{"id":4002,"date":"2025-06-17T00:01:21","date_gmt":"2025-06-16T15:01:21","guid":{"rendered":"https:\/\/best-biostatistics.com\/toukei-er\/?p=4002"},"modified":"2025-06-17T00:01:22","modified_gmt":"2025-06-16T15:01:22","slug":"equivalence-test-and-sample-size-calculation-practical-approach-in-clinical-research","status":"publish","type":"post","link":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/equivalence-test-and-sample-size-calculation-practical-approach-in-clinical-research\/","title":{"rendered":"\u540c\u7b49\u6027\u691c\u5b9a\u3068\u5fc5\u8981\u30b5\u30f3\u30d7\u30eb\u6570\u8a08\u7b97\uff1a\u81e8\u5e8a\u7814\u7a76\u306b\u304a\u3051\u308b\u5b9f\u8df5\u7684\u30a2\u30d7\u30ed\u30fc\u30c1"},"content":{"rendered":"\n<p>\u65b0\u3057\u3044\u6cbb\u7642\u6cd5\u304c\u65e2\u5b58\u306e\u3082\u306e\u3068\u540c\u7b49\u3067\u3042\u308b\u3053\u3068\u3092\u8a3c\u660e\u3057\u305f\u3044\u3002\u305d\u3093\u306a\u6642\u3001\u5f93\u6765\u306e\u300c\u512a\u308c\u3066\u3044\u308b\u304b\u300d\u3092\u554f\u3046\u7814\u7a76\u3060\u3051\u3067\u306f\u4e0d\u5341\u5206\u3067\u3042\u308b\u3002\u672c\u8a18\u4e8b\u3067\u306f\u3001\u81e8\u5e8a\u73fe\u5834\u3067\u5f79\u7acb\u3064<strong>\u540c\u7b49\u6027\u691c\u5b9a<\/strong>\u306e\u57fa\u672c\u304b\u3089\u3001\u533b\u5e2b\u304c\u76f4\u9762\u3059\u308b\u5177\u4f53\u7684\u306a\u30b1\u30fc\u30b9\u3067\u306e\u6d3b\u7528\u6cd5\u3001\u305d\u3057\u3066\u7814\u7a76\u306e\u6210\u529f\u306b\u4e0d\u53ef\u6b20\u306a<strong>\u5fc5\u8981\u30b5\u30f3\u30d7\u30eb\u6570<\/strong>\u306e\u7b97\u51fa\u65b9\u6cd5\u307e\u3067\u3092\u3001R\u3092\u7528\u3044\u305f\u5b9f\u8df5\u7684\u306a\u8a08\u7b97\u4f8b\u3092\u4ea4\u3048\u3066\u8a73\u3057\u304f\u89e3\u8aac\u3059\u308b\u3002\u3042\u306a\u305f\u306e\u81e8\u5e8a\u7814\u7a76\u3092\u3088\u308a\u78ba\u5b9f\u306a\u3082\u306e\u306b\u3059\u308b\u305f\u3081\u306e\u5b9f\u8df5\u7684\u77e5\u8b58\u304c\u3053\u3053\u306b\u3042\u308b\u3002<\/p>\n\n\n\n<!--more-->\n\n\n\n<h2 class=\"wp-block-heading\">\u540c\u7b49\u6027\u691c\u5b9a\u306e\u6982\u8981<\/h2>\n\n\n\n<p>\u81e8\u5e8a\u7814\u7a76\u306b\u304a\u3044\u3066\u3001\u65b0\u3057\u3044\u6cbb\u7642\u6cd5\u3084\u85ac\u5264\u304c\u65e2\u5b58\u306e\u3082\u306e\u3068\u540c\u7b49\u3067\u3042\u308b\u304b\u3092\u691c\u8a3c\u3057\u305f\u3044\u5834\u5408\u304c\u3042\u308b\u3002\u4f8b\u3048\u3070\u3001\u526f\u4f5c\u7528\u304c\u5c11\u306a\u3044\u65b0\u3057\u3044\u85ac\u5264\u304c\u3001\u65e2\u5b58\u306e\u85ac\u5264\u3068\u540c\u7b49\u306e\u52b9\u679c\u3092\u6301\u3064\u3053\u3068\u3092\u793a\u3057\u305f\u3044\u5834\u5408\u306a\u3069\u304c\u3053\u308c\u306b\u8a72\u5f53\u3059\u308b\u3002\u3053\u306e\u3088\u3046\u306a\u72b6\u6cc1\u3067\u7528\u3044\u3089\u308c\u308b\u306e\u304c\u300c\u540c\u7b49\u6027\u691c\u5b9a\uff08Equivalence Test\uff09\u300d\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<p>\u5f93\u6765\u306e\u512a\u8d8a\u6027\u691c\u5b9a\uff08Superiority Test\uff09\u304c\u300c\u65b0\u3057\u3044\u6cbb\u7642\u6cd5\u304c\u65e2\u5b58\u306e\u6cbb\u7642\u6cd5\u3088\u308a\u3082\u512a\u308c\u3066\u3044\u308b\u304b\u300d\u3092\u554f\u3046\u306e\u306b\u5bfe\u3057\u3001\u540c\u7b49\u6027\u691c\u5b9a\u306f\u300c2\u3064\u306e\u6cbb\u7642\u6cd5\u9593\u306b\u81e8\u5e8a\u7684\u306b\u610f\u5473\u306e\u3042\u308b\u5dee\u304c\u306a\u3044\u304b\u300d\u3092\u554f\u3046\u3002\u3053\u3053\u3067\u91cd\u8981\u306a\u306e\u306f\u3001\u300c\u81e8\u5e8a\u7684\u306b\u610f\u5473\u306e\u3042\u308b\u5dee\u300d\u3068\u3044\u3046\u6982\u5ff5\u3067\u3042\u308b\u3002\u7d71\u8a08\u7684\u306b\u6709\u610f\u5dee\u304c\u306a\u3044\u5834\u5408\u3067\u3082\u3001\u305d\u306e\u5dee\u304c\u81e8\u5e8a\u7684\u306b\u8a31\u5bb9\u7bc4\u56f2\u5185\u3067\u3042\u308b\u304b\u3069\u3046\u304b\u306f\u5225\u9014\u8003\u616e\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\u3002\u3053\u306e\u8a31\u5bb9\u7bc4\u56f2\u3092\u300c\u540c\u7b49\u6027\u30de\u30fc\u30b8\u30f3\uff08Equivalence Margin\uff09\u300d\u3068\u547c\u3073\u3001\u901a\u5e38\u3001\u4e8b\u524d\u306b\u81e8\u5e8a\u7684\u306a\u5224\u65ad\u306b\u57fa\u3065\u3044\u3066\u8a2d\u5b9a\u3055\u308c\u306a\u3051\u308c\u3070\u306a\u3089\u306a\u3044\u3002<\/p>\n\n\n\n<p>\u540c\u7b49\u6027\u691c\u5b9a\u3067\u306f\u3001\u5e30\u7121\u4eee\u8aac\uff08H0\u200b\uff09\u3068\u5bfe\u7acb\u4eee\u8aac\uff08H1\u200b\uff09\u306e\u8a2d\u5b9a\u304c\u512a\u8d8a\u6027\u691c\u5b9a\u3068\u306f\u9006\u306b\u306a\u308b\u3002<\/p>\n\n\n\n<p><strong>\u512a\u8d8a\u6027\u691c\u5b9a\u306e\u5834\u5408\uff1a <\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>H0\u200b: 2\u7fa4\u9593\u306b\u5dee\u304c\u306a\u3044 <\/li>\n\n\n\n<li>H1\u200b: 2\u7fa4\u9593\u306b\u5dee\u304c\u3042\u308b<\/li>\n<\/ul>\n\n\n\n<p><strong>\u540c\u7b49\u6027\u691c\u5b9a\u306e\u5834\u5408\uff1a <\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>H0\u200b: 2\u7fa4\u9593\u306b\u81e8\u5e8a\u7684\u306b\u610f\u5473\u306e\u3042\u308b\u5dee\u304c\u3042\u308b\uff08\u3064\u307e\u308a\u3001\u540c\u7b49\u3067\u306f\u306a\u3044\uff09 <\/li>\n\n\n\n<li>H1\u200b: 2\u7fa4\u9593\u306b\u81e8\u5e8a\u7684\u306b\u610f\u5473\u306e\u3042\u308b\u5dee\u304c\u306a\u3044\uff08\u3064\u307e\u308a\u3001\u540c\u7b49\u3067\u3042\u308b\uff09<\/li>\n<\/ul>\n\n\n\n<p>\u540c\u7b49\u6027\u691c\u5b9a\u306e\u4e3b\u306a\u624b\u6cd5\u3068\u3057\u3066\u306f\u3001Two One-Sided Tests (TOST) \u30d7\u30ed\u30b7\u30fc\u30b8\u30e3\u304c\u5e83\u304f\u7528\u3044\u3089\u308c\u308b\u3002\u3053\u308c\u306f\u3001\u4e8b\u524d\u306b\u8a2d\u5b9a\u3055\u308c\u305f\u540c\u7b49\u6027\u30de\u30fc\u30b8\u30f3\uff08\u0394\uff09\u3092\u7528\u3044\u3066\u3001\u4ee5\u4e0b\u306e2\u3064\u306e\u7247\u5074\u691c\u5b9a\u3092\u540c\u6642\u306b\u884c\u3044\u3001\u4e21\u65b9\u306e\u691c\u5b9a\u3067\u5e30\u7121\u4eee\u8aac\u304c\u68c4\u5374\u3055\u308c\u305f\u5834\u5408\u306b\u540c\u7b49\u3067\u3042\u308b\u3068\u7d50\u8ad6\u3065\u3051\u308b\u65b9\u6cd5\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u6cbb\u7642A\u304c\u6cbb\u7642B\u3088\u308a\u2212\u0394\u4ee5\u4e0a\u5927\u304d\u3044\u304b <\/li>\n\n\n\n<li>\u6cbb\u7642A\u304c\u6cbb\u7642B\u3088\u308a+\u0394\u4ee5\u4e0b\u5c0f\u3055\u3044\u304b<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">\u81e8\u5e8a\u7814\u7a76\u306e\u5177\u4f53\u4f8b<\/h2>\n\n\n\n<p>\u6574\u5f62\u5916\u79d1\u533b\u306eA\u533b\u5e2b\u306f\u3001\u5909\u5f62\u6027\u819d\u95a2\u7bc0\u75c7\u306e\u60a3\u8005\u306b\u5bfe\u3059\u308b\u65b0\u3057\u3044\u30ea\u30cf\u30d3\u30ea\u30c6\u30fc\u30b7\u30e7\u30f3\u30d7\u30ed\u30b0\u30e9\u30e0\uff08\u30d7\u30ed\u30b0\u30e9\u30e0Y\uff09\u3092\u691c\u8a0e\u3057\u3066\u3044\u308b\u3002\u65e2\u5b58\u306e\u30ea\u30cf\u30d3\u30ea\u30c6\u30fc\u30b7\u30e7\u30f3\u30d7\u30ed\u30b0\u30e9\u30e0\uff08\u30d7\u30ed\u30b0\u30e9\u30e0X\uff09\u3068\u6bd4\u8f03\u3057\u3066\u3001\u30d7\u30ed\u30b0\u30e9\u30e0Y\u306f\u3088\u308a\u77ed\u671f\u9593\u3067\u5b9f\u65bd\u3067\u304d\u3001\u60a3\u8005\u306e\u901a\u9662\u8ca0\u62c5\u304c\u5c11\u306a\u3044\u3068\u3044\u3046\u30e1\u30ea\u30c3\u30c8\u304c\u3042\u308b\u3002A\u533b\u5e2b\u306f\u3001\u30d7\u30ed\u30b0\u30e9\u30e0Y\u304c\u30d7\u30ed\u30b0\u30e9\u30e0X\u3068<strong>\u540c\u7b49\u306a\u75bc\u75db\u6539\u5584\u52b9\u679c\uff08VAS\u30b9\u30b3\u30a2\u306e\u5909\u5316\u91cf\uff09\u3092\u3082\u305f\u3089\u3059\u3053\u3068\u3092\u78ba\u8a8d\u3057\u305f\u3044\u3068\u8003\u3048\u3066\u3044\u308b\u3002\u3053\u3053\u3067\u3001\u30d7\u30ed\u30b0\u30e9\u30e0Y\u306f\u30d7\u30ed\u30b0\u30e9\u30e0X\u3088\u308a\u3082\u5e73\u5747\u3067\u308f\u305a\u304b\u306b\u4f4e\u3044\uff08\u4f8b\u3048\u30702\u30dd\u30a4\u30f3\u30c8\u4f4e\u3044\uff09<\/strong>\u75bc\u75db\u6539\u5584\u52b9\u679c\u3092\u793a\u3059\u53ef\u80fd\u6027\u304c\u3042\u308b\u3082\u306e\u306e\u3001\u305d\u306e\u5dee\u304c\u81e8\u5e8a\u7684\u306b\u8a31\u5bb9\u7bc4\u56f2\u5185\u3067\u3042\u308c\u3070\u3001\u30d7\u30ed\u30b0\u30e9\u30e0Y\u3092\u5c0e\u5165\u3059\u308b\u4fa1\u5024\u304c\u3042\u308b\u3068\u8003\u3048\u3066\u3044\u308b\u3002<\/p>\n\n\n\n<p><strong>\u7814\u7a76\u30c7\u30b6\u30a4\u30f3:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u5bfe\u8c61\u75be\u60a3:<\/strong> \u5909\u5f62\u6027\u819d\u95a2\u7bc0\u75c7 <\/li>\n\n\n\n<li><strong>\u4ecb\u5165:<\/strong> \u65b0\u3057\u3044\u30ea\u30cf\u30d3\u30ea\u30c6\u30fc\u30b7\u30e7\u30f3\u30d7\u30ed\u30b0\u30e9\u30e0Y <\/li>\n\n\n\n<li><strong>\u5bfe\u7167:<\/strong> \u65e2\u5b58\u306e\u30ea\u30cf\u30d3\u30ea\u30c6\u30fc\u30b7\u30e7\u30f3\u30d7\u30ed\u30b0\u30e9\u30e0X <\/li>\n\n\n\n<li><strong>\u4e3b\u8981\u8a55\u4fa1\u9805\u76ee:<\/strong> 8\u9031\u6642\u70b9\u3067\u306eVAS\u30b9\u30b3\u30a2\u306e\u5909\u5316\u91cf\uff08\u30d9\u30fc\u30b9\u30e9\u30a4\u30f3\u304b\u3089\u306e\u6539\u5584\u5ea6\uff09\n<ul class=\"wp-block-list\">\n<li>VAS\u30b9\u30b3\u30a2\u306f0\uff08\u75db\u307f\u306a\u3057\uff09\u304b\u3089100\uff08\u60f3\u50cf\u3057\u3046\u308b\u6700\u60aa\u306e\u75db\u307f\uff09\u3067\u8a55\u4fa1\u3055\u308c\u308b\u3002\u5909\u5316\u91cf\u306f\u30d9\u30fc\u30b9\u30e9\u30a4\u30f3\u30b9\u30b3\u30a2\u304b\u30898\u9031\u5f8c\u30b9\u30b3\u30a2\u3092\u5f15\u3044\u305f\u5024\u3068\u3059\u308b\uff08\u5024\u304c\u5927\u304d\u3044\u307b\u3069\u6539\u5584\u304c\u5927\u304d\u3044\uff09\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>\u540c\u7b49\u6027\u30de\u30fc\u30b8\u30f3:<\/strong> \u81e8\u5e8a\u7684\u306b\u8a31\u5bb9\u3067\u304d\u308bVAS\u30b9\u30b3\u30a2\u5909\u5316\u91cf\u306e\u5dee\u3092<strong>\u00b17\u30dd\u30a4\u30f3\u30c8<\/strong>\u3068\u8a2d\u5b9a\u3057\u305f\u3002\u3053\u308c\u306f\u3001\u30d7\u30ed\u30b0\u30e9\u30e0Y\u306eVAS\u30b9\u30b3\u30a2\u5909\u5316\u91cf\u304c\u30d7\u30ed\u30b0\u30e9\u30e0X\u3068\u6bd4\u8f03\u3057\u30667\u30dd\u30a4\u30f3\u30c8\u4ee5\u4e0a\u60aa\u5316\u3057\u306a\u3051\u308c\u3070\u3001\u81e8\u5e8a\u7684\u306b\u540c\u7b49\u3068\u307f\u306a\u3059\u3068\u3044\u3046\u5224\u65ad\u3067\u3042\u308b\u3002<\/li>\n\n\n\n<li> <strong>\u671f\u5f85\u3055\u308c\u308b\u5e73\u5747\u5dee:<\/strong> \u30d7\u30ed\u30b0\u30e9\u30e0X\u306e\u5e73\u5747VAS\u30b9\u30b3\u30a2\u5909\u5316\u91cf\u3092<strong>40\u30dd\u30a4\u30f3\u30c8<\/strong>\u3001\u30d7\u30ed\u30b0\u30e9\u30e0Y\u306e\u5e73\u5747VAS\u30b9\u30b3\u30a2\u5909\u5316\u91cf\u3092<strong>38\u30dd\u30a4\u30f3\u30c8<\/strong>\uff08X\u3088\u308a2\u30dd\u30a4\u30f3\u30c8\u4f4e\u3044\u304c\u3001\u81e8\u5e8a\u7684\u306b\u8a31\u5bb9\u7bc4\u56f2\u5185\uff09\u3068\u4eee\u5b9a\u3059\u308b\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u3053\u306e\u7814\u7a76\u306e\u76ee\u7684\u306f\u3001\u30d7\u30ed\u30b0\u30e9\u30e0Y\u304c\u30d7\u30ed\u30b0\u30e9\u30e0X\u306b\u512a\u308c\u3066\u3044\u308b\u3053\u3068\u3092\u793a\u3059\u3053\u3068\u3067\u306f\u306a\u304f\u3001\u30d7\u30ed\u30b0\u30e9\u30e0Y\u304c\u30d7\u30ed\u30b0\u30e9\u30e0X\u306e\u75bc\u75db\u6539\u5584\u52b9\u679c\u3068\u540c\u7b49\u3067\u3042\u308a\u3001\u308f\u305a\u304b\u306a\u52a3\u6027\u304c\u81e8\u5e8a\u7684\u306b\u8a31\u5bb9\u3055\u308c\u308b\u7bc4\u56f2\u5185\u3067\u3042\u308b\u3053\u3068\u3092\u793a\u3059\u3053\u3068\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<div id=\"biost-2757951239\" 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\">\u5177\u4f53\u4f8b\u306b\u304a\u3051\u308b\u540c\u7b49\u6027\u691c\u5b9a R\u3067\u306e\u8a08\u7b97\u4f8b<\/h2>\n\n\n\n<p>\u4e0a\u8a18\u306e\u4f8b\u306b\u57fa\u3065\u304d\u3001R\u3067\u306e\u540c\u7b49\u6027\u691c\u5b9a\u306e\u8a08\u7b97\u4f8b\u3092\u793a\u3059\u3002\u3053\u3053\u3067\u306f\u3001\u5e73\u5747\u5024\u306b\u5bfe\u3059\u308b\u540c\u7b49\u6027\u691c\u5b9a\u3092\u884c\u3046\u3002R\u306e<code>equivalence<\/code>\u30d1\u30c3\u30b1\u30fc\u30b8\u3092\u4f7f\u7528\u3059\u308b\u3002<\/p>\n\n\n\n<p>\u307e\u305a\u3001\u67b6\u7a7a\u306e\u30c7\u30fc\u30bf\u3092\u4f5c\u6210\u3057\u3001<code>tost<\/code>\u95a2\u6570\u3092\u7528\u3044\u3066\u540c\u7b49\u6027\u691c\u5b9a\u3092\u5b9f\u884c\u3059\u308b\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code> \u5fc5\u8981\u306a\u30d1\u30c3\u30b1\u30fc\u30b8\u3092\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\uff08\u521d\u56de\u306e\u307f\uff09\n# install.packages(\"equivalence\")\n\nlibrary(equivalence)\n\n# \u30c7\u30fc\u30bf\u4f5c\u6210\n# \u30d7\u30ed\u30b0\u30e9\u30e0X\u7fa4\u306eVAS\u30b9\u30b3\u30a2\u5909\u5316\u91cf (\u6539\u5584\u5ea6)\nset.seed(1) # \u518d\u73fe\u6027\u306e\u305f\u3081\u306e\u30b7\u30fc\u30c9\u8a2d\u5b9a\nn_x &lt;- 50 # \u5404\u7fa4\u306e\u60a3\u8005\u6570\nmean_x &lt;- 40 # \u671f\u5f85\u3055\u308c\u308b\u5e73\u5747VAS\u5909\u5316\u91cf\nsd_x &lt;- 15 # \u6a19\u6e96\u504f\u5dee\n\n# \u30d7\u30ed\u30b0\u30e9\u30e0Y\u7fa4\u306eVAS\u30b9\u30b3\u30a2\u5909\u5316\u91cf (\u6539\u5584\u5ea6)\nn_y &lt;- 50 # \u5404\u7fa4\u306e\u60a3\u8005\u6570\nmean_y &lt;- 38 # \u671f\u5f85\u3055\u308c\u308b\u5e73\u5747VAS\u5909\u5316\u91cf\nsd_y &lt;- 15 # \u6a19\u6e96\u504f\u5dee (\u4e21\u7fa4\u3067\u540c\u3058\u3068\u4eee\u5b9a)\n\n# \u6b63\u898f\u5206\u5e03\u306b\u5f93\u3046\u30e9\u30f3\u30c0\u30e0\u30c7\u30fc\u30bf\u3092\u751f\u6210\ndata_x &lt;- rnorm(n_x, mean = mean_x, sd = sd_x)\ndata_y &lt;- rnorm(n_y, mean = mean_y, sd = sd_y)\n\n# \u30c7\u30fc\u30bf\u306e\u8981\u7d04\ncat(\"\u30d7\u30ed\u30b0\u30e9\u30e0X\u7fa4 \u5e73\u5747VAS\u5909\u5316\u91cf:\", mean(data_x), \", \u6a19\u6e96\u504f\u5dee:\", sd(data_x), \"\\n\")\ncat(\"\u30d7\u30ed\u30b0\u30e9\u30e0Y\u7fa4 \u5e73\u5747VAS\u5909\u5316\u91cf:\", mean(data_y), \", \u6a19\u6e96\u504f\u5dee:\", sd(data_y), \"\\n\")\ncat(\"\u4e21\u7fa4\u306e\u5e73\u5747\u5dee:\", mean(data_y) - mean(data_x), \"\\n\\n\")\n\n# \u540c\u7b49\u6027\u30de\u30fc\u30b8\u30f3\u3092\u5b9a\u7fa9\n# \u81e8\u5e8a\u7684\u306b\u8a31\u5bb9\u3067\u304d\u308b\u5dee\u30927\u30dd\u30a4\u30f3\u30c8\u3068\u8a2d\u5b9a\nepsilon &lt;- 7\n\n# 2\u7fa4\u306e\u5e73\u5747\u5024\u306e\u540c\u7b49\u6027\u691c\u5b9a (TOST)\n# `tost`\u95a2\u6570\u3092\u4f7f\u7528\n# H0: diff &lt;= -epsilon or diff >= epsilon\n# H1: -epsilon &lt; diff &lt; epsilon (\u5dee\u304c\u540c\u7b49\u6027\u30de\u30fc\u30b8\u30f3\u5185\u306b\u53ce\u307e\u308b)\n# alpha = \u6709\u610f\u6c34\u6e96 (TOST\u3067\u306f\u3001\u5404\u7247\u5074\u691c\u5b9a\u306b alpha \u304c\u5272\u308a\u5f53\u3066\u3089\u308c\u308b\u305f\u3081\u3001\u4e21\u5074\u3067 alpha * 2)\n# conf.level = \u4fe1\u983c\u6c34\u6e96 (1 - alpha_total)\n# default_alpha\u306f0.05\u3002TOST\u3067\u306f\u3001\u4e21\u5074\u691c\u5b9a\u306e\u4fe1\u983c\u6c34\u6e96\u30921-alpha\u3068\u3057\u305f\u3044\u5834\u5408\u3001\n# \u7247\u5074\u691c\u5b9a\u306e\u6709\u610f\u6c34\u6e96\u3092alpha\/2\u306b\u8a2d\u5b9a\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\u3002\n# tost\u306econf.level\u306f\u4e21\u5074\u4fe1\u983c\u533a\u9593\u306e\u4fe1\u983c\u6c34\u6e96\u3092\u6307\u5b9a\u3059\u308b\u3002\n# \u3053\u3053\u3067\u306f\u3001\u4fe1\u983c\u6c34\u6e9690% (\u7247\u5074\u6709\u610f\u6c34\u6e960.05) \u3067\u540c\u7b49\u6027\u691c\u5b9a\u3092\u884c\u3046\u3002\nresult_equivalence &lt;- tost(\n  x = data_x,\n  y = data_y,\n  epsilon = epsilon, # \u540c\u7b49\u6027\u30de\u30fc\u30b8\u30f3\n  conf.level = 0.90 # \u4e21\u5074\u4fe1\u983c\u533a\u959390% (\u5404\u7247\u5074\u691c\u5b9a\u3067\u6709\u610f\u6c34\u6e960.05\u306b\u5bfe\u5fdc)\n)\n\nprint(result_equivalence)\n\n# \u7d50\u679c\u306e\u89e3\u91c8\n# 90%\u4fe1\u983c\u533a\u9593 (confidence interval) \u304c &#91;-epsilon, +epsilon] \u306e\u7bc4\u56f2\u306b\u5b8c\u5168\u306b\u542b\u307e\u308c\u3066\u3044\u308b\u304b\u3092\u78ba\u8a8d\u3057\u307e\u3059\u3002<\/code><\/pre>\n\n\n\n<p><strong>\u5b9f\u884c\u7d50\u679c\uff1a<\/strong><\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>> cat(\"\u30d7\u30ed\u30b0\u30e9\u30e0X\u7fa4 \u5e73\u5747VAS\u5909\u5316\u91cf:\", mean(data_x), \", \u6a19\u6e96\u504f\u5dee:\", sd(data_x), \"\\n\")\n\u30d7\u30ed\u30b0\u30e9\u30e0X\u7fa4 \u5e73\u5747VAS\u5909\u5316\u91cf: 41.50672 , \u6a19\u6e96\u504f\u5dee: 12.47091 \n\n> cat(\"\u30d7\u30ed\u30b0\u30e9\u30e0Y\u7fa4 \u5e73\u5747VAS\u5909\u5316\u91cf:\", mean(data_y), \", \u6a19\u6e96\u504f\u5dee:\", sd(data_y), \"\\n\")\n\u30d7\u30ed\u30b0\u30e9\u30e0Y\u7fa4 \u5e73\u5747VAS\u5909\u5316\u91cf: 39.7599 , \u6a19\u6e96\u504f\u5dee: 14.53242 \n\n> cat(\"\u4e21\u7fa4\u306e\u5e73\u5747\u5dee:\", mean(data_y) - mean(data_x), \"\\n\\n\")\n\u4e21\u7fa4\u306e\u5e73\u5747\u5dee: -1.746827 \n\n> print(result_equivalence)\n\n        Welch Two Sample TOST\n\ndata:  data_x and data_y\ndf = 95.793\nsample estimates:\nmean of x mean of y \n 41.50672  39.75990 \n\nEpsilon: 7 \n90 percent two one-sided confidence interval (TOST interval):\n -1.747962  5.241616\nNull hypothesis of statistical difference is: rejected \nTOST p-value: 0.0276767 <\/code><\/pre>\n\n\n\n<p>\u4e21\u7fa4\u306e\u5e73\u5747\u5dee\u306f\u3001-1.7 \u3068 \u7d04 2 \u3067\u3042\u308b\u3002\u540c\u7b49\u6027\u30de\u30fc\u30b8\u30f3\u3092 7 \u3068\u3057\u3066\u3001TOST \u3092\u5b9f\u884c\u3059\u308b\u3068\u3001\u5e73\u5747\u5dee\u306e 90\uff05 \u4fe1\u983c\u533a\u9593\u304c\u3001-1.7 \u304b\u3089 5.2 \u3067\u3042\u308a\u3001-7 \u304b\u3089 +7 \u306b\u53ce\u307e\u3063\u3066\u304a\u308a\u3001\u4e21\u5074\u3068\u30825\uff05\u3067\u7d71\u8a08\u5b66\u7684\u6709\u610f\u306b\u540c\u7b49\u6027\u30de\u30fc\u30b8\u30f3\u3092\u8d85\u3048\u306a\u3044\u3053\u3068\u304c\u308f\u304b\u308b\u3002\u3086\u3048\u306b\u3001\u7247\u50745\uff05\u306e2\u3064\u306e\u691c\u5b9a\u3001\u4e0a\u5074\u30fb\u4e0b\u5074\u3068\u3082\u306b\u6709\u610f\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u3053\u306e\u7d50\u679c\u304b\u3089\u300c\u30d7\u30ed\u30b0\u30e9\u30e0X\u3068\u30d7\u30ed\u30b0\u30e9\u30e0Y\u306e\u75bc\u75db\u6539\u5584\u52b9\u679c\u306f\u540c\u7b49\u3067\u3042\u308b\u300d\u3068\u7d50\u8ad6\u3065\u3051\u3089\u308c\u308b\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u5fc5\u8981\u30b5\u30f3\u30d7\u30eb\u6570 R\u3067\u306e\u8a08\u7b97\u4f8b<\/h2>\n\n\n\n<p>\u540c\u7b49\u6027\u691c\u5b9a\u3092\u884c\u3046\u306b\u3042\u305f\u308a\u3001\u9069\u5207\u306a\u30b5\u30f3\u30d7\u30eb\u6570\u3092\u4e8b\u524d\u306b\u7b97\u51fa\u3059\u308b\u3053\u3068\u306f\u975e\u5e38\u306b\u91cd\u8981\u3067\u3042\u308b\u3002\u30b5\u30f3\u30d7\u30eb\u6570\u304c\u4e0d\u8db3\u3057\u3066\u3044\u308b\u3068\u3001\u305f\u3068\u3048\u771f\u306b\u540c\u7b49\u3067\u3042\u3063\u3066\u3082\u540c\u7b49\u6027\u3092\u8a3c\u660e\u3067\u304d\u306a\u3044\uff08\u30bf\u30a4\u30d7II\u30a8\u30e9\u30fc\uff09\u53ef\u80fd\u6027\u304c\u9ad8\u307e\u308b\u3002<\/p>\n\n\n\n<p>\u3053\u3053\u3067\u306f\u3001\u5e73\u5747\u5024\u306e\u540c\u7b49\u6027\u691c\u5b9a\u306b\u304a\u3051\u308b\u5fc5\u8981\u30b5\u30f3\u30d7\u30eb\u6570\u3092\u8a08\u7b97\u3059\u308b\u3002TOST\u30d7\u30ed\u30b7\u30fc\u30b8\u30e3\u306e\u8003\u3048\u65b9\u306b\u57fa\u3065\u304d\u3001<code>pwr<\/code>\u30d1\u30c3\u30b1\u30fc\u30b8\u306e<code>pwr.t.test<\/code>\u95a2\u6570\u3092\u5fdc\u7528\u3057\u305f\u4f8b\u3092\u793a\u3059\u3002<\/p>\n\n\n\n<p><strong>\u5fc5\u8981\u30b5\u30f3\u30d7\u30eb\u6570\u8a08\u7b97\u306e\u524d\u63d0\u6761\u4ef6:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u30d7\u30ed\u30b0\u30e9\u30e0X\u306e\u671f\u5f85\u3055\u308c\u308bVAS\u5909\u5316\u91cf:<\/strong> 40\u30dd\u30a4\u30f3\u30c8 <\/li>\n\n\n\n<li><strong>\u30d7\u30ed\u30b0\u30e9\u30e0Y\u306e\u671f\u5f85\u3055\u308c\u308bVAS\u5909\u5316\u91cf:<\/strong> 38\u30dd\u30a4\u30f3\u30c8\uff08\u5dee\u304c-2\u30dd\u30a4\u30f3\u30c8\u3068\u4eee\u5b9a\uff09 <\/li>\n\n\n\n<li><strong>\u671f\u5f85\u3055\u308c\u308b\u6a19\u6e96\u504f\u5dee (\u03c3):<\/strong> 15\u30dd\u30a4\u30f3\u30c8\uff08\u4e21\u7fa4\u3067\u540c\u3058\u3068\u4eee\u5b9a\uff09 <\/li>\n\n\n\n<li><strong>\u540c\u7b49\u6027\u30de\u30fc\u30b8\u30f3 (\u0394):<\/strong> 7\u30dd\u30a4\u30f3\u30c8 <\/li>\n\n\n\n<li><strong>\u6709\u610f\u6c34\u6e96 (\u03b1):<\/strong> 0.05 (\u7247\u5074\u691c\u5b9a\u3054\u3068\u306b0.05\u3001TOST\u3067\u306f\u4e21\u5074\u30670.10\u3001\u3064\u307e\u308a\u7247\u50740.05\u304c2\u56de) <\/li>\n\n\n\n<li><strong>\u691c\u51fa\u529b (Power):<\/strong> 0.80 (80%)<\/li>\n<\/ul>\n\n\n\n<p>\u540c\u7b49\u6027\u691c\u5b9a\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\u3067\u306f\u3001\u771f\u306e\u5dee\u304c\u540c\u7b49\u6027\u30de\u30fc\u30b8\u30f3\u306e\u4e00\u65b9\u306e\u7aef\u306b\u3042\u308b\u3068\u304d\u306b\u3001\u305d\u306e\u4eee\u8aac\u3092\u68c4\u5374\u3067\u304d\u308b\u30d1\u30ef\u30fc\u3092\u78ba\u4fdd\u3059\u308b\u3068\u3044\u3046\u8003\u3048\u65b9\u3092\u3059\u308b\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code># \u5fc5\u8981\u30b5\u30f3\u30d7\u30eb\u6570\u8a08\u7b97\u306e\u305f\u3081\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u8a2d\u5b9a\nmean_x_expected &lt;- 40 # \u30d7\u30ed\u30b0\u30e9\u30e0X\u306e\u671f\u5f85\u3055\u308c\u308b\u5e73\u5747\nmean_y_expected &lt;- 38 # \u30d7\u30ed\u30b0\u30e9\u30e0Y\u306e\u671f\u5f85\u3055\u308c\u308b\u5e73\u5747 (\u671f\u5f85\u3055\u308c\u308b\u5dee\u306f -2)\nsd_pooled &lt;- 15 # \u30d7\u30fc\u30eb\u3055\u308c\u305f\u6a19\u6e96\u504f\u5dee (\u4e21\u7fa4\u3067\u540c\u3058\u3068\u4eee\u5b9a)\n\nepsilon_margin &lt;- 7 # \u540c\u7b49\u6027\u30de\u30fc\u30b8\u30f3\n\nalpha_one_sided &lt;- 0.05 # \u7247\u5074\u691c\u5b9a\u306e\u6709\u610f\u6c34\u6e96\npower_target &lt;- 0.80 # \u76ee\u6a19\u3068\u3059\u308b\u691c\u51fa\u529b\n\n# TOST\u30d7\u30ed\u30b7\u30fc\u30b8\u30e3\u306b\u304a\u3051\u308b\u5fc5\u8981\u30b5\u30f3\u30d7\u30eb\u6570\u8a08\u7b97\u306e\u8003\u3048\u65b9\n# 2\u3064\u306e\u7247\u5074\u691c\u5b9a\u306e\u305d\u308c\u305e\u308c\u306b\u5bfe\u3057\u3066\u5fc5\u8981\u30b5\u30f3\u30d7\u30eb\u6570\u3092\u8a08\u7b97\u3059\u308b\u3002\n# \u3053\u306e\u5834\u5408\u3001\u771f\u306e\u5dee\u304c -epsilon_margin \u306e\u6642\u306b\u3001\n# \u5dee\u304c -epsilon_margin \u3088\u308a\u5927\u304d\u3044\u3053\u3068\u3092\u793a\u3059\u691c\u5b9a\u306e\u30d1\u30ef\u30fc\u3092\u8a08\u7b97\u3002\n# \u307e\u305f\u306f\u3001\u771f\u306e\u5dee\u304c +epsilon_margin \u306e\u6642\u306b\u3001\n# \u5dee\u304c +epsilon_margin \u3088\u308a\u5c0f\u3055\u3044\u3053\u3068\u3092\u793a\u3059\u691c\u5b9a\u306e\u30d1\u30ef\u30fc\u3092\u8a08\u7b97\u3002\n\n# effect size (Cohen's d) \u306e\u8a08\u7b97\n# d = |(mu1 - mu2) - delta| \/ sigma_pooled\n# \u3053\u3053\u3067\u306f\u3001\u671f\u5f85\u3055\u308c\u308b\u771f\u306e\u5dee\u3092 -2 \u3068\u8a2d\u5b9a\u3057\u3066\u3044\u308b\u305f\u3081\u3001\n# \u4ee5\u4e0b\u306e2\u3064\u306e\u30b7\u30ca\u30ea\u30aa\u3067\u6700\u3082\u5927\u304d\u3044\u30b5\u30f3\u30d7\u30eb\u6570\u3092\u63a1\u7528\u3059\u308b\u3002\n# \u30b7\u30ca\u30ea\u30aa1: (mu_Y - mu_X) \u304c -epsilon_margin \u306e\u3068\u304d\u306b\u3001\u691c\u51fa\u529b0.80\u3067\u305d\u306e\u5dee\u304c-epsilon_margin\u3088\u308a\u5927\u304d\u3044\u3053\u3068\u3092\u793a\u3059\u3002\n# \u771f\u306e\u5dee\u306f -2 \u3068\u4eee\u5b9a\u3002\n# \u691c\u51fa\u3057\u305f\u3044\u5dee (delta) = (\u671f\u5f85\u3055\u308c\u308b\u771f\u306e\u5dee) - (-epsilon_margin) = -2 - (-7) = 5\nd1 &lt;- abs((mean_y_expected - mean_x_expected) - (-epsilon_margin)) \/ sd_pooled\n# \u307e\u305f\u306f\n# \u691c\u51fa\u3057\u305f\u3044\u5dee (delta) = epsilon_margin - (\u671f\u5f85\u3055\u308c\u308b\u771f\u306e\u5dee) = 7 - (-2) = 9 (\u3053\u308c\u306f\u5dee\u304c +epsilon_margin \u304b\u3089\u3069\u308c\u3060\u3051\u96e2\u308c\u3066\u3044\u308b\u304b)\nd2 &lt;- abs(epsilon_margin - (mean_y_expected - mean_x_expected)) \/ sd_pooled\n\n# \u3069\u3061\u3089\u304b\u5927\u304d\u3044\u65b9\u306e\u52b9\u679c\u91cf\u3067\u8a08\u7b97\u3059\u308b\n# effect_size &lt;- max(d1, d2) # \u3053\u3053\u3067\u306f\u3001\u771f\u306e\u5dee\u3092\u8003\u616e\u3057\u306a\u3044\u30b7\u30f3\u30d7\u30eb\u306a\u30b1\u30fc\u30b9\u3067\u8a08\u7b97\n\n# \u3053\u3053\u3067\u306f\u3001\u771f\u306e\u5dee\u30920\u3068\u3057\u3066\u3001epsilon_margin\u306e\u5dee\u3092\u691c\u51fa\u3059\u308b\u30d1\u30ef\u30fc\u8a08\u7b97\u3068\u306f\u7570\u306a\u308b\u3002\n# \u540c\u7b49\u6027\u691c\u5b9a\u306b\u304a\u3051\u308b\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u306f\u3001\u901a\u5e38\u3001\n# \u300c\u771f\u306e\u5dee\u304c\u540c\u7b49\u6027\u30de\u30fc\u30b8\u30f3\u306e\u7aef\uff08\u4f8b: -epsilon_margin \u307e\u305f\u306f +epsilon_margin\uff09\u306b\u3042\u308a\u3001\n# \u304b\u3064\u691c\u51fa\u529b\u304c\u76ee\u6a19\u5024\u3067\u3042\u308b\u3068\u304d\u306b\u3001\u540c\u7b49\u6027\u304c\u68c4\u5374\u3055\u308c\u306a\u3044\uff08\u3064\u307e\u308a\u3001\u4fe1\u983c\u533a\u9593\u304c\u30de\u30fc\u30b8\u30f3\u5185\u306b\u53ce\u307e\u308b\uff09\n# \u305f\u3081\u306b\u5fc5\u8981\u306a\u30b5\u30f3\u30d7\u30eb\u6570\u300d\u3068\u3057\u3066\u8a08\u7b97\u3055\u308c\u308b\u3002\n\n# \u3088\u308a\u53b3\u5bc6\u306a\u540c\u7b49\u6027\u691c\u5b9a\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\n# pwr.t.test\u3067\u306f\u76f4\u63a5\u540c\u7b49\u6027\u691c\u5b9a\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u3092\u8a08\u7b97\u3067\u304d\u306a\u3044\u305f\u3081\u3001\n# TOST\u306e\u8003\u3048\u65b9\u306b\u57fa\u3065\u3044\u3066\u3001\u7247\u5074\u691c\u5b9a\u306e\u30d1\u30ef\u30fc\u8a08\u7b97\u3092\u5fdc\u7528\u3059\u308b\u3002\n\n# Scenario 1: H0: mu_Y - mu_X &lt;= -epsilon_margin\n# Alternative: mu_Y - mu_X > -epsilon_margin\n# effect size = (\u771f\u306e\u5dee - H0\u306e\u5883\u754c\u5024) \/ \u6a19\u6e96\u504f\u5dee\n#               = (-2 - (-7)) \/ 15 = 5 \/ 15 = 0.333\nd_scenario1 &lt;- (mean_y_expected - mean_x_expected - (-epsilon_margin)) \/ sd_pooled\n\nprint(d_scenario1)\n\n# Scenario 2: H0: mu_Y - mu_X >= epsilon_margin\n# Alternative: mu_Y - mu_X &lt; epsilon_margin\n# effect size = (H0\u306e\u5883\u754c\u5024 - \u771f\u306e\u5dee) \/ \u6a19\u6e96\u504f\u5dee\n#               = (7 - (-2)) \/ 15 = 9 \/ 15 = 0.6\nd_scenario2 &lt;- (epsilon_margin - (mean_y_expected - mean_x_expected)) \/ sd_pooled\n\nprint(d_scenario2)\n\n# \u4e21\u65b9\u306e\u7247\u5074\u691c\u5b9a\u3067\u30d1\u30ef\u30fc\u304c\u76ee\u6a19\u5024\u306b\u9054\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\u305f\u3081\u3001\u3088\u308a\u53b3\u3057\u3044\u6761\u4ef6\uff08effect size\u304c\u5c0f\u3055\u3044\u65b9\uff09\u3067\u8a08\u7b97\u3059\u308b\u3002\n# \u305f\u3060\u3057\u3001pwr.t.test\u306edelta\u5f15\u6570\u306f\u3001\u671f\u5f85\u3055\u308c\u308b\u5dee\u306e\u7d76\u5bfe\u5024\u3002\n# \u3053\u3053\u3067\u306f\u3001TOST\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\u306e\u30ed\u30b8\u30c3\u30af\u306b\u57fa\u3065\u3044\u3066\u3001\u6700\u3082\u53b3\u3057\u3044\u30b7\u30ca\u30ea\u30aa\u3067\u8a08\u7b97\u3059\u308b\u3002\n# \u3064\u307e\u308a\u3001\u771f\u306e\u5dee\u304c\u671f\u5f85\u3055\u308c\u308b\u5dee\uff08-2\uff09\u306e\u6642\u306b\u3001\n# \u4fe1\u983c\u533a\u9593\u304c &#91;-7, 7] \u306e\u7bc4\u56f2\u306b\u53ce\u307e\u308b\u78ba\u7387\u3092\u8a08\u7b97\u3059\u308b\u3002\n\n# \u7c21\u6613\u7684\u306a\u8a08\u7b97\u3068\u3057\u3066\u3001pwr.t.test\u3092\u5fdc\u7528\u3059\u308b\u3002\n# effect size\u3068\u3057\u3066\u3001\u540c\u7b49\u6027\u30de\u30fc\u30b8\u30f3\u3068\u671f\u5f85\u3055\u308c\u308b\u5dee\u306e\u9593\u306e\u8ddd\u96e2\u3092\u7528\u3044\u308b\u3002\n# \u4f8b\u3048\u3070\u3001\u671f\u5f85\u3055\u308c\u308b\u5dee\u304c -2\u3001\u540c\u7b49\u6027\u30de\u30fc\u30b8\u30f3\u304c 7 \u306e\u5834\u5408\u3001\n# -7 \u3068 -2 \u306e\u5dee (5) \u307e\u305f\u306f +7 \u3068 -2 \u306e\u5dee (9) \u306e\u3046\u3061\u3001\u3088\u308a\u5c0f\u3055\u3044\u65b9\u306e\u5dee\u3092\u691c\u51fa\u3067\u304d\u308b\u3088\u3046\u306a\u30b5\u30f3\u30d7\u30eb\u6570\u3092\u6c42\u3081\u308b\u3002\n# \u3053\u308c\u3089\u3092\u6a19\u6e96\u504f\u5dee\u3067\u5272\u3063\u305f\u3082\u306e\u304cCohen's d\u3002\n\n# \u540c\u7b49\u6027\u691c\u5b9a\u306b\u304a\u3051\u308b\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\u306e\u4e00\u822c\u7684\u306a\u30ed\u30b8\u30c3\u30af\n# H0: |mu1 - mu2| >= epsilon_margin\n# H1: |mu1 - mu2| &lt; epsilon_margin\n# \u691c\u51fa\u529b\u306f\u3001\u771f\u306e\u5dee\u304cdelta_0\u306e\u3068\u304d\u306bH1\u3092\u63a1\u629e\u3059\u308b\u78ba\u7387\n\n# Cohen's d for equivalence test\n# d_equiv = (epsilon - |mu1 - mu2|) \/ sigma_pooled\n# \u3053\u3053\u3067\u306f\u3001\u671f\u5f85\u3055\u308c\u308b\u771f\u306e\u5dee\u3092 `mean_y_expected - mean_x_expected` \u3068\u8a2d\u5b9a\n# `delta` in `pwr.t.test` is `mean1 - mean2`.\n# \u540c\u7b49\u6027\u691c\u5b9a\u3067\u306f\u3001`delta = epsilon_margin - expected_diff` \u307e\u305f\u306f `expected_diff - (-epsilon_margin)`\n# \u306e\u3046\u3061\u3001\u5c0f\u3055\u3044\u65b9\u306e\u7d76\u5bfe\u5024\u3092\u53d6\u308b\u3002\n\n# d = min(abs(epsilon_margin - (mean_y_expected - mean_x_expected)), abs(-epsilon_margin - (mean_y_expected - mean_x_expected))) \/ sd_pooled\n# d = min(abs(7 - (-2)), abs(-7 - (-2))) \/ 15\n# d = min(abs(9), abs(-5)) \/ 15\n# d = 5 \/ 15 = 0.3333\n\nd_calc &lt;- min(abs(epsilon_margin - (mean_y_expected - mean_x_expected)), abs(-epsilon_margin - (mean_y_expected - mean_x_expected))) \/ sd_pooled\n\nprint(d_calc)\n\n# \u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\u306e\u305f\u3081\u306b pwr \u30d1\u30c3\u30b1\u30fc\u30b8\u3092\u547c\u3073\u51fa\u3059\n# install.packages(\"pwr\") # \u672a\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u3067\u3042\u308c\u3070\u521d\u56de\u306e\u307f\u5b9f\u884c\nlibrary(pwr)\n\n# \u5404\u7fa4\u306e\u5fc5\u8981\u30b5\u30f3\u30d7\u30eb\u6570\nn_each_group &lt;- pwr.t.test(\n    d = d_calc, # \u52b9\u679c\u91cf\n    sig.level = alpha_one_sided, # \u7247\u5074\u691c\u5b9a\u306e\u6709\u610f\u6c34\u6e96\n    power = power_target, # \u76ee\u6a19\u691c\u51fa\u529b\n    type = \"two.sample\",\n    alternative = \"greater\" # TOST\u306e\u7247\u5074\u691c\u5b9a\u306e\u4e00\u3064\u3092\u60f3\u5b9a (H0: diff &lt;= -epsilon \u3092\u68c4\u5374\u3059\u308b)\n)$n\n\ncat(\"\u5404\u7fa4\u306e\u5fc5\u8981\u30b5\u30f3\u30d7\u30eb\u6570 (\u8fd1\u4f3c\u5024): \", ceiling(n_each_group), \"\\n\")\n<\/code><\/pre>\n\n\n\n<p><strong>\u5b9f\u884c\u7d50\u679c\uff1a<\/strong><\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>> cat(\"\u5404\u7fa4\u306e\u5fc5\u8981\u30b5\u30f3\u30d7\u30eb\u6570 (\u8fd1\u4f3c\u5024): \", ceiling(n_each_group), \"\\n\")\n\u5404\u7fa4\u306e\u5fc5\u8981\u30b5\u30f3\u30d7\u30eb\u6570 (\u8fd1\u4f3c\u5024):  112 <\/code><\/pre>\n\n\n\n<p>\u4f8b\u3048\u3070\u3001\u4e0a\u8a18\u306e\u8a08\u7b97\u306b\u3088\u308a\u3001\u300c\u5404\u7fa4\u306e\u5fc5\u8981\u30b5\u30f3\u30d7\u30eb\u6570 (\u8fd1\u4f3c\u5024): 112\u300d\u3068\u3044\u3046\u7d50\u679c\u304c\u5f97\u3089\u308c\u308b\u3002\u3053\u308c\u306f\u3001\u5404\u7fa4\u306b112\u4eba\u306e\u60a3\u8005\u3092\u7d44\u307f\u5165\u308c\u308c\u3070\u3001\u8a2d\u5b9a\u3057\u305f\u6761\u4ef6\uff08\u671f\u5f85\u3055\u308c\u308b\u5e73\u5747\u5dee-2\u3001\u6a19\u6e96\u504f\u5dee15\u3001\u540c\u7b49\u6027\u30de\u30fc\u30b8\u30f3\u00b17\u3001\u6709\u610f\u6c34\u6e960.05\u3001\u691c\u51fa\u529b0.80\uff09\u3067\u540c\u7b49\u6027\u3092\u691c\u8a3c\u3059\u308b\u305f\u3081\u306b\u306f\u5341\u5206\u3067\u3042\u308b\u3068\u3044\u3046\u76ee\u5b89\u3092\u793a\u3057\u3066\u3044\u308b\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u307e\u3068\u3081<\/h2>\n\n\n\n<p>\u672c\u8a18\u4e8b\u3067\u306f\u3001\u5e73\u5747\u5024\u30a2\u30a6\u30c8\u30ab\u30e0\u306b\u7126\u70b9\u3092\u5f53\u3066\u3001\u81e8\u5e8a\u7814\u7a76\u306b\u304a\u3051\u308b\u540c\u7b49\u6027\u691c\u5b9a\u3068\u5fc5\u8981\u30b5\u30f3\u30d7\u30eb\u6570\u8a08\u7b97\u306b\u3064\u3044\u3066\u89e3\u8aac\u3057\u305f\u3002\u540c\u7b49\u6027\u691c\u5b9a\u306f\u3001\u65b0\u3057\u3044\u4ecb\u5165\u304c\u65e2\u5b58\u306e\u4ecb\u5165\u3068\u540c\u7b49\u3067\u3042\u308b\u3053\u3068\u3092\u300c\u81e8\u5e8a\u7684\u306b\u610f\u5473\u306e\u3042\u308b\u5dee\u304c\u306a\u3044\u300d\u3068\u3044\u3046\u89b3\u70b9\u304b\u3089\u8a3c\u660e\u3059\u308b\u969b\u306b\u4e0d\u53ef\u6b20\u306a\u624b\u6cd5\u3067\u3042\u308b\u3002\u3053\u306e\u969b\u306b\u3001\u7814\u7a76\u958b\u59cb\u524d\u306b\u8a2d\u5b9a\u3059\u308b<strong>\u540c\u7b49\u6027\u30de\u30fc\u30b8\u30f3<\/strong>\u304c\u6975\u3081\u3066\u91cd\u8981\u306a\u5f79\u5272\u3092\u679c\u305f\u3059\u3002<\/p>\n\n\n\n<p>\u5177\u4f53\u4f8b\u3068\u3057\u3066\u3001\u6574\u5f62\u5916\u79d1\u9818\u57df\u306b\u304a\u3051\u308b\u5909\u5f62\u6027\u819d\u95a2\u7bc0\u75c7\u306e\u65b0\u3057\u3044\u30ea\u30cf\u30d3\u30ea\u30c6\u30fc\u30b7\u30e7\u30f3\u30d7\u30ed\u30b0\u30e9\u30e0\u304c\u3001\u65e2\u5b58\u30d7\u30ed\u30b0\u30e9\u30e0\u3068\u540c\u7b49\u306eVAS\u30b9\u30b3\u30a2\u6539\u5584\u52b9\u679c\u3092\u793a\u3059\u304b\u3092\u691c\u8a3c\u3059\u308b\u30b7\u30ca\u30ea\u30aa\u3092\u63d0\u793a\u3057\u305f\u3002\u7279\u306b\u3001\u65b0\u3057\u3044\u30d7\u30ed\u30b0\u30e9\u30e0\u304c\u308f\u305a\u304b\u306b\u52a3\u308b\u53ef\u80fd\u6027\uff08\u5e73\u5747\u30672\u30dd\u30a4\u30f3\u30c8\u4f4e\u3044\u6539\u5584\u52b9\u679c\uff09\u304c\u3042\u308b\u3082\u306e\u306e\u3001\u305d\u308c\u304c\u81e8\u5e8a\u7684\u306b\u8a31\u5bb9\u7bc4\u56f2\u5185\u3067\u3042\u308b\u5834\u5408\u306b\u3001\u540c\u7b49\u6027\u3092\u8a3c\u660e\u3059\u308b\u610f\u7fa9\u304c\u3042\u308b\u3053\u3068\u3092\u793a\u3057\u305f\u3002<\/p>\n\n\n\n<p>R\u3092\u7528\u3044\u305f\u8a08\u7b97\u4f8b\u3067\u306f\u3001<code>equivalence<\/code>\u30d1\u30c3\u30b1\u30fc\u30b8\u306e<code>tost<\/code>\u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u5e73\u5747\u5024\u306e\u540c\u7b49\u6027\u691c\u5b9a\u3092\u5b9f\u884c\u3059\u308b\u65b9\u6cd5\u3001\u304a\u3088\u3073<code>pwr<\/code>\u30d1\u30c3\u30b1\u30fc\u30b8\u306e<code>pwr.t.test<\/code>\u95a2\u6570\u3092\u5fdc\u7528\u3057\u3066\u5fc5\u8981\u30b5\u30f3\u30d7\u30eb\u6570\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5\u3092\u793a\u3057\u305f\u3002\u540c\u7b49\u6027\u691c\u5b9a\u306b\u304a\u3051\u308b\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\u306f\u3001\u512a\u8d8a\u6027\u691c\u5b9a\u3068\u6bd4\u8f03\u3057\u3066\u3084\u3084\u8907\u96d1\u3067\u3042\u308a\u3001\u671f\u5f85\u3055\u308c\u308b\u771f\u306e\u5dee\u3084\u540c\u7b49\u6027\u30de\u30fc\u30b8\u30f3\u3092\u8003\u616e\u3057\u305f\u52b9\u679c\u91cf\u306e\u8a2d\u5b9a\u304c\u91cd\u8981\u3068\u306a\u308b\u3002<\/p>\n\n\n\n<p>\u540c\u7b49\u6027\u691c\u5b9a\u3092\u9069\u5207\u306b\u5b9f\u65bd\u3059\u308b\u305f\u3081\u306b\u306f\u3001\u81e8\u5e8a\u7684\u610f\u7fa9\u306b\u57fa\u3065\u3044\u305f\u540c\u7b49\u6027\u30de\u30fc\u30b8\u30f3\u306e\u8a2d\u5b9a\u3001\u671f\u5f85\u3055\u308c\u308b\u771f\u306e\u5dee\u306e\u628a\u63e1\u3001\u305d\u3057\u3066\u5341\u5206\u306a\u691c\u51fa\u529b\u3092\u78ba\u4fdd\u3059\u308b\u305f\u3081\u306e\u9069\u5207\u306a\u30b5\u30f3\u30d7\u30eb\u6570\u8a08\u7b97\u304c\u4e0d\u53ef\u6b20\u3067\u3042\u308b\u3002\u3053\u308c\u3089\u306e\u7d71\u8a08\u7684\u624b\u6cd5\u3092\u7406\u89e3\u3057\u3001\u9069\u5207\u306b\u9069\u7528\u3059\u308b\u3053\u3068\u3067\u3001\u3088\u308a\u4fe1\u983c\u6027\u306e\u9ad8\u3044\u81e8\u5e8a\u7814\u7a76\u3092\u884c\u3046\u3053\u3068\u304c\u3067\u304d\u308b\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u65b0\u3057\u3044\u6cbb\u7642\u6cd5\u304c\u65e2\u5b58\u306e\u3082\u306e\u3068\u540c\u7b49\u3067\u3042\u308b\u3053\u3068\u3092\u8a3c\u660e\u3057\u305f\u3044\u3002\u305d\u3093\u306a\u6642\u3001\u5f93\u6765\u306e\u300c\u512a\u308c\u3066\u3044\u308b\u304b\u300d\u3092\u554f\u3046\u7814\u7a76\u3060\u3051\u3067\u306f\u4e0d\u5341\u5206\u3067\u3042\u308b\u3002\u672c\u8a18\u4e8b\u3067\u306f\u3001\u81e8\u5e8a\u73fe\u5834\u3067\u5f79\u7acb\u3064\u540c\u7b49\u6027\u691c\u5b9a\u306e\u57fa\u672c\u304b\u3089\u3001\u533b\u5e2b\u304c\u76f4\u9762\u3059\u308b\u5177\u4f53\u7684\u306a\u30b1\u30fc\u30b9\u3067\u306e\u6d3b\u7528\u6cd5\u3001\u305d\u3057\u3066\u7814\u7a76\u306e [&hellip;]<\/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":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[16,29],"tags":[],"class_list":["post-4002","post","type-post","status-publish","format-standard","hentry","category-16","category-29"],"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\/4002","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=4002"}],"version-history":[{"count":4,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts\/4002\/revisions"}],"predecessor-version":[{"id":4006,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts\/4002\/revisions\/4006"}],"wp:attachment":[{"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/media?parent=4002"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/categories?post=4002"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/tags?post=4002"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}