{"id":4459,"date":"2025-06-17T14:14:11","date_gmt":"2025-06-17T05:14:11","guid":{"rendered":"https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/?p=4459"},"modified":"2026-01-09T16:45:57","modified_gmt":"2026-01-09T07:45:57","slug":"%e3%83%8e%e3%83%b3%e3%83%91%e3%83%a9%e3%83%a1%e3%83%88%e3%83%aa%e3%83%83%e3%82%af%e6%a4%9c%e5%ae%9a%e3%81%ab%e9%96%a2%e3%81%99%e3%82%8b%e3%82%88%e3%81%8f%e3%81%82%e3%82%8b%e8%aa%a4%e8%a7%a3","status":"publish","type":"post","link":"https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/2025\/06\/17\/%e3%83%8e%e3%83%b3%e3%83%91%e3%83%a9%e3%83%a1%e3%83%88%e3%83%aa%e3%83%83%e3%82%af%e6%a4%9c%e5%ae%9a%e3%81%ab%e9%96%a2%e3%81%99%e3%82%8b%e3%82%88%e3%81%8f%e3%81%82%e3%82%8b%e8%aa%a4%e8%a7%a3\/","title":{"rendered":"\u30ce\u30f3\u30d1\u30e9\u30e1\u30c8\u30ea\u30c3\u30af\u691c\u5b9a\u306b\u95a2\u3059\u308b\u3088\u304f\u3042\u308b\u8aa4\u89e3"},"content":{"rendered":"\n\n\n\n<p>\uff082026\u5e741\u67089\u65e5\u66f4\u65b0\uff09<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u30ce\u30f3\u30d1\u30e9\u30e1\u30c8\u30ea\u30c3\u30af\u6cd5\u306b\u95a2\u3059\u308b\u8aa4\u89e3\u3068\u5229\u70b9<\/h2>\n\n\n\n<p><a href=\"https:\/\/scientist-press.com\/2019\/06\/12\/igaku-015\/\" title=\"\">\u6c38\u7530\u9756\u30fb&#134071;\u7530\u9053\u5f18\u300c\u7d71\u8a08\u7684\u591a\u91cd\u6bd4\u8f03\u6cd5\u306e\u57fa\u790e\u300d1997\u5e74\u3001\u30b5\u30a4\u30c6\u30f3\u30c6\u30a3\u30b9\u30c8\u793e<\/a>\u3001\u306e\u7b2c5\u7ae0\u300c\u30ce\u30f3\u30d1\u30e9\u30e1\u30c8\u30ea\u30c3\u30af\u6cd5\u300dpp.63\u201364\u306e\u307e\u3068\u3081\u3002<\/p>\n\n\n\n<p><strong>&#8220;\u8aa4\u89e3&#8221;<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u300c\u30c7\u30fc\u30bf\u306f\u4e92\u3044\u306b\u72ec\u7acb\u306b\u4f55\u3089\u304b\u306e\u5206\u5e03\u306b\u3057\u305f\u304c\u3063\u3066\u3044\u308c\u3070\u3088\u3044\u300d\u306f\u8aa4\u308a\u3002\u5b9f\u969b\u306b\u306fa\u500b\u306e\u6bcd\u96c6\u56e3\u306e\u5206\u5e03\u5f62\u306f\u3059\u3079\u3066\u7b49\u3057\u304f\u3001\u305d\u306e\u4f4d\u7f6e\u3060\u3051\u304c\u7570\u306a\u3063\u3066\u3044\u308b\u3053\u3068\u3092\u60f3\u5b9a\u3057\u3066\u3044\u308b\u3002<\/li>\n\n\n\n<li>\u300c\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u304c\u5c0f\u3055\u3044\u5834\u5408\u306b\u306f\u30ce\u30f3\u30d1\u30e9\u30e1\u30c8\u30ea\u30c3\u30af\u6cd5\u3092\u7528\u3044\u308b\u300d\u306f\u66f2\u89e3\u3002\u5b9f\u969b\u306b\u306f\u5927\u6a19\u672c\u8fd1\u4f3c\u306b\u57fa\u3065\u3044\u3066\u3044\u308b\u306e\u3067\u3001\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u304c\u5c0f\u3055\u3044\u3068\u5206\u5e03\u306e\u8fd1\u4f3c\u7cbe\u5ea6\u306b\u554f\u984c\u304c\u3042\u308b\u3002<\/li>\n\n\n\n<li>\u300c\u7fa4\u3054\u3068\u306e\u6bcd\u5206\u6563\u304c\u7570\u306a\u308b\u5834\u5408\u306b\u306f\u30ce\u30f3\u30d1\u30e9\u30e1\u30c8\u30ea\u30c3\u30af\u6cd5\u3092\u7528\u3044\u308c\u3070\u3088\u3044\u300d\u306f\u66f2\u89e3\u3002\u5b9f\u969b\u306b\u306f\u307b\u3068\u3093\u3069\u306e\u691c\u5b9a\u6cd5\u3067\u5404\u7fa4\u306e\u6bcd\u5206\u6563\u304c\u7b49\u3057\u3044\u3053\u3068\u3092\u4eee\u5b9a\u3059\u308b\u3002<\/li>\n<\/ul>\n\n\n\n<p><strong>&#8220;\u5229\u70b9&#8221;<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u9806\u4f4d\u3068\u3057\u3066\u3057\u304b\u30c7\u30fc\u30bf\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u306a\u3044\u5834\u5408\u3084\u9806\u5e8f\u30ab\u30c6\u30b4\u30ea\u30ab\u30eb\u30c7\u30fc\u30bf\u3067\u3082\u53d6\u308a\u6271\u3046\u3053\u3068\u304c\u3067\u304d\u308b\u3002<\/li>\n\n\n\n<li>\u5916\u308c\u5024\u306b\u3088\u3063\u3066\u7d50\u679c\u304c\u3042\u307e\u308a\u5f71\u97ff\u3055\u308c\u306a\u3044\u3002<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">\u30c6\u30ad\u30b9\u30c8\u3092\u8aad\u3093\u3067\u3044\u3066\u6c17\u306b\u306a\u3063\u305f\u3053\u3068<\/h2>\n\n\n\n<p>\u5b9f\u9a13\u30c6\u30ad\u30b9\u30c8\u3092\u898b\u3066\u3044\u305f\u3089\u3001\u5c11\u3057\u6c17\u306b\u306a\u308b\u8a18\u8ff0\u304c\u3042\u3063\u3066\u8abf\u3079\u7269\u3092\u3057\u305f\u306e\u3067\u30e1\u30e2\u3002<a href=\"https:\/\/biolab.sakura.ne.jp\/welch-test.html\">\u4e95\u53e3\u8c4a\uff082025-02-17\uff09\u7b49\u5206\u6563\u691c\u5b9a\u304b\u3089 t\u691c\u5b9a\uff0c\u30a6\u30a7\u30eb\u30c1\u691c\u5b9a\uff0cU\u691c\u5b9a\u3078\u306e\u554f\u984c\u70b9<\/a>\u304c\u5927\u5909\u53c2\u8003\u306b\u306a\u308a\u307e\u3057\u305f\u3002\u30c6\u30ad\u30b9\u30c8\u3067\u306f\u6559\u80b2\u7684\u306b\u6b63\u898f\u6027\u306e\u691c\u5b9a\uff08Shapiro\u2013Wilk\u691c\u5b9a\uff09\u3001\u7b49\u5206\u6563\u6027\u306e\u691c\u5b9a\uff08<em>F<\/em>\u691c\u5b9a\uff09\u3001\u5206\u6563\u5206\u6790\u3001<em>t<\/em>\u691c\u5b9a\u3001Welch\u306e<em>t<\/em>\u691c\u5b9a\u3001\u30ce\u30f3\u30d1\u30e9\u30e1\u30c8\u30ea\u30c3\u30af\u6cd5\uff08Wilcoxon\u306e\u7b26\u53f7\u4ed8\u304d\u9806\u4f4d\u691c\u5b9a\u3001Kruskal\u2013Wallis\u691c\u5b9a\uff09\u3001\u305d\u3057\u3066\u7b2c\u4e00\u7a2e\u306e\u904e\u8aa4\u3092\u5236\u5fa1\u3059\u308b\u65b9\u6cd5\u3068\u3057\u3066Bonferroni\u306e\u65b9\u6cd5\u304c\u8aac\u660e\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u6559\u80b2\u7684\u3067\u3088\u3044\u306e\u3067\u3059\u304c\u30011) \u691c\u5b9a\u306e\u591a\u91cd\u6027\u306e\u554f\u984c\uff08\u4f8b\u3048\u3070<em>F<\/em>\u691c\u5b9a\u2192<em>t<\/em>\u691c\u5b9a\u3068\u3044\u3046\u624b\u9806\uff09\u30012) \u5206\u6563\u5206\u6790\u2192\u591a\u91cd\u6bd4\u8f03\u3068\u3044\u3046\u624b\u9806\u30013) \u30ce\u30f3\u30d1\u30e9\u30e1\u30c8\u30ea\u30c3\u30af\u691c\u5b9a\u306b\u3064\u3044\u3066\u30014) \u6b63\u898f\u6027\u306e\u691c\u5b9a\u306e\u5fc5\u8981\u6027\u3001\u306e4\u70b9\u304c\u6c17\u306b\u306a\u308a\u307e\u3057\u305f\u3002\u8b1b\u7fa9\u3084\u5b9f\u7fd2\u4e2d\u3067\u306f\u304d\u3061\u3093\u3068\u8aac\u660e\u3055\u308c\u3066\u3044\u308b\u304b\u3082\u3057\u308c\u307e\u305b\u3093\u304c\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u305d\u306e1) \u691c\u5b9a\u306e\u591a\u91cd\u6027\u306e\u554f\u984c<\/h3>\n\n\n\n<p>\u7b49\u5206\u6563\u6027\u306e\u691c\u5b9a\uff082\u7fa4\u306e\u5834\u5408\u306f<strong><em>F<\/em>\u691c\u5b9a<\/strong>\u30013\u7fa4\u4ee5\u4e0a\u3067\u306f<strong>\u5206\u6563\u5206\u6790\uff08ANOVA\uff09<\/strong>\uff09\u2192F\u691c\u5b9a\u306e\u7d50\u679c\u3092\u53d7\u3051\u3066Welch\u306e\u88dc\u6b63\u3092\u52a0\u3048\u308b\u304b\u6c7a\u5b9a\u3059\u308b\u3001\u3068\u3044\u3046\u624b\u9806\u304c\u66f8\u304b\u308c\u3066\u3044\u307e\u3059\u3002\u3053\u308c\u306f\u4ee5\u4e0b\u306e\u7406\u7531\u3067\u3088\u304f\u306a\u3044\u3067\u3059\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><em>F<\/em>\u691c\u5b9a\u3068<em>t<\/em>\u691c\u5b9a\u3092\u305d\u308c\u305e\u308c\u3042\u308b\u6709\u610f\u6c34\u6e96\uff08\u4f8b\u3048\u30705%\uff09\u3067\u884c\u3063\u305f\u5834\u5408\u3001\u691c\u5b9a\u5168\u4f53\u306e\u7b2c\u4e00\u7a2e\u306e\u904e\u8aa4\u3092\uff085%\u4ee5\u5185\u306b\uff09\u5236\u5fa1\u3067\u304d\u306a\u3044<strong>\u691c\u5b9a\u306e\u591a\u91cd\u6027<\/strong>\u306e\u554f\u984c\u304c\u751f\u3058\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>\u7b49\u5206\u6563\u3067\u3042\u308b\u304b\u3069\u3046\u304b\u3092\u78ba\u304b\u3081\u3066\u304b\u3089\uff0c\u666e\u901a\u306e t \u691c\u5b9a\u3092\u4f7f\u3046\u304b\uff0cWelch \u306e\u65b9\u6cd5\u306b\u3088\u308b t \u691c\u5b9a\u306b\u3059\u308b\u304b\u3092\u6c7a\u3081\u308b\u3068\u3044\u3046\u306e\u306f\uff0c\u3088\u304f\u306a\u3044\u3002\u6700\u521d\u304b\u3089 Welch \u306e\u65b9\u6cd5\u306b\u3088\u308b t \u691c\u5b9a\u3092\u4f7f\u3048\u3070\u3088\u3044\u3002\uff08<a href=\"http:\/\/aoki2.si.gunma-u.ac.jp\/lecture\/Average\/bunsan1.html\">\u9752\u6728\u7e41\u4f38\uff082007-02-08\uff09\u4e8c\u7fa4\u306e\u7b49\u5206\u6563\u6027\u306e\u691c\u5b9a<\/a>; <a href=\"https:\/\/biolab.sakura.ne.jp\/welch-test.html\">\u4e95\u53e3\u8c4a\uff082025-02-17\uff09\u7b49\u5206\u6563\u691c\u5b9a\u304b\u3089 t\u691c\u5b9a\uff0c\u30a6\u30a7\u30eb\u30c1\u691c\u5b9a\uff0cU\u691c\u5b9a\u3078\u306e\u554f\u984c\u70b9<\/a>\uff09<\/p>\n<\/blockquote>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>\u7dcf\u3058\u3066\u3001Welch\u306et\u691c\u5b9a\u3092\u4f7f\u3046\u3053\u3068\u3067\u8aa4\u3063\u305f\u5224\u65ad\u3092\u4e0b\u3059\u78ba\u7387\u304c\u6e1b\u308b\u305f\u3081\u3001\u57fa\u672c\u7684\u306b\u306f<strong>\u7b49\u5206\u6563\u6027\u306e\u4eee\u5b9a\u304c\u6210\u308a\u7acb\u3064\u304b\u306b\u95a2\u308f\u3089\u305aWelch\u306et\u691c\u5b9a\u306e\u4f7f\u7528\u304c\u63a8\u5968<\/strong>\u3055\u308c\u3066\u3044\u308b\u3002R\u306e\u30c7\u30d5\u30a9\u30eb\u30c8\u306et\u691c\u5b9a\u3082Welch\u306et\u691c\u5b9a\u3067\u3042\u308b\u3002\uff08<a href=\"https:\/\/sites.google.com\/view\/ynomura\/stats\/Welch_t_test\">\u91ce\u6751\u5eb7\u4e4b\u3001t\u691c\u5b9a\u306e\u518d\u80031: \u7b49\u5206\u6563\u6027<\/a>\uff09<\/p>\n<\/blockquote>\n\n\n\n<p>\u3053\u306e<strong>\u691c\u5b9a\u306e\u591a\u91cd\u6027<\/strong>\u306e\u554f\u984c\u3067\u3059\u304c\u3001\u4f8b\u3048\u3070\u540c\u3058\u78ba\u7387\u5206\u5e03\u306b\u5f93\u30462\u3064\u306e\u7fa4\u306b\u3064\u3044\u3066\u3001<em>F<\/em>\u691c\u5b9a\u3068<em>t<\/em>\u691c\u5b9a\u3092\u305d\u308c\u305e\u308c\u6709\u610f\u6c34\u6e965%\u3067\u9023\u7d9a\u3057\u3066\u884c\u3063\u305f\u3068\u3057\u307e\u3059\u3002\u3053\u306e\u5834\u5408\u306e<strong>\u5e30\u7121\u4eee\u8aac\u304c\u6b63\u3057\u3044\u306b\u3082\u304b\u304b\u308f\u3089\u305a\u305d\u308c\u3092\u8aa4\u3063\u3066\u68c4\u5374\u3057\u3066\u3057\u307e\u3046\u78ba\u7387<\/strong>\uff08\u7b2c\u4e00\u7a2e\u306e\u904e\u8aa4\u3001\u03b1\u30a8\u30e9\u30fc\uff09\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002\u4e21\u691c\u5b9a\u3068\u3082\u6b63\u3057\u304f\u5e30\u7121\u4eee\u8aac\u3092\u63a1\u629e\u3059\u308b\u78ba\u7387\u306f\\(0.95 \\times 0.95 = 0.95^2\\)\u3067\u3059\u3002\u4e21\u65b9\u3082\u3057\u304f\u306f\u7247\u65b9\u306e\u691c\u5b9a\u3067\u8aa4\u3063\u3066\u5e30\u7121\u4eee\u8aac\u3092\u68c4\u5374\u3059\u308b\u78ba\u7387\u306f\\(1 &#8211; 0.95^2 = 0.0975\\)\u3068\u306a\u308a\u307e\u3059\u3002\u5143\u3005\u306f\u7b2c\u4e00\u7a2e\u306e\u904e\u8aa4\u30925%\u4ee5\u5185\u306b\u6291\u3048\u305f\u304b\u3063\u305f\u306e\u306b\u3001\u691c\u5b9a\u5168\u4f53\u3068\u3057\u3066\u306f9.75%\u306810%\u8fd1\u3044\u5024\u306b\u306a\u3063\u3066\u3057\u307e\u3046\u306e\u304c\u691c\u5b9a\u306e\u591a\u91cd\u6027\u306e\u554f\u984c\u3067\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u305d\u306e2) \u5206\u6563\u5206\u6790\u2192\u591a\u91cd\u6bd4\u8f03\u3068\u3044\u3046\u624b\u9806<\/h3>\n\n\n\n<p>\u57fa\u672c\u7684\u306b\u591a\u91cd\u6bd4\u8f03\u691c\u5b9a\u3088\u308a\u3082\u5206\u6563\u5206\u6790\u306e\u65b9\u304c\u691c\u51fa\u529b\u304c\u9ad8\u3044\u306e\u3067\u3001\u3053\u306e\u624b\u9806\u306b\u5b9f\u7528\u4e0a\u554f\u984c\u306f\u307b\u3068\u3093\u3069\u306a\u3044\u3068\u601d\u3044\u307e\u3059\u3002\u3057\u304b\u3057\u3001<strong>\u5206\u6563\u5206\u6790\u3067\u6709\u610f\u5dee\u304c\u306a\u304f\u3066\u3082\u3001\u7fa4\u9593\u591a\u91cd\u6bd4\u8f03\u3067\u6709\u610f\u3068\u306a\u308b\u5834\u5408\u304c\uff08\u3054\u304f\u7a00\u306b\uff09\u3042\u308a\u307e\u3059<\/strong>\uff08<em>vice versa<\/em>\u3001<a href=\"https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/2025\/06\/20\/%e5%88%86%e6%95%a3%e5%88%86%e6%9e%90%e3%81%a7%e6%9c%89%e6%84%8f%e3%81%ab%e3%81%aa%e3%82%89%e3%81%aa%e3%81%84%e3%81%8c%e3%80%81%e5%a4%9a%e9%87%8d%e6%af%94%e8%bc%83%e6%a4%9c%e5%ae%9a%e3%81%a7%e6%9c%89\/\">\u5206\u6563\u5206\u6790\u3067\u6709\u610f\u306b\u306a\u3089\u306a\u3044\u304c\u3001\u591a\u91cd\u6bd4\u8f03\u691c\u5b9a\u3067\u6709\u610f\u3068\u306a\u308b\u3088\u3046\u306a\u30c7\u30fc\u30bf\u306e\u4f8b<\/a>\uff09\u3002A\u3001B\u3001C\u306e3\u3064\u306e\u7fa4\u3092\u6bd4\u8f03\u3059\u308b\u5834\u5408\u3092\u8003\u3048\u308b\u3068\u3001\u5206\u6563\u5206\u6790\u306e\u5e30\u7121\u4eee\u8aac\u306f\u3059\u3079\u3066\u306e\u7fa4\u306e\u6bcd\u5e73\u5747\uff08\\(\\mu_A, \\mu_B, \\mu_C\\)\uff09\u304c\u7b49\u3057\u3044\uff08\\(\\mu_A = \\mu_B = \\mu_C\\)\uff09\u306a\u306e\u306b\u5bfe\u3057\u3066\u3001\u591a\u91cd\u6bd4\u8f03\uff08\u4f8b\u3048\u3070Tukey\u306eHSD\u691c\u5b9a\uff09\u306e\u5e30\u7121\u4eee\u8aac\u65cf\uff08\u30d5\u30a1\u30df\u30ea\u30fc\uff09\u306f\\(\\mu_A = \\mu_B, \\mu_B = \\mu_C, \\mu_A= \\mu_C\\)\u3067\u3042\u308a\u7570\u306a\u3063\u3066\u3044\u308b\u305f\u3081\u3067\u3059\u3002<\/p>\n\n\n\n<p>\u591a\u91cd\u6bd4\u8f03\u6cd5\u306e\u4e2d\u3067<strong>Scheffe\u306e\u65b9\u6cd5<\/strong>\u3001<strong>Fisher\u306e\u5236\u7d04\u4ed8\u304dLSD\u6cd5<\/strong> (Fisher&#8217;s Protected Least Significant Difference) \u306f<em>F<\/em>\u5206\u5e03\u3092\u4f7f\u7528\u3059\u308b\u306e\u3067\u3001\u624b\u9806\u306b\u5206\u6563\u5206\u6790\u304c\u7d44\u8fbc\u307e\u308c\u3066\u3044\u307e\u3059\u3002\u5206\u6563\u5206\u6790\u3067\u6709\u610f\u5dee\u304c\u51fa\u306a\u3051\u308c\u3070\u3001\u3053\u308c\u3089\u306e\u65b9\u6cd5\u3067\u3082\u6709\u610f\u5dee\u306f\u51fa\u307e\u305b\u3093\u3002\u305d\u306e\u4ed6\u306e\u591a\u91cd\u6bd4\u8f03\u6cd5\uff08Tukey\u306eHSD\u6cd5\u3001Games\u2013Howell\u6cd5\u3001Dunnett\u306e\u65b9\u6cd5\u3001Dunnett\u306eC\u6cd5\u3001Welch\u306e<em>t<\/em>\u691c\u5b9a\u306eBonferroni\u88dc\u6b63\u3001Welch\u306e<em>t<\/em>\u691c\u5b9a\u306eHolm\u2013Bonferroni\u88dc\u6b63\u306a\u3069\uff09\u306f<em>F<\/em>\u5206\u5e03\u3092\u4f7f\u7528\u3057\u306a\u3044\u306e\u3067\u5206\u6563\u5206\u6790\u3092\u4e8b\u524d\u306b\u884c\u308f\u306a\u3044\u306e\u304c\u539f\u5247\u3067\u3059\uff08\u3064\u307e\u308a\u3053\u308c\u3089\u306f\u5206\u6563\u5206\u6790\u306epost-hoc\uff08\u4e8b\u5f8c\uff09\u89e3\u6790\u6cd5\u3067\u306f\u306a\u3044\uff09\u3002<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>\u4e00\u8a00\u3067\u7b54\u3048\u308b\u3068\u3001\u300c\u7528\u3044\u308b\u591a\u91cd\u6bd4\u8f03\u6cd5\u306e\u624b\u9806\u306e\u4e2d\u306b\u542b\u307e\u308c\u3066\u3044\u308b\u5834\u5408\u306e\u307f\u4e00\u5143\u914d\u7f6e\u5206\u6563\u5206\u6790\u3092\u884c\u3046\u300d\u3068\u306a\u308b\u3002\u305d\u308c\u4ee5\u5916\u306e\u5834\u5408\u306b\u306f\u3001\u5206\u6563\u5206\u6790\u306f\u4e0d\u8981\u306a\u306e\u3067\u306f\u306a\u304f\u3001\u884c\u308f\u306a\u3044\u3053\u3068\u304c\u539f\u5247\u3067\u3042\u308b\u3002\uff08<a href=\"https:\/\/www.jstage.jst.go.jp\/article\/jappstat1971\/27\/2\/27_2_93\/_article\/-char\/ja\/\">\u6c38\u7530\u9756. \u591a\u91cd\u6bd4\u8f03\u6cd5\u306e\u5b9f\u969b\u3000\u5fdc\u7528\u7d71\u8a08\u5b66\u30011998 \u5e74 27 \u5dfb 2 \u53f7 p. 93-108<\/a>\uff09<\/p>\n<\/blockquote>\n\n\n\n<h3 class=\"wp-block-heading\">\u305d\u306e3) \u30ce\u30f3\u30d1\u30e9\u30e1\u30c8\u30ea\u30c3\u30af\u306a\u691c\u5b9a\u306b\u3064\u3044\u3066\u306e\u6ce8\u610f\u70b9<\/h3>\n\n\n\n<p>\u6a19\u672c\uff08\u7fa4\uff09\u306b\u6bcd\u96c6\u56e3\u304c\u6b63\u898f\u5206\u5e03\u306b\u5f93\u308f\u306a\u3044\u3082\u306e\u304c\u3042\u308b\u5834\u5408\u306f\u3001Wilcoxon\u306e\u9806\u4f4d\u548c\u691c\u5b9a\uff08Mann\u2013Whitney\u306e<em>U<\/em>\u691c\u5b9a\u3068\u7b49\u4fa1\uff09\u3084Kruskal\u2013Wallis\u691c\u5b9a\u3068\u3044\u3063\u305f\u30ce\u30f3\u30d1\u30e9\u30e1\u30c8\u30ea\u30c3\u30af\u306a\u691c\u5b9a\u3092\u884c\u3046\u65e8\u304c\u66f8\u304b\u308c\u3066\u3044\u307e\u3059\u3002\u3053\u308c\u306f\u5371\u967a\u3067\u3059\u3002<\/p>\n\n\n\n<p>Mann\u2013Whitney\u306e<em>U<\/em>\u691c\u5b9a\uff08Wilcoxon\u306e\u9806\u4f4d\u548c\u691c\u5b9a\uff09\u306e\u5e30\u7121\u4eee\u8aac\u306f\u300c<strong>2\u3064\u306e\u6a19\u672c\u306e\u9806\u4f4d\u306e\u5e73\u5747\u304c\u7b49\u3057\u3044 = 2\u3064\u306e\u6a19\u672c\u306e\u6bcd\u96c6\u56e3\u306e\u5206\u5e03\u304c\u540c\u3058<\/strong>\u300d\u3067\u3059\u3002\u300c2\u3064\u306e\u6a19\u672c\u306e\u6bcd\u96c6\u56e3\u306e\u5e73\u5747\u3084\u4e2d\u592e\u5024\u304c\u7b49\u3057\u3044\u300d\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u30022\u3064\u306e\u6a19\u672c\u306f\u540c\u3058\u78ba\u7387\u5206\u5e03\u304b\u3089\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u3055\u308c\u3066\u3044\u308b\u3053\u3068\u304c\u60f3\u5b9a\u3055\u308c\u307e\u3059\u3002\u5bfe\u7acb\u4eee\u8aac\u306f\u300c2\u3064\u306e\u6a19\u672c\u306e\u9806\u4f4d\u306e\u5e73\u5747\u306f\u7570\u306a\u308b \u2252 \u3042\u308b\u7fa4\u304b\u3089\u306e\u89b3\u6e2c\u5024\u304c\u3001\u3082\u3046\u4e00\u65b9\u306e\u7fa4\u304b\u3089\u306e\u89b3\u6e2c\u5024\u3088\u308a\u5927\u304d\u304f\u306a\u308b\u300d\u3068\u306a\u308a\u307e\u3059\u3002\u305d\u3082\u305d\u3082\u5e73\u5747\u5024\u3084\u4e2d\u592e\u5024\u306e\u5dee\u3092\u691c\u5b9a\u3057\u305f\u3044\u6642\u306b\u306fMann\u2013Whitney\u306e<em>U<\/em>\u691c\u5b9a\u3092\u4f7f\u3046\u3079\u304d\u3067\u306f\u306a\u3044\u3068\u3044\u3046\u3053\u3068\u3067\u3059\u3002<strong>\u5e73\u5747\u5024\u306e\u691c\u5b9a\u306b\u306fWelch\u306e<em>t<\/em>\u691c\u5b9a<\/strong>\u3092\u3001<strong>\u4e2d\u592e\u5024\u306e\u7b49\u3057\u3055\u3092\u691c\u5b9a\u3057\u305f\u3044\u5834\u5408\u306f\u5206\u4f4d\u70b9\u56de\u5e30<\/strong>\u3092\u4f7f\u7528\u3059\u308b\u3079\u304d\u3067\u3059\u3002\u554f\u984c\u306e\u3084\u3084\u3053\u3057\u3055\u306f\u30012\u3064\u306e\u96c6\u56e3\u306e<strong>\u5206\u5e03\u5f62\u72b6\u304c\u540c\u4e00\u3067\u3042\u308b\u5834\u5408\u306bMann\u2013Whitney\u306e<em>U<\/em>\u691c\u5b9a\u3092\u300c\u4e2d\u592e\u5024\u306e\u7b49\u3057\u3055\u306e\u691c\u5b9a\u300d\u3068\u89e3\u91c8\u3067\u304d\u3066\u3057\u307e\u3046<\/strong>\u70b9\u306b\u3042\u308a\u307e\u3059\u3002\u3057\u304b\u3057\u5b9f\u969b\u306e\u30c7\u30fc\u30bf\u3067\u306f\u3001\u5206\u5e03\u5f62\u72b6\u304c\u540c\u4e00\u3067\u4f4d\u7f6e\u304c\u30b7\u30d5\u30c8\u3057\u3066\u3044\u308b\u3060\u3051\u3068\u4eee\u5b9a\u3067\u304d\u308b\u3053\u3068\u306f\u307b\u3068\u3093\u3069\u306a\u3044\u3068\u601d\u3044\u307e\u3059\u3002\u5f8c\u3067\u4e0d\u7b49\u5206\u6563\u306e\u5834\u5408\u306b\u3069\u3046\u306a\u308b\u304b\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u3057\u3066\u3044\u307e\u3059\u304c\u3001\u4e0d\u7b49\u5206\u6563\u306e\u5834\u5408\u306f\u7fa4\u9593\u306e\u9055\u3044\u306b\u3064\u3044\u3066\u691c\u5b9a\u7d50\u679c\u304b\u3089\u89e3\u91c8\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u305b\u3093\uff08\u53c2\u8003: <a href=\"http:\/\/kasuya.ecology1.org\/stats\/utest01.html\">\u7c95\u8c37\u82f1\u4e00\uff082001-11-04\uff09Mann\u2013Whitney\u306eU\u691c\u5b9a\u3068\u4e0d\u7b49\u5206\u6563\u306e\u30da\u30fc\u30b8<\/a>\uff09\u3002Google\u3067\u691c\u7d22\u3059\u308b\u3068\u3001\u30ce\u30f3\u30d1\u30e9\u30e1\u30c8\u30ea\u30c3\u30af\u691c\u5b9a\u304c\u6b63\u898f\u6027\u3082\u7b49\u5206\u6563\u6027\u3082\u5fc5\u8981\u3068\u3057\u306a\u3044\u3001\u3068\u306e\u8aa4\u89e3\u304c\u66f8\u304b\u308c\u3066\u3044\u308b\uff08\u3082\u3057\u304f\u306f\u305d\u306e\u3088\u3046\u306b\u8aad\u3081\u308b\uff09\u8a18\u4e8b\u3082\u3061\u3089\u307b\u3089\u3042\u308a\u307e\u3059\u3002\u307e\u305f\u3001\u300c\u7b49\u5206\u6563\u6027\u3092\u5fc5\u8981\u3068\u3059\u308b\u300d\u3068\u3044\u3046\u306e\u3082\u9593\u9055\u3044\u3067\u3001\u5206\u6563\u306b\u3064\u3044\u3066\u306f\u4f55\u306e\u4eee\u5b9a\u3082\u7f6e\u304b\u308c\u307e\u305b\u3093\u3002<\/p>\n\n\n\n<p>\u975e\u6b63\u898f\u5206\u5e03\u3001\u975e\u7b49\u5206\u6563\u306e\u30c7\u30fc\u30bf\u306b\u3066\u9069\u7528\u3067\u304d\u308b\u30ce\u30f3\u30d1\u30e9\u30e1\u30c8\u30ea\u30c3\u30af\u691c\u5b9a\u3068\u3057\u3066\u306fBrunner\u2013Munzel\u691c\u5b9a\u304c\u63a8\u5968\u3055\u308c\u3066\u3044\u307e\u3059\uff08<a href=\"https:\/\/biolab.sakura.ne.jp\/welch-test.html\">\u4e95\u53e3\u8c4a\uff082025-02-17\uff09\u7b49\u5206\u6563\u691c\u5b9a\u304b\u3089 t\u691c\u5b9a\uff0c\u30a6\u30a7\u30eb\u30c1\u691c\u5b9a\uff0cU\u691c\u5b9a\u3078\u306e\u554f\u984c\u70b9<\/a>\uff09\u3002Brunner\u2013Munzel\u691c\u5b9a\u306e\u5e30\u7121\u4eee\u8aac\u306f\u300c2\u7fa4\u304b\u30891\u500b\u305a\u3064\u53d6\u308a\u51fa\u3057\u305f\u3068\u304d\u3001\u3042\u308b\u7fa4\u304b\u3089\u306e\u5024\u304c\u5225\u306e\u7fa4\u306e\u5024\u3088\u308a\u3082\u5927\u304d\u304f\u306a\u308b\u78ba\u7387\u3068\u540c\u3058\u306b\u306a\u308b\u78ba\u7387\u306e\u534a\u5206\u306e\u5408\u7b97\u304c1\/2\u306b\u306a\u308b\u300d\u3053\u3068\u3067\u3001\u5bfe\u7acb\u4eee\u8aac\u306f\u300c\u3069\u3061\u3089\u304b\u306e\u7fa4\u304c\u5168\u4f53\u7684\u306b\u5927\u304d\u306a\u5024\u3092\u6301\u3064\u300d\u3067\u3059\uff08<a href=\"https:\/\/www.jstage.jst.go.jp\/article\/psj\/30\/1\/30_30.006\/_article\/-char\/ja\/\" title=\"\">\u540d\u53d6\u771f\u4eba. \u30de\u30f3\u30fb\u30db\u30a4\u30c3\u30c8\u30cb\u30fc\u306eU\u691c\u5b9a\u3068\u4e0d\u7b49\u5206\u6563\u6642\u306b\u304a\u3051\u308b\u4ee3\u8868\u5024\u306e\u691c\u5b9a\u6cd5\u3000\u970a\u9577\u985e\u7814\u7a76\u30012014 \u5e74 30 \u5dfb 1 \u53f7 p. 173-185<\/a>\uff09\u3002<\/p>\n\n\n\n<p>\u5bfe\u3057\u3066<em>t<\/em>\u691c\u5b9a\u306b\u3088\u308b2\u7fa4\u6bd4\u8f03\u306e\u5e30\u7121\u4eee\u8aac\u306f\u300c\u4e00\u3064\u76ee\u306e\u6bcd\u96c6\u56e3\u306e<strong>\u5e73\u5747\u5024<i>\u03bc<\/i><sub>1<\/sub><\/strong>\u304c2\u3064\u76ee\u306e\u6bcd\u96c6\u56e3\u306e<strong>\u5e73\u5747\u5024<i>\u03bc<\/i><sub>2<\/sub><\/strong>\u3068\u7b49\u3057\u3044\u300d\u3067\u3059\u3002\u300c\u5e73\u5747\u5024\u306e\u5dee\u306e\u691c\u5b9a\u300d\u3067\u3042\u308a\u300c<strong>\u4e2d\u5fc3\u6975\u9650\u5b9a\u7406<\/strong>\u300d\u304c\u52b9\u3044\u3066\u304f\u308b\u305f\u3081\u3001<em>t<\/em>\u691c\u5b9a\u306f\u6b63\u898f\u5206\u5e03\u3057\u3066\u306a\u3044\u30c7\u30fc\u30bf\u306b\u5bfe\u3057\u3066\u3082<strong>\u9811\u5065<\/strong>\uff08robust\uff09\u3067\u3042\u308b\u3068\u8a00\u308f\u308c\u3066\u3044\u307e\u3059\u3002\u305f\u3060\u3057\u3001\u6b63\u898f\u6bcd\u96c6\u56e3\u306b\u5bfe\u3057\u3066\u306f<em>n <\/em>= 2\u3067\u3082\u5927\u4e08\u592b\u306a\u306e\u306b\u5bfe\u3057\u3066\u3001\u300c\u6307\u6570\u6bcd\u96c6\u56e3\u306e\u5834\u5408\u306f\uff0c\u9069\u5207\u306a\u7d50\u679c\u3092\u5f97\u308b\u306b\u306f\uff0c\u6a19\u672c\u30b5\u30a4\u30ba\u304c100\u4ee5\u4e0a\u5fc5\u8981\u300d\uff08<a href=\"https:\/\/biolab.sakura.ne.jp\/small-sample-t-test-glm.html\">\u4e95\u53e3\u8c4a\uff082022-12-06\uff09\u5c0f\u6a19\u672c t \u691c\u5b9a\u306e\u8aa4\u89e3\uff1a\u4e2d\u5fc3\u6975\u9650\u5b9a\u7406\u3068\u4e00\u822c\u5316\u7dda\u5f62\u30e2\u30c7\u30eb<\/a>\uff09\u3002<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>\u6b63\u898f\u6027\u3082\u7b49\u5206\u6563\u6027\u3082\u6210\u308a\u7acb\u305f\u306a\u3044\u72b6\u6cc1\u3067\u306f\u3001\u5e73\u5747\u5024\u306e\u6bd4\u8f03\u306a\u3089Welch\u306et\u691c\u5b9a\u3001\u4e2d\u592e\u5024\u306e\u6bd4\u8f03\u306a\u3089Brunner-Munzel\u691c\u5b9a\u304c\u691c\u5b9a\u7cbe\u5ea6\u304c\u3088\u3044\u50be\u5411\u306b\u3042\u308b\u3002\uff08<a href=\"https:\/\/www.pu-hiroshima.ac.jp\/p\/ttetsuji\/R\/[73]bmtest.html\">\u51a8\u7530 \u54f2\u6cbb\u3001Brunner-Munzel\u691c\u5b9a<\/a>\uff09<\/p>\n<\/blockquote>\n\n\n\n<p>Welch\u306e<em>t<\/em>\u691c\u5b9a\u306f\u975e\u6b63\u898f\u6027\u306b\u5bfe\u3057\u3066\u3082\u975e\u7b49\u5206\u6563\u6027\u306b\u5bfe\u3057\u3066\u3082\u9811\u5065\u306a\u306e\u306b\u5bfe\u3057\u3066\u3001Wilcoxon\u306e\u9806\u4f4d\u548c\u691c\u5b9a\u306a\u3069\u306f\u8106\u5f31\u306a\u65b9\u6cd5\u3067\u3042\u308b\u3068\u8a00\u308f\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u305d\u306e4) \u6b63\u898f\u6027\u306e\u691c\u5b9a\u306e\u7d50\u679c\u3092\u53d7\u3051\u3066<em>t<\/em>\u691c\u5b9a\u304b\u30ce\u30f3\u30d1\u30e9\u30e1\u30c8\u30ea\u30c3\u30af\u306a\u691c\u5b9a\u304b\u3092\u9078\u629e\u3059\u308b\u554f\u984c\u70b9<\/h3>\n\n\n\n<p>\u300c\u6a19\u672c\uff08\u7fa4\uff09\u3054\u3068\u306b<strong>Shapiro\u2013Wilk\u691c\u5b9a<\/strong>\u3092\u304a\u3053\u306a\u3063\u3066\u5404\u6a19\u672c\uff08\u7fa4\uff09\u306e\u6bcd\u96c6\u56e3\u304c\u6b63\u898f\u5206\u5e03\u306b\u5f93\u3046\u304b\u3092\u691c\u5b9a\u300d\u3057\u3066\u3001<em>t<\/em>\u691c\u5b9a\u304b\u30ce\u30f3\u30d1\u30e9\u30e1\u30c8\u30ea\u30c3\u30af\u306a\u691c\u5b9a\u304b\u3092\u9078\u629e\u3059\u308b\u65e8\u304c\u66f8\u304b\u308c\u3066\u3044\u307e\u3057\u305f\u3002<\/p>\n\n\n\n<p>Shapiro\u2013Wilk\u691c\u5b9a\u3092\u4e8b\u524d\u306b\u884c\u3046\u3053\u3068\u3082\u300c<strong>\u591a\u91cd\u6027\u306e\u554f\u984c<\/strong>\u300d\u3068\u300c<strong>\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u3067\u691c\u5b9a\u7d50\u679c\u306f\u5de6\u53f3<\/strong>\u300d\u3055\u308c\u308b\u305f\u3081\u3001\u63a8\u5968\u3055\u308c\u3066\u3044\u307e\u305b\u3093\u3002<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>\u7fa4\u3054\u3068\u3084\uff0c\u8981\u56e0\u306e\u6c34\u6e96\u3054\u3068\u306b\u6b63\u898f\u6027\u3092\u691c\u5b9a\u3059\u308b\u3068\uff0c\u4f55\u304c\u554f\u984c\u306a\u306e\u304b\uff1f\u3054\u304f\u7c21\u5358\u306a\u3053\u3068\u3067\uff0c\u691c\u5b9a\u306e\u591a\u91cd\u6027\u304c\u554f\u984c\u306b\u306a\u308b\u306e\u3067\u3042\u308b\u3002\uff08<a href=\"https:\/\/biolab.sakura.ne.jp\/normality-test-for-anova.html\">\u4e95\u53e3\u8c4a\uff082022-09-12\uff09\u5206\u6563\u5206\u6790\u306e\u6b63\u898f\u6027\u306f\u6b8b\u5dee\u3092\u8abf\u3079\u308b\uff1a\u691c\u5b9a\u306e\u591a\u91cd\u6027\u554f\u984c<\/a>\uff09<\/p>\n<\/blockquote>\n\n\n\n<p>\u3067\u306f\u3069\u3046\u3084\u3063\u3066\u6b63\u898f\u6027\u3092\u5224\u65ad\u3059\u308b\u304b\u3068\u3044\u3046\u3068<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>\u57fa\u672c\u7684\u306b\u306f\u3001\u30d2\u30b9\u30c8\u30b0\u30e9\u30e0\u3092\u63cf\u3044\u3066\u91e3\u308a\u9418\u72b6\u306b\u306a\u3063\u3066\u3044\u308b\u304b\u3092\u89b3\u5bdf\u3057\u307e\u3059\u3002\u7d4c\u9a13\u7684\u77e5\u898b\u304b\u3089\u300c\u3053\u306e\u30c7\u30fc\u30bf\u306f\u6b63\u898f\u5206\u5e03\u306b\u5f93\u3046\u306f\u305a\u3060\u300d\u3068\u601d\u3048\u3070\u3001\u6b63\u898f\u5206\u5e03\u3068\u3057\u3066\u89e3\u6790\u3057\u3066\u3082\u304b\u307e\u3044\u307e\u305b\u3093\u3002\uff08<a href=\"https:\/\/best-biostatistics.com\/spss\/spss-norm-test.html\">\u300c\u3044\u3061\u3070\u3093\u3084\u3055\u3057\u3044\u3001\u533b\u7642\u7d71\u8a08\u300d\uff082024-05-07\uff09SPSS\u3067\u6b63\u898f\u6027\u306e\u691c\u5b9a\uff08\u30b7\u30e3\u30d4\u30ed\u30a6\u30a3\u30eb\u30af\u3084Kolmogorov-Smirnov\uff09\u3092\u5b9f\u65bd\u3059\u308b\u65b9\u6cd5\uff01<\/a>\uff09<\/p>\n<\/blockquote>\n\n\n\n<h2 class=\"wp-block-heading\">\u7528\u8a9e\u306e\u304a\u3055\u3089\u3044<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u6b63\u898f\u5206\u5e03<\/strong>\uff08\u305b\u3044\u304d\u3076\u3093\u3077\uff09\u2014 \u30ac\u30a6\u30b9\u95a2\u6570\\(f(x) = e^{-x^2}\\)\u306e\u5206\u5e03\u3002\u5e73\u5747\\(\\mu\\)\u3001\u5206\u6563\\(\\sigma^2 &gt; 0\\)\u306e\u6b63\u898f\u5206\u5e03\u306f\u3001$$f(x) = \\frac{1}{\\sqrt{2\\pi\\sigma^2}}\\exp\\left(-\\frac{(x-\\mu)^2}{2\\sigma^2}\\right)$$<\/li>\n\n\n\n<li><strong>\u5927\u6570\u306e\u6cd5\u5247<\/strong>\uff08\u305f\u3044\u3059\u3046\u306e\u307b\u3046\u305d\u304f\uff09 \u2014 \u6a19\u672c\u6570\u3092\u5897\u3084\u3057\u3066\u3044\u3051\u3070\u540c\u4e00\u306a\u5206\u5e03\u304b\u3089\u751f\u6210\u3057\u305f\u78ba\u7387\u5909\u6570\u306e\u7b97\u8853\u5e73\u5747\uff08\u6a19\u672c\u5e73\u5747\uff09\u304c\u3001\u6bcd\u96c6\u56e3\u306e\u5e73\u5747\uff08\u671f\u5f85\u5024\uff09\u304c\u5b58\u5728\u3059\u308b\u306a\u3089\u3070\u3001\u3053\u306e\u6bcd\u5e73\u5747\u306b\u53ce\u675f\u3059\u308b\u3001\u3068\u3044\u3046\u4e3b\u5f35\uff08\u5927\u6570\u306e\u6cd5\u5247\u306b\u306f\u5f37\u6cd5\u5247\u3068\u5f31\u6cd5\u5247\u304c\u3042\u308a\u3001\u3053\u308c\u306f\u5927\u6570\u306e\u5f37\u6cd5\u5247\uff09\u3002<\/li>\n\n\n\n<li><strong>\u4e2d\u5fc3\u6975\u9650\u5b9a\u7406<\/strong>\uff08\u3061\u3085\u3046\u3057\u3093\u304d\u3087\u304f\u3052\u3093\u3066\u3044\u308a\uff09\u2014 \u6bcd\u96c6\u56e3\u306e\u78ba\u7387\u5206\u5e03\u304c\u6709\u9650\u306e\u5206\u6563\u3092\u6301\u3064\u306a\u3089\u3070\u3001\u3069\u306e\u3088\u3046\u306a\u5f62\u306e\u306e\u78ba\u7387\u5206\u5e03\u3092\u6301\u3064\u6bcd\u96c6\u56e3\u304b\u3089\u53d6\u3089\u308c\u305f\u6a19\u672c\u3067\u3082\u3001\u305d\u306e\u6a19\u672c\u5e73\u5747\u306e\u78ba\u7387\u5206\u5e03\u306f\u6b63\u898f\u5206\u5e03\u306b\u306a\u308b\u3001\u3068\u3044\u3046\u5b9a\u7406\u3002<\/li>\n\n\n\n<li><strong><em>t<\/em>\u691c\u5b9a<\/strong>\uff08\u30c6\u30a3\u30fc\u3051\u3093\u3066\u3044\uff09\u2014 \u5927\u96d1\u628a\u306b\u8a00\u3046\u3068\u30012\u3064\u306e\u7fa4\u306e\u5e73\u5747\u5024\u306e\u5dee\u3092\u5168\u4f53\u306e\u6a19\u6e96\u8aa4\u5dee\u3067\u5272\u3063\u305f\u5024\u3092\u691c\u5b9a\u7d71\u8a08\u91cf<em>t<\/em>&nbsp;$$t_0 = \\frac{|\\bar{X} &#8211; \\bar{Y}|}{\\sqrt{U_e\\left(\\frac{1}{m}+\\frac{1}{n}\\right)}}$$ \u3068\u3057\u3066\u3001\u5e73\u5747\u5024\u304c\u540c\u3058\u5834\u5408\uff08\u5e30\u7121\u4eee\u8aac\uff09\u306b\u3053\u306et\u304c\u5f93\u3046\u5206\u5e03\u3001<em>t<\/em>\u5206\u5e03\u3092\u5143\u306b\u3057\u3066\u5f97\u3089\u308c\u305f\u691c\u5b9a\u7d71\u8a08\u91cf\u304c\u3069\u308c\u307b\u3069\u8d77\u3053\u308a\u3065\u3089\u3044\u304b\u3001\u3092\u5224\u65ad\u3059\u308b\u3002<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">\u898b\u3066\u304a\u304f\u3079\u304d\u52d5\u753b<\/h2>\n\n\n\n<p><a href=\"https:\/\/www.channel.pr.kyoto-u.ac.jp\/video\/13525\">KyotoU Channel\uff082018-01-11\uff09\u81e8\u5e8a\u7814\u7a76\u8005\u306e\u305f\u3081\u306e\u751f\u7269\u7d71\u8a08\u5b66\u300c\u4eee\u8aac\u691c\u5b9a\u3068P\u5024\u306e\u8aa4\u89e3\u300d\u4f50\u85e4\u4fca\u54c9(\u533b\u5b66\u7814\u7a76\u79d1\u6559\u6388)<\/a><\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>\u7d71\u8a08\u30e2\u30c7\u30eb\u306f\u4e00\u9023\u306e\u4eee\u5b9a\uff08\u30e9\u30f3\u30c0\u30e0\u5316\u30fb\u30e9\u30f3\u30c0\u30e0\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u304c\u306a\u3055\u308c\u3066\u3044\u308b\u3001\u7814\u7a76\u8a08\u753b\u304c\u9075\u5b88\u3055\u308c\u3066\u3044\u308b\u3001\u3059\u3079\u3066\u306e\u89e3\u6790\u7d50\u679c\u304c\u5831\u544a\u3055\u308c\u3066\u3044\u308b\u3001\u306a\u3069\uff09\u3067\u69cb\u6210\u3055\u308c\u3066\u3044\u308b\u3002\u5e30\u7121\u4eee\u8aac\u306f\u305d\u306e\u4eee\u5b9a\u306e\u4e00\u3064\u306b\u904e\u304e\u306a\u3044\u3002P\u5024\u304c\u5c0f\u3055\u3044\u3053\u3068\u306f\u300c\u305f\u304f\u3055\u3093\u3042\u308b\u7d71\u8a08\u30e2\u30c7\u30eb\u306b\u5fc5\u8981\u306a\u4eee\u5b9a\u306e\u3046\u3061\u3069\u308c\u304b1\u3064\u3042\u308b\u3044\u306f\u8907\u6570\u304c\u9593\u9055\u3063\u3066\u3044\u308b\u300d\u3053\u3068\u3092\u610f\u5473\u3059\u308b\u3002\u6c7a\u3057\u3066\u5e30\u7121\u4eee\u8aac\u3060\u3051\u304c\u9593\u9055\u3044\u306e\u5bfe\u8c61\u3067\u306f\u306a\u3044\u3002<\/p>\n<\/blockquote>\n\n\n\n<h2 class=\"wp-block-heading\">R\u3092\u4f7f\u3063\u305f\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3<\/h2>\n\n\n\n<p>\u53c2\u8003\u30b5\u30a4\u30c8: <a href=\"https:\/\/biolab.sakura.ne.jp\/small-sample-t-test-glm.html\">\u4e95\u53e3\u8c4a\uff082022-12-06\uff09\u5c0f\u6a19\u672c t \u691c\u5b9a\u306e\u8aa4\u89e3\uff1a\u4e2d\u5fc3\u6975\u9650\u5b9a\u7406\u3068\u4e00\u822c\u5316\u7dda\u5f62\u30e2\u30c7\u30eb<\/a><\/p>\n\n\n\n<p>R 4.5.1 (macOS) \u3092\u4f7f\u7528\u3002\u6bd4\u8f03\u3059\u308b2\u7fa4\u306f\u5168\u3066\u6a19\u672c\u30b5\u30a4\u30ba (<em>n<\/em>) \u304c\u540c\u3058\u3002<\/p>\n\n\n\n<p>\u5148\u306b\u81ea\u5206\u306a\u308a\u306e\u7d50\u8ad6\uff08\u6559\u8a13\u3001\u53cd\u7701\uff09:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><em>n<\/em> = 2\u30843\u3067\u3069\u3046\u306e\u3053\u3046\u306e\u3044\u3046\u306e\u306f\u5371\u306a\u3044\u3002<\/li>\n\n\n\n<li>\u30ce\u30f3\u30d1\u30e9\u30e1\u30c8\u30ea\u30c3\u30af\u306a\u65b9\u6cd5\u3068\u3057\u3066\u4ee3\u8868\u7684\u306aMann\u2013Whitney\u306e<em>U<\/em>\u691c\u5b9a\uff08Wilcoxon\u306e\u9806\u4f4d\u548c\u691c\u5b9a\uff09\u306f\u5e73\u5747\u5024\u3084\u4e2d\u592e\u5024\u306b\u5dee\u304c\u3042\u308b\u304b\u3092\u691c\u5b9a\u3059\u308b\u65b9\u6cd5\u3067\u306f\u306a\u3044\u305f\u3081\u3001\u305d\u306e\u3088\u3046\u306a\u7528\u9014\u3067\u4f7f\u7528\u3059\u3079\u304d\u3067\u306f\u306a\u3044\u3002<\/li>\n\n\n\n<li>Welch\u306e<em>t<\/em>\u691c\u5b9a\u306f\u78ba\u304b\u306b\u9811\u5065\u3002<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">\u6bcd\u96c6\u56e3\u304c\u6b63\u898f\u5206\u5e03\u306e\u5834\u5408\uff08\u7b49\u5206\u6563\uff09<\/h3>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"239\" src=\"https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2025\/06\/dnorm-300x239.png\" alt=\"\" class=\"wp-image-4865\" srcset=\"https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2025\/06\/dnorm-300x239.png 300w, https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2025\/06\/dnorm-1024x815.png 1024w, https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2025\/06\/dnorm-768x611.png 768w, https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2025\/06\/dnorm.png 1392w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading\">Student\u306e<em>t<\/em>\u691c\u5b9a<\/h4>\n\n\n\n<pre class=\"prettyprint\">k &lt;- 100000 # \u6a19\u672c\u53d6\u308a\u51fa\u3057\u53cd\u5fa9\u56de\u6570\nn &lt;- 4 # \u6a19\u672c\u30b5\u30a4\u30ba\nr &lt;- replicate(k, {\n     x &lt;- rnorm(n, mean=0, sd=1)\n     y &lt;- rnorm(n, mean=0, sd=1)\n     c(mean(x), t.test(x, y, var.equal=TRUE)$p.value)\n})\nm &lt;- r&#091;1, &#093; # \u5e73\u5747\u5024\np &lt;- r&#091;2, &#093; # 5%\u6c34\u6e96\u68c4\u5374\u6570\nreject_rate &lt;- length(p&#091;p&lt;=0.05&#093;)&#47;k # 5%\u6c34\u6e96\u68c4\u5374\u7387\nprint (reject_rate)\n&#091;1&#093; 0.04981<\/pre>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"187\" src=\"https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2025\/06\/student-300x187.png\" alt=\"\" class=\"wp-image-4514\" srcset=\"https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2025\/06\/student-300x187.png 300w, https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2025\/06\/student.png 1370w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><figcaption class=\"wp-element-caption\"><em>p<\/em>\u5024\u306e\u5206\u5e03<\/figcaption><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading\">Welch\u306e<em>t<\/em>\u691c\u5b9a<\/h4>\n\n\n\n<pre class=\"prettyprint\">k &lt;- 100000 # \u6a19\u672c\u53d6\u308a\u51fa\u3057\u53cd\u5fa9\u56de\u6570\nn &lt;- 4 # \u6a19\u672c\u30b5\u30a4\u30ba\nr &lt;- replicate(k, {\n     x &lt;- rnorm(n, mean=0, sd=1)\n     y &lt;- rnorm(n, mean=0, sd=1)\n     c(mean(x), t.test(x, y, var.equal=FALSE)$p.value)\n})\nm &lt;- r&#091;1, &#093; # \u5e73\u5747\u5024\np &lt;- r&#091;2, &#093; # 5%\u6c34\u6e96\u68c4\u5374\u6570\nreject_rate &lt;- length(p&#091;p&lt;=0.05&#093;)&#47;k # 5%\u6c34\u6e96\u68c4\u5374\u7387\nprint (reject_rate)\n&#091;1&#093; 0.0413\n<\/pre>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"169\" src=\"https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2025\/06\/welch-300x169.png\" alt=\"\" class=\"wp-image-4520\" srcset=\"https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2025\/06\/welch-300x169.png 300w, https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2025\/06\/welch.png 1558w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><figcaption class=\"wp-element-caption\"><em>p<\/em>\u5024\u306e\u5206\u5e03<\/figcaption><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading\">Mann\u2013Whitney\u306e<em>U<\/em>\u691c\u5b9a<\/h4>\n\n\n\n<pre class=\"prettyprint\">k &lt;- 100000 # \u6a19\u672c\u53d6\u308a\u51fa\u3057\u53cd\u5fa9\u56de\u6570\nn &lt;- 4 # \u6a19\u672c\u30b5\u30a4\u30ba\nr &lt;- replicate(k,{\n     x &lt;- rnorm(n, mean=0, sd=1) #\u5e73\u57470\u3001\u6a19\u6e96\u504f\u5dee1\u306e\u6b63\u898f\u5206\u5e03\u304b\u3089\u30e9\u30f3\u30c0\u30e0\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\n     y &lt;- rnorm(n, mean=0, sd=1)\n     c(mean(x), wilcox.test(x, y)$p.value)\n})\nm &lt;- r&#091;1, &#093; # \u5e73\u5747\u5024\np &lt;- r&#091;2, &#093; # 5%\u6c34\u6e96\u68c4\u5374\u6570\nreject_rate &lt;- length(p&#091;p&lt;=0.05&#093;)&#47;k # 5%\u6c34\u6e96\u68c4\u5374\u7387\nprint (reject_rate)\n&#091;1&#093; 0.02919\n<\/pre>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"169\" src=\"https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2025\/06\/wilcox-300x169.png\" alt=\"\" class=\"wp-image-4521\" srcset=\"https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2025\/06\/wilcox-300x169.png 300w, https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2025\/06\/wilcox.png 1556w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><figcaption class=\"wp-element-caption\"><em>p<\/em>\u5024\u306e\u5206\u5e03<\/figcaption><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading\"><span style=\"font-size: revert;\">\u7d50\u679c<\/span><\/h4>\n\n\n\n<p>\u540c\u4e00\u306e\u78ba\u7387\u5206\u5e03\u304b\u3089<em>n<\/em>\u500b\u306e\u6a19\u672c\u30922\u56de\u53d6\u308a\u51fa\u3057\u30662\u3064\u306e\u7fa4\u306b\u5dee\u304c\u3042\u308b\u304b\u3092\u691c\u5b9a\u3059\u308b (<em>p<\/em>\u5024\u3092\u8a08\u7b97\u3059\u308b)\u3001\u309210\u4e07\u56de\u7e70\u308a\u8fd4\u3057\u3066<em>p<\/em> \u2266 0.05\u3068\u306a\u3063\u305f\u78ba\u7387\u3002<\/p>\n\n\n\n<figure class=\"wp-block-table is-style-stripes\">\n<table class=\"has-fixed-layout\" style=\"width: 100%; height: 371px;\">\n<tbody>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">&nbsp;<\/td>\n<td style=\"height: 19px; width: 75%;\" colspan=\"3\">5%\u6c34\u6e96\u68c4\u5374\u7387<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\"><em>n<\/em><\/td>\n<td style=\"height: 19px; width: 25%;\">Student\u306e<em>t<\/em>\u691c\u5b9a<\/td>\n<td style=\"height: 19px; width: 25%;\">Welch\u306e<em>t<\/em>\u691c\u5b9a<\/td>\n<td style=\"height: 19px; width: 25%;\">Mann\u2013Whitney\u306e<em>U<\/em>\u691c\u5b9a<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">2<\/td>\n<td style=\"height: 19px; width: 25%;\">0.05012<\/td>\n<td style=\"height: 19px; width: 25%;\">0.02321<\/td>\n<td style=\"height: 19px; width: 25%;\">\u2013<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">3<\/td>\n<td style=\"height: 19px; width: 25%;\">0.05059<\/td>\n<td style=\"height: 19px; width: 25%;\">0.03456<\/td>\n<td style=\"height: 19px; width: 25%;\">\u2013<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">4<\/td>\n<td style=\"height: 19px; width: 25%;\">0.04981<\/td>\n<td style=\"height: 19px; width: 25%;\">0.0413<\/td>\n<td style=\"height: 19px; width: 25%;\">0.02919<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">5<\/td>\n<td style=\"height: 19px; width: 25%;\">0.04999<\/td>\n<td style=\"height: 19px; width: 25%;\">0.04404<\/td>\n<td style=\"height: 19px; width: 25%;\">0.03144<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">6<\/td>\n<td style=\"height: 19px; width: 25%;\">0.5104<\/td>\n<td style=\"height: 19px; width: 25%;\">0.04493<\/td>\n<td style=\"height: 19px; width: 25%;\">0.04067<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">7<\/td>\n<td style=\"height: 19px; width: 25%;\">0.04942<\/td>\n<td style=\"height: 19px; width: 25%;\">0.0475<\/td>\n<td style=\"height: 19px; width: 25%;\">0.03808<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">8<\/td>\n<td style=\"height: 19px; width: 25%;\">0.04975<\/td>\n<td style=\"height: 19px; width: 25%;\">0.04699<\/td>\n<td style=\"height: 19px; width: 25%;\">0.05012<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">9<\/td>\n<td style=\"height: 19px; width: 25%;\">0.04983<\/td>\n<td style=\"height: 19px; width: 25%;\">0.04841<\/td>\n<td style=\"height: 19px; width: 25%;\">0.03832<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">10<\/td>\n<td style=\"height: 19px; width: 25%;\">0.5097<\/td>\n<td style=\"height: 19px; width: 25%;\">0.04846<\/td>\n<td style=\"height: 19px; width: 25%;\">0.04357<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">20<\/td>\n<td style=\"height: 19px; width: 25%;\">0.04845<\/td>\n<td style=\"height: 19px; width: 25%;\">0.05003<\/td>\n<td style=\"height: 19px; width: 25%;\">0.04874<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">30<\/td>\n<td style=\"height: 19px; width: 25%;\">0.05017<\/td>\n<td style=\"height: 19px; width: 25%;\">0.04939<\/td>\n<td style=\"height: 19px; width: 25%;\">0.05059<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">40<\/td>\n<td style=\"height: 19px; width: 25%;\">0.04979<\/td>\n<td style=\"height: 19px; width: 25%;\">0.04889<\/td>\n<td style=\"height: 19px; width: 25%;\">0.05027<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">50<\/td>\n<td style=\"height: 19px; width: 25%;\">0.04945<\/td>\n<td style=\"height: 19px; width: 25%;\">0.05065<\/td>\n<td style=\"height: 19px; width: 25%;\">0.04892<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 10px; width: 25%;\">60<\/td>\n<td style=\"height: 10px; width: 25%;\">0.04934<\/td>\n<td style=\"height: 10px; width: 25%;\">0.04954<\/td>\n<td style=\"height: 10px; width: 25%;\">0.05057<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">70<\/td>\n<td style=\"height: 19px; width: 25%;\">0.0502<\/td>\n<td style=\"height: 19px; width: 25%;\">0.0482<\/td>\n<td style=\"height: 19px; width: 25%;\">0.05015<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">80<\/td>\n<td style=\"height: 19px; width: 25%;\">0.05082<\/td>\n<td style=\"height: 19px; width: 25%;\">0.05107<\/td>\n<td style=\"height: 19px; width: 25%;\">0.05006<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">90<\/td>\n<td style=\"height: 19px; width: 25%;\">0.05024<\/td>\n<td style=\"height: 19px; width: 25%;\">0.04976<\/td>\n<td style=\"height: 19px; width: 25%;\">0.05034<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">100<\/td>\n<td style=\"height: 19px; width: 25%;\">0.04899<\/td>\n<td style=\"height: 19px; width: 25%;\">0.04974<\/td>\n<td style=\"height: 19px; width: 25%;\">0.04987<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\n\n\n\n<p>\u30e2\u30c7\u30eb\u901a\u308a\u306a\u306e\u3067Student\u306e<em>t<\/em>\u691c\u5b9a\u306f<em>n<\/em> = 2\u3067\u3082\u6b63\u78ba\u3067\u3059\u3002Welch\u306e<em>t<\/em>\u691c\u5b9a\u306f<em>n<\/em>\u6570\u304c\u5c11\u306a\u3044\u6642\u306f\u68c4\u5374\u7387\u304c\u4f4e\u3044\u3067\u3059\u3002\u540c\u3058\u5206\u5e03\u306e\u6bd4\u8f03\u306a\u306e\u3067Mann\u2013Whitney\u306e<em>U<\/em>\u691c\u5b9a\u3082\u4e2d\u592e\u5024\u306e\u691c\u5b9a\u3068\u3057\u3066\u632f\u308b\u821e\u3063\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u6bcd\u96c6\u56e3\u304c\u6b63\u898f\u5206\u5e03\u3067\u5206\u6563\u304c\u7570\u306a\u308b\u5834\u5408<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\">\u6a19\u672c\u30b5\u30a4\u30ba\u304c\u7b49\u3057\u3044\u5834\u5408<\/h4>\n\n\n\n<p>\u6b63\u898f\u5206\u5e03A\uff08\u5e73\u57470\u3001\u6a19\u6e96\u504f\u5dee=1\u3001\u8d64\uff09vs. \u6b63\u898f\u5206\u5e03B\uff08\u5e73\u5747\u5024=0\u3001\u6a19\u6e96\u504f\u5dee=3\u3001\u9ed2\uff09\u3002<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"236\" src=\"https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2025\/06\/two_norm_equalmean-300x236.png\" alt=\"\" class=\"wp-image-4659\" srcset=\"https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2025\/06\/two_norm_equalmean-300x236.png 300w, https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2025\/06\/two_norm_equalmean.png 1374w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/figure>\n<\/div>\n\n\n<figure class=\"wp-block-table is-style-stripes\">\n<table class=\"has-fixed-layout\" style=\"width: 98.5714%; height: 380px;\">\n<tbody>\n<tr style=\"height: 19px;\">\n<td style=\"width: 25%; height: 19px;\">&nbsp;<\/td>\n<td style=\"width: 73.5714%; height: 19px;\" colspan=\"3\">5%\u6c34\u6e96\u68c4\u5374\u7387<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"width: 25%; height: 19px;\"><em>n<\/em><\/td>\n<td style=\"width: 25%; height: 19px;\">Student\u306e<em>t<\/em>\u691c\u5b9a<\/td>\n<td style=\"width: 25%; height: 19px;\">Welch\u306e<em>t<\/em>\u691c\u5b9a<\/td>\n<td style=\"width: 23.5714%; height: 19px;\">Mann\u2013Whitney\u306e<em>U<\/em>\u691c\u5b9a<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"width: 25%; height: 19px;\">2<\/td>\n<td style=\"width: 25%; height: 19px;\">0.07343<\/td>\n<td style=\"width: 25%; height: 19px;\">0.03688<\/td>\n<td style=\"width: 23.5714%; height: 19px;\">\u2013<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"width: 25%; height: 19px;\">3<\/td>\n<td style=\"width: 25%; height: 19px;\">0.07413<\/td>\n<td style=\"width: 25%; height: 19px;\">0.05227<\/td>\n<td style=\"width: 23.5714%; height: 19px;\">\u2013<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"width: 25%; height: 19px;\">4<\/td>\n<td style=\"width: 25%; height: 19px;\">0.07121<\/td>\n<td style=\"width: 25%; height: 19px;\">0.05398<\/td>\n<td style=\"width: 23.5714%; height: 19px;\">0.04841<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"width: 25%; height: 19px;\">5<\/td>\n<td style=\"width: 25%; height: 19px;\">0.06767<\/td>\n<td style=\"width: 25%; height: 19px;\">0.05187<\/td>\n<td style=\"width: 23.5714%; height: 19px;\">0.04509<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"width: 25%; height: 19px;\">6<\/td>\n<td style=\"width: 25%; height: 19px;\">0.06437<\/td>\n<td style=\"width: 25%; height: 19px;\">0.05248<\/td>\n<td style=\"width: 23.5714%; height: 19px;\">0.0494<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"width: 25%; height: 19px;\">7<\/td>\n<td style=\"width: 25%; height: 19px;\">0.06227<\/td>\n<td style=\"width: 25%; height: 19px;\">0.05126<\/td>\n<td style=\"width: 23.5714%; height: 19px;\">0.054<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"width: 25%; height: 19px;\">8<\/td>\n<td style=\"width: 25%; height: 19px;\">0.06005<\/td>\n<td style=\"width: 25%; height: 19px;\">0.0508<\/td>\n<td style=\"width: 23.5714%; height: 19px;\">0.0671<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"width: 25%; height: 19px;\">9<\/td>\n<td style=\"width: 25%; height: 19px;\">0.0599<\/td>\n<td style=\"width: 25%; height: 19px;\">0.05179<\/td>\n<td style=\"width: 23.5714%; height: 19px;\">0.05365<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"width: 25%; height: 19px;\">10<\/td>\n<td style=\"width: 25%; height: 19px;\">0.06025<\/td>\n<td style=\"width: 25%; height: 19px;\">0.05017<\/td>\n<td style=\"width: 23.5714%; height: 19px;\">0.0605<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"width: 25%; height: 19px;\">20<\/td>\n<td style=\"width: 25%; height: 19px;\">0.05343<\/td>\n<td style=\"width: 25%; height: 19px;\">0.05068<\/td>\n<td style=\"width: 23.5714%; height: 19px;\">0.06728<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"width: 25%; height: 19px;\">30<\/td>\n<td style=\"width: 25%; height: 19px;\">0.05162<\/td>\n<td style=\"width: 25%; height: 19px;\">0.05059<\/td>\n<td style=\"width: 23.5714%; height: 19px;\">0.06818<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"width: 25%; height: 19px;\">40<\/td>\n<td style=\"width: 25%; height: 19px;\">0.05231<\/td>\n<td style=\"width: 25%; height: 19px;\">0.05047<\/td>\n<td style=\"width: 23.5714%; height: 19px;\">0.06974<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"width: 25%; height: 19px;\">50<\/td>\n<td style=\"width: 25%; height: 19px;\">0.05168<\/td>\n<td style=\"width: 25%; height: 19px;\">0.05018<\/td>\n<td style=\"width: 23.5714%; height: 19px;\">0.06915<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"width: 25%; height: 19px;\">60<\/td>\n<td style=\"width: 25%; height: 19px;\">0.05254<\/td>\n<td style=\"width: 25%; height: 19px;\">0.04984<\/td>\n<td style=\"width: 23.5714%; height: 19px;\">0.06906<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"width: 25%; height: 19px;\">70<\/td>\n<td style=\"width: 25%; height: 19px;\">0.05084<\/td>\n<td style=\"width: 25%; height: 19px;\">0.05022<\/td>\n<td style=\"width: 23.5714%; height: 19px;\">0.0694<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"width: 25%; height: 19px;\">80<\/td>\n<td style=\"width: 25%; height: 19px;\">0.04975<\/td>\n<td style=\"width: 25%; height: 19px;\">0.04894<\/td>\n<td style=\"width: 23.5714%; height: 19px;\">0.06913<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"width: 25%; height: 19px;\">90<\/td>\n<td style=\"width: 25%; height: 19px;\">0.0505<\/td>\n<td style=\"width: 25%; height: 19px;\">0.05116<\/td>\n<td style=\"width: 23.5714%; height: 19px;\">0.06784<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"width: 25%; height: 19px;\">100<\/td>\n<td style=\"width: 25%; height: 19px;\">0.0503<\/td>\n<td style=\"width: 25%; height: 19px;\">0.05021<\/td>\n<td style=\"width: 23.5714%; height: 19px;\">0.06722<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\n\n\n\n<p>Welch\u306e<em>t<\/em>\u691c\u5b9a\u306f\u7406\u8ad6\u901a\u308a\u4e0d\u7b49\u5206\u6563\u306e\u5834\u5408\u3067\u3082\u5927\u4e08\u592b\u3067\u3057\u305f\u3002Student\u306e<em>t<\/em>\u691c\u5b9a\u306f<em>n<\/em>\u304c\u5927\u304d\u3051\u308c\u3070\u6b63\u3057\u304f\u632f\u308b\u821e\u3063\u3066\u3044\u307e\u3059\u3002\u3053\u308c\u306f\u306a\u305c\u304b\u3068\u3044\u3048\u3070<strong>\u6a19\u672c\u30b5\u30a4\u30ba\uff08<em>n<\/em>\uff09\u304c\u7b49\u3057\u3044<\/strong>\u304b\u3089\u3067\u3059\u3002\u751f\u7269\u7cfb\u306e\u5b9f\u9a13\u306e\u5834\u5408\u306f<em>n<\/em>\u6570\u3092\u63c3\u3048\u308b\u306e\u304c\u666e\u901a\u306a\u306e\u3067\u3042\u307e\u308a\u610f\u8b58\u3055\u308c\u307e\u305b\u3093\u304c\u3001\u3053\u308c\u306f\u304b\u306a\u308a\u5927\u4e8b\u3067\u3059\u3002<em>n<\/em>\u304c\u5341\u5206\u5927\u304d\u304f\u3001<em>n<\/em>\u3092\u63c3\u3048\u3066\u3044\u308c\u3070\u3001Student\u306e<em>t<\/em>\u691c\u5b9a\u3084Tukey\u306eHSD\u691c\u5b9a\u306f\u4e0d\u7b49\u5206\u6563\u306b\u5bfe\u3057\u3066\u9811\u5065\u3067\u3059\u3002\u9006\u306b\u8a00\u3046\u3068<em>n<\/em>\u6570\u304c\u7570\u306a\u308b\u5834\u5408\u306f\u7b49\u5206\u6563\u6027\u306b\u6ce8\u610f\u3092\u6255\u3046\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<br><\/p>\n\n\n\n<p>\u5927\u4e8b\u306a\u3053\u3068\u3067\u3059\u304c\u3001<strong><em>n<\/em>\u304c\u63c3\u3063\u3066\u3044\u308c\u3070Student\u306e<em>t<\/em>\u691c\u5b9a\u3068Welch\u306e<em>t<\/em>\u691c\u5b9a\u306e\u7d71\u8a08\u91cf<em>t<\/em>\u306f\u7b49\u3057\u3044<\/strong>\u3067\u3059\u3002\u7d71\u8a08\u91cf<em>t<\/em>\u306e\u8a08\u7b97\u5f0f\u3092\u4e0b\u306b\u793a\u3057\u307e\u3059\u3002<br><\/p>\n\n\n\n<p>Student\u306e<em>t<\/em>\u691c\u5b9a\u306e\u7d71\u8a08\u91cf<em>t<\/em>\uff08\\(m\\)\u3068\\(n\\)\u306f\u6a19\u672c\u30b5\u30a4\u30ba\u3001\\(\\bar{X}\\)\u3068\\(\\bar{Y}\\)\u306f\u6a19\u672c\u5e73\u5747\u3001\\(U_x\\)\u3068\\(U_y\\)\u306f\u4e0d\u504f\u5206\u6563\uff09<br><\/p>\n\n\n\n<p>$$t_0 = \\frac{|\\bar{X} - \\bar{Y}|}{\\sqrt{U_e\\left(\\frac{1}{m}+\\frac{1}{n}\\right)}} $$ $$U_e = \\frac{(m-1)U_x + (n-1)U_y}{m+n-2} $$ \u4e21\u7fa4\u306e\u6bcd\u5e73\u5747\u304c\u7b49\u3057\u3044\u5834\u5408\u306b\u306f\u300c\u7d71\u8a08\u91cf\\(t_0\\)\u306f\u81ea\u7531\u5ea6\\(\\nu = m+n-2\\)\u306e<em>t<\/em>\u5206\u5e03\u306b\u5f93\u3046\u300d\u3002<br><\/p>\n\n\n\n<p>Welch\u306e<em>t<\/em>\u691c\u5b9a\u306e\u7d71\u8a08\u91cf<em>t<\/em>:<br><\/p>\n\n\n\n<p>$$t_0 = \\frac{|\\bar{X} - \\bar{Y}|}{\\sqrt{\\frac{U_x}{m}+\\frac{U_y}{n}}} $$ \u4e21\u7fa4\u306e\u6bcd\u5e73\u5747\u304c\u7b49\u3057\u3044\u5834\u5408\u306b\u306f\u300c\u7d71\u8a08\u91cf\\(t_0\\)\u306f\u81ea\u7531\u5ea6 $$\\nu \\simeq \\frac{\\left(\\frac{U_x}{m} + \\frac{U_y}{n}\\right)^2}{\\frac{U_x^2}{m^2(m-1)}+\\frac{U_y^2}{n^2(n-1)}}$$ \u306e<em>t<\/em>\u5206\u5e03\u306b\u5f93\u3046\u300d\u3002<\/p>\n\n\n\n<p>\\(m = n\\) \u306e\u6642\u306f\u3001Student\u306e<em>t<\/em>\u691c\u5b9a\u306e\u81ea\u7531\u5ea6:$$ \\nu_{Student} = 2(m-1)$$<\/p>\n\n\n\n<p>Welch\u306e<em>t<\/em>\u691c\u5b9a\u306e\u81ea\u7531\u5ea6:$$ \\nu_{Welch} = \\left(1+\\frac{2U_x U_y}{U_x^2 + U_y^2}\\right)(m-1)$$<\/p>\n\n\n\n<p>\u3067\u3059\u3002\\(U_x = U_y\\) \u306a\u3089\u3070\u4e21\u691c\u5b9a\u306e\u81ea\u7531\u5ea6\u3082\u7b49\u3057\u304f\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u6a19\u672c\u30b5\u30a4\u30ba\u304c\u7570\u306a\u308b\u5834\u5408<\/h4>\n\n\n\n<p>\u6b21\u306b\u7247\u65b9\uff08\u6a19\u6e96\u504f\u5dee\u304c\u5927\u304d\u3044\u65b9\uff09\u306e<em>n<\/em>\u30922\u500d\u306b\u3057\u3066\u540c\u69d8\u306b5%\u6c34\u6e96\u68c4\u5374\u7387\u304c\u3069\u3046\u306a\u308b\u304b\u8a66\u3057\u3066\u307f\u307e\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-table is-style-stripes\">\n<table class=\"has-fixed-layout\" style=\"width: 99.1665%; height: 380px;\">\n<tbody>\n<tr style=\"height: 19px;\">\n<td style=\"width: 8.16929%; height: 19px;\">&nbsp;<\/td>\n<td style=\"width: 8.07083%; height: 19px;\">&nbsp;<\/td>\n<td style=\"width: 64.4677%; height: 19px;\" colspan=\"3\">5%\u6c34\u6e96\u68c4\u5374\u7387<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"width: 8.16929%; height: 19px;\"><em>n<\/em><sub>A<\/sub><\/td>\n<td style=\"width: 8.07083%; height: 19px;\"><em>n<sub>B<\/sub><\/em><\/td>\n<td style=\"width: 38.4843%; height: 19px;\">Student\u306e<em>t<\/em>\u691c\u5b9a<\/td>\n<td style=\"width: 19.1929%; height: 19px;\">Welch\u306e<em>t<\/em>\u691c\u5b9a<\/td>\n<td style=\"width: 6.79046%; height: 19px;\">Mann\u2013Whitney\u306e<em>U<\/em>\u691c\u5b9a<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"width: 8.16929%; height: 19px;\">2<\/td>\n<td style=\"width: 8.07083%; height: 19px;\">4<\/td>\n<td style=\"width: 38.4843%; height: 19px;\">0.02764<\/td>\n<td style=\"width: 19.1929%; height: 19px;\">0.03732<\/td>\n<td style=\"width: 6.79046%; height: 19px;\">\u2013<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"width: 8.16929%; height: 19px;\">3<\/td>\n<td style=\"width: 8.07083%; height: 19px;\">6<\/td>\n<td style=\"width: 38.4843%; height: 19px;\">0.02481<\/td>\n<td style=\"width: 19.1929%; height: 19px;\">0.04337<\/td>\n<td style=\"width: 6.79046%; height: 19px;\">0.02842<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"width: 8.16929%; height: 19px;\">4<\/td>\n<td style=\"width: 8.07083%; height: 19px;\">8<\/td>\n<td style=\"width: 38.4843%; height: 19px;\">0.02256<\/td>\n<td style=\"width: 19.1929%; height: 19px;\">0.04636<\/td>\n<td style=\"width: 6.79046%; height: 19px;\">0.03206<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"width: 8.16929%; height: 19px;\">5<\/td>\n<td style=\"width: 8.07083%; height: 19px;\">10<\/td>\n<td style=\"width: 38.4843%; height: 19px;\">0.02192<\/td>\n<td style=\"width: 19.1929%; height: 19px;\">0.04828<\/td>\n<td style=\"width: 6.79046%; height: 19px;\">0.02558<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"width: 8.16929%; height: 19px;\">6<\/td>\n<td style=\"width: 8.07083%; height: 19px;\">12<\/td>\n<td style=\"width: 38.4843%; height: 19px;\">0.02114<\/td>\n<td style=\"width: 19.1929%; height: 19px;\">0.04861<\/td>\n<td style=\"width: 6.79046%; height: 19px;\">0.02713<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"width: 8.16929%; height: 19px;\">7<\/td>\n<td style=\"width: 8.07083%; height: 19px;\">14<\/td>\n<td style=\"width: 38.4843%; height: 19px;\">0.01966<\/td>\n<td style=\"width: 19.1929%; height: 19px;\">0.04846<\/td>\n<td style=\"width: 6.79046%; height: 19px;\">0.02961<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"width: 8.16929%; height: 19px;\">8<\/td>\n<td style=\"width: 8.07083%; height: 19px;\">16<\/td>\n<td style=\"width: 38.4843%; height: 19px;\">0.01961<\/td>\n<td style=\"width: 19.1929%; height: 19px;\">0.04942<\/td>\n<td style=\"width: 6.79046%; height: 19px;\">0.02801<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"width: 8.16929%; height: 19px;\">9<\/td>\n<td style=\"width: 8.07083%; height: 19px;\">18<\/td>\n<td style=\"width: 38.4843%; height: 19px;\">0.01904<\/td>\n<td style=\"width: 19.1929%; height: 19px;\">0.04894<\/td>\n<td style=\"width: 6.79046%; height: 19px;\">0.02933<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"width: 8.16929%; height: 19px;\">10<\/td>\n<td style=\"width: 8.07083%; height: 19px;\">20<\/td>\n<td style=\"width: 38.4843%; height: 19px;\">0.01779<\/td>\n<td style=\"width: 19.1929%; height: 19px;\">0.04861<\/td>\n<td style=\"width: 6.79046%; height: 19px;\">0.03106<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"width: 8.16929%; height: 19px;\">20<\/td>\n<td style=\"width: 8.07083%; height: 19px;\">40<\/td>\n<td style=\"width: 38.4843%; height: 19px;\">0.01712<\/td>\n<td style=\"width: 19.1929%; height: 19px;\">0.0498<\/td>\n<td style=\"width: 6.79046%; height: 19px;\">0.03161<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"width: 8.16929%; height: 19px;\">30<\/td>\n<td style=\"width: 8.07083%; height: 19px;\">60<\/td>\n<td style=\"width: 38.4843%; height: 19px;\">0.0172<\/td>\n<td style=\"width: 19.1929%; height: 19px;\">0.05002<\/td>\n<td style=\"width: 6.79046%; height: 19px;\">0.03247<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"width: 8.16929%; height: 19px;\">40<\/td>\n<td style=\"width: 8.07083%; height: 19px;\">80<\/td>\n<td style=\"width: 38.4843%; height: 19px;\">0.01693<\/td>\n<td style=\"width: 19.1929%; height: 19px;\">0.05006<\/td>\n<td style=\"width: 6.79046%; height: 19px;\">0.03308<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"width: 8.16929%; height: 19px;\">50<\/td>\n<td style=\"width: 8.07083%; height: 19px;\">100<\/td>\n<td style=\"width: 38.4843%; height: 19px;\">0.01711<\/td>\n<td style=\"width: 19.1929%; height: 19px;\">0.04997<\/td>\n<td style=\"width: 6.79046%; height: 19px;\">0.03287<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"width: 8.16929%; height: 19px;\">60<\/td>\n<td style=\"width: 8.07083%; height: 19px;\">120<\/td>\n<td style=\"width: 38.4843%; height: 19px;\">0.01738<\/td>\n<td style=\"width: 19.1929%; height: 19px;\">0.05036<\/td>\n<td style=\"width: 6.79046%; height: 19px;\">0.03274<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"width: 8.16929%; height: 19px;\">70<\/td>\n<td style=\"width: 8.07083%; height: 19px;\">140<\/td>\n<td style=\"width: 38.4843%; height: 19px;\">0.01668<\/td>\n<td style=\"width: 19.1929%; height: 19px;\">0.05035<\/td>\n<td style=\"width: 6.79046%; height: 19px;\">0.03205<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"width: 8.16929%; height: 19px;\">80<\/td>\n<td style=\"width: 8.07083%; height: 19px;\">160<\/td>\n<td style=\"width: 38.4843%; height: 19px;\">0.01672<\/td>\n<td style=\"width: 19.1929%; height: 19px;\">0.04971<\/td>\n<td style=\"width: 6.79046%; height: 19px;\">0.03289<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"width: 8.16929%; height: 19px;\">90<\/td>\n<td style=\"width: 8.07083%; height: 19px;\">180<\/td>\n<td style=\"width: 38.4843%; height: 19px;\">0.01651<\/td>\n<td style=\"width: 19.1929%; height: 19px;\">0.05049<\/td>\n<td style=\"width: 6.79046%; height: 19px;\">0.03343<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"width: 8.16929%; height: 19px;\">100<\/td>\n<td style=\"width: 8.07083%; height: 19px;\">200<\/td>\n<td style=\"width: 38.4843%; height: 19px;\">0.01684<\/td>\n<td style=\"width: 19.1929%; height: 19px;\">0.05071<\/td>\n<td style=\"width: 6.79046%; height: 19px;\">0.03394<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\n<p>Welch\u306e<em>t<\/em>\u691c\u5b9a\u3060\u3051\u304c\u7b2c\u4e00\u7a2e\u306e\u904e\u8aa4\u3092\u5236\u5fa1\u3067\u304d\u3066\u3044\u307e\u3057\u305f\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u6bcd\u96c6\u56e3\u304c\u6b63\u898f\u5206\u5e03\u3067\u306a\u3044\u5834\u5408\uff08\u4e8c\u5cf0\u5206\u5e03\uff09\uff08\u7b49\u5206\u6563\uff09<\/h3>\n\n\n\n<p>\u30d4\u30fc\u30af\u304c2\u3064\u3042\u308b\u30d5\u30bf\u30b3\u30d6\u30e9\u30af\u30c0\u306e\u3088\u3046\u306a\u5206\u5e03\uff08\u4e8c\u5cf0\u5206\u5e03\uff09\u3092\u8003\u3048\u307e\u3059\uff08\u53c2\u8003: <a href=\"https:\/\/amphipod.hatenablog.com\/entry\/2015\/02\/23\/201935\">\u5099\u5fd8\u9332 a record of inner life\uff082015-02-23\uff09R\u3067\u306e\u5206\u5e03\u4f5c\u6210\u3068\u81ea\u4f5c\u5206\u5e03\u306b\u5f93\u3046\u4e71\u6570\u751f\u6210<\/a>\uff09\u3002<\/p>\n\n\n\n<pre class=\"prettyprint\">fx &lt;- function(x) dnorm(x, mean=2, sd=1)\ngx &lt;- function(x) dnorm(x, mean=-2, sd=2)\nhx &lt;- function(x) 1&#47;2*(fx(x)+gx(x))\nplot(hx, xlim=c(-10, 10))<\/pre>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"225\" src=\"https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2025\/06\/two-humped_camel-300x225.png\" alt=\"\" class=\"wp-image-4537\" srcset=\"https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2025\/06\/two-humped_camel-300x225.png 300w, https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2025\/06\/two-humped_camel.png 1014w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/figure>\n<\/div>\n\n\n<p>$$h(x) = \\frac{1}{2}\\left(\\frac{1}{\\sqrt{2\\pi 1^2}}\\exp\\left(-\\frac{(x-2)^2}{2\\times 1^2}\\right) + \\frac{1}{\\sqrt{2\\pi 2^2}}\\exp\\left(-\\frac{(x+2)^2}{2\\times 2^2}\\right)\\right)\\;\\;\\;(-10 &lt; x &lt; 10)$$\u3068\u3044\u3046\u5206\u5e03\u306b\u5f93\u3046\u4e71\u6570\u3092\u751f\u6210\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<pre class=\"prettyprint\">rbimodal &lt;- function(x, m1=2, s1=1, m2=-2, s2=2) {\n  u &lt;- rbinom(x, 1, 0.5)\n  v &lt;- sum(u == 0)\n  w &lt;- x - v\n  y &lt;- c(rnorm(v, mean=m1, sd=s1), rnorm(w, mean=m2, sd=s2))\n  return(y)\n}\n<\/pre>\n\n\n\n<h4 class=\"wp-block-heading\"><span style=\"font-size: revert;\">\u7d50\u679c\uff08\u4e8c\u5cf0\u5206\u5e03\uff09<\/span><\/h4>\n\n\n\n<figure class=\"wp-block-table is-style-stripes\">\n<table class=\"has-fixed-layout\" style=\"width: 100%; height: 380px;\">\n<tbody>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">&nbsp;<\/td>\n<td style=\"height: 19px; width: 75%;\" colspan=\"3\">5%\u6c34\u6e96\u68c4\u5374\u7387<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\"><em>n<\/em><\/td>\n<td style=\"height: 19px; width: 1.19048%;\">Student\u306e<em>t<\/em>\u691c\u5b9a<\/td>\n<td style=\"height: 19px; width: 48.8095%;\">Welch\u306e<em>t<\/em>\u691c\u5b9a<\/td>\n<td style=\"height: 19px; width: 25%;\">Mann\u2013Whitney\u306e<em>U<\/em>\u691c\u5b9a<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">2<\/td>\n<td style=\"height: 19px; width: 1.19048%;\">0.06412<\/td>\n<td style=\"height: 19px; width: 48.8095%;\">0.03159<\/td>\n<td style=\"height: 19px; width: 25%;\">\u2013<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">3<\/td>\n<td style=\"height: 19px; width: 1.19048%;\">0.05416<\/td>\n<td style=\"height: 19px; width: 48.8095%;\">0.0378<\/td>\n<td style=\"height: 19px; width: 25%;\">\u2013<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">4<\/td>\n<td style=\"height: 19px; width: 1.19048%;\">0.05186<\/td>\n<td style=\"height: 19px; width: 48.8095%;\">0.0386<\/td>\n<td style=\"height: 19px; width: 25%;\">0.02903<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">5<\/td>\n<td style=\"height: 19px; width: 1.19048%;\">0.05066<\/td>\n<td style=\"height: 19px; width: 48.8095%;\">0.04235<\/td>\n<td style=\"height: 19px; width: 25%;\">0.3167<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">6<\/td>\n<td style=\"height: 19px; width: 1.19048%;\">0.05317<\/td>\n<td style=\"height: 19px; width: 48.8095%;\">0.04427<\/td>\n<td style=\"height: 19px; width: 25%;\">0.04131<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">7<\/td>\n<td style=\"height: 19px; width: 1.19048%;\">0.05143<\/td>\n<td style=\"height: 19px; width: 48.8095%;\">0.04655<\/td>\n<td style=\"height: 19px; width: 25%;\">0.03748<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">8<\/td>\n<td style=\"height: 19px; width: 1.19048%;\">0.05117<\/td>\n<td style=\"height: 19px; width: 48.8095%;\">0.04831<\/td>\n<td style=\"height: 19px; width: 25%;\">0.0502<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">9<\/td>\n<td style=\"height: 19px; width: 1.19048%;\">0.05075<\/td>\n<td style=\"height: 19px; width: 48.8095%;\">0.04865<\/td>\n<td style=\"height: 19px; width: 25%;\">0.03999<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">10<\/td>\n<td style=\"height: 19px; width: 1.19048%;\">0.05224<\/td>\n<td style=\"height: 19px; width: 48.8095%;\">0.04889<\/td>\n<td style=\"height: 19px; width: 25%;\">0.04317<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">20<\/td>\n<td style=\"height: 19px; width: 1.19048%;\">0.05087<\/td>\n<td style=\"height: 19px; width: 48.8095%;\">0.04944<\/td>\n<td style=\"height: 19px; width: 25%;\">0.0492<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">30<\/td>\n<td style=\"height: 19px; width: 1.19048%;\">0.04999<\/td>\n<td style=\"height: 19px; width: 48.8095%;\">0.04898<\/td>\n<td style=\"height: 19px; width: 25%;\">0.05071<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">40<\/td>\n<td style=\"height: 19px; width: 1.19048%;\">0.05004<\/td>\n<td style=\"height: 19px; width: 48.8095%;\">0.04958<\/td>\n<td style=\"height: 19px; width: 25%;\">0.04987<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">50<\/td>\n<td style=\"height: 19px; width: 1.19048%;\">0.04907<\/td>\n<td style=\"height: 19px; width: 48.8095%;\">0.05007<\/td>\n<td style=\"height: 19px; width: 25%;\">0.04913<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">60<\/td>\n<td style=\"height: 19px; width: 1.19048%;\">0.04973<\/td>\n<td style=\"height: 19px; width: 48.8095%;\">0.05102<\/td>\n<td style=\"height: 19px; width: 25%;\">0.04896<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">70<\/td>\n<td style=\"height: 19px; width: 1.19048%;\">0.0507<\/td>\n<td style=\"height: 19px; width: 48.8095%;\">0.04947<\/td>\n<td style=\"height: 19px; width: 25%;\">0.04822<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">80<\/td>\n<td style=\"height: 19px; width: 1.19048%;\">0.05108<\/td>\n<td style=\"height: 19px; width: 48.8095%;\">0.0495<\/td>\n<td style=\"height: 19px; width: 25%;\">0.04966<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">90<\/td>\n<td style=\"height: 19px; width: 1.19048%;\">0.05016<\/td>\n<td style=\"height: 19px; width: 48.8095%;\">0.04983<\/td>\n<td style=\"height: 19px; width: 25%;\">0.04975<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">100<\/td>\n<td style=\"height: 19px; width: 1.19048%;\">0.05063<\/td>\n<td style=\"height: 19px; width: 48.8095%;\">0.04968<\/td>\n<td style=\"height: 19px; width: 25%;\">0.04878<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u6b63\u898f\u5206\u5e03\u3067\u306a\u304f\u3066\u3082<em>t<\/em>\u691c\u5b9a\u306f\u4f7f\u3048\u308b\u3053\u3068\u304c\u5206\u304b\u308a\u307e\u3059\u3002<\/p>\n<\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">\u6bcd\u96c6\u56e3\u306e\u7247\u65b9\u304c\u6b63\u898f\u5206\u5e03\u3067\u306a\u3044\u5834\u5408\uff08\u4e8c\u5cf0\u5206\u5e03\uff09<\/h3>\n\n\n\n<p>\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u6b63\u898f\u5206\u5e03\uff08\u8d64\uff09\u3068\u4e8c\u5cf0\u5206\u5e03\uff08\u9ed2\uff09\u304b\u3089\u53d6\u51fa\u3057\u305f\u6a19\u672c\u540c\u58eb\u3092\u6bd4\u3079\u307e\u3059\u3002<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"293\" src=\"https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2025\/06\/dnorm_camel-300x293.png\" alt=\"\" class=\"wp-image-4622\" srcset=\"https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2025\/06\/dnorm_camel-300x293.png 300w, https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2025\/06\/dnorm_camel.png 1408w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/figure>\n<\/div>\n\n\n<p>\u203b\u6ce8\u610f\u66f8\u304d<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>\u3053\u306e\u3088\u3046\u306a\u6a19\u672c\u304c\u53d6\u308c\u305f\u3068\u304d\u306b\u3001<strong>\u307e\u305a\u8003\u3048\u3066\u307b\u3057\u3044\u306e\u306f\u3053\u308c\u3089\u306e\u6a19\u672c\u306f\u672c\u5f53\u306b\u6bd4\u8f03\u3059\u308b\u3079\u304d\u304b<\/strong>\u3001\u3068\u3044\u3046\u3053\u3068\u3067\u3042\u308b\u3002\u7279\u306b\u4e8c\u5cf0\u5206\u5e03\u306e\u307b\u3046\u306f\u3001\u3082\u3057\u304b\u3057\u305f\u3089\u5206\u3051\u3089\u308c\u308b\u3079\u304d\u6a19\u672c\u304c\u6df7\u3058\u3063\u3066\u3044\u308b\u53ef\u80fd\u6027\u3082\u8003\u3048\u308b\u3079\u304d\u3067\u3042\u308b\u3002<strong>\u306a\u306b\u3082\u8003\u3048\u305a\u306b\u305f\u3060\u691c\u5b9a\u3059\u308b\u306e\u306f\u826f\u3044\u624b\u3068\u306f\u8a00\u3048\u306a\u3044<\/strong>\u3002\uff08<a href=\"https:\/\/sites.google.com\/view\/ynomura\/stats\/Brunner_Munzel\">\u91ce\u6751\u5eb7\u4e4b. Brunner-Munzel\u691c\u5b9a<\/a>\uff09<\/p>\n<\/blockquote>\n\n\n\n<figure class=\"wp-block-table is-style-stripes\">\n<table class=\"has-fixed-layout\" style=\"width: 100%; height: 362px;\">\n<tbody>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 20.7143%;\">&nbsp;<\/td>\n<td style=\"height: 19px; width: 84.4048%;\" colspan=\"3\">5%\u6c34\u6e96\u68c4\u5374\u7387<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 20.7143%;\"><em>n<\/em><\/td>\n<td style=\"height: 19px; width: 34.4048%;\">Student\u306e<em>t<\/em>\u691c\u5b9a<\/td>\n<td style=\"height: 19px; width: 25%;\">Welch\u306e<em>t<\/em>\u691c\u5b9a<\/td>\n<td style=\"height: 19px; width: 25%;\">Mann\u2013Whitney\u306e<em>U<\/em>\u691c\u5b9a<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 20.7143%;\">2<\/td>\n<td style=\"height: 19px; width: 34.4048%;\">0.09888<\/td>\n<td style=\"height: 19px; width: 25%;\">0.04859<\/td>\n<td style=\"height: 19px; width: 25%;\">\u2013<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 20.7143%;\">3<\/td>\n<td style=\"height: 19px; width: 34.4048%;\">0.10786<\/td>\n<td style=\"height: 19px; width: 25%;\">0.08199<\/td>\n<td style=\"height: 19px; width: 25%;\">\u2013<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 20.7143%;\">4<\/td>\n<td style=\"height: 19px; width: 34.4048%;\">0.09623<\/td>\n<td style=\"height: 19px; width: 25%;\">0.08372<\/td>\n<td style=\"height: 19px; width: 25%;\">0.06325<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 10px; width: 20.7143%;\">5<\/td>\n<td style=\"height: 10px; width: 34.4048%;\">0.0827<\/td>\n<td style=\"height: 10px; width: 25%;\">0.07315<\/td>\n<td style=\"height: 10px; width: 25%;\">0.05605<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 20.7143%;\">6<\/td>\n<td style=\"height: 19px; width: 34.4048%;\">0.07439<\/td>\n<td style=\"height: 19px; width: 25%;\">0.06804<\/td>\n<td style=\"height: 19px; width: 25%;\">0.0574<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 20.7143%;\">7<\/td>\n<td style=\"height: 19px; width: 34.4048%;\">0.0723<\/td>\n<td style=\"height: 19px; width: 25%;\">0.06359<\/td>\n<td style=\"height: 19px; width: 25%;\">0.07345<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 20.7143%;\">8<\/td>\n<td style=\"height: 19px; width: 34.4048%;\">0.06735<\/td>\n<td style=\"height: 19px; width: 25%;\">0.06174<\/td>\n<td style=\"height: 19px; width: 25%;\">0.08358<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 20.7143%;\">9<\/td>\n<td style=\"height: 19px; width: 34.4048%;\">0.06505<\/td>\n<td style=\"height: 19px; width: 25%;\">0.05893<\/td>\n<td style=\"height: 19px; width: 25%;\">0.07089<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 20.7143%;\">10<\/td>\n<td style=\"height: 19px; width: 34.4048%;\">0.06399<\/td>\n<td style=\"height: 19px; width: 25%;\">0.05903<\/td>\n<td style=\"height: 19px; width: 25%;\">0.08386<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 10px; width: 20.7143%;\">20<\/td>\n<td style=\"height: 10px; width: 34.4048%;\">0.05663<\/td>\n<td style=\"height: 10px; width: 25%;\">0.05369<\/td>\n<td style=\"height: 10px; width: 25%;\">0.1107<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 20.7143%;\">30<\/td>\n<td style=\"height: 19px; width: 34.4048%;\">0.05363<\/td>\n<td style=\"height: 19px; width: 25%;\">0.0525<\/td>\n<td style=\"height: 19px; width: 25%;\">0.13456<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 20.7143%;\">40<\/td>\n<td style=\"height: 19px; width: 34.4048%;\">0.05371<\/td>\n<td style=\"height: 19px; width: 25%;\">0.05193<\/td>\n<td style=\"height: 19px; width: 25%;\">0.15399<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 20.7143%;\">50<\/td>\n<td style=\"height: 19px; width: 34.4048%;\">0.05201<\/td>\n<td style=\"height: 19px; width: 25%;\">0.05032<\/td>\n<td style=\"height: 19px; width: 25%;\">0.17493<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 20.7143%;\">60<\/td>\n<td style=\"height: 19px; width: 34.4048%;\">0.05266<\/td>\n<td style=\"height: 19px; width: 25%;\">0.05315<\/td>\n<td style=\"height: 19px; width: 25%;\">0.19635<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 20.7143%;\">70<\/td>\n<td style=\"height: 19px; width: 34.4048%;\">0.05169<\/td>\n<td style=\"height: 19px; width: 25%;\">0.04962<\/td>\n<td style=\"height: 19px; width: 25%;\">0.21546<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 20.7143%;\">80<\/td>\n<td style=\"height: 19px; width: 34.4048%;\">0.05188<\/td>\n<td style=\"height: 19px; width: 25%;\">0.05155<\/td>\n<td style=\"height: 19px; width: 25%;\">0.23806<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 20.7143%;\">90<\/td>\n<td style=\"height: 19px; width: 34.4048%;\">0.05183<\/td>\n<td style=\"height: 19px; width: 25%;\">0.04997<\/td>\n<td style=\"height: 19px; width: 25%;\">0.25626<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 20.7143%;\">100<\/td>\n<td style=\"height: 19px; width: 34.4048%;\">0.0522<\/td>\n<td style=\"height: 19px; width: 25%;\">0.05032<\/td>\n<td style=\"height: 19px; width: 25%;\">0.27582<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><em>n<\/em> \u2267 50\u3067Welch\u306e<em>t<\/em>\u691c\u5b9a\u306f\u3088\u3044\u7d50\u679c\u3002<\/p>\n<p>&nbsp;<\/p>\n<\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">\u6bcd\u96c6\u56e3\u306e\u7247\u65b9\u304c\u6b63\u898f\u5206\u5e03\u3067\u306a\u3044\u5834\u5408\uff08\u30b3\u30fc\u30b7\u30fc\u5206\u5e03\uff09<\/h3>\n\n\n\n<p>\u6b63\u898f\u5206\u5e03 (\u8d64) vs. \u30b3\u30fc\u30b7\u30fc\u5206\u5e03\uff08\u9ed2\uff09\u3002\u30b3\u30fc\u30b7\u30fc\u5206\u5e03\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u88fe\u304c\u91cd\u3044\u95a2\u6570\u3067\u3059\u3002<br>$$ f(x;x_0,\\gamma) = \\frac{1}{\\pi}\\frac{\\gamma}{(x-x_0)^2 + \\gamma^2} $$<br>\u88fe\u304c\u91cd\u304f\u3001\u671f\u5f85\u5024\uff08\u5e73\u5747\uff09\u3068\u5206\u6563\u304c\u5b9a\u7fa9\u3055\u308c\u307e\u305b\u3093\uff08\\(x_0\\)\u306f\u6700\u983b\u5024\u3001\\(\\gamma\\)\u306f\u534a\u5024\u534a\u5e45\u3092\u4e0e\u3048\u308b\u5024\uff09\u3002\u305d\u306e\u305f\u3081\u3001\u5927\u6570\u306e\u6cd5\u5247\u3068\u4e2d\u5fc3\u6975\u9650\u5b9a\u7406\u304c\u6210\u7acb\u3057\u307e\u305b\u3093\u3002\u95a2\u6570\u5f62\u306f\u30ed\u30fc\u30ec\u30f3\u30c4\u95a2\u6570\u3068\u3082\u547c\u3070\u308c\u308b\u5f62\u3067\u3001\u30d5\u30fc\u30ea\u30a8\u5909\u63dbNMR\u306e\u52c9\u5f37\u3092\u3057\u3066\u3044\u308b\u6642\u306b\u7247\u5074\u6307\u6570\u95a2\u6570\u306e\u30d5\u30fc\u30ea\u30a8\u5909\u63db\u304c\u8907\u7d20\u30ed\u30fc\u30ec\u30f3\u30c4\u95a2\u6570\u3068\u306a\u308b\uff08\u3064\u307e\u308aNMR\u30d4\u30fc\u30af\u306e\u5f62\u72b6\u306f\u30ed\u30fc\u30ec\u30f3\u30c4\u95a2\u6570\u3068\u3044\u3046\u3053\u3068\uff09\u306e\u3067\u99b4\u67d3\u304c\u3042\u308b\u304b\u3068\u601d\u3044\u307e\u3059\u3002<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2025\/06\/norm_cauchy-300x276.png\" alt=\"\" class=\"wp-image-4622\"\/><\/figure>\n<\/div>\n\n\n<figure class=\"wp-block-table is-style-stripes\">\n<table class=\"has-fixed-layout\" style=\"width: 105.26%; height: 400px;\">\n<tbody>\n<tr style=\"height: 20px;\">\n<td style=\"width: 9.27606%; height: 20px;\">&nbsp;<\/td>\n<td style=\"width: 62.6696%; height: 20px;\" colspan=\"3\">5%\u6c34\u6e96\u68c4\u5374\u7387<\/td>\n<td style=\"width: 28.1674%; height: 20px;\">&nbsp;<\/td>\n<\/tr>\n<tr style=\"height: 20px;\">\n<td style=\"width: 9.27606%; height: 20px;\"><em>n<\/em><\/td>\n<td style=\"width: 26.6968%; height: 20px;\">Student\u306e<em>t<\/em>\u691c\u5b9a<\/td>\n<td style=\"width: 18.7782%; height: 20px;\">Welch\u306e<em>t<\/em>\u691c\u5b9a<\/td>\n<td style=\"width: 17.1946%; height: 20px;\">Mann\u2013Whitney\u306e<em>U<\/em>\u691c\u5b9a<\/td>\n<td style=\"width: 28.1674%; height: 20px;\">Brunner\u2013Munzel\u691c\u5b9a<\/td>\n<\/tr>\n<tr style=\"height: 20px;\">\n<td style=\"width: 9.27606%; height: 20px;\">2<\/td>\n<td style=\"width: 26.6968%; height: 20px;\">0.03864<\/td>\n<td style=\"width: 18.7782%; height: 20px;\">0.0178<\/td>\n<td style=\"width: 17.1946%; height: 20px;\">\u2013<\/td>\n<td style=\"width: 28.1674%; height: 20px;\">0.034374<\/td>\n<\/tr>\n<tr style=\"height: 20px;\">\n<td style=\"width: 9.27606%; height: 20px;\">3<\/td>\n<td style=\"width: 26.6968%; height: 20px;\">0.03061<\/td>\n<td style=\"width: 18.7782%; height: 20px;\">0.01983<\/td>\n<td style=\"width: 17.1946%; height: 20px;\">\u2013<\/td>\n<td style=\"width: 28.1674%; height: 20px;\">0.10554<\/td>\n<\/tr>\n<tr style=\"height: 20px;\">\n<td style=\"width: 9.27606%; height: 20px;\">4<\/td>\n<td style=\"width: 26.6968%; height: 20px;\">0.02931<\/td>\n<td style=\"width: 18.7782%; height: 20px;\">0.0208<\/td>\n<td style=\"width: 17.1946%; height: 20px;\">0.3132<\/td>\n<td style=\"width: 28.1674%; height: 20px;\">0.06119<\/td>\n<\/tr>\n<tr style=\"height: 20px;\">\n<td style=\"width: 9.27606%; height: 20px;\">5<\/td>\n<td style=\"width: 26.6968%; height: 20px;\">0.02926<\/td>\n<td style=\"width: 18.7782%; height: 20px;\">0.02222<\/td>\n<td style=\"width: 17.1946%; height: 20px;\">0.03513<\/td>\n<td style=\"width: 28.1674%; height: 20px;\">0.08471<\/td>\n<\/tr>\n<tr style=\"height: 20px;\">\n<td style=\"width: 9.27606%; height: 20px;\">6<\/td>\n<td style=\"width: 26.6968%; height: 20px;\">0.02839<\/td>\n<td style=\"width: 18.7782%; height: 20px;\">0.02215<\/td>\n<td style=\"width: 17.1946%; height: 20px;\">0.04258<\/td>\n<td style=\"width: 28.1674%; height: 20px;\">0.06577<\/td>\n<\/tr>\n<tr style=\"height: 20px;\">\n<td style=\"width: 9.27606%; height: 20px;\">7<\/td>\n<td style=\"width: 26.6968%; height: 20px;\">0.02742<\/td>\n<td style=\"width: 18.7782%; height: 20px;\">0.2202<\/td>\n<td style=\"width: 17.1946%; height: 20px;\">0.03998<\/td>\n<td style=\"width: 28.1674%; height: 20px;\">0.05692<\/td>\n<\/tr>\n<tr style=\"height: 20px;\">\n<td style=\"width: 9.27606%; height: 20px;\">8<\/td>\n<td style=\"width: 26.6968%; height: 20px;\">0.02784<\/td>\n<td style=\"width: 18.7782%; height: 20px;\">0.02232<\/td>\n<td style=\"width: 17.1946%; height: 20px;\">0.05294<\/td>\n<td style=\"width: 28.1674%; height: 20px;\">0.05751<\/td>\n<\/tr>\n<tr style=\"height: 20px;\">\n<td style=\"width: 9.27606%; height: 20px;\">9<\/td>\n<td style=\"width: 26.6968%; height: 20px;\">0.0277<\/td>\n<td style=\"width: 18.7782%; height: 20px;\">0.0225<\/td>\n<td style=\"width: 17.1946%; height: 20px;\">0.04167<\/td>\n<td style=\"width: 28.1674%; height: 20px;\">0.05662<\/td>\n<\/tr>\n<tr style=\"height: 20px;\">\n<td style=\"width: 9.27606%; height: 20px;\">10<\/td>\n<td style=\"width: 26.6968%; height: 20px;\">0.02598<\/td>\n<td style=\"width: 18.7782%; height: 20px;\">0.02123<\/td>\n<td style=\"width: 17.1946%; height: 20px;\">0.04524<\/td>\n<td style=\"width: 28.1674%; height: 20px;\">0.0542<\/td>\n<\/tr>\n<tr style=\"height: 20px;\">\n<td style=\"width: 9.27606%; height: 20px;\">20<\/td>\n<td style=\"width: 26.6968%; height: 20px;\">0.02532<\/td>\n<td style=\"width: 18.7782%; height: 20px;\">0.0221<\/td>\n<td style=\"width: 17.1946%; height: 20px;\">0.05336<\/td>\n<td style=\"width: 28.1674%; height: 20px;\">0.05326<\/td>\n<\/tr>\n<tr style=\"height: 20px;\">\n<td style=\"width: 9.27606%; height: 20px;\">30<\/td>\n<td style=\"width: 26.6968%; height: 20px;\">0.02341<\/td>\n<td style=\"width: 18.7782%; height: 20px;\">0.02129<\/td>\n<td style=\"width: 17.1946%; height: 20px;\">0.05273<\/td>\n<td style=\"width: 28.1674%; height: 20px;\">0.05124<\/td>\n<\/tr>\n<tr style=\"height: 20px;\">\n<td style=\"width: 9.27606%; height: 20px;\">40<\/td>\n<td style=\"width: 26.6968%; height: 20px;\">0.02425<\/td>\n<td style=\"width: 18.7782%; height: 20px;\">0.02222<\/td>\n<td style=\"width: 17.1946%; height: 20px;\">0.05483<\/td>\n<td style=\"width: 28.1674%; height: 20px;\">0.05229<\/td>\n<\/tr>\n<tr style=\"height: 20px;\">\n<td style=\"width: 9.27606%; height: 20px;\">50<\/td>\n<td style=\"width: 26.6968%; height: 20px;\">0.02291<\/td>\n<td style=\"width: 18.7782%; height: 20px;\">0.02155<\/td>\n<td style=\"width: 17.1946%; height: 20px;\">0.05373<\/td>\n<td style=\"width: 28.1674%; height: 20px;\">0.05132<\/td>\n<\/tr>\n<tr style=\"height: 20px;\">\n<td style=\"width: 9.27606%; height: 20px;\">60<\/td>\n<td style=\"width: 26.6968%; height: 20px;\">0.02309<\/td>\n<td style=\"width: 18.7782%; height: 20px;\">0.02169<\/td>\n<td style=\"width: 17.1946%; height: 20px;\">0.05439<\/td>\n<td style=\"width: 28.1674%; height: 20px;\">0.05169<\/td>\n<\/tr>\n<tr style=\"height: 20px;\">\n<td style=\"width: 9.27606%; height: 20px;\">70<\/td>\n<td style=\"width: 26.6968%; height: 20px;\">0.02168<\/td>\n<td style=\"width: 18.7782%; height: 20px;\">0.0206<\/td>\n<td style=\"width: 17.1946%; height: 20px;\">0.05398<\/td>\n<td style=\"width: 28.1674%; height: 20px;\">0.05109<\/td>\n<\/tr>\n<tr style=\"height: 20px;\">\n<td style=\"width: 9.27606%; height: 20px;\">80<\/td>\n<td style=\"width: 26.6968%; height: 20px;\">0.02199<\/td>\n<td style=\"width: 18.7782%; height: 20px;\">0.0209<\/td>\n<td style=\"width: 17.1946%; height: 20px;\">0.05407<\/td>\n<td style=\"width: 28.1674%; height: 20px;\">0.05177<\/td>\n<\/tr>\n<tr style=\"height: 20px;\">\n<td style=\"width: 9.27606%; height: 20px;\">90<\/td>\n<td style=\"width: 26.6968%; height: 20px;\">0.02217<\/td>\n<td style=\"width: 18.7782%; height: 20px;\">0.02134<\/td>\n<td style=\"width: 17.1946%; height: 20px;\">0.05409<\/td>\n<td style=\"width: 28.1674%; height: 20px;\">0.05088<\/td>\n<\/tr>\n<tr style=\"height: 20px;\">\n<td style=\"width: 9.27606%; height: 20px;\">100<\/td>\n<td style=\"width: 26.6968%; height: 20px;\">0.02186<\/td>\n<td style=\"width: 18.7782%; height: 20px;\">0.02106<\/td>\n<td style=\"width: 17.1946%; height: 20px;\">0.05457<\/td>\n<td style=\"width: 28.1674%; height: 20px;\">0.05151<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">\u6bcd\u96c6\u56e3\u304c\u6b63\u898f\u5206\u5e03\u3067\u306a\u3044\u5834\u5408: \u4e8c\u5cf0\u5206\u5e03 vs. \u30b3\u30fc\u30b7\u30fc\u5206\u5e03<\/h3>\n\n\n\n<p>\u30b3\u30fc\u30b7\u30fc\u5206\u5e03\uff08\u8d64\uff09vs. \u4e8c\u5cf0\u5206\u5e03\uff08\u9ed2\uff09\u3002<\/p>\n\n\n\n<pre class=\"prettyprint\">x &lt;- seq(-10,10,by=0.1)\nplot(dcauchy, -10, 10, n=1001, col=&#39;red&#39;) #\u30b3\u30fc\u30b7\u30fc\u5206\u5e03\uff08\u8d64\uff09\nlines(x, hx(x),col=&#34;black&#34;) #\u30d5\u30bf\u30b3\u30d6\u5206\u5e03\uff08\u9ed2\uff09\n<\/pre>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"288\" src=\"https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2025\/06\/cauchy-300x288.png\" alt=\"\" class=\"wp-image-4575\" srcset=\"https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2025\/06\/cauchy-300x288.png 300w, https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2025\/06\/cauchy.png 1426w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/figure>\n<\/div>\n\n\n<pre class=\"prettyprint\">k &lt;- 100000\nN = c(2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100)\nfor (n in N){\n     r &lt;- replicate(k, {\n          x &lt;- rbimodal(n)\n          y &lt;- rcauchy(n) # \u30b3\u30fc\u30b7\u30fc\u5206\u5e03\u306b\u5f93\u3046\u4e71\u6570\u767a\u751f\n          c(t.test(x, y, var.equal=TRUE)$p.value,\n            t.test(x, y, var.equal=FALSE)$p.value,\n            wilcox.test(x, y)$p.value)\n          })\n     p_1 &lt;- r&#091;1, &#093;\n     p_2 &lt;- r&#091;2, &#093;\n     p_3 &lt;- r&#091;3, &#093;\n     reject_1 &lt;- length(p_1&#091;p_1&lt;=0.05&#093;)&#47;k # 5%\u6c34\u6e96\u68c4\u5374\u7387\n     reject_2 &lt;- length(p_2&#091;p_2&lt;=0.05&#093;)&#47;k\n     reject_3 &lt;- length(p_3&#091;p_3&lt;=0.05&#093;)&#47;k\n     cat(n, format(reject_1, 5), format(reject_2, 5), format(reject_3, 5), &#34;\\n&#34;)\n}  <\/pre>\n\n\n\n<h4 class=\"wp-block-heading\"><span style=\"font-size: revert;\">\u7d50\u679c\uff08\u4e8c\u5cf0\u5206\u5e03\u3068\u30b3\u30fc\u30b7\u30fc\u5206\u5e03\uff09<\/span><\/h4>\n\n\n\n<figure class=\"wp-block-table is-style-stripes\">\n<table class=\"has-fixed-layout\" style=\"width: 100%; height: 379px;\">\n<tbody>\n<tr style=\"height: 19px;\">\n<td style=\"height: 18px; width: 25%;\">&nbsp;<\/td>\n<td style=\"height: 18px; width: 92.0239%;\" colspan=\"3\">5%\u6c34\u6e96\u68c4\u5374\u7387<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\"><em>n<\/em><\/td>\n<td style=\"height: 19px; width: 34.2857%;\">Student\u306e<em>t<\/em>\u691c\u5b9a<\/td>\n<td style=\"height: 19px; width: 31.3096%;\">Welch\u306e<em>t<\/em>\u691c\u5b9a<\/td>\n<td style=\"height: 19px; width: 26.4286%;\">Mann\u2013Whitney\u306e<em>U<\/em>\u691c\u5b9a<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">2<\/td>\n<td style=\"height: 19px; width: 34.2857%;\">0.06123<\/td>\n<td style=\"height: 19px; width: 31.3096%;\">0.03007<\/td>\n<td style=\"height: 19px; width: 26.4286%;\">\u2013<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">3<\/td>\n<td style=\"height: 19px; width: 34.2857%;\">0.05921<\/td>\n<td style=\"height: 19px; width: 31.3096%;\">0.04252<\/td>\n<td style=\"height: 19px; width: 26.4286%;\">\u2013<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">4<\/td>\n<td style=\"height: 19px; width: 34.2857%;\">0.049<\/td>\n<td style=\"height: 19px; width: 31.3096%;\">0.03999<\/td>\n<td style=\"height: 19px; width: 26.4286%;\">0.04217<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">5<\/td>\n<td style=\"height: 19px; width: 34.2857%;\">0.04399<\/td>\n<td style=\"height: 19px; width: 31.3096%;\">0.03709<\/td>\n<td style=\"height: 19px; width: 26.4286%;\">0.03969<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">6<\/td>\n<td style=\"height: 19px; width: 34.2857%;\">0.03881<\/td>\n<td style=\"height: 19px; width: 31.3096%;\">0.03345<\/td>\n<td style=\"height: 19px; width: 26.4286%;\">0.05023<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">7<\/td>\n<td style=\"height: 19px; width: 34.2857%;\">0.03627<\/td>\n<td style=\"height: 19px; width: 31.3096%;\">0.03327<\/td>\n<td style=\"height: 19px; width: 26.4286%;\">0.04951<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">8<\/td>\n<td style=\"height: 19px; width: 34.2857%;\">0.03615<\/td>\n<td style=\"height: 19px; width: 31.3096%;\">0.03138<\/td>\n<td style=\"height: 19px; width: 26.4286%;\">0.06096<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">9<\/td>\n<td style=\"height: 19px; width: 34.2857%;\">0.03367<\/td>\n<td style=\"height: 19px; width: 31.3096%;\">0.03047<\/td>\n<td style=\"height: 19px; width: 26.4286%;\">0.05204<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">10<\/td>\n<td style=\"height: 19px; width: 34.2857%;\">0.03342<\/td>\n<td style=\"height: 19px; width: 31.3096%;\">0.02977<\/td>\n<td style=\"height: 19px; width: 26.4286%;\">0.05697<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">20<\/td>\n<td style=\"height: 19px; width: 34.2857%;\">0.02933<\/td>\n<td style=\"height: 19px; width: 31.3096%;\">0.02661<\/td>\n<td style=\"height: 19px; width: 26.4286%;\">0.07293<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">30<\/td>\n<td style=\"height: 19px; width: 34.2857%;\">0.02776<\/td>\n<td style=\"height: 19px; width: 31.3096%;\">0.02695<\/td>\n<td style=\"height: 19px; width: 26.4286%;\">0.08275<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">40<\/td>\n<td style=\"height: 19px; width: 34.2857%;\">0.02662<\/td>\n<td style=\"height: 19px; width: 31.3096%;\">0.02555<\/td>\n<td style=\"height: 19px; width: 26.4286%;\">0.09228<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">50<\/td>\n<td style=\"height: 19px; width: 34.2857%;\">0.02531<\/td>\n<td style=\"height: 19px; width: 31.3096%;\">0.02464<\/td>\n<td style=\"height: 19px; width: 26.4286%;\">0.10031<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">60<\/td>\n<td style=\"height: 19px; width: 34.2857%;\">0.02519<\/td>\n<td style=\"height: 19px; width: 31.3096%;\">0.02456<\/td>\n<td style=\"height: 19px; width: 26.4286%;\">0.10849<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">70<\/td>\n<td style=\"height: 19px; width: 34.2857%;\">0.02444<\/td>\n<td style=\"height: 19px; width: 31.3096%;\">0.02405<\/td>\n<td style=\"height: 19px; width: 26.4286%;\">0.11873<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">80<\/td>\n<td style=\"height: 19px; width: 34.2857%;\">0.02441<\/td>\n<td style=\"height: 19px; width: 31.3096%;\">0.02401<\/td>\n<td style=\"height: 19px; width: 26.4286%;\">0.12666<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">90<\/td>\n<td style=\"height: 19px; width: 34.2857%;\">0.02444<\/td>\n<td style=\"height: 19px; width: 31.3096%;\">0.02302<\/td>\n<td style=\"height: 19px; width: 26.4286%;\">0.13748<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">100<\/td>\n<td style=\"height: 19px; width: 34.2857%;\">0.02375<\/td>\n<td style=\"height: 19px; width: 31.3096%;\">0.02377<\/td>\n<td style=\"height: 19px; width: 26.4286%;\">0.14521<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">\u6bcd\u96c6\u56e3\u304c\u6b63\u898f\u5206\u5e03\u3067\u5e73\u5747\u5024\u3068\u5206\u6563\u304c\u7570\u306a\u308b\u5834\u5408<\/h3>\n\n\n\n<p>\u6b63\u898f\u5206\u5e03\uff08\u5e73\u5747=1\u3001\u6a19\u6e96\u504f\u5dee=2\u3001\u8d64\uff09vs. \u6b63\u898f\u5206\u5e03\uff08\u5e73\u5747\u5024=-1\u3001\u6a19\u6e96\u504f\u5dee=4\u3001\u9ed2\uff09\u3002\u52b9\u679c\u91cf\uff08\u5e73\u5747\u306e\u5dee\u00f7\u6a19\u6e96\u504f\u5dee\uff09\u306f$$\\frac{|1-(-1)|}{\\sqrt{\\frac{2^2+4^2}{2}}} \\fallingdotseq 0.632$$\u3067\u4e2d\u7a0b\u5ea6\u3068\u8a00\u3048\u307e\u3059\uff08<em>d<\/em> = 0.2\uff08\u5c0f\u3055\u3044\u52b9\u679c\uff09\u30010.5\uff08\u4e2d\u7a0b\u5ea6\u306e\u52b9\u679c\uff09\u30010.8\uff08\u5927\u304d\u3044\u52b9\u679c\uff09\uff09\u3002<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"246\" src=\"https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2025\/06\/two_norm2-300x246.png\" alt=\"\" class=\"wp-image-4695\" srcset=\"https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2025\/06\/two_norm2-300x246.png 300w, https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2025\/06\/two_norm2-1024x840.png 1024w, https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2025\/06\/two_norm2-768x630.png 768w, https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2025\/06\/two_norm2.png 1388w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/figure>\n<\/div>\n\n\n<figure class=\"wp-block-table is-style-stripes\">\n<table class=\"has-fixed-layout\" style=\"width: 99.5238%; height: 378px;\">\n<tbody>\n<tr style=\"height: 19px;\">\n<td style=\"height: 18px; width: 25%;\">&nbsp;<\/td>\n<td style=\"height: 18px; width: 97.2832%;\" colspan=\"3\">5%\u6c34\u6e96\u68c4\u5374\u7387<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\"><em>n<\/em><\/td>\n<td style=\"height: 19px; width: 34.2857%;\">Student\u306e<em>t<\/em>\u691c\u5b9a<\/td>\n<td style=\"height: 19px; width: 31.3096%;\">Welch\u306e<em>t<\/em>\u691c\u5b9a<\/td>\n<td style=\"height: 19px; width: 31.6879%;\">Mann\u2013Whitney\u306e<em>U<\/em>\u691c\u5b9a<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">2<\/td>\n<td style=\"height: 19px; width: 34.2857%;\">0.08122<\/td>\n<td style=\"height: 19px; width: 31.3096%;\">0.03849<\/td>\n<td style=\"height: 19px; width: 31.6879%;\">\u2013<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 10px; width: 25%;\">3<\/td>\n<td style=\"height: 10px; width: 34.2857%;\">0.10877<\/td>\n<td style=\"height: 10px; width: 31.3096%;\">0.07941<\/td>\n<td style=\"height: 10px; width: 31.6879%;\">\u2013<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">4<\/td>\n<td style=\"height: 19px; width: 34.2857%;\">0.13293<\/td>\n<td style=\"height: 19px; width: 31.3096%;\">0.10722<\/td>\n<td style=\"height: 19px; width: 31.6879%;\">0.08771<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">5<\/td>\n<td style=\"height: 19px; width: 34.2857%;\">0.15622<\/td>\n<td style=\"height: 19px; width: 31.3096%;\">0.13357<\/td>\n<td style=\"height: 19px; width: 31.6879%;\">0.10983<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">6<\/td>\n<td style=\"height: 19px; width: 34.2857%;\">0.17949<\/td>\n<td style=\"height: 19px; width: 31.3096%;\">0.16056<\/td>\n<td style=\"height: 19px; width: 31.6879%;\">0.14395<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">7<\/td>\n<td style=\"height: 19px; width: 34.2857%;\">0.20341<\/td>\n<td style=\"height: 19px; width: 31.3096%;\">0.18465<\/td>\n<td style=\"height: 19px; width: 31.6879%;\">0.16496<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">8<\/td>\n<td style=\"height: 19px; width: 34.2857%;\">0.22851<\/td>\n<td style=\"height: 19px; width: 31.3096%;\">0.20847<\/td>\n<td style=\"height: 19px; width: 31.6879%;\">0.21961<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">9<\/td>\n<td style=\"height: 19px; width: 34.2857%;\">0.25064<\/td>\n<td style=\"height: 19px; width: 31.3096%;\">0.23274<\/td>\n<td style=\"height: 19px; width: 31.6879%;\">0.2131<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">10<\/td>\n<td style=\"height: 19px; width: 34.2857%;\">0.27669<\/td>\n<td style=\"height: 19px; width: 31.3096%;\">0.25696<\/td>\n<td style=\"height: 19px; width: 31.6879%;\">0.24706<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">20<\/td>\n<td style=\"height: 19px; width: 34.2857%;\">0.499<\/td>\n<td style=\"height: 19px; width: 31.3096%;\">0.48885<\/td>\n<td style=\"height: 19px; width: 31.6879%;\">0.47347<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 27px; width: 25%;\">30<\/td>\n<td style=\"height: 27px; width: 34.2857%;\">0.6711<\/td>\n<td style=\"height: 27px; width: 31.3096%;\">0.66596<\/td>\n<td style=\"height: 27px; width: 31.6879%;\">0.64369<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">40<\/td>\n<td style=\"height: 19px; width: 34.2857%;\">0.79825<\/td>\n<td style=\"height: 19px; width: 31.3096%;\">0.79321<\/td>\n<td style=\"height: 19px; width: 31.6879%;\">0.76642<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">50<\/td>\n<td style=\"height: 19px; width: 34.2857%;\">0.87752<\/td>\n<td style=\"height: 19px; width: 31.3096%;\">0.87767<\/td>\n<td style=\"height: 19px; width: 31.6879%;\">0.85248<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">60<\/td>\n<td style=\"height: 19px; width: 34.2857%;\">0.9303<\/td>\n<td style=\"height: 19px; width: 31.3096%;\">0.927<\/td>\n<td style=\"height: 19px; width: 31.6879%;\">0.9094<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">70<\/td>\n<td style=\"height: 19px; width: 34.2857%;\">0.95973<\/td>\n<td style=\"height: 19px; width: 31.3096%;\">0.95921<\/td>\n<td style=\"height: 19px; width: 31.6879%;\">0.94547<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">80<\/td>\n<td style=\"height: 19px; width: 34.2857%;\">0.97866<\/td>\n<td style=\"height: 19px; width: 31.3096%;\">0.97803<\/td>\n<td style=\"height: 19px; width: 31.6879%;\">0.96824<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">90<\/td>\n<td style=\"height: 19px; width: 34.2857%;\">0.9882<\/td>\n<td style=\"height: 19px; width: 31.3096%;\">0.98743<\/td>\n<td style=\"height: 19px; width: 31.6879%;\">0.98103<\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 25%;\">100<\/td>\n<td style=\"height: 19px; width: 34.2857%;\">0.99358<\/td>\n<td style=\"height: 19px; width: 31.3096%;\">0.99353<\/td>\n<td style=\"height: 19px; width: 31.6879%;\">0.98912<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">\u53c2\u8003\u6587\u732e<\/h2>\n\n\n\n<p>1) \u6c38\u7530\u9756\u30fb&#134071;\u7530\u9053\u5f18\uff081997\uff09\uff0e\u7d71\u8a08\u7684\u591a\u91cd\u6bd4\u8f03\u6cd5\u306e\u57fa\u790e\u3000\u30b5\u30a4\u30a8\u30f3\u30c6\u30a3\u30b9\u30c8\u793e<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\uff082026\u5e741\u67089\u65e5\u66f4\u65b0\uff09 \u30ce\u30f3\u30d1\u30e9\u30e1\u30c8\u30ea\u30c3\u30af\u6cd5\u306b\u95a2\u3059\u308b\u8aa4\u89e3 &#8230;<\/p>\n","protected":false},"author":1,"featured_media":4476,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"om_disable_all_campaigns":false,"_uag_custom_page_level_css":"","_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"_uf_show_specific_survey":0,"_uf_disable_surveys":false,"_locale":"ja","_original_post":"https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/?p=4459","footnotes":""},"categories":[9],"tags":[],"class_list":["post-4459","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-9","ja"],"aioseo_notices":[],"uagb_featured_image_src":{"full":["https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2025\/06\/Student_t_pdf.svg_-1.png",650,520,false],"thumbnail":["https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2025\/06\/Student_t_pdf.svg_-1-150x150.png",150,150,true],"medium":["https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2025\/06\/Student_t_pdf.svg_-1-300x240.png",300,240,true],"medium_large":["https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2025\/06\/Student_t_pdf.svg_-1.png",650,520,false],"large":["https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2025\/06\/Student_t_pdf.svg_-1.png",650,520,false],"1536x1536":["https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2025\/06\/Student_t_pdf.svg_-1.png",650,520,false],"2048x2048":["https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2025\/06\/Student_t_pdf.svg_-1.png",650,520,false],"onepress-blog-small":["https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2025\/06\/Student_t_pdf.svg_-1-300x150.png",300,150,true],"onepress-small":["https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2025\/06\/Student_t_pdf.svg_-1-480x300.png",480,300,true],"onepress-medium":["https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp\/wp-content\/uploads\/2025\/06\/Student_t_pdf.svg_-1-640x400.png",640,400,true]},"uagb_author_info":{"display_name":"RCY","author_link":"https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/author\/charlesy\/"},"uagb_comment_info":0,"uagb_excerpt":"\uff082026\u5e741\u67089\u65e5\u66f4\u65b0\uff09 \u30ce\u30f3\u30d1\u30e9\u30e1\u30c8\u30ea\u30c3\u30af\u6cd5\u306b\u95a2\u3059\u308b\u8aa4\u89e3 ...","_links":{"self":[{"href":"https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp-json\/wp\/v2\/posts\/4459","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp-json\/wp\/v2\/comments?post=4459"}],"version-history":[{"count":240,"href":"https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp-json\/wp\/v2\/posts\/4459\/revisions"}],"predecessor-version":[{"id":6837,"href":"https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp-json\/wp\/v2\/posts\/4459\/revisions\/6837"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp-json\/wp\/v2\/media\/4476"}],"wp:attachment":[{"href":"https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp-json\/wp\/v2\/media?parent=4459"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp-json\/wp\/v2\/categories?post=4459"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/wp-json\/wp\/v2\/tags?post=4459"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}