{"id":483,"date":"2023-07-29T18:29:23","date_gmt":"2023-07-29T18:29:23","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e4%ba%8b%e5%90%8e%e6%96%b9%e5%b7%ae%e5%88%86%e6%9e%90%e6%a3%80%e9%aa%8c\/"},"modified":"2023-07-29T18:29:23","modified_gmt":"2023-07-29T18:29:23","slug":"%e4%ba%8b%e5%90%8e%e6%96%b9%e5%b7%ae%e5%88%86%e6%9e%90%e6%a3%80%e9%aa%8c","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e4%ba%8b%e5%90%8e%e6%96%b9%e5%b7%ae%e5%88%86%e6%9e%90%e6%a3%80%e9%aa%8c\/","title":{"rendered":"\u4f7f\u7528\u65b9\u5dee\u5206\u6790\u8fdb\u884c\u4e8b\u540e\u6d4b\u8bd5\u7684\u6307\u5357"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>\u65b9\u5dee\u5206\u6790<\/strong>\u662f\u4e00\u79cd\u7edf\u8ba1\u68c0\u9a8c\uff0c\u7528\u4e8e\u786e\u5b9a\u4e09\u4e2a\u6216\u66f4\u591a\u72ec\u7acb\u7ec4\u7684\u5e73\u5747\u503c\u4e4b\u95f4\u662f\u5426\u5b58\u5728\u7edf\u8ba1\u663e\u7740\u5dee\u5f02\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u65b9\u5dee\u5206\u6790\u4e2d\u4f7f\u7528\u7684<a href=\"https:\/\/statorials.org\/cn\/\u7edf\u8ba1\u5b66\u4ee5\u7b80\u5355\u76f4\u63a5\u7684\u65b9\u5f0f\u89e3\u91ca\u6982\u5ff5\uff0c\u6211\u4eec\u4f7f\u5b66\u4e60\u7edf\u8ba1\u53d8\u5f97\u66f4\u5bb9\u6613\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u5047\u8bbe<\/a>\u5982\u4e0b\uff1a<\/span><\/p>\n<p><span style=\"color: #000000;\">\u539f\u5047\u8bbe (H <sub>0<\/sub> )\uff1a \u00b5 <sub>1<\/sub> = \u00b5 <sub>2<\/sub> = \u00b5 <sub>3<\/sub> = \u2026 = \u00b5 <sub>k<\/sub> \uff08\u6bcf\u7ec4\u7684\u5e73\u5747\u503c\u76f8\u7b49\uff09<\/span><\/p>\n<p><span style=\"color: #000000;\">\u5907\u62e9\u5047\u8bbe\uff1a(Ha)\uff1a\u81f3\u5c11\u5176\u4e2d\u4e00\u4e2a\u5747\u503c\u4e0e\u5176\u4ed6\u5747\u503c\u4e0d\u540c<\/span><\/p>\n<p><span style=\"color: #000000;\">\u5982\u679c\u65b9\u5dee\u5206\u6790\u7684<a href=\"https:\/\/statorials.org\/cn\/\u7edf\u8ba1\u5b66\u4ee5\u7b80\u5355\u76f4\u63a5\u7684\u65b9\u5f0f\u89e3\u91ca\u6982\u5ff5\uff0c\u6211\u4eec\u4f7f\u5b66\u4e60\u7edf\u8ba1\u53d8\u5f97\u66f4\u5bb9\u6613\/\" target=\"_blank\" rel=\"noopener noreferrer\">p \u503c<\/a>\u4f4e\u4e8e\u663e\u7740\u6027\u6c34\u5e73\uff0c\u6211\u4eec\u53ef\u4ee5\u62d2\u7edd\u539f\u5047\u8bbe\uff0c\u5e76\u5f97\u51fa\u7ed3\u8bba\uff1a\u6211\u4eec\u6709\u8db3\u591f\u7684\u8bc1\u636e\u8868\u660e\u7ec4\u5747\u503c\u4e2d\u81f3\u5c11\u6709\u4e00\u4e2a\u4e0e\u5176\u4ed6\u5747\u503c\u4e0d\u540c\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u7136\u800c\uff0c\u8fd9\u5e76\u6ca1\u6709\u544a\u8bc9\u6211\u4eec<em>\u54ea\u4e9b<\/em>\u7fa4\u4f53\u5f7c\u6b64\u4e0d\u540c\u3002\u8fd9\u53ea\u662f\u544a\u8bc9\u6211\u4eec\u5e76\u975e\u6240\u6709\u7ec4\u7684\u5e73\u5747\u503c\u90fd\u662f\u76f8\u7b49\u7684\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4e3a\u4e86\u51c6\u786e\u5730\u77e5\u9053\u54ea\u4e9b\u7ec4\u5f7c\u6b64\u4e0d\u540c\uff0c\u6211\u4eec\u9700\u8981\u6267\u884c<strong>\u4e8b\u540e\u68c0\u9a8c<\/strong>\uff08\u4e5f\u79f0\u4e3a\u591a\u91cd\u6bd4\u8f83\u68c0\u9a8c\uff09\uff0c\u8fd9\u5c06\u4f7f\u6211\u4eec\u80fd\u591f\u63a2\u7d22\u591a\u4e2a\u7ec4\u7684\u5e73\u5747\u503c\u4e4b\u95f4\u7684\u5dee\u5f02\uff0c\u540c\u65f6\u4e5f\u63a7\u5236\u5bb6\u5ead\u3002\u5408\u7406\u7684\u9519\u8bef\u7387\u3002<\/span><\/p>\n<blockquote>\n<p><span style=\"color: #000000;\"><strong>\u6280\u672f\u8bf4\u660e\uff1a<\/strong>\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u53ea\u6709\u5f53\u65b9\u5dee\u5206\u6790 p \u503c\u5177\u6709\u7edf\u8ba1\u663e\u7740\u6027\u65f6\uff0c\u6211\u4eec\u624d\u5e94\u6267\u884c\u4e8b\u540e\u68c0\u9a8c\u3002\u5982\u679c p \u503c\u4e0d\u5177\u6709\u7edf\u8ba1\u663e\u7740\u6027\uff0c\u5219\u8868\u660e\u6240\u6709\u7ec4\u7684\u5e73\u5747\u503c\u5f7c\u6b64\u6ca1\u6709\u5dee\u5f02\u3002\u56e0\u6b64\uff0c\u65e0\u9700\u6267\u884c\u4e8b\u540e\u6d4b\u8bd5\u6765\u786e\u5b9a\u54ea\u4e9b\u7ec4\u5f7c\u6b64\u4e0d\u540c\u3002<\/span><\/p>\n<\/blockquote>\n<h2><strong><span style=\"color: #000000;\">\u5bb6\u5ead\u9519\u8bef\u7387<\/span><\/strong><\/h2>\n<p><span style=\"color: #000000;\">\u5982\u524d\u6240\u8ff0\uff0c\u4e8b\u540e\u68c0\u9a8c\u4f7f\u6211\u4eec\u80fd\u591f\u68c0\u9a8c\u591a\u4e2a\u7ec4\u5747\u503c\u4e4b\u95f4\u7684\u5dee\u5f02\uff0c\u540c\u65f6\u8fd8\u63a7\u5236<strong>\u6bcf\u4e2a\u65cf\u7684\u9519\u8bef\u7387<\/strong>\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u5728<a href=\"https:\/\/statorials.org\/cn\/\u7edf\u8ba1\u5b66\u4ee5\u7b80\u5355\u76f4\u63a5\u7684\u65b9\u5f0f\u89e3\u91ca\u6982\u5ff5\uff0c\u6211\u4eec\u4f7f\u5b66\u4e60\u7edf\u8ba1\u53d8\u5f97\u66f4\u5bb9\u6613\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u5047\u8bbe\u68c0\u9a8c<\/a>\u4e2d\uff0c\u603b\u662f\u5b58\u5728 I \u7c7b\u9519\u8bef\u7387\uff0c\u5b83\u7531\u6211\u4eec\u7684\u663e\u7740\u6027\u6c34\u5e73 (alpha) \u5b9a\u4e49\uff0c\u5e76\u544a\u8bc9\u6211\u4eec\u62d2\u7edd\u5b9e\u9645\u4e0a\u4e3a\u771f\u7684\u539f\u5047\u8bbe\u7684\u6982\u7387\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u5b83\u662f\u83b7\u5f97\u201c\u5047\u9633\u6027\u201d\u7684\u6982\u7387\uff0c\u4e5f\u5c31\u662f\u8bf4\uff0c\u5f53\u6211\u4eec\u58f0\u79f0\u5404\u7ec4\u4e4b\u95f4\u5b58\u5728\u7edf\u8ba1\u663e\u7740\u5dee\u5f02\u65f6\uff0c\u4f46\u5b9e\u9645\u4e0a\u60c5\u51b5\u5e76\u975e\u5982\u6b64\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u5f53\u6211\u4eec\u8fdb\u884c\u5047\u8bbe\u68c0\u9a8c\u65f6\uff0cI \u7c7b\u9519\u8bef\u7387\u7b49\u4e8e\u663e\u7740\u6027\u6c34\u5e73\uff0c\u901a\u5e38\u9009\u62e9 0.01\u30010.05 \u6216 0.10\u3002\u7136\u800c\uff0c\u5f53\u6211\u4eec\u540c\u65f6\u8fd0\u884c\u591a\u4e2a\u5047\u8bbe\u68c0\u9a8c\u65f6\uff0c\u5f97\u5230\u5047\u9633\u6027\u7684\u53ef\u80fd\u6027\u5c31\u4f1a\u589e\u52a0\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4f8b\u5982\uff0c\u5047\u8bbe\u6211\u4eec\u63b7\u51fa\u4e00\u4e2a 20 \u9762\u7684\u9ab0\u5b50\u3002\u9ab0\u5b50\u843d\u5728\u201c1\u201d\u4e0a\u7684\u6982\u7387\u4ec5\u4e3a 5%\u3002\u4f46\u5982\u679c\u4f60\u540c\u65f6\u63b7\u4e24\u4e2a\u9ab0\u5b50\uff0c\u5176\u4e2d\u4e00\u4e2a\u9ab0\u5b50\u843d\u5728\u201c1\u201d\u4e0a\u7684\u6982\u7387\u5c31\u4f1a\u589e\u52a0\u5230 9.75%\u3002\u5982\u679c\u6211\u4eec\u540c\u65f6\u63b7 5 \u4e2a\u9ab0\u5b50\uff0c\u6982\u7387\u5c31\u4f1a\u589e\u52a0\u5230 22.6%\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u6211\u4eec\u63b7\u7684\u9ab0\u5b50\u8d8a\u591a\uff0c\u5176\u4e2d\u4e00\u4e2a\u9ab0\u5b50\u843d\u5230\u201c1\u201d\u7684\u6982\u7387\u5c31\u8d8a\u9ad8\u3002\u540c\u6837\uff0c\u5982\u679c\u6211\u4eec\u4f7f\u7528 0.05 \u7684\u663e\u7740\u6027\u6c34\u5e73\u540c\u65f6\u8fd0\u884c\u591a\u4e2a\u5047\u8bbe\u68c0\u9a8c\uff0c\u5219\u5f97\u5230\u5047\u9633\u6027\u7684\u6982\u7387\u4f1a\u589e\u52a0\u5230\u8d85\u8fc7 0.05\u3002<\/span><\/p>\n<h2><span style=\"color: #000000;\"><strong>\u65b9\u5dee\u5206\u6790\u4e2d\u7684\u591a\u91cd\u6bd4\u8f83<\/strong><\/span><\/h2>\n<p><span style=\"color: #000000;\">\u5f53\u6211\u4eec\u8fdb\u884c\u65b9\u5dee\u5206\u6790\u65f6\uff0c\u6211\u4eec\u7ecf\u5e38\u6bd4\u8f83\u4e09\u4e2a\u6216\u66f4\u591a\u7ec4\u3002\u56e0\u6b64\uff0c\u5f53\u6211\u4eec\u8fdb\u884c\u4e8b\u540e\u68c0\u9a8c\u6765\u63a2\u7d22\u7ec4\u5747\u503c\u4e4b\u95f4\u7684\u5dee\u5f02\u65f6\uff0c\u6211\u4eec\u60f3\u8981\u63a2\u7d22\u591a\u4e2a<strong>\u6210\u5bf9<\/strong>\u6bd4\u8f83\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4f8b\u5982\uff0c\u5047\u8bbe\u6211\u4eec\u6709\u56db\u4e2a\u7ec4\uff1aA\u3001B\u3001C \u548c D\u3002\u8fd9\u610f\u5473\u7740\u6211\u4eec\u8981\u901a\u8fc7\u4e8b\u540e\u68c0\u9a8c\u68c0\u67e5\u603b\u5171\u516d\u4e2a\u6210\u5bf9\u6bd4\u8f83\uff1a<\/span><\/p>\n<p> <span style=\"color: #000000;\">A \u2013 B\uff08A\u7ec4\u5e73\u5747\u503c\u4e0eB\u7ec4\u5e73\u5747\u503c\u4e4b\u5dee\uff09<\/span><br \/><span style=\"color: #000000;\">\u4ea4\u6d41\u7535<\/span><br \/><span style=\"color: #000000;\">\u516c\u544a<\/span><br \/><span style=\"color: #000000;\">\u516c\u5143\u524d<\/span><br \/><span style=\"color: #000000;\">\u6f2b\u753b<\/span><br \/><span style=\"color: #000000;\">\u5149\u76d8<\/span><\/p>\n<p><span style=\"color: #000000;\">\u5982\u679c\u6211\u4eec\u6709\u56db\u4e2a\u4ee5\u4e0a\u7684\u7ec4\uff0c\u6211\u4eec\u60f3\u8981\u6267\u884c\u7684\u6210\u5bf9\u6bd4\u8f83\u7684\u6570\u91cf\u53ea\u4f1a\u589e\u52a0\u66f4\u591a\u3002\u4e0b\u8868\u8bf4\u660e\u4e86\u4e0e\u6bcf\u4e2a\u7ec4\u6570\u76f8\u5173\u7684\u6210\u5bf9\u6bd4\u8f83\u7684\u6570\u91cf\u4ee5\u53ca\u6bcf\u4e2a\u65cf\u7684\u9519\u8bef\u7387\uff1a<\/span><\/p>\n<p><span style=\"color: #000000;\">\u8bf7\u6ce8\u610f\uff0c\u6bcf\u4e2a\u7cfb\u5217\u7684\u9519\u8bef\u7387\u968f\u7740\u7ec4\u6570\uff08\u4ee5\u53ca\u56e0\u6b64\u6210\u5bf9\u6bd4\u8f83\u7684\u6570\u91cf\uff09\u7684\u589e\u52a0\u800c\u8fc5\u901f\u589e\u52a0\u3002\u4e8b\u5b9e\u4e0a\uff0c\u4e00\u65e6\u6211\u4eec\u8fbe\u5230\u516d\u7ec4\uff0c\u6211\u4eec\u5f97\u5230\u5047\u9633\u6027\u7684\u51e0\u7387\u5b9e\u9645\u4e0a\u5c31\u8d85\u8fc7 50%\uff01<\/span><\/p>\n<p><span style=\"color: #000000;\">\u8fd9\u610f\u5473\u7740\uff0c\u5982\u679c\u6211\u4eec\u5fc5\u987b\u8fdb\u884c\u5982\u6b64\u591a\u7684\u6210\u5bf9\u6bd4\u8f83\uff0c\u5e76\u4e14\u77e5\u9053\u6211\u4eec\u7684\u5bb6\u5ead\u9519\u8bef\u7387\u5982\u6b64\u4e4b\u9ad8\uff0c\u6211\u4eec\u5c31\u4f1a\u5bf9\u6211\u4eec\u7684\u7ed3\u679c\u4ea7\u751f\u4e25\u91cd\u6000\u7591\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u5e78\u8fd0\u7684\u662f\uff0c\u4e8b\u540e\u6d4b\u8bd5\u4f7f\u6211\u4eec\u80fd\u591f\u5728\u7ec4\u4e4b\u95f4\u8fdb\u884c\u591a\u91cd\u6bd4\u8f83\uff0c\u540c\u65f6\u6309\u5bb6\u5ead\u63a7\u5236\u9519\u8bef\u7387\u3002<\/span><\/p>\n<h2><span style=\"color: #000000;\"><strong>\u793a\u4f8b\uff1a\u4f7f\u7528\u4e8b\u540e\u68c0\u9a8c\u7684\u5355\u5411\u65b9\u5dee\u5206\u6790<\/strong><\/span><\/h2>\n<p><span style=\"color: #000000;\">\u4ee5\u4e0b\u793a\u4f8b\u8bf4\u660e\u5982\u4f55\u4f7f\u7528\u4e8b\u540e\u68c0\u9a8c\u6267\u884c <a href=\"https:\/\/statorials.org\/cn\/\u5355\u5411\u65b9\u5dee\u5206\u6790\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u5355\u5411\u65b9\u5dee\u5206\u6790<\/a>\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\"><em><strong>\u6ce8\u610f\uff1a<\/strong>\u6b64\u793a\u4f8b\u4f7f\u7528 R \u7f16\u7a0b\u8bed\u8a00\uff0c\u4f46\u60a8\u65e0\u9700\u4e86\u89e3 R \u5373\u53ef\u7406\u89e3\u6d4b\u8bd5\u7ed3\u679c\u6216\u5173\u952e\u8981\u70b9\u3002<\/em><\/span><\/p>\n<p><span style=\"color: #000000;\">\u9996\u5148\uff0c\u6211\u4eec\u5c06\u521b\u5efa\u4e00\u4e2a\u5305\u542b\u56db\u7ec4\uff08A\u3001B\u3001C\u3001D\uff09\u7684\u6570\u636e\u96c6\uff0c\u6bcf\u7ec4\u6709 20 \u4e2a\u89c2\u6d4b\u503c\uff1a<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#make this example reproducible\n<span style=\"color: #000000;\">set.seed(1)<\/span>\n\n#load <em>tidyr<\/em> library to convert data from wide to long format<\/span>\nlibrary(tidyr)\n\n<span style=\"color: #008080;\">#create wide dataset\n<\/span>data &lt;- data.frame(A = runif(20, 2, 5),\n                   B = runif(20, 3, 5),\n                   C = runif(20, 3, 6),\n                   D = runif(20, 4, 6))\n\n<span style=\"color: #008080;\">#convert to long dataset for ANOVA\n<\/span>data_long &lt;- gather(data, key = \"group\", value = \"amount\", A, B, C, D)\n\n<span style=\"color: #008080;\">#view first six lines of dataset\n<\/span>head(data_long)\n\n# group amount\n#1 To 2.796526\n#2 A 3.116372\n#3 A 3.718560\n#4 A 4.724623\n#5 A 2.605046\n#6 A 4.695169\n<\/strong><\/pre>\n<p><span style=\"color: #000000;\">\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u5c06\u5bf9\u6570\u636e\u96c6\u8fdb\u884c\u5355\u5411\u65b9\u5dee\u5206\u6790\uff1a<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#fit anova model\n<\/span>anova_model &lt;- aov(amount ~ group, data = data_long)\n\n<span style=\"color: #008080;\">#view summary of anova model\n<\/span>summary(anova_model)\n\n# Df Sum Sq Mean Sq F value Pr(&gt;F)    \n#group 3 25.37 8.458 17.66 8.53e-09 ***\n#Residuals 76 36.39 0.479            \n<\/strong><\/pre>\n<p><span style=\"color: #000000;\">\u4ece\u65b9\u5dee\u5206\u6790\u8868\u7ed3\u679c\u4e2d\uff0c\u6211\u4eec\u770b\u5230 F \u7edf\u8ba1\u91cf\u4e3a 17.66\uff0c\u76f8\u5e94\u7684 p \u503c\u975e\u5e38\u5c0f\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u8fd9\u610f\u5473\u7740\u6211\u4eec\u6709\u8db3\u591f\u7684\u8bc1\u636e\u6765\u62d2\u7edd\u6240\u6709\u7ec4\u5747\u503c\u76f8\u7b49\u7684\u539f\u5047\u8bbe\u3002\u7136\u540e\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u4e8b\u540e\u68c0\u9a8c\u6765\u786e\u5b9a\u54ea\u4e9b\u7ec4\u5747\u503c\u5f7c\u6b64\u4e0d\u540c\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u6211\u4eec\u5c06\u56de\u987e\u4ee5\u4e0b\u4e8b\u540e\u6d4b\u8bd5\u7684\u793a\u4f8b\uff1a<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Tukey \u6d4b\u8bd5<\/strong>\u2013 \u5f53\u60a8\u60f3\u8981\u8fdb\u884c\u6240\u6709\u53ef\u80fd\u7684\u6210\u5bf9\u6bd4\u8f83\u65f6\u5f88\u6709\u7528<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>Holm \u65b9\u6cd5<\/strong>\u2013 \u6bd4 Tukey \u6d4b\u8bd5\u7a0d\u5fae\u4fdd\u5b88\u7684\u6d4b\u8bd5<\/span><\/p>\n<p><span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/cn\/\u9093\u5c3c\u7279\u68c0\u9a8c\/\" target=\"_blank\" rel=\"noopener noreferrer\"><strong>Dunnett \u6821\u6b63<\/strong><\/a>\u2013 \u5f53\u60a8\u60f3\u8981\u5c06\u6bcf\u4e2a\u7ec4\u7684\u5747\u503c\u4e0e\u63a7\u5236\u5747\u503c\u8fdb\u884c\u6bd4\u8f83\u5e76\u4e14\u4e0d\u60f3\u5c06\u5904\u7406\u5747\u503c\u76f8\u4e92\u6bd4\u8f83\u65f6\u975e\u5e38\u6709\u7528\u3002<\/span><\/p>\n<h2><span style=\"color: #000000;\"><strong>\u56fe\u57fa\u6d4b\u8bd5<\/strong><\/span><\/h2>\n<p><span style=\"color: #000000;\">\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u5185\u7f6e\u7684 R \u51fd\u6570<strong>TukeyHSD()<\/strong>\u8fdb\u884c\u591a\u91cd\u6bd4\u8f83\u7684 Tukey \u6d4b\u8bd5\uff0c\u5982\u4e0b\u6240\u793a\uff1a<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#perform Tukey's Test for multiple comparisons\n<\/span>TukeyHSD(anova_model, conf.level=.95) \n\n#Tukey multiple comparisons of means\n# 95% family-wise confidence level\n#\n#Fit: aov(formula = amount ~ group, data = data_long)\n#\n#$group\n# diff lwr upr p adj\n#BA 0.2822630 -0.292540425 0.8570664 0.5721402\n#CA 0.8561388 0.281335427 1.4309423 0.0011117\n#DA 1.4676027 0.892799258 2.0424061 0.0000000\n#CB 0.5738759 -0.000927561 1.1486793 0.0505270\n#DB 1.1853397 0.610536271 1.7601431 0.0000041\n#DC 0.6114638 0.036660419 1.1862672 0.0326371\n<\/strong><\/pre>\n<p><span style=\"color: #000000;\">\u8bf7\u6ce8\u610f\uff0c\u6211\u4eec\u6307\u5b9a\u7f6e\u4fe1\u5ea6\u4e3a 95%\uff0c\u8fd9\u610f\u5473\u7740\u6211\u4eec\u5e0c\u671b\u6bcf\u4e2a\u65cf\u7684\u9519\u8bef\u7387\u4e3a 0.05\u3002 R \u4e3a\u6211\u4eec\u63d0\u4f9b\u4e86\u4e24\u4e2a\u6307\u6807\u6765\u6bd4\u8f83\u6bcf\u4e2a\u6210\u5bf9\u5dee\u5f02\uff1a<\/span><\/p>\n<ul>\n<li><span style=\"color: #000000;\">\u5e73\u5747\u5dee\u7684\u7f6e\u4fe1\u533a\u95f4\uff08\u7531<em>lwr<\/em>\u548c<em>upr<\/em>\u7684\u503c\u7ed9\u51fa\uff09<\/span><\/li>\n<li><span style=\"color: #000000;\">\u6839\u636e\u5747\u503c\u5dee\u8c03\u6574 p \u503c<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u7f6e\u4fe1\u533a\u95f4\u548c p \u503c\u5c06\u5f97\u51fa\u76f8\u540c\u7684\u7ed3\u8bba\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4f8b\u5982\uff0cC \u7ec4\u548c A \u7ec4\u4e4b\u95f4\u7684\u5747\u503c\u5dee\u7684 95% \u7f6e\u4fe1\u533a\u95f4\u4e3a (0.2813, 1.4309)\uff0c\u5e76\u4e14\u7531\u4e8e\u8be5\u533a\u95f4\u4e0d\u5305\u542b\u96f6\uff0c\u6240\u4ee5\u6211\u4eec\u77e5\u9053\u8fd9\u4e24\u7ec4\u5747\u503c\u4e4b\u95f4\u7684\u5dee\u5f02\u5177\u6709\u7edf\u8ba1\u663e\u7740\u6027\u3002\u7279\u522b\u662f\uff0c\u6211\u4eec\u77e5\u9053\u5dee\u5f02\u662f\u6b63\u7684\uff0c\u56e0\u4e3a\u7f6e\u4fe1\u533a\u95f4\u7684\u4e0b\u9650\u5927\u4e8e\u96f6\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u540c\u6837\uff0cC \u7ec4\u548c A \u7ec4\u4e4b\u95f4\u7684\u5747\u503c\u5dee\u5f02\u7684 p \u503c\u4e3a 0.0011\uff0c\u4f4e\u4e8e\u6211\u4eec\u7684\u663e\u7740\u6027\u6c34\u5e73 0.05\uff0c\u8fd9\u4e5f\u8868\u660e\u8fd9\u4e24\u7ec4\u5747\u503c\u4e4b\u95f4\u7684\u5dee\u5f02\u5177\u6709\u7edf\u8ba1\u663e\u7740\u6027\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u6211\u4eec\u8fd8\u53ef\u4ee5\u4f7f\u7528 R \u4e2d\u7684<strong>plot()<\/strong>\u51fd\u6570\u53ef\u89c6\u5316 Tukey \u6d4b\u8bd5\u4ea7\u751f\u7684 95% \u7f6e\u4fe1\u533a\u95f4\uff1a<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong>plot(TukeyHSD(anova_model, conf.level=.95))\n<\/strong><\/pre>\n<p><span style=\"color: #000000;\">\u5982\u679c\u533a\u95f4\u5305\u542b\u96f6\uff0c\u5219\u6211\u4eec\u77e5\u9053\u7ec4\u5747\u503c\u4e4b\u95f4\u7684\u5dee\u5f02\u4e0d\u5177\u6709\u7edf\u8ba1\u663e\u7740\u6027\u3002\u5728\u4e0a\u9762\u7684\u793a\u4f8b\u4e2d\uff0cBA \u548c CB \u7684\u5dee\u5f02\u4e0d\u5177\u6709\u7edf\u8ba1\u663e\u7740\u6027\uff0c\u4f46\u5176\u4ed6\u56db\u4e2a\u6210\u5bf9\u6bd4\u8f83\u7684\u5dee\u5f02\u5177\u6709\u7edf\u8ba1\u663e\u7740\u6027\u3002<\/span><\/p>\n<h2><span style=\"color: #000000;\"><strong>\u970d\u5c14\u59c6\u6cd5<\/strong><\/span><\/h2>\n<p><span style=\"color: #000000;\">\u6211\u4eec\u53ef\u4ee5\u6267\u884c\u7684\u53e6\u4e00\u4e2a\u4e8b\u540e\u6d4b\u8bd5\u662f\u970d\u5c14\u59c6\u65b9\u6cd5\u3002\u8be5\u68c0\u9a8c\u901a\u5e38\u88ab\u8ba4\u4e3a\u6bd4 Tukey \u68c0\u9a8c\u66f4\u4e3a\u4fdd\u5b88\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u6211\u4eec\u53ef\u4ee5\u5728 R \u4e2d\u4f7f\u7528\u4ee5\u4e0b\u4ee3\u7801\u6765\u8fd0\u884c Holm \u65b9\u6cd5\u8fdb\u884c\u591a\u4e2a\u6210\u5bf9\u6bd4\u8f83\uff1a<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#perform holm's method for multiple comparisons<\/span>\npairwise.t.test(data_long$amount, data_long$group, p.adjust=\"holm\") \n# Pairwise comparisons using t tests with pooled SD \n#\n#data: data_long$amount and data_long$group \n#\n#ABC\n#B 0.20099 - -      \n#C 0.00079 0.02108 -      \n#D 1.9e-08 3.4e-06 0.01974\n#\n#P value adjustment method: holm<\/strong><\/pre>\n<p><span style=\"color: #000000;\">\u8be5\u6d4b\u8bd5\u4e3a\u6bcf\u4e2a\u6210\u5bf9\u6bd4\u8f83\u63d0\u4f9b p \u503c\u7f51\u683c\u3002\u4f8b\u5982\uff0cA \u7ec4\u548c B \u7ec4\u5e73\u5747\u503c\u4e4b\u95f4\u5dee\u5f02\u7684 p \u503c\u4e3a 0.20099\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u5982\u679c\u5c06\u6b64\u68c0\u9a8c\u7684 p \u503c\u4e0e Tukey \u68c0\u9a8c\u7684 p \u503c\u8fdb\u884c\u6bd4\u8f83\uff0c\u60a8\u4f1a\u53d1\u73b0\u9664\u4e86 C \u7ec4\u548c D \u7ec4\u4e4b\u95f4\u7684\u5dee\u5f02\u5916\uff0c\u6bcf\u4e2a\u6210\u5bf9\u6bd4\u8f83\u90fd\u4f1a\u5f97\u51fa\u76f8\u540c\u7684\u7ed3\u8bba\u3002 &#8211; Tukey \u6d4b\u8bd5\u4e2d\u7684\u5dee\u5f02\u503c\u4e3a 0.0505\uff0c\u800c Holm \u65b9\u6cd5\u4e2d\u7684\u5dee\u5f02\u503c\u4e3a 0.02108\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u56e0\u6b64\uff0c\u4f7f\u7528Tukey&#8217;s\u68c0\u9a8c\uff0c\u6211\u4eec\u5f97\u51fa\u7ed3\u8bba\uff0cC\u7ec4\u548cD\u7ec4\u4e4b\u95f4\u7684\u5dee\u5f02\u57280.05\u663e\u7740\u6027\u6c34\u5e73\u4e0a\u4e0d\u5177\u6709\u7edf\u8ba1\u5b66\u663e\u7740\u6027\uff0c\u4f46\u4f7f\u7528Holm&#8217;s\u65b9\u6cd5\uff0c\u6211\u4eec\u5f97\u51fa\u7ed3\u8bba\uff0cC\u7ec4\u548cD\u7ec4\u4e4b\u95f4\u7684\u5dee\u5f02<em>\u5177\u6709<\/em>\u7edf\u8ba1\u5b66\u663e\u7740\u6027\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4e00\u822c\u6765\u8bf4\uff0cHolm \u65b9\u6cd5\u4ea7\u751f\u7684 p \u503c\u5f80\u5f80\u4f4e\u4e8e Tukey \u68c0\u9a8c\u4ea7\u751f\u7684 p \u503c\u3002<\/span><\/p>\n<h2><span style=\"color: #000000;\"><strong>\u9093\u5c3c\u7279\u4fee\u6b63<\/strong><\/span><\/h2>\n<p><span style=\"color: #000000;\">\u6211\u4eec\u53ef\u4ee5\u7528\u4e8e\u591a\u91cd\u6bd4\u8f83\u7684\u53e6\u4e00\u79cd\u65b9\u6cd5\u662f Dunett \u6821\u6b63\u3002\u5f53\u6211\u4eec\u60f3\u8981\u5c06\u6bcf\u4e2a\u7ec4\u7684\u5747\u503c\u4e0e\u63a7\u5236\u5747\u503c\u8fdb\u884c\u6bd4\u8f83\u5e76\u4e14\u6211\u4eec\u4e0d\u60f3\u5c06\u6cbb\u7597\u5747\u503c\u76f8\u4e92\u6bd4\u8f83\u65f6\uff0c\u6211\u4eec\u4f1a\u4f7f\u7528\u8fd9\u79cd\u65b9\u6cd5\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4f8b\u5982\uff0c\u4f7f\u7528\u4e0b\u9762\u7684\u4ee3\u7801\uff0c\u6211\u4eec\u5c06 B\u3001C \u548c D \u7ec4\u7684\u5747\u503c\u4e0e A \u7ec4\u7684\u5747\u503c\u8fdb\u884c\u6bd4\u8f83\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u4f7f\u7528 A \u7ec4\u4f5c\u4e3a\u5bf9\u7167\u7ec4\uff0c\u5e76\u4e14\u5bf9 B\u3001C \u7ec4\u4e4b\u95f4\u7684\u5dee\u5f02\u4e0d\u611f\u5174\u8da3., \u548c D.<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#load multcomp library necessary for using Dunnett's Correction<\/span>\nlibrary(multicomp)\n\n<span style=\"color: #008080;\">#convert group variable to factor \n<\/span>data_long$group &lt;- as.factor(data_long$group)\n\n<span style=\"color: #008080;\">#fit anova model\n<\/span>anova_model &lt;- aov(amount ~ group, data = data_long)\n\n<span style=\"color: #008080;\">#performcomparisons\n<\/span>dunnet_comparison &lt;- glht(anova_model, linfct = mcp(group = \"Dunnett\"))\n\n<span style=\"color: #008080;\">#view summary of comparisons\n<\/span>summary(dunnet_comparison)\n\n#Multiple Comparisons of Means: Dunnett Contrasts\n#\n#Fit: aov(formula = amount ~ group, data = data_long)\n#\n#Linear Assumptions:\n#Estimate Std. Error t value Pr(&gt;|t|)    \n#B - A == 0 0.2823 0.2188 1.290 0.432445    \n#C - A == 0 0.8561 0.2188 3.912 0.000545 ***\n#D - A == 0 1.4676 0.2188 6.707 &lt; 1e-04 ***<\/strong><\/pre>\n<p><span style=\"color: #000000;\">\u4ece\u8f93\u51fa\u4e2d\u7684 p \u503c\uff0c\u6211\u4eec\u53ef\u4ee5\u770b\u5230\u4ee5\u4e0b\u5185\u5bb9\uff1a<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">B \u7ec4\u4e0e A \u7ec4\u5747\u503c\u4e4b\u95f4\u7684\u5dee\u5f02\u5728 0.05 \u663e\u7740\u6027\u6c34\u5e73\u4e0a<em>\u4e0d\u5177\u6709<\/em>\u7edf\u8ba1\u5b66\u663e\u7740\u6027\u3002\u6b64\u6d4b\u8bd5\u7684 p \u503c\u4e3a<strong>0.4324<\/strong> \u3002<\/span><\/li>\n<li> <span style=\"color: #000000;\">C\u7ec4\u548cA\u7ec4\u5e73\u5747\u503c\u4e4b\u95f4\u7684\u5dee\u5f02<em>\u5177\u6709<\/em>\u7edf\u8ba1\u5b66\u663e\u7740\u6027\uff0c\u663e\u7740\u6027\u6c34\u5e73\u4e3a0.05\u3002\u6b64\u6d4b\u8bd5\u7684 p \u503c\u4e3a<strong>0.0005<\/strong> \u3002<\/span><\/li>\n<li> <span style=\"color: #000000;\">D \u7ec4\u548c A \u7ec4\u5e73\u5747\u503c\u4e4b\u95f4\u7684\u5dee\u5f02<em>\u5177\u6709<\/em>\u7edf\u8ba1\u663e\u7740\u6027\uff0c\u663e\u7740\u6027\u6c34\u5e73\u4e3a 0.05\u3002\u6b64\u6d4b\u8bd5\u7684 p \u503c\u4e3a<strong>0.00004<\/strong> \u3002<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u5982\u524d\u6240\u8ff0\uff0c\u6b64\u65b9\u6cd5\u5c06 A \u7ec4\u89c6\u4e3a\u201c\u5bf9\u7167\u201d\u7ec4\uff0c\u5e76\u7b80\u5355\u5730\u5c06\u6240\u6709\u5176\u4ed6\u7ec4\u7684\u5e73\u5747\u503c\u4e0e A \u7ec4\u7684\u5e73\u5747\u503c\u8fdb\u884c\u6bd4\u8f83\u3002\u8bf7\u6ce8\u610f\uff0c\u6ca1\u6709\u5bf9 B\u3001C \u548c D \u7ec4\u4e4b\u95f4\u7684\u5dee\u5f02\u8fdb\u884c\u6d4b\u8bd5\uff0c\u56e0\u4e3a\u6211\u4eec\u4e0d\u8fd9\u6837\u505a\u4e0d\u8981\u8fd9\u6837\u505a\u3002\u6211\u5bf9\u8fd9\u4e9b\u7fa4\u4f53\u4e4b\u95f4\u7684\u5dee\u5f02\u4e0d\u611f\u5174\u8da3\u3002<\/span><\/p>\n<h2><strong><span style=\"color: #000000;\">\u5173\u4e8e\u4e8b\u540e\u6d4b\u8bd5\u548c\u7edf\u8ba1\u529f\u6548\u7684\u8bf4\u660e<\/span><\/strong><\/h2>\n<p><span style=\"color: #000000;\">\u4e8b\u540e\u6d4b\u8bd5\u5728\u63a7\u5236\u65cf\u9519\u8bef\u7387\u65b9\u9762\u505a\u5f97\u975e\u5e38\u51fa\u8272\uff0c\u4f46\u4ee3\u4ef7\u662f\u5b83\u4eec\u964d\u4f4e\u4e86\u6bd4\u8f83\u7684\u7edf\u8ba1\u529f\u6548\u3002\u4e8b\u5b9e\u4e0a\uff0c\u964d\u4f4e\u5bb6\u65cf\u9519\u8bef\u7387\u7684\u552f\u4e00\u65b9\u6cd5\u662f\u5bf9\u6240\u6709\u4e2a\u4f53\u6bd4\u8f83\u4f7f\u7528\u8f83\u4f4e\u7684\u663e\u7740\u6027\u6c34\u5e73\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4f8b\u5982\uff0c\u5f53\u6211\u4eec\u4f7f\u7528 Tukey \u68c0\u9a8c\u8fdb\u884c\u516d\u6b21\u914d\u5bf9\u6bd4\u8f83\u5e76\u4e14\u5e0c\u671b\u5c06\u65cf\u9519\u8bef\u7387\u4fdd\u6301\u5728 0.05 \u65f6\uff0c\u6211\u4eec\u5e94\u8be5\u5bf9\u6bcf\u4e2a\u5355\u72ec\u7684\u663e\u7740\u6027\u6c34\u5e73\u4f7f\u7528\u5927\u7ea6 0.011 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#000000;\">\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u5728\u6267\u884c\u65b9\u5dee\u5206\u6790<em>\u4e4b\u524d\uff0c<\/em>\u60a8\u5fc5\u987b\u51c6\u786e\u786e\u5b9a\u8981\u8fdb\u884c\u6bd4\u8f83\u7684\u7ec4\u4ee5\u53ca\u5c06\u4f7f\u7528\u54ea\u4e2a\u4e8b\u540e\u68c0\u9a8c\u6765\u8fdb\u884c\u8fd9\u4e9b\u6bd4\u8f83\u3002\u5426\u5219\uff0c\u5982\u679c\u60a8\u53ea\u662f\u770b\u5230\u54ea\u4e2a\u4e8b\u540e\u6d4b\u8bd5\u4ea7\u751f\u4e86\u7edf\u8ba1\u4e0a\u663e\u7740\u7684\u7ed3\u679c\uff0c\u5c31\u4f1a\u964d\u4f4e\u7814\u7a76\u7684\u5b8c\u6574\u6027\u3002<\/span><\/p>\n<h2><span style=\"color: #000000;\"><strong>\u7ed3\u8bba<\/strong><\/span><\/h2>\n<p><span style=\"color: #000000;\">\u5728\u8fd9\u7bc7\u6587\u7ae0\u4e2d\uff0c\u6211\u4eec\u4e86\u89e3\u4e86\u4ee5\u4e0b\u5185\u5bb9\uff1a<\/span><\/p>\n<ul>\n<li><span style=\"color: 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