068\u3057\u3066\u53d7\u3051\u5165\u308c\u3089\u308c\u3084\u3059\u304f\u3001\u8aac\u660e\u30b3\u30b9\u30c8\u304c\u4e0b\u304c\u308b\u3002<\/li>\n<\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\u307e\u3068\u3081<\/h2>\n\n\n\n<p>\u30a2\u30f3\u30d0\u30e9\u30f3\u30b9\u306a2\u7fa4\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\u306f\u3001\u300c<span class=\"swl-marker mark_orange\">1:1\u306e\u6642\u306e\u5fc5\u8981\u4eba\u6570\u3092\u30d9\u30fc\u30b9\u306b\u3001\u5272\u308a\u4ed8\u3051\u6bd4 $k$ \u3092\u52a0\u5473\u3057\u3066\u8abf\u6574\u3059\u308b\u300d<\/span>\u306e\u304c\u57fa\u672c\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u5e73\u5747\u30fb\u5272\u5408\uff1a<\/strong> \u5408\u8a08\u4eba\u6570\u306f\u5897\u3048\u308b\u304c\u3001\u30bd\u30d5\u30c8\u3092\u4f7f\u3048\u3070\u8a08\u7b97\u81ea\u4f53\u306f\u5bb9\u6613\u3002<\/li>\n\n\n\n<li><strong>\u751f\u5b58\u7387\uff1a<\/strong> \u5206\u6563\u52b9\u7387\u304c\u4f4e\u4e0b\u3057\u3001\u30a4\u30d9\u30f3\u30c8\u78ba\u4fdd\u306e\u305f\u3081\u306e\u89b3\u5bdf\u671f\u9593\u304c\u5ef6\u3073\u308b\u30ea\u30b9\u30af\u304c\u3042\u308b\u3002<\/li>\n\n\n\n<li><strong>\u9244\u5247\uff1a<\/strong> \u53ef\u80fd\u306a\u9650\u308a1:1\u3092\u76ee\u6307\u3057\u3001\u3084\u3080\u3092\u5f97\u306a\u3044\u5834\u5408\u306e\u307f\u30a2\u30f3\u30d0\u30e9\u30f3\u30b9\u3092\u53d7\u3051\u5165\u308c\u308b\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u307e\u305a\u306f\u3001\u624b\u6301\u3061\u306e\u7d71\u8a08\u30bd\u30d5\u30c8\u3084\u30aa\u30f3\u30e9\u30a4\u30f3\u8a08\u7b97\u30c4\u30fc\u30eb\u306b\u300cAllocation Ratio = 2\u300d\u306a\u3069\u3092\u5165\u529b\u3057\u3001\u4eba\u6570\u304c\u3069\u3046\u5909\u5316\u3059\u308b\u304b\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u3057\u3066\u307f\u308b\u3053\u3068\u304b\u3089\u59cb\u3081\u3066\u307b\u3057\u3044\u3002<\/p>\n\n\n\n\n\n\n\n<h2 class=\"wp-block-heading\">\u304a\u3059\u3059\u3081\u66f8\u7c4d<\/h2>\n\n\n\n<p><a href=\"https:\/\/amzn.to\/4phQ2bU\">\u8ab0\u3082\u6559\u3048\u3066\u304f\u308c\u306a\u304b\u3063\u305f\u3000\u533b\u7642\u7d71\u8a08\u306e\u4f7f\u3044\u5206\u3051\u301c\u8ff7\u3044\u3084\u3059\u3044\u89e3\u6790\u624b\u6cd5\u306e\u9078\u3073\u65b9\u304c\uff0cR\u3067\u5b9f\u611f\u3057\u306a\u304c\u3089\u308f\u304b\u308b\uff01<\/a><\/p>\n\n\n\n<hr class=\"wp-block-separator 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