{"id":4777,"date":"2026-08-28T07:37:14","date_gmt":"2026-08-27T22:37:14","guid":{"rendered":"https:\/\/best-biostatistics.com\/toukei-er\/?p=4777"},"modified":"2026-08-28T07:37:14","modified_gmt":"2026-08-27T22:37:14","slug":"ever-get-lost-in-sensory-evaluation-a-guide-to-selecting-scheffes-paired-comparison-methods-and-scaling-with-hagas-modification","status":"publish","type":"post","link":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/ever-get-lost-in-sensory-evaluation-a-guide-to-selecting-scheffes-paired-comparison-methods-and-scaling-with-hagas-modification\/","title":{"rendered":"\u5b98\u80fd\u8a55\u4fa1\u30fb\u55dc\u597d\u30c6\u30b9\u30c8\u3067\u8ff7\u308f\u306a\u3044\uff01\u30b7\u30a7\u30c3\u30d5\u30a7\u306e\u4e00\u5bfe\u6bd4\u8f03\u6cd5\uff08\u539f\u6cd5\u30fb\u82b3\u8cc0\u30fb\u4e2d\u5c4b\u30fb\u6d66\uff09\u306e\u9078\u3073\u65b9\u3068\u82b3\u8cc0\u306e\u5909\u6cd5\u306b\u3088\u308b\u5fc3\u7406\u5c3a\u5ea6\u5316\u30ac\u30a4\u30c9"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">\u88fd\u54c1\u958b\u767a\u306e\u73fe\u5834\u3067\u3001\u98f2\u6599\u306e\u5473\u3084\u5316\u7ca7\u54c1\u306e\u808c\u89e6\u308a\u3068\u3044\u3063\u305f\u300c\u4eba\u9593\u306e\u611f\u899a\u3084\u55dc\u597d\u300d\u3092\u5ba2\u89b3\u7684\u306a\u6570\u5024\u3068\u3057\u3066\u8a55\u4fa1\u3057\u305f\u3044\u5834\u9762\u306f\u975e\u5e38\u306b\u591a\u3044\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u305d\u306e\u969b\u3001\u6700\u3082\u4fe1\u983c\u6027\u304c\u9ad8\u3044\u624b\u6cd5\u306e1\u3064\u304c\u300c2\u3064\u306e\u30b5\u30f3\u30d7\u30eb\u3092\u63d0\u793a\u3057\u3066 $-2 \\sim +2$ \u70b9\u3067\u8a55\u4fa1\u3055\u305b\u308b\u300d<strong>\u30b7\u30a7\u30c3\u30d5\u30a7\u306e\u4e00\u5bfe\u6bd4\u8f03\u6cd5<\/strong>\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u3057\u304b\u3057\u3001\u3044\u3056\u6587\u732e\u3084\u7d71\u8a08\u30bd\u30d5\u30c8\u3092\u8abf\u3079\u308b\u3068\u300c\u30b7\u30a7\u30c3\u30d5\u30a7\u306e\u539f\u6cd5\u300d\u300c\u82b3\u8cc0\u306e\u5909\u6cd5\u300d\u300c\u4e2d\u5c4b\u306e\u5909\u6cd5\u300d\u300c\u6d66\u306e\u5909\u6cd5\u300d\u3068\u3044\u30464\u3064\u306e\u30d0\u30ea\u30a8\u30fc\u30b7\u30e7\u30f3\u304c\u767b\u5834\u3057\u3001\u3069\u308c\u3092\u9078\u3076\u3079\u304d\u304b\u56f0\u60d1\u3057\u305f\u7d4c\u9a13\u306f\u306a\u3044\u3060\u308d\u3046\u304b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u7d50\u8ad6\u304b\u3089\u8a00\u3048\u3070\u3001\u98df\u54c1\u30fb\u98f2\u6599\u30fb\u5316\u7ca7\u54c1\u306e\u3088\u3046\u306b\u300c1\u4eba\u306e\u8a55\u4fa1\u8005\u304c\u4f55\u7a2e\u985e\u3082\u8a66\u3059\u3068\u611f\u899a\u304c\u9ebb\u75fa\u3057\u3066\u3057\u307e\u3046\u300d\u73fe\u5834\u3067\u306f\u3001\u82b3\u8cc0\u306e\u5909\u6cd5\uff08Haga&#8217;s modification\uff09\u304c\u6700\u3082\u73fe\u5b9f\u7684\u304b\u3064\u5f37\u529b\u306a\u30a2\u30d7\u30ed\u30fc\u30c1\u3068\u306a\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u672c\u8a18\u4e8b\u3067\u306f\u30014\u3064\u306e\u5909\u6cd5\u306e\u9055\u3044\u3092\u76f4\u611f\u7684\u306a\u4f8b\u3048\u3067\u6574\u7406\u3057\u305f\u4e0a\u3067\u3001\u306a\u305c\u82b3\u8cc0\u306e\u5909\u6cd5\u304c\u5b9f\u52d9\u6700\u5f37\u306a\u306e\u304b\u3001\u305d\u306e\u7d71\u8a08\u30e2\u30c7\u30eb\u306e\u4ed5\u7d44\u307f\u3001\u591a\u91cd\u6bd4\u8f03\u306e\u6b66\u5668\u3067\u3042\u308b\u300c\u30e4\u30fc\u30c9\u30b9\u30c6\u30a3\u30c3\u30af\uff08Yardstick\uff09\u691c\u5b9a\u300d\u3001\u305d\u3057\u3066R\u306b\u3088\u308b\u5b8c\u5168\u81ea\u52d5\u89e3\u6790\u30fb\u53ef\u8996\u5316\u30b3\u30fc\u30c9\u307e\u3067\u3092\u5fb9\u5e95\u89e3\u8aac\u3059\u308b\u3002<\/p>\n\n\n\n<!--more-->\n\n\n\n<h2 class=\"wp-block-heading\">1. \u306a\u305c\u4e00\u5bfe\u6bd4\u8f03\u6cd5\u3067\u8ff7\u3046\u306e\u304b\uff1f\u30b7\u30a7\u30c3\u30d5\u30a7\u306e4\u3064\u306e\u5909\u6cd5\uff08\u539f\u6cd5\u30fb\u82b3\u8cc0\u30fb\u4e2d\u5c4b\u30fb\u6d66\uff09\u306e\u9055\u3044\u3068\u9078\u3073\u65b9\u30d5\u30ed\u30fc\u30c1\u30e3\u30fc\u30c8<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e00\u5bfe\u6bd4\u8f03\u6cd5\u3067\u8ff7\u3063\u3066\u3057\u307e\u3046\u6700\u5927\u306e\u539f\u56e0\u306f\u3001\u300c\u5b9f\u9a13\u306e\u5236\u7d04\uff081\u4eba\u304c\u4f55\u7d44\u8a55\u4fa1\u3067\u304d\u308b\u304b\uff09\u300d<strong>\u3068<\/strong>\u300c\u8003\u616e\u3057\u305f\u3044\u52b9\u679c\uff08\u8a66\u98f2\u306e\u9806\u756a\u3084\u500b\u4eba\u306e\u7656\uff09\u300d\u306e\u7d44\u307f\u5408\u308f\u305b\u306b\u3088\u3063\u3066\u3001\u6570\u5b66\u7684\u306a\u30e2\u30c7\u30eb\u304c4\u30d1\u30bf\u30fc\u30f3\u306b\u5206\u304b\u308c\u308b\u305f\u3081\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u308f\u304b\u308a\u3084\u3059\u304f\u4f8b\u3048\u308b\u306a\u3089\u3001\u5909\u6cd5\u306e\u9078\u629e\u306f\u300c\u7dcf\u5f53\u305f\u308a\u6226\u306e\u5bfe\u6226\u30eb\u30fc\u30eb\u6c7a\u3081\u300d\u306b\u4f3c\u3066\u3044\u308b\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">4\u3064\u306e\u5909\u6cd5\u3092\u6c7a\u3081\u308b\u300c2\u3064\u306e\u8ef8\u300d<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">4\u3064\u306e\u5909\u6cd5\u306e\u9055\u3044\u306f\u3001\u4ee5\u4e0b\u306e2\u3064\u306e\u8cea\u554f\u306b\u7b54\u3048\u308b\u3060\u3051\u3067\u4e00\u77ac\u3067\u6574\u7406\u3067\u304d\u308b\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u8ef81\uff08\u8a55\u4fa1\u91cf\uff09<\/strong>: 1\u4eba\u306e\u88ab\u9a13\u8005\uff08\u30d1\u30cd\u30eb\uff09\u304c\u300c1\u30da\u30a2\uff081\u7d44\uff09\u3060\u3051\u300d\u8a55\u4fa1\u3059\u308b\u306e\u304b\u3001\u305d\u308c\u3068\u3082\u300c\u5168\u30da\u30a2\uff08\u5168\u7d44\u307f\u5408\u308f\u305b\uff09\u300d\u3092\u8a55\u4fa1\u3059\u308b\u306e\u304b\uff1f<\/li>\n\n\n\n<li><strong>\u8ef82\uff08\u8003\u616e\u3059\u308b\u52b9\u679c\uff09<\/strong>: \u63d0\u793a\u3059\u308b\u300c\u9806\u5e8f\u52b9\u679c\uff08\u5148\u306b\u8a66\u3059\u304b\u5f8c\u3067\u8a66\u3059\u304b\uff09\u300d\u3084\u300c\u30d1\u30cd\u30eb\u306e\u500b\u4f53\u5dee\uff08\u8a55\u4fa1\u306e\u7518\u3055\u30fb\u8f9b\u3055\u306e\u7656\uff09\u300d\u3092\u30e2\u30c7\u30eb\u306b\u7d44\u307f\u8fbc\u307f\u305f\u3044\u304b\uff1f<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">\u3053\u306e2\u8ef8\u306b\u3088\u3063\u3066\u30014\u3064\u306e\u624b\u6cd5\u306f\u660e\u78ba\u306b\u30de\u30c8\u30ea\u30af\u30b9\u5316\u3055\u308c\u308b\u3002<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td><strong>\u624b\u6cd5\u540d<\/strong><\/td><td><strong>1\u4eba\u306e\u8a55\u4fa1\u8005\u306e\u8a55\u4fa1\u6570<\/strong><\/td><td><strong>\u63d0\u793a\u9806\u5e8f\u52b9\u679c<\/strong><\/td><td><strong>\u30d1\u30cd\u30eb\u306e\u500b\u4f53\u5dee<\/strong><\/td><td><strong>\u4f8b\u3048\u3067\u308f\u304b\u308b\u5b9f\u9a13\u30c7\u30b6\u30a4\u30f3<\/strong><\/td><\/tr><tr><td><strong>\u30b7\u30a7\u30c3\u30d5\u30a7\u306e\u539f\u6cd5<\/strong><\/td><td><strong>1\u7d44\u306e\u307f<\/strong><\/td><td><strong>\u8003\u616e\u3059\u308b<\/strong><\/td><td>\u8003\u616e\u3057\u306a\u3044<\/td><td>\u8a55\u4fa1\u8005\u304c\u5927\u52e2\u304a\u308a\u3001\u300cA $\\rightarrow$ B\u300d\u3068\u300cB $\\rightarrow$ A\u300d\u306e\u9806\u756a\u306e\u9055\u3044\u307e\u3067\u53b3\u5bc6\u306b\u8abf\u3079\u305f\u3044\u5834\u5408<\/td><\/tr><tr><td><strong>\u82b3\u8cc0\u306e\u5909\u6cd5\uff08\u2605\u672c\u8a18\u4e8b\u306e\u4e3b\u5f79\uff09<\/strong><\/td><td><strong>1\u7d44\u306e\u307f<\/strong><\/td><td><strong>\u8003\u616e\u3057\u306a\u3044\uff08\u30e9\u30f3\u30c0\u30e0\u5316\uff09<\/strong><\/td><td>\u8003\u616e\u3057\u306a\u3044<\/td><td><strong>\u8a55\u4fa1\u8005\u304c\u5927\u52e2\u3044\u308b\u304c\u3001\u75b2\u52b4\u3092\u907f\u3051\u308b\u305f\u30811\u4eba1\u7d44\u3068\u3057\u3001\u9806\u5e8f\u306f\u30e9\u30f3\u30c0\u30e0\u306b\u5165\u308c\u66ff\u3048\u3066\u6253\u3061\u6d88\u3059\u5834\u5408<\/strong><\/td><\/tr><tr><td><strong>\u4e2d\u5c4b\u306e\u5909\u6cd5<\/strong><\/td><td><strong>\u5168\u7d44\u307f\u5408\u308f\u305b<\/strong><\/td><td>\u8003\u616e\u3057\u306a\u3044\uff08\u30e9\u30f3\u30c0\u30e0\u5316\uff09<\/td><td><strong>\u8003\u616e\u3059\u308b<\/strong><\/td><td>1\u4eba\u304c\u5168\u7d44\u307f\u5408\u308f\u305b\u3092\u8a55\u4fa1\u3067\u304d\uff08\u30c7\u30b6\u30a4\u30f3\u3084\u753b\u50cf\u8a55\u4fa1\u306a\u3069\uff09\u3001\u8a55\u4fa1\u8005\u306e\u300c\u70b9\u306e\u7518\u3055\u30fb\u8f9b\u3055\u300d\u3092\u88dc\u6b63\u3057\u305f\u3044\u5834\u5408<\/td><\/tr><tr><td><strong>\u6d66\u306e\u5909\u6cd5<\/strong><\/td><td><strong>\u5168\u7d44\u307f\u5408\u308f\u305b<\/strong><\/td><td><strong>\u8003\u616e\u3059\u308b<\/strong><\/td><td><strong>\u8003\u616e\u3059\u308b<\/strong><\/td><td>1\u4eba\u304c\u5168\u7d44\u3092\u8a55\u4fa1\u3067\u304d\u3001\u3055\u3089\u306b\u9806\u5e8f\u52b9\u679c\u3082\u8a55\u4fa1\u8005\u306e\u7656\u3082\u3059\u3079\u3066\u5b8c\u74a7\u306b\u30e2\u30c7\u30eb\u5316\u3057\u305f\u3044\u300c\u5168\u90e8\u4e57\u305b\u300d\u30e2\u30c7\u30eb<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">\u4e00\u767a\u3067\u6c7a\u307e\u308b\u9078\u629e\u30d5\u30ed\u30fc\u30c1\u30e3\u30fc\u30c8<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u5b9f\u52d9\u3067\u8ff7\u3063\u305f\u3068\u304d\u306f\u3001\u4ee5\u4e0b\u306e\u30d5\u30ed\u30fc\u306b\u5f93\u3063\u3066\u9078\u629e\u3059\u308c\u3070\u9593\u9055\u3044\u304c\u306a\u3044\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>\u3010\u8cea\u554f1\u30111\u4eba\u306e\u8a55\u4fa1\u8005\u306b\u3001\u3059\u3079\u3066\u306e\u7d44\u307f\u5408\u308f\u305b\uff08\u5168\u30da\u30a2\uff09\u3092\u8a66\u3055\u305b\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u304b\uff1f\n  \u2502\n  \u251c\u2500\u2500\uff3b NO \uff3d\u2500\u2500\uff1e\u3010\u8cea\u554f2\u3011\u8a66\u3059\u9806\u756a\uff08A\u2192B \u304b B\u2192A \u304b\uff09\u306e\u5f71\u97ff\u3092\u8a08\u7b97\u3067\u62bd\u51fa\u3057\u305f\u3044\u3067\u3059\u304b\uff1f\n  \u2502                \u2502\n  \u2502                \u251c\u2500\u2500\uff3b YES \uff3d\u2500\u2500\uff1e \u3010\u30b7\u30a7\u30c3\u30d5\u30a7\u306e\u539f\u6cd5\u3011\n  \u2502                \u2514\u2500\u2500\uff3b NO \uff3d \u2500\u2500\uff1e \u3010\u82b3\u8cc0\u306e\u5909\u6cd5\uff08\u2605\u30d9\u30b9\u30c8\u9078\u629e\uff09\u3011\n  \u2502\n  \u2514\u2500\u2500\uff3b YES \uff3d\u2500\u2500\uff1e\u3010\u8cea\u554f3\u3011\u8a66\u3059\u9806\u756a\uff08\u9806\u5e8f\u52b9\u679c\uff09\u306e\u5f71\u97ff\u3092\u8a08\u7b97\u3067\u62bd\u51fa\u3057\u305f\u3044\u3067\u3059\u304b\uff1f\n                   \u2502\n                   \u251c\u2500\u2500\uff3b YES \uff3d\u2500\u2500\uff1e \u3010\u6d66\u306e\u5909\u6cd5\u3011\n                   \u2514\u2500\u2500\uff3b NO \uff3d \u2500\u2500\uff1e \u3010\u4e2d\u5c4b\u306e\u5909\u6cd5\u3011\n<\/code><\/pre>\n\n\n\n<h2 class=\"wp-block-heading\">2. \u98df\u54c1\u30fb\u30b3\u30b9\u30e1\u958b\u767a\u306e\u73fe\u5834\u3067\u300c\u82b3\u8cc0\u306e\u5909\u6cd5\u300d\u304c\u6700\u5f37\u3067\u3042\u308b\u7406\u7531\uff081\u4eba1\u7d44\u30fb\u9806\u5e8f\u30e9\u30f3\u30c0\u30e0\u5316\u306e\u5fc5\u7136\u6027\uff09<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u306a\u305c\u98df\u54c1\u3084\u30b3\u30b9\u30e1\u306e\u5b98\u80fd\u8a55\u4fa1\uff08Sensory Evaluation\uff09\u306b\u304a\u3044\u3066\u3001\u82b3\u8cc0\u306e\u5909\u6cd5\u304c\u3053\u308c\u307b\u3069\u91cd\u5b9d\u3055\u308c\u308b\u306e\u3060\u308d\u3046\u304b\u3002\u305d\u3053\u306b\u306f\u73fe\u5834\u306a\u3089\u3067\u306f\u306e\u5207\u5b9f\u306a\u7269\u7406\u7684\u5236\u7d04\u304c\u3042\u308b\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u5b98\u80fd\u8a55\u4fa1\u306e\u6700\u5927\u306e\u6575\u300c\u611f\u5ea6\u306e\u75b2\u52b4\uff08Sensory Fatigue\uff09\u300d<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u4f8b\u3048\u3070\u30015\u7a2e\u985e\u306e\u65b0\u5546\u54c1\u30ab\u30ec\u30fc\uff08A, B, C, D, E\uff09\u306e\u304a\u3044\u3057\u3055\u3092\u6bd4\u8f03\u3057\u305f\u3044\u3068\u3059\u308b\u30025\u7a2e\u985e\u304b\u30892\u3064\u3092\u9078\u3076\u7d44\u307f\u5408\u308f\u305b\u306f\u5168\u90e8\u3067 10 \u30da\u30a2\uff08$\\frac{5 \\times 4}{2} = 10$\uff09\u5b58\u5728\u3059\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u3082\u30571\u4eba\u306e\u88ab\u9a13\u8005\u306b10\u30da\u30a2\uff08\u8a0820\u76bf\u306e\u30ab\u30ec\u30fc\uff09\u3092\u98df\u3079\u6bd4\u3079\u3055\u305b\u305f\u3089\u3069\u3046\u306a\u308b\u3060\u308d\u3046\u304b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u3069\u3093\u306a\u306b\u7f8e\u98df\u5bb6\u3067\u3042\u3063\u3066\u3082\u30013\u30da\u30a2\u76ee\u3042\u305f\u308a\u3067\u820c\u304c\u9ebb\u75fa\u3057\u3001\u304a\u8179\u304c\u3044\u3063\u3071\u3044\u306b\u306a\u308a\u3001\u5f8c\u534a\u306e\u8a55\u4fa1\u306f\u9069\u5f53\u306b\u306a\u308b\u306f\u305a\u3060\u3002\u9999\u6c34\u3084\u53e3\u7d05\u306e\u30c6\u30b9\u30c8\u3067\u3082\u540c\u69d8\u3067\u3001\u9f3b\u3084\u808c\u306e\u611f\u899a\u306f\u3059\u3050\u306b\u9ebb\u75fa\u3057\u3066\u3057\u307e\u3046\u3002\u3053\u308c\u304c\u300c\u611f\u5ea6\u306e\u75b2\u52b4\u300d\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4fe1\u983c\u3067\u304d\u308b\u5b98\u80fd\u8a55\u4fa1\u30c7\u30fc\u30bf\u3092\u5f97\u308b\u305f\u3081\u306e\u7d76\u5bfe\u6761\u4ef6\u306f\u3001\u300c1\u4eba\u306e\u88ab\u9a13\u8005\u306b\u306f1\u30da\u30a2\uff081\u7d44\uff09\u3060\u3051\u3092\u8a55\u4fa1\u3057\u3066\u3082\u3089\u3046\u300d\u3053\u3068\u3067\u3042\u308b\u3002200\u4eba\u306e\u88ab\u9a13\u8005\u3092\u78ba\u4fdd\u3057\u300120\u4eba\u305a\u306410\u500b\u306e\u30da\u30a2\u306b\u5272\u308a\u5f53\u3066\u308b\u4e0d\u5b8c\u5099\u306a\u8a2d\u8a08\uff08\u5206\u5272\u8a55\u4fa1\uff09\u306b\u3059\u308b\u306e\u304c\u6700\u3082\u7406\u306b\u304b\u306a\u3063\u3066\u3044\u308b\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u9806\u5e8f\u52b9\u679c\u306f\u300c\u30e9\u30f3\u30c0\u30e0\u5316\uff08\u30ab\u30a6\u30f3\u30bf\u30fc\u30d0\u30e9\u30f3\u30b9\uff09\u300d\u3067\u6d88\u305b\u3070\u3044\u3044<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u300c\u5148\u306b\u5473\u308f\u3063\u305f\u30b5\u30f3\u30d7\u30eb\u306e\u5473\u304c\u53e3\u306b\u6b8b\u3063\u3066\u30012\u756a\u76ee\u306e\u30b5\u30f3\u30d7\u30eb\u306e\u8a55\u4fa1\u306b\u5f71\u97ff\u3059\u308b\u306e\u3067\u306f\u306a\u3044\u304b\uff1f\u300d\u3068\u3044\u3046\u61f8\u5ff5\uff08\u63d0\u793a\u9806\u5e8f\u52b9\u679c\uff09\u306f\u5f53\u7136\u751f\u3058\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u3057\u304b\u3057\u3001\u3053\u306e\u9806\u5e8f\u52b9\u679c\u306f<strong>\u7d71\u8a08\u30e2\u30c7\u30eb\u306e\u5f0f\u306b\u5165\u308c\u3066\u308f\u3056\u308f\u3056\u8a08\u7b97\u3057\u306a\u304f\u3066\u3082\u3001\u5b9f\u9a13\u306e\u8a2d\u8a08\u6bb5\u968e\u3067\u6d88\u3057\u53bb\u308b\u3053\u3068\u304c\u3067\u304d\u308b<\/strong>\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4f8b\u3048\u3070 A \u3068 B \u306e\u30da\u30a2\u3092\u8a55\u4fa1\u3059\u308b20\u4eba\u306e\u3046\u3061\u3001<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>10\u4eba\u306b\u306f\u300cA $\\rightarrow$ B\u300d\u306e\u9806\u3067\u8a66\u98f2\u3055\u305b\u308b<\/li>\n\n\n\n<li>\u6b8b\u308a10\u4eba\u306b\u306f\u300cB $\\rightarrow$ A\u300d\u306e\u9806\u3067\u8a66\u98f2\u3055\u305b\u308b<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u3053\u306e\u3088\u3046\u306b\u9806\u756a\u3092\u534a\u3005\uff08\u30e9\u30f3\u30c0\u30e0\u5316\u30fb\u30ab\u30a6\u30f3\u30bf\u30fc\u30d0\u30e9\u30f3\u30b9\uff09\u306b\u3059\u308c\u3070\u3001\u9806\u5e8f\u306b\u3088\u308b\u6709\u5229\u30fb\u4e0d\u5229\u306f\u76f8\u6bba\u3055\u308c\u3066\u6d88\u3048\u3066\u3057\u307e\u3046\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u9806\u5e8f\u52b9\u679c\u3092\u30e2\u30c7\u30eb\u304b\u3089\u9664\u5916\u3059\u308b\u3053\u3068\u3067\u8a08\u7b97\u30ed\u30b8\u30c3\u30af\u304c\u6975\u3081\u3066\u30b7\u30f3\u30d7\u30eb\u306b\u306a\u308a\u3001\u30c7\u30fc\u30bf\u5206\u6790\u306e\u900f\u660e\u6027\u3068\u5831\u544a\u306e\u3057\u3084\u3059\u3055\u304c\u98db\u8e8d\u7684\u306b\u5411\u4e0a\u3059\u308b\u3002\u3053\u308c\u3053\u305d\u304c\u3001\u5b9f\u52d9\u3067<strong>\u82b3\u8cc0\u306e\u5909\u6cd5<\/strong>\u304c\u6700\u5f37\u3068\u547c\u3070\u308c\u308b\u7406\u7531\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<div id=\"biost-2971281931\" 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\">3. \u82b3\u8cc0\u306e\u5909\u6cd5\u306e\u7d71\u8a08\u30e2\u30c7\u30eb\u3068\u5206\u6563\u5206\u6790\uff08ANOVA\uff09\u306e\u4ed5\u7d44\u307f\uff1a\u4e3b\u52b9\u679c\u30fb\u7d44\u307f\u5408\u308f\u305b\u52b9\u679c\u30fb\u8aa4\u5dee\u3078\u306e\u5206\u89e3<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u82b3\u8cc0\u306e\u5909\u6cd5\u3067\u306f\u3001\u5f97\u3089\u308c\u305f\u8a55\u70b9\u30c7\u30fc\u30bf\u3092\u3069\u306e\u3088\u3046\u306b\u5206\u89e3\u3057\u3066\u7d71\u8a08\u7684\u306b\u691c\u8a3c\u3059\u308b\u306e\u3060\u308d\u3046\u304b\u3002\u305d\u306e\u6570\u5f0f\u30e2\u30c7\u30eb\u3068\u4ed5\u7d44\u307f\u3092\u7d10\u89e3\u3044\u3066\u3044\u304f\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u6570\u5f0f\u30e2\u30c7\u30eb\u306e\u5206\u89e3\uff08\u5f97\u3089\u308c\u305f\u70b9\u6570\u306e\u300c\u5185\u8a33\u300d\uff09<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u88ab\u9a13\u8005 $l$ \u304c\u8a66\u6599 $i$ \u3068 \u8a66\u6599 $j$ \u3092\u6bd4\u8f03\u3057\u305f\u3068\u304d\u306e\u8a55\u70b9 $x_{ijl}$\uff08\u4f8b: $-2, -1, 0, +1, +2$\uff09\u306f\u3001\u4ee5\u4e0b\u306e3\u3064\u306e\u8981\u7d20\u306e\u8db3\u3057\u7b97\u3068\u3057\u3066\u8868\u3055\u308c\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$x_{ijl} = (\\alpha_i &#8211; \\alpha_j) + \\gamma_{ij} + e_{ijl}$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u3053\u306e\u5f0f\u306f\u3001\u4e00\u898b\u96e3\u3057\u305d\u3046\u306b\u898b\u3048\u308b\u304c\u3001\u300c\u3042\u308b\u4eba\u304c\u3064\u3051\u305f\u70b9\u6570\u306f\u3001\u4f55\u306b\u3088\u3063\u3066\u6c7a\u307e\u3063\u305f\u306e\u304b\uff1f\u300d\u306e\u5185\u8a33\u3092\u793a\u3057\u3066\u3044\u308b\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>$\\alpha_i &#8211; \\alpha_j$\uff08\u4e3b\u52b9\u679c\u306e\u5dee\uff09<\/strong>:\u8a66\u6599 $i$ \u304c\u672c\u6765\u6301\u3064\u5b9f\u529b\uff08\u5e73\u5747\u55dc\u597d\u5ea6\uff09\u3068\u3001\u8a66\u6599 $j$ \u306e\u5b9f\u529b\u3068\u306e\u7d20\u76f4\u306a\u5dee\u3002\u79c1\u305f\u3061\u304c\u6700\u3082\u77e5\u308a\u305f\u3044\u300c\u672c\u5f53\u306e\u5fc3\u7406\u7684\u8ddd\u96e2\u300d\u3067\u3042\u308b\u3002<\/li>\n\n\n\n<li><strong>$\\gamma_{ij}$\uff08\u7d44\u307f\u5408\u308f\u305b\u52b9\u679c \/ \u4ea4\u4e92\u4f5c\u7528\uff09<\/strong>:\u300c\u7279\u5b9a\u306e2\u3064\u3092\u4e26\u3079\u305f\u3068\u304d\u3060\u3051\u306b\u751f\u3058\u308b\u7279\u6709\u306e\u76f8\u4e57\u30fb\u76f8\u6bba\u52b9\u679c\u300d\u3067\u3042\u308b\u3002\u4f8b\u3048\u308b\u306a\u3089\u3001\u300c\u5358\u4f53\u3067\u898b\u308b\u3068\u5730\u5473\u306a\u9078\u624b\uff08\u8a66\u6599 $i$\uff09\u304c\u3001\u7279\u5b9a\u306e\u30e9\u30a4\u30d0\u30eb\uff08\u8a66\u6599 $j$\uff09\u3068\u4e26\u3093\u3060\u3068\u304d\u3060\u3051\u6025\u306b\u5f15\u304d\u7acb\u3063\u3066\u898b\u3048\u308b\u73fe\u8c61\u300d\u306e\u3088\u3046\u306a\u3082\u306e\u3067\u3042\u308b\u3002<\/li>\n\n\n\n<li><strong>$e_{ijl}$\uff08\u8aa4\u5dee\uff09<\/strong>:\u500b\u4eba\u306e\u4f53\u8abf\u3084\u305d\u306e\u5834\u306e\u6c17\u307e\u3050\u308c\u306b\u3088\u308b\u8a55\u4fa1\u306e\u3070\u3089\u3064\u304d\uff08\u30ce\u30a4\u30ba\uff09\u3002<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">\u5168\u5909\u52d5\uff08\u5e73\u65b9\u548c\uff09\u306e\u5206\u89e3\u3068ANOVA\u8868<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u82b3\u8cc0\u306e\u5909\u6cd5\u3067\u306f\u3001\u30c7\u30fc\u30bf\u5168\u4f53\u306e\u3070\u3089\u3064\u304d\uff08\u5168\u5e73\u65b9\u548c $S_T$\uff09\u3092\u3001\u4e0a\u306e\u8981\u7d20\u306b\u5bfe\u5fdc\u3055\u305b\u3066\u4ee5\u4e0b\u306e\u3088\u3046\u306b3\u3064\u306b\u5206\u89e3\u3057\u3001F\u691c\u5b9a\u3092\u884c\u3046\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$\\text{\u5168\u3070\u3089\u3064\u304d }(S_T) = \\text{\u4e3b\u52b9\u679c\u306e\u3070\u3089\u3064\u304d }(S_\\alpha) + \\text{\u7d44\u307f\u5408\u308f\u305b\u52b9\u679c\u306e\u3070\u3089\u3064\u304d }(S_\\gamma) + \\text{\u8aa4\u5dee\u306e\u3070\u3089\u3064\u304d }(S_e)$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u8a66\u6599\u6570\u3092 $t$\u30011\u30da\u30a2\u3042\u305f\u308a\u306e\u8a55\u4fa1\u8005\u6570\u3092 $n$ \u3068\u3057\u305f\u3068\u304d\u306e\u5206\u6563\u5206\u6790\u8868\uff08ANOVA\u8868\uff09\u306e\u69cb\u9020\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><td><strong>\u5206\u6563\u6e90\uff08\u8981\u56e0\uff09<\/strong><\/td><td><strong>\u5e73\u65b9\u548c\uff08SS\uff09<\/strong><\/td><td><strong>\u81ea\u7531\u5ea6\uff08df\uff09<\/strong><\/td><td><strong>\u5e73\u5747\u5e73\u65b9\uff08MS\uff09<\/strong><\/td><td><strong>F \u5024<\/strong><\/td><td><strong>\u610f\u5473\u3068\u5224\u5b9a\u5185\u5bb9<\/strong><\/td><\/tr><\/thead><tbody><tr><td><strong>\u4e3b\u52b9\u679c\uff08\u8a66\u6599\u9593\u306e\u5dee\uff09<\/strong><\/td><td>$S_\\alpha$<\/td><td>$t &#8211; 1$<\/td><td>$MS_\\alpha = \\frac{S_\\alpha}{t &#8211; 1}$<\/td><td>$\\frac{MS_\\alpha}{MS_e}$<\/td><td><strong>\u8a66\u6599\u9593\u306b\u7d71\u8a08\u5b66\u7684\u306a\u55dc\u597d\u30fb\u8a55\u4fa1\u306e\u5dee\u304c\u5b58\u5728\u3059\u308b\u304b\uff1f<\/strong>\uff08\u4e3b\u76ee\u7684\uff09<\/td><\/tr><tr><td><strong>\u7d44\u307f\u5408\u308f\u305b\u52b9\u679c<\/strong><\/td><td>$S_\\gamma$<\/td><td>$\\frac{(t-1)(t-2)}{2}$<\/td><td>$MS_\\gamma = \\frac{S_\\gamma}{df_\\gamma}$<\/td><td>$\\frac{MS_\\gamma}{MS_e}$<\/td><td><strong>\u7279\u5b9a\u306e\u30da\u30a2\u3060\u3051\u3067\u8d77\u304d\u308b\u7279\u6709\u306e\u76f8\u4e57\u52b9\u679c\u3084\u76f8\u6bba\u52b9\u679c\u304c\u3042\u308b\u304b\uff1f<\/strong><\/td><\/tr><tr><td><strong>\u8aa4\u5dee\uff08\u6b8b\u5dee\uff09<\/strong><\/td><td>$S_e$<\/td><td>$\\frac{t(t-1)(n-1)}{2}$<\/td><td>$MS_e = \\frac{S_e}{df_e}$<\/td><td>&#8211;<\/td><td>\u8a55\u4fa1\u8005\u500b\u4eba\u306e\u6c17\u307e\u3050\u308c\u3084\u6e2c\u5b9a\u8aa4\u5dee<\/td><\/tr><tr><td><strong>\u5168\u4f53<\/strong><\/td><td>$S_T$<\/td><td>$\\frac{t(t-1)n}{2}$<\/td><td>&#8211;<\/td><td>&#8211;<\/td><td>\u53ce\u96c6\u3057\u305f\u5168\u30c7\u30fc\u30bf\u306e\u3070\u3089\u3064\u304d<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e3b\u52b9\u679c\u306e $F$ \u5024\u306e $P$ \u5024\u304c $0.05$ \u672a\u6e80\u3067\u3042\u308c\u3070\u3001\u300c\u8a66\u6599\u306e\u9593\u306b\u5076\u7136\u3068\u306f\u8a00\u3048\u306a\u3044\u660e\u78ba\u306a\u611f\u899a\u30fb\u55dc\u597d\u306e\u5dee\u304c\u5b58\u5728\u3059\u308b\u300d\u3068\u7d50\u8ad6\u4ed8\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">4. \u5e73\u5747\u55dc\u597d\u5ea6\u306e\u7b97\u51fa\u3068\u591a\u91cd\u6bd4\u8f03\u306e\u6b66\u5668\u300c\u30e4\u30fc\u30c9\u30b9\u30c6\u30a3\u30c3\u30af\uff08Yardstick\uff09\u300d\u691c\u5b9a<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u5206\u6563\u5206\u6790\u3067\u300c\u8a66\u6599\u9593\u306b\u6709\u610f\u5dee\u3042\u308a\u300d\u3068\u5206\u304b\u3063\u305f\u3089\u3001\u6b21\u306f\u300c\u5177\u4f53\u7684\u306b\u3069\u306e\u30b5\u30f3\u30d7\u30eb\u3068\u3069\u306e\u30b5\u30f3\u30d7\u30eb\u306e\u9593\u306b\u5dee\u304c\u3042\u308b\u306e\u304b\uff1f\u300d<strong>\u3092\u7a81\u304d\u6b62\u3081\u308b\u30d5\u30a7\u30fc\u30ba\u306b\u5165\u308b\u3002\u3053\u3053\u3067\u767b\u5834\u3059\u308b\u306e\u304c<\/strong>\u300c\u5e73\u5747\u55dc\u597d\u5ea6\uff08\u5fc3\u7406\u7684\u5c3a\u5ea6\u5024\uff09\u300d<strong>\u3068<\/strong>\u300c\u30e4\u30fc\u30c9\u30b9\u30c6\u30a3\u30c3\u30af\uff08Yardstick\uff09\u300d\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u5e73\u5747\u55dc\u597d\u5ea6\uff08$\\hat{\\alpha}_i$\uff09\u306e\u7b97\u51fa\uff1a\u611f\u899a\u3092\u300c1\u6b21\u5143\u306e\u7269\u5dee\u3057\u300d\u306b\u4e57\u305b\u308b<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u5404\u8a66\u6599 $i$ \u306e\u5e73\u5747\u55dc\u597d\u5ea6\u306e\u63a8\u5b9a\u91cf $\\hat{\\alpha}_i$ \u306f\u3001\u8a66\u6599 $i$ \u304c\u7372\u5f97\u3057\u305f\u7dcf\u5408\u8a55\u70b9\u548c $X_{i.}$ \u3092\u7528\u3044\u3066\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3055\u308c\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$\\hat{\\alpha}_i = \\frac{X_{i.}}{t \\cdot n}$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u3059\u3079\u3066\u306e\u8a66\u6599\u306e\u5e73\u5747\u55dc\u597d\u5ea6\u3092\u5408\u8a08\u3059\u308b\u3068\u3001\u5fc5\u305a\u3061\u3087\u3046\u3069\u30bc\u30ed\uff08$\\sum_{i=1}^t \\hat{\\alpha}_i = 0$\uff09\u306b\u306a\u308b\u3068\u3044\u3046\u7f8e\u3057\u3044\u6027\u8cea\u3092\u6301\u3064\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u30d7\u30e9\u30b9\u306e\u5024\u304c\u5927\u304d\u3044\u307b\u3069\u300c\u5e73\u5747\u3057\u3066\u3088\u308a\u597d\u307e\u3057\u3044\u30fb\u611f\u899a\u304c\u5f37\u3044\u300d\u3053\u3068\u3092\u793a\u3057\u3001\u30de\u30a4\u30ca\u30b9\u306b\u5927\u304d\u3044\u307b\u3069\u300c\u597d\u307e\u3057\u304f\u306a\u3044\u30fb\u611f\u899a\u304c\u5f31\u3044\u300d\u3053\u3068\u3092\u793a\u3059\u3002\u3053\u308c\u306b\u3088\u308a\u3001\u5b9a\u6027\u7684\u306a\u597d\u304d\u5acc\u3044\u304c\u300c\u6570\u5024\u5316\u3055\u308c\u305f\u30dd\u30b8\u30b7\u30e7\u30cb\u30f3\u30b0\u30de\u30c3\u30d7\u300d\u3078\u5909\u63db\u3055\u308c\u308b\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u6709\u610f\u5dee\u5224\u5b9a\u306e\u7d76\u5bfe\u7684\u7269\u5dee\u3057\u300c\u30e4\u30fc\u30c9\u30b9\u30c6\u30a3\u30c3\u30af\uff08$Y_\\alpha$\uff09\u300d<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u5e73\u5747\u55dc\u597d\u5ea6\u306e\u4f4d\u7f6e\u304c\u6c42\u307e\u3063\u305f\u3089\u30012\u3064\u306e\u8a66\u6599\u306e\u5dee $\\vert{}\\hat{\\alpha}_i &#8211; \\hat{\\alpha}_j\\vert{}$ \u304c\u300c\u610f\u5473\u306e\u3042\u308b\u5dee\u306a\u306e\u304b\u3001\u5076\u7136\u306e\u8aa4\u5dee\u7bc4\u56f2\u306a\u306e\u304b\u300d\u3092\u5224\u5b9a\u3057\u306a\u3051\u308c\u3070\u306a\u3089\u306a\u3044\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u901a\u5e38\u306e\u591a\u91cd\u6bd4\u8f03\uff08Tukey\u6cd5\u306a\u3069\uff09\u3067\u306f\u306a\u304f\u3001\u4e00\u5bfe\u6bd4\u8f03\u6cd5\u5c02\u7528\u306e\u9650\u754c\u5024\u3068\u3057\u3066\u7b97\u51fa\u3055\u308c\u308b\u5224\u5b9a\u306e\u7269\u5dee\u3057\u3001\u305d\u308c\u304c\u30e4\u30fc\u30c9\u30b9\u30c6\u30a3\u30c3\u30af\uff08Yardstick\uff09\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u30e4\u30fc\u30c9\u30b9\u30c6\u30a3\u30c3\u30af\u9650\u754c\u5024 $Y_\\alpha$ \u306e\u516c\u5f0f\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$Y_\\alpha = q(t, df_e, \\alpha) \\cdot \\sqrt{\\frac{\\hat{\\sigma}^2}{2 t n}}$$<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>$q(t, df_e, \\alpha)$: \u8a66\u6599\u6570 $t$\u3001\u8aa4\u5dee\u81ea\u7531\u5ea6 $df_e$\u3001\u6709\u610f\u6c34\u6e96 $\\alpha$\uff08\u901a\u5e38 $0.05$\uff09\u306b\u304a\u3051\u308b\u30b9\u30c6\u30e5\u30fc\u30c7\u30f3\u30c8\u5316\u3055\u308c\u305f\u7bc4\u56f2\u306e\u9650\u754c\u5024\uff08R\u306e <code>qtukey<\/code> \u95a2\u6570\u3067\u7b97\u51fa\uff09\u3002<\/li>\n\n\n\n<li>$\\hat{\\sigma}^2$: \u5206\u6563\u5206\u6790\u8868\u304b\u3089\u5f97\u3089\u308c\u305f\u8aa4\u5dee\u306e\u4e0d\u504f\u5206\u6563\uff08$MS_e$\uff09\u3002<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u4f8b\u3048\u308b\u306a\u3089\u3001\u30e4\u30fc\u30c9\u30b9\u30c6\u30a3\u30c3\u30af\u3068\u306f\u300c\u7d71\u8a08\u5b66\u7684\u306b\u5f15\u304b\u308c\u305f\u5224\u5b9a\u7528\u30ab\u30fc\u30bd\u30eb\u300d\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2\u3064\u306e\u8a66\u6599\u306e\u5e73\u5747\u55dc\u597d\u5ea6\u306e\u8ddd\u96e2\uff08\u5dee\uff09\u304c\u3001\u3053\u306e\u30e4\u30fc\u30c9\u30b9\u30c6\u30a3\u30c3\u30af\u306e\u9577\u3055 $Y_{0.05}$ \u3088\u308a\u5927\u304d\u3051\u308c\u3070\u3001\u300c\u305d\u306e2\u3064\u306e\u30b5\u30f3\u30d7\u30eb\u306b\u306f 5% \u6c34\u6e96\u3067\u6709\u610f\u306a\u9078\u597d\u5dee\u304c\u3042\u308b\u300d\u3068\u5224\u5b9a\u3067\u304d\u308b\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>\u3010\u30e4\u30fc\u30c9\u30b9\u30c6\u30a3\u30c3\u30af\u691c\u5b9a\u306e\u5224\u5b9a\u30a4\u30e1\u30fc\u30b8\u3011\n\n  \u8a66\u6599A (\u03b1_A = +0.65)         \u8a66\u6599B (\u03b1_B = +0.10)       \u8a66\u6599C (\u03b1_C = -0.75)\n \u2500\u2500\u2500\u2500\u253c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u253c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u253c\u2500\u2500\u2500\u2500\u2500\u2500\uff1e \u5fc3\u7406\u7684\u5c3a\u5ea6\n     \u2514\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 \u5dee = 0.55 \u2500\u2500\u2500\u2500\u2500\u2500\u2518\n     &#91;==== \u30e4\u30fc\u30c9\u30b9\u30c6\u30a3\u30c3\u30af Y_0.05 = 0.35 ====]\n\n \u2794 \u8a66\u6599A\u3068\u8a66\u6599B\u306e\u5dee\uff080.55\uff09 \uff1e \u30e4\u30fc\u30c9\u30b9\u30c6\u30a3\u30c3\u30af\uff080.35\uff09 \n \u2794 A \u3068 B \u306e\u9593\u306b\u306f\u300c\u6709\u610f\u5dee\u3042\u308a\uff01\u300d\u3068\u5224\u5b9a\u3067\u304d\u308b\u3002<\/code><\/pre>\n\n\n\n<h2 class=\"wp-block-heading\">5. \u3010\u5b9f\u8df5R\u30b3\u30fc\u30c9\u3011\u82b3\u8cc0\u306e\u5909\u6cd5\u306b\u3088\u308b\u5206\u6563\u5206\u6790\u8868\u306e\u4f5c\u6210\u30fb\u30e4\u30fc\u30c9\u30b9\u30c6\u30a3\u30c3\u30af\u9650\u754c\u5024\u8a08\u7b97\u30fb\u5c3a\u5ea6\u56f3\u63cf\u753b\uff08Step by Step\uff09<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u3053\u3053\u304b\u3089\u306f\u3001\u5b9f\u969b\u306bR\u3092\u7528\u3044\u3066\u3001\u7591\u4f3c\u30c7\u30fc\u30bf\u306e\u4f5c\u6210\u304b\u3089\u5206\u6563\u5206\u6790\u8868\uff08ANOVA\uff09\u306e\u51fa\u529b\u3001\u30e4\u30fc\u30c9\u30b9\u30c6\u30a3\u30c3\u30af\u9650\u754c\u5024\u306e\u7b97\u51fa\u3001\u305d\u3057\u3066\u76f4\u611f\u7684\u306a\u5fc3\u7406\u7684\u5c3a\u5ea6\u56f3\uff08<code>ggplot2<\/code>\uff09\u306e\u63cf\u753b\u307e\u3067\u3092\u884c\u3046\u624b\u9806\u3092\u89e3\u8aac\u3059\u308b\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: \u7591\u4f3c\u5b98\u80fd\u8a55\u4fa1\u30c7\u30fc\u30bf\u306e\u4f5c\u6210<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">5\u7a2e\u985e\u306e\u6e05\u6dbc\u98f2\u6599\u6c34\uff08Sample_A, B, C, D, E\uff09\u3092\u8a55\u4fa1\u3059\u308b\u5b9f\u9a13\u3092\u60f3\u5b9a\u3059\u308b\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u8a66\u6599\u6570 $t = 5$\uff08\u30da\u30a2\u6570 = $\\frac{5 \\times 4}{2} = 10$ \u30da\u30a2\uff09<\/li>\n\n\n\n<li>1\u30da\u30a2\u3042\u305f\u308a\u306e\u8a55\u4fa1\u8005\u6570 $n = 20$ \u4eba\uff08\u7dcf\u88ab\u9a13\u8005\u6570 200 \u4eba\uff09<\/li>\n\n\n\n<li>\u8a55\u4fa1\u70b9: $-2$\uff08\u975e\u5e38\u306b\u60aa\u3044\uff09 $\\sim$ $+2$\uff08\u975e\u5e38\u306b\u3088\u3044\uff09<\/li>\n<\/ul>\n\n\n\n<pre class=\"wp-block-code\"><code>library(tidyverse)\n\n# \u4e71\u6570\u30b7\u30fc\u30c9\u306e\u8a2d\u5b9a\nset.seed(123)\n\nt &lt;- 5  # \u8a66\u6599\u6570\nn &lt;- 20 # 1\u30da\u30a2\u3042\u305f\u308a\u306e\u8a55\u4fa1\u8005\u6570\nsample_names &lt;- paste0(\"Sample_\", LETTERS&#91;1:t])\n\n# \u516810\u30da\u30a2\u306e\u7d44\u307f\u5408\u308f\u305b\u3092\u4f5c\u6210\npairs &lt;- combn(sample_names, 2)\n\n# \u7591\u4f3c\u8a55\u70b9\u30c7\u30fc\u30bf\u306e\u751f\u6210\u95a2\u6570\ngenerate_data &lt;- function() {\n  data_list &lt;- list()\n  \n  # \u8a2d\u5b9a\u3059\u308b\u771f\u306e\u55dc\u597d\u5ea6\uff08A\u304c\u6700\u3082\u9ad8\u304f\u3001E\u304c\u6700\u3082\u4f4e\u3044\uff09\n  true_alpha &lt;- c(0.8, 0.3, 0.0, -0.3, -0.8)\n  names(true_alpha) &lt;- sample_names\n  \n  for (k in 1:ncol(pairs)) {\n    s1 &lt;- pairs&#91;1, k]\n    s2 &lt;- pairs&#91;2, k]\n    \n    # \u771f\u306e\u5dee + \u30ce\u30a4\u30ba\u304b\u3089\u8a55\u70b9\uff08-2 ~ +2\uff09\u3092\u751f\u6210\n    diff &lt;- true_alpha&#91;s1] - true_alpha&#91;s2]\n    scores &lt;- round(rnorm(n, mean = diff * 1.5, sd = 0.9))\n    scores &lt;- pmax(-2, pmin(2, scores)) # -2~+2\u306e\u7bc4\u56f2\u306b\u53ce\u3081\u308b\n    \n    df_pair &lt;- tibble(\n      sample1 = s1,\n      sample2 = s2,\n      score = scores\n    )\n    data_list&#91;&#91;k]] &lt;- df_pair\n  }\n  bind_rows(data_list)\n}\n\nraw_data &lt;- generate_data()\nhead(raw_data)<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: \u5404\u30da\u30a2\u306e\u5408\u8a08\u70b9\u884c\u5217\u3068\u8a66\u6599\u3054\u3068\u306e\u7dcf\u5408\u8a55\u70b9\u548c\u306e\u96c6\u8a08<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u82b3\u8cc0\u306e\u5909\u6cd5\u306e\u8a08\u7b97\u306b\u5fc5\u8981\u306a\u3001\u5404\u30da\u30a2\u306e\u8a55\u70b9\u548c $X_{ij}$ \u3068\u3001\u5404\u8a66\u6599\u306e\u7dcf\u5408\u8a55\u70b9\u548c $X_{i.}$ \u3092\u8a08\u7b97\u3059\u308b\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code># t \u00d7 t \u306e\u8a55\u70b9\u548c\u884c\u5217 X_ij \u306e\u4f5c\u6210\nX_matrix &lt;- matrix(0, nrow = t, ncol = t, dimnames = list(sample_names, sample_names))\n\nfor (i in 1:nrow(raw_data)) {\n  s1 &lt;- raw_data$sample1&#91;i]\n  s2 &lt;- raw_data$sample2&#91;i]\n  sc &lt;- raw_data$score&#91;i]\n  \n  s1_idx &lt;- match(s1, sample_names)\n  s2_idx &lt;- match(s2, sample_names)\n  \n  X_matrix&#91;s1_idx, s2_idx] &lt;- X_matrix&#91;s1_idx, s2_idx] + sc\n  X_matrix&#91;s2_idx, s1_idx] &lt;- X_matrix&#91;s2_idx, s1_idx] - sc # \u5bfe\u79f0\u6210\u5206\u306f\u7b26\u53f7\u53cd\u8ee2\n}\n\n# \u5404\u8a66\u6599\u306e\u7dcf\u5408\u8a55\u70b9\u548c X_i. \u306e\u7b97\u51fa\nX_i_dot &lt;- rowSums(X_matrix)\n\nprint(X_matrix)\nprint(X_i_dot)<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: \u82b3\u8cc0\u306e\u5909\u6cd5\u306b\u3088\u308b\u5206\u6563\u5206\u6790\uff08ANOVA\uff09\u8868\u306e\u69cb\u7bc9<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u5e73\u65b9\u548c $S_T, S_\\alpha, S_\\gamma, S_e$ \u304a\u3088\u3073\u81ea\u7531\u5ea6\u3092\u8a08\u7b97\u3057\u3001\u5206\u6563\u5206\u6790\u8868\u3092\u4f5c\u6210\u3059\u308b\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code># \u7dcf\u5e73\u65b9\u548c S_T \u306e\u8a08\u7b97\nS_T &lt;- sum(raw_data$score^2)\n\n# \u4e3b\u52b9\u679c\u306e\u5e73\u65b9\u548c S_alpha \u306e\u8a08\u7b97\nS_alpha &lt;- sum(X_i_dot^2) \/ (t * n)\n\n# \u7d44\u307f\u5408\u308f\u305b\u52b9\u679c\u3092\u542b\u3080\u30da\u30a2\u5e73\u65b9\u548c S_pair \u306e\u8a08\u7b97\n# (\u4e0a\u4e09\u89d2\u6210\u5206\u306e\u307f\u3092\u4f7f\u7528)\nX_ij_upper &lt;- X_matrix&#91;upper.tri(X_matrix)]\nS_pair &lt;- sum(X_ij_upper^2) \/ n\n\n# \u7d44\u307f\u5408\u308f\u305b\u52b9\u679c\u306e\u5e73\u65b9\u548c S_gamma\nS_gamma &lt;- S_pair - S_alpha\n\n# \u8aa4\u5dee\u5e73\u65b9\u548c S_e\nS_e &lt;- S_T - S_alpha - S_gamma\n\n# \u81ea\u7531\u5ea6 (df) \u306e\u8a08\u7b97\ndf_alpha &lt;- t - 1\ndf_gamma &lt;- (t - 1) * (t - 2) \/ 2\ndf_e &lt;- (t * (t - 1) \/ 2) * (n - 1)\ndf_total &lt;- t * (t - 1) * n \/ 2\n\n# \u5e73\u5747\u5e73\u65b9 (MS) \u3068 F\u5024\u306e\u8a08\u7b97\nMS_alpha &lt;- S_alpha \/ df_alpha\nMS_gamma &lt;- S_gamma \/ df_gamma\nMS_e &lt;- S_e \/ df_e\n\nF_alpha &lt;- MS_alpha \/ MS_e\nF_gamma &lt;- MS_gamma \/ MS_e\n\np_alpha &lt;- pf(F_alpha, df_alpha, df_e, lower.tail = FALSE)\np_gamma &lt;- pf(F_gamma, df_gamma, df_e, lower.tail = FALSE)\n\n# ANOVA\u8868\u306e\u30c7\u30fc\u30bf\u30d5\u30ec\u30fc\u30e0\u4f5c\u6210\nanova_table &lt;- tibble(\n  Source = c(\"\u4e3b\u52b9\u679c (\u8a66\u6599\u5dee)\", \"\u7d44\u307f\u5408\u308f\u305b\u52b9\u679c\", \"\u8aa4\u5dee (\u6b8b\u5dee)\", \"\u5168\u4f53\"),\n  SS = c(S_alpha, S_gamma, S_e, S_T),\n  df = c(df_alpha, df_gamma, df_e, df_total),\n  MS = c(MS_alpha, MS_gamma, MS_e, NA),\n  F_value = c(F_alpha, F_gamma, NA, NA),\n  p_value = c(p_alpha, p_gamma, NA, NA)\n)\n\nprint(anova_table)<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\">Step 4: \u5e73\u5747\u55dc\u597d\u5ea6 $\\hat{\\alpha}_i$ \u3068\u30e4\u30fc\u30c9\u30b9\u30c6\u30a3\u30c3\u30af\u9650\u754c\u5024 $Y_{0.05}$ \u306e\u7b97\u51fa<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u5e73\u5747\u55dc\u597d\u5ea6\uff08\u5fc3\u7406\u7684\u5c3a\u5ea6\u5024\uff09\u3068\u3001\u591a\u91cd\u6bd4\u8f03\u306e\u57fa\u6e96\u3068\u306a\u308b\u30e4\u30fc\u30c9\u30b9\u30c6\u30a3\u30c3\u30af\u9650\u754c\u5024\u3092\u7b97\u51fa\u3059\u308b\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code># \u5e73\u5747\u55dc\u597d\u5ea6 (\u03b1_hat) \u306e\u7b97\u51fa\nalpha_hat &lt;- X_i_dot \/ (t * n)\n\n# 5%\u6c34\u6e96\u306e\u30e4\u30fc\u30c9\u30b9\u30c6\u30a3\u30c3\u30af\u9650\u754c\u5024 Y_0.05 \u306e\u8a08\u7b97\n# qtukey(p, nmeans, df) \u3092\u4f7f\u7528\nq_val &lt;- qtukey(p = 0.95, nmeans = t, df = df_e)\nyardstick_05 &lt;- q_val * sqrt(MS_e \/ (2 * t * n))\n\ncat(\"--- \u5e73\u5747\u55dc\u597d\u5ea6 (\u5fc3\u7406\u7684\u5c3a\u5ea6\u5024) ---\\n\")\nprint(round(alpha_hat, 4))\n\ncat(sprintf(\"\\n\u30e4\u30fc\u30c9\u30b9\u30c6\u30a3\u30c3\u30af\u9650\u754c\u5024 (Y_0.05): %.4f\\n\", yardstick_05))<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\">Step 5: \u5fc3\u7406\u7684\u5c3a\u5ea6\u56f3\uff08\u30dd\u30b8\u30b7\u30e7\u30cb\u30f3\u30b0\u30de\u30c3\u30d7\uff09\u306e <code>ggplot2<\/code> \u53ef\u8996\u5316<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u6c42\u307e\u3063\u305f\u5e73\u5747\u55dc\u597d\u5ea6\u3068\u30e4\u30fc\u30c9\u30b9\u30c6\u30a3\u30c3\u30af\u5e45\u30921\u6b21\u5143\u306e\u30dd\u30b8\u30b7\u30e7\u30cb\u30f3\u30b0\u30de\u30c3\u30d7\u3068\u3057\u3066\u7f8e\u3057\u304f\u30b0\u30e9\u30d5\u5316\u3059\u308b\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code># \u53ef\u8996\u5316\u7528\u30c7\u30fc\u30bf\u30d5\u30ec\u30fc\u30e0\u306e\u4f5c\u6210\ndf_plot &lt;- tibble(\n  Sample = names(alpha_hat),\n  Alpha = as.numeric(alpha_hat)\n) %>% \n  mutate(Sample = factor(Sample, levels = Sample&#91;order(Alpha)]))\n\n# \u5c3a\u5ea6\u56f3\u306e\u63cf\u753b\nggplot(df_plot, aes(x = Alpha, y = 1, label = Sample)) +\n  geom_hline(yintercept = 1, color = \"gray60\", linetype = \"dashed\") +\n  geom_point(size = 5, color = \"steelblue\") +\n  ggrepel::geom_text_repel(size = 5, vjust = -1.5, fontface = \"bold\") +\n  scale_y_continuous(limits = c(0.5, 1.5)) +\n  theme_minimal(base_size = 14) +\n  labs(\n    title = \"Mean Preference Scores &amp; Yardstick Comparison\",\n    subtitle = sprintf(\"Yardstick (Y_0.05) = %.4f\", yardstick_05),\n    x = \"Mean Preference Score (\u2190 Lower | Higher \u2192)\",\n    y = \"\"\n  ) +\n  theme(\n    axis.text.y = element_blank(),\n    axis.ticks.y = element_blank(),\n    panel.grid.major.y = element_blank(),\n    panel.grid.minor.y = element_blank()\n  )<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"575\" height=\"483\" src=\"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2026\/08\/image-15.png\" alt=\"\" class=\"wp-image-4779\" srcset=\"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2026\/08\/image-15.png 575w, https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2026\/08\/image-15-300x252.png 300w\" sizes=\"(max-width: 575px) 100vw, 575px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">6. \u307e\u3068\u3081\uff06\u4e00\u62ec\u30b3\u30d4\u30da\u7528R\u30b9\u30af\u30ea\u30d7\u30c8<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">\u672c\u8a18\u4e8b\u306e\u30dd\u30a4\u30f3\u30c8\u304a\u3055\u3089\u3044<\/h3>\n\n\n\n<ol start=\"1\" class=\"wp-block-list\">\n<li><strong>\u30b7\u30a7\u30c3\u30d5\u30a7\u306e4\u3064\u306e\u5909\u6cd5\u306f\u5b9f\u9a13\u5236\u7d04\u3067\u9078\u3076<\/strong>: \u98df\u54c1\u30fb\u30b3\u30b9\u30e1\u306a\u3069\u30011\u4eba\u306e\u88ab\u9a13\u8005\u306b1\u30da\u30a2\u3057\u304b\u8a66\u3055\u305b\u3089\u308c\u306a\u3044\u5834\u5408\u306f\u300c\u82b3\u8cc0\u306e\u5909\u6cd5\u300d\u304c\u30d9\u30b9\u30c8\u30a2\u30d7\u30ed\u30fc\u30c1\u3002<\/li>\n\n\n\n<li><strong>\u9806\u5e8f\u52b9\u679c\u306f\u30e9\u30f3\u30c0\u30e0\u5316\u3067\u76f8\u6bba\u3059\u308b<\/strong>: \u63d0\u793a\u9806\u5e8f\u306e\u6709\u5229\u30fb\u4e0d\u5229\u306f\u30ab\u30a6\u30f3\u30bf\u30fc\u30d0\u30e9\u30f3\u30b9\uff08\u30e9\u30f3\u30c0\u30e0\u5316\uff09\u3067\u6d88\u3059\u3053\u3068\u3067\u3001\u30e2\u30c7\u30eb\u304b\u3089\u6392\u9664\u3057\u3066\u30b7\u30f3\u30d7\u30eb\u306b\u89e3\u6790\u3067\u304d\u308b\u3002<\/li>\n\n\n\n<li><strong>\u4e3b\u52b9\u679c\u3068\u7d44\u307f\u5408\u308f\u305b\u52b9\u679c\u3092\u5206\u3051\u308b<\/strong>: ANOVA\u306b\u3088\u3063\u3066\u300c\u5546\u54c1\u81ea\u4f53\u306e\u5b9f\u529b\u5dee\u300d\u3068\u300c\u7279\u5b9a\u306e\u4e26\u3073\u306b\u3088\u308b\u76f8\u4e57\u30fb\u76f8\u6bba\u52b9\u679c\u300d\u3092\u660e\u78ba\u306b\u5206\u96e2\u3057\u3066\u691c\u5b9a\u3067\u304d\u308b\u3002<\/li>\n\n\n\n<li><strong>\u30e4\u30fc\u30c9\u30b9\u30c6\u30a3\u30c3\u30af\uff08Yardstick\uff09\u3067\u5dee\u3092\u5224\u5b9a<\/strong>: \u5e73\u5747\u55dc\u597d\u5ea6\uff08\u5fc3\u7406\u7684\u5c3a\u5ea6\u5024\uff09\u306e\u5dee\u304c\u30e4\u30fc\u30c9\u30b9\u30c6\u30a3\u30c3\u30af\u9650\u754c\u5024 $Y_{0.05}$ \u3088\u308a\u5927\u304d\u3051\u308c\u3070\u7d71\u8a08\u7684\u6709\u610f\u5dee\u3042\u308a\u3068\u5224\u5b9a\u3059\u308b\u3002<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">\u4e00\u62ec\u5b9f\u884c\u7528R\u30b9\u30af\u30ea\u30d7\u30c8<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u4ee5\u4e0b\u306e\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\uff06\u30da\u30fc\u30b9\u30c8\u3059\u308b\u3053\u3068\u3067\u3001\u30c7\u30fc\u30bf\u306e\u96c6\u8a08\u304b\u3089\u5206\u6563\u5206\u6790\u8868\u306e\u51fa\u529b\u3001\u5e73\u5747\u55dc\u597d\u5ea6\u306e\u7b97\u51fa\u3001\u30e4\u30fc\u30c9\u30b9\u30c6\u30a3\u30c3\u30af\u9650\u754c\u5024\u306e\u8868\u793a\u3001\u5c3a\u5ea6\u56f3\u30d7\u30ed\u30c3\u30c8\u307e\u3067\u3092\u4e00\u6c17\u901a\u8cab\u3067\u8d70\u3089\u305b\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code># ==============================================================================\n# \u30b7\u30a7\u30c3\u30d5\u30a7\u306e\u4e00\u5bfe\u6bd4\u8f03\u6cd5\uff08\u82b3\u8cc0\u306e\u5909\u6cd5\uff09\u4e00\u62ec\u89e3\u6790\u30b9\u30af\u30ea\u30d7\u30c8\n# \u30d1\u30c3\u30b1\u30fc\u30b8: tidyverse, ggrepel\n# ==============================================================================\n\nif (!requireNamespace(\"tidyverse\", quietly = TRUE)) install.packages(\"tidyverse\")\nif (!requireNamespace(\"ggrepel\", quietly = TRUE)) install.packages(\"ggrepel\")\n\nlibrary(tidyverse)\nlibrary(ggrepel)\n\n# --- 1. \u7591\u4f3c\u5b98\u80fd\u8a55\u4fa1\u30c7\u30fc\u30bf\u306e\u751f\u6210 ---\nset.seed(123)\nt &lt;- 5  # \u8a66\u6599\u6570\nn &lt;- 20 # 1\u30da\u30a2\u3042\u305f\u308a\u306e\u8a55\u4fa1\u8005\u6570\nsample_names &lt;- paste0(\"Sample_\", LETTERS&#91;1:t])\npairs &lt;- combn(sample_names, 2)\n\ntrue_alpha &lt;- c(0.8, 0.3, 0.0, -0.3, -0.8)\nnames(true_alpha) &lt;- sample_names\n\ndata_list &lt;- list()\nfor (k in 1:ncol(pairs)) {\n  s1 &lt;- pairs&#91;1, k]\n  s2 &lt;- pairs&#91;2, k]\n  diff &lt;- true_alpha&#91;s1] - true_alpha&#91;s2]\n  scores &lt;- round(rnorm(n, mean = diff * 1.5, sd = 0.9))\n  scores &lt;- pmax(-2, pmin(2, scores))\n  data_list&#91;&#91;k]] &lt;- tibble(sample1 = s1, sample2 = s2, score = scores)\n}\nraw_data &lt;- bind_rows(data_list)\n\n# --- 2. \u8a55\u70b9\u548c\u884c\u5217\u304a\u3088\u3073\u7dcf\u5408\u8a55\u70b9\u548c\u306e\u7b97\u51fa ---\nX_matrix &lt;- matrix(0, nrow = t, ncol = t, dimnames = list(sample_names, sample_names))\nfor (i in 1:nrow(raw_data)) {\n  s1_idx &lt;- match(raw_data$sample1&#91;i], sample_names)\n  s2_idx &lt;- match(raw_data$sample2&#91;i], sample_names)\n  sc &lt;- raw_data$score&#91;i]\n  X_matrix&#91;s1_idx, s2_idx] &lt;- X_matrix&#91;s1_idx, s2_idx] + sc\n  X_matrix&#91;s2_idx, s1_idx] &lt;- X_matrix&#91;s2_idx, s1_idx] - sc\n}\nX_i_dot &lt;- rowSums(X_matrix)\n\n# --- 3. \u5206\u6563\u5206\u6790 (ANOVA) \u8868\u306e\u69cb\u7bc9 ---\nS_T &lt;- sum(raw_data$score^2)\nS_alpha &lt;- sum(X_i_dot^2) \/ (t * n)\nS_pair &lt;- sum(X_matrix&#91;upper.tri(X_matrix)]^2) \/ n\nS_gamma &lt;- S_pair - S_alpha\nS_e &lt;- S_T - S_alpha - S_gamma\n\ndf_alpha &lt;- t - 1\ndf_gamma &lt;- (t - 1) * (t - 2) \/ 2\ndf_e &lt;- (t * (t - 1) \/ 2) * (n - 1)\ndf_total &lt;- t * (t - 1) * n \/ 2\n\nMS_alpha &lt;- S_alpha \/ df_alpha\nMS_gamma &lt;- S_gamma \/ df_gamma\nMS_e &lt;- S_e \/ df_e\n\nF_alpha &lt;- MS_alpha \/ MS_e\nF_gamma &lt;- MS_gamma \/ MS_e\n\np_alpha &lt;- pf(F_alpha, df_alpha, df_e, lower.tail = FALSE)\np_gamma &lt;- pf(F_gamma, df_gamma, df_e, lower.tail = FALSE)\n\nanova_table &lt;- tibble(\n  Source = c(\"\u4e3b\u52b9\u679c (\u8a66\u6599\u5dee)\", \"\u7d44\u307f\u5408\u308f\u305b\u52b9\u679c\", \"\u8aa4\u5dee (\u6b8b\u5dee)\", \"\u5168\u4f53\"),\n  SS = c(S_alpha, S_gamma, S_e, S_T),\n  df = c(df_alpha, df_gamma, df_e, df_total),\n  MS = c(MS_alpha, MS_gamma, MS_e, NA),\n  F_value = c(F_alpha, F_gamma, NA, NA),\n  p_value = c(p_alpha, p_gamma, NA, NA)\n)\n\n# --- 4. \u5e73\u5747\u55dc\u597d\u5ea6\u3068\u30e4\u30fc\u30c9\u30b9\u30c6\u30a3\u30c3\u30af\u7b97\u51fa ---\nalpha_hat &lt;- X_i_dot \/ (t * n)\nq_val &lt;- qtukey(p = 0.95, nmeans = t, df = df_e)\nyardstick_05 &lt;- q_val * sqrt(MS_e \/ (2 * t * n))\n\n# \u51fa\u529b\u8868\u793a\ncat(\"==================================================================\\n\")\ncat(\"          \u30b7\u30a7\u30c3\u30d5\u30a7\u306e\u4e00\u5bfe\u6bd4\u8f03\u6cd5\uff08\u82b3\u8cc0\u306e\u5909\u6cd5\uff09\u89e3\u6790\u7d50\u679c            \\n\")\ncat(\"==================================================================\\n\\n\")\ncat(\"\u3010\u5206\u6563\u5206\u6790\u8868 (ANOVA)\u3011\\n\")\nprint(anova_table)\ncat(\"\\n\u3010\u5e73\u5747\u55dc\u597d\u5ea6 (\u5fc3\u7406\u7684\u5c3a\u5ea6\u5024)\u3011\\n\")\nprint(round(alpha_hat, 4))\ncat(sprintf(\"\\n\u3010\u30e4\u30fc\u30c9\u30b9\u30c6\u30a3\u30c3\u30af\u9650\u754c\u5024 (Y_0.05)\u3011: %.4f\\n\", yardstick_05))\ncat(\"==================================================================\\n\")\n\n# --- 5. \u5fc3\u7406\u7684\u5c3a\u5ea6\u56f3\u306e\u63cf\u753b ---\ndf_plot &lt;- tibble(\n  Sample = names(alpha_hat),\n  Alpha = as.numeric(alpha_hat)\n) %&gt;% mutate(Sample = factor(Sample, levels = Sample&#91;order(Alpha)]))\n\np_map &lt;- ggplot(df_plot, aes(x = Alpha, y = 1, label = Sample)) +\n  geom_hline(yintercept = 1, color = \"gray60\", linetype = \"dashed\") +\n  geom_point(size = 5, color = \"steelblue\") +\n  geom_text_repel(size = 5, vjust = -1.5, fontface = \"bold\") +\n  scale_y_continuous(limits = c(0.5, 1.5)) +\n  theme_minimal(base_size = 14) +\n  labs(\n    title = \"\u5e73\u5747\u55dc\u597d\u5ea6\uff08\u5fc3\u7406\u7684\u5c3a\u5ea6\u56f3\uff09\u3068\u30e4\u30fc\u30c9\u30b9\u30c6\u30a3\u30c3\u30af\u6bd4\u8f03\",\n    subtitle = sprintf(\"Yardstick (Y_0.05) = %.4f\", yardstick_05),\n    x = \"\u5e73\u5747\u55dc\u597d\u5ea6 (\u2190 \u8a55\u4fa1\u4f4e\u3044 | \u8a55\u4fa1\u9ad8\u3044 \u2192)\",\n    y = \"\"\n  ) +\n  theme(\n    axis.text.y = element_blank(),\n    axis.ticks.y = element_blank(),\n    panel.grid.major.y = element_blank(),\n    panel.grid.minor.y = element_blank()\n  )\n\nprint(p_map)<\/code><\/pre>\n\n\n\n<h2 class=\"wp-block-heading\">\u304a\u3059\u3059\u3081\u66f8\u7c4d<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/amzn.to\/4gyToF5\">\u7d71\u8a08\u7684\u5b98\u80fd\u691c\u67fb\u6cd5<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u305f\u3060\u3057\u3001\u304b\u306a\u308a\u53e4\u304f\u4e2d\u53e4\u3057\u304b\u306a\u3044<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u88fd\u54c1\u958b\u767a\u306e\u73fe\u5834\u3067\u3001\u98f2\u6599\u306e\u5473\u3084\u5316\u7ca7\u54c1\u306e\u808c\u89e6\u308a\u3068\u3044\u3063\u305f\u300c\u4eba\u9593\u306e\u611f\u899a\u3084\u55dc\u597d\u300d\u3092\u5ba2\u89b3\u7684\u306a\u6570\u5024\u3068\u3057\u3066\u8a55\u4fa1\u3057\u305f\u3044\u5834\u9762\u306f\u975e\u5e38\u306b\u591a\u3044\u3002 \u305d\u306e\u969b\u3001\u6700\u3082\u4fe1\u983c\u6027\u304c\u9ad8\u3044\u624b\u6cd5\u306e1\u3064\u304c\u300c2\u3064\u306e\u30b5\u30f3\u30d7\u30eb\u3092\u63d0\u793a\u3057\u3066 $-2 \\sim +2$ \u70b9\u3067\u8a55\u4fa1\u3055 [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":4780,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"swell_btn_cv_data":"","_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_feature_clip_id":0,"_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},"jetpack_post_was_ever_published":false},"categories":[70],"tags":[],"class_list":["post-4777","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-70"],"jetpack_publicize_connections":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2026\/08\/\u82b3\u8cc0\u306e\u5909\u6cd5-scaled.jpeg","_links":{"self":[{"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts\/4777","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=4777"}],"version-history":[{"count":2,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts\/4777\/revisions"}],"predecessor-version":[{"id":4781,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts\/4777\/revisions\/4781"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/media\/4780"}],"wp:attachment":[{"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/media?parent=4777"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/categories?post=4777"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/tags?post=4777"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}