{"id":593,"date":"2023-07-29T09:47:17","date_gmt":"2023-07-29T09:47:17","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e8%82%af%e5%be%b7%e5%b0%94%e6%96%af%e5%a4%b4\/"},"modified":"2023-07-29T09:47:17","modified_gmt":"2023-07-29T09:47:17","slug":"%e8%82%af%e5%be%b7%e5%b0%94%e6%96%af%e5%a4%b4","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e8%82%af%e5%be%b7%e5%b0%94%e6%96%af%e5%a4%b4\/","title":{"rendered":"Kendall \u7684 tau\uff1a\u5b9a\u4e49 + \u793a\u4f8b"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">\u5728\u7edf\u8ba1\u5b66\u4e2d\uff0c<strong>\u76f8\u5173\u6027<\/strong>\u662f\u6307\u4e24\u4e2a\u53d8\u91cf\u4e4b\u95f4\u5173\u7cfb\u7684\u5f3a\u5ea6\u548c\u65b9\u5411\u3002\u76f8\u5173\u7cfb\u6570\u7684\u503c\u8303\u56f4\u4e3a -1 \u5230 1\uff0c\u5176\u4e2d -1 \u8868\u793a\u5b8c\u5168\u8d1f\u5173\u7cfb\uff0c0 \u8868\u793a\u6ca1\u6709\u5173\u7cfb\uff0c1 \u8868\u793a\u5b8c\u5168\u6b63\u5173\u7cfb\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u6700\u5e38\u7528\u7684\u76f8\u5173\u7cfb\u6570\u662f<a href=\"https:\/\/statorials.org\/cn\/\u76ae\u5c14\u900a\u76f8\u5173\u7cfb\u6570-1\/\" target=\"_blank\" rel=\"noopener\">\u76ae\u5c14\u900a\u76f8\u5173\u7cfb\u6570<\/a>\uff0c\u5b83\u8861\u91cf\u4e24\u4e2a\u6570\u503c\u53d8\u91cf\u4e4b\u95f4\u7684\u7ebf\u6027\u5173\u8054\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4e0d\u592a\u5e38\u7528\u7684\u76f8\u5173\u7cfb\u6570\u662f<strong>Kendall \u7684 Tau<\/strong> \uff0c\u5b83\u8861\u91cf\u4e24\u5217\u6392\u540d\u6570\u636e\u4e4b\u95f4\u7684\u5173\u7cfb\u3002<\/span><\/p>\n<p> <span style=\"color: #000000;\">Kendall&#8217;s Tau\uff08\u901a\u5e38\u7f29\u5199\u4e3a \u03c4\uff09\u7684\u8ba1\u7b97\u516c\u5f0f\u5982\u4e0b\uff1a<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u03c4 = (CD) \/ (C+D)<\/span><\/p>\n<p><span style=\"color: #000000;\">\u91d1\u5b50\uff1a<\/span><\/p>\n<p> <span style=\"color: #000000;\">C = \u5339\u914d\u5bf9\u7684\u6570\u91cf<\/span><\/p>\n<p><span style=\"color: #000000;\">D = \u4e0d\u4e00\u81f4\u5bf9\u7684\u6570\u91cf<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4ee5\u4e0b\u793a\u4f8b\u8bf4\u660e\u5982\u4f55\u4f7f\u7528\u6b64\u516c\u5f0f\u8ba1\u7b97\u4e24\u5217\u6392\u540d\u6570\u636e\u7684 Kendall&#8217;s Tau \u6392\u540d\u76f8\u5173\u7cfb\u6570\u3002<\/span><\/p>\n<h2><span style=\"color: #000000;\"><strong>\u8ba1\u7b97 Kendall&#8217;s Tau \u7684\u793a\u4f8b<\/strong><\/span><\/h2>\n<p><span style=\"color: #000000;\">\u5047\u8bbe\u4e24\u4f4d\u7bee\u7403\u6559\u7ec3\u5c06 12 \u540d\u7403\u5458\u4ece\u6700\u5dee\u5230\u6700\u597d\u6392\u540d\u3002\u4e0b\u8868\u662f\u5404\u6559\u7ec3\u7ed9\u7403\u5458\u5206\u914d\u7684\u6392\u540d\uff1a<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-5441 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/kendall1.png\" alt=\"\u80af\u5fb7\u5c14\u7684 Tau \u793a\u4f8b\" width=\"233\" height=\"281\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p><span style=\"color: #000000;\">\u7531\u4e8e\u6211\u4eec\u5904\u7406\u7684\u662f\u4e24\u5217\u6392\u540d\u6570\u636e\uff0c\u56e0\u6b64\u4f7f\u7528 Kendall \u7684 Tau \u6765\u8ba1\u7b97\u4e24\u4f4d\u6559\u7ec3\u6392\u540d\u4e4b\u95f4\u7684\u76f8\u5173\u6027\u662f\u5408\u9002\u7684\u3002\u8bf7\u6309\u7167\u4ee5\u4e0b\u6b65\u9aa4\u8ba1\u7b97 Kendall \u7684 Tau\uff1a<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>\u6b65\u9aa41\uff1a\u8ba1\u7b97\u5339\u914d\u5bf9\u7684\u6570\u91cf\u3002<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u53ea\u770b\u6559\u7ec3#2 \u7684\u6392\u540d\u3002\u4ece\u7b2c\u4e00\u4e2a\u73a9\u5bb6\u5f00\u59cb\uff0c\u6570\u4e00\u4e0b\u4ed6\u4e0b\u9762\u6709\u591a\u5c11\u4e2a\u7b49\u7ea7<em>\u9ad8<\/em>\u3002\u4f8b\u5982\u201c1\u201d\u4e0b\u9762\u670911\u4e2a\u6570\u5b57\u8f83\u5927\uff0c\u6240\u4ee5\u6211\u4eec\u5c31\u519911\uff1a<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-5443 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/kendall2.png\" alt=\"Kendall tau \u6570\u636e\u96c6\" width=\"308\" height=\"271\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p><span style=\"color: #000000;\">\u79fb\u52a8\u5230\u4e0b\u4e00\u4e2a\u73a9\u5bb6\u5e76\u91cd\u590d\u8be5\u8fc7\u7a0b\u3002 \u201c2\u201d\u4e0b\u9762\u6709 10 \u4e2a\u66f4\u5927\u7684\u6570\u5b57\uff0c\u6240\u4ee5\u6211\u4eec\u5199 10\uff1a<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-5444 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/kendall3.png\" alt=\"Kendalls tau \u4e00\u81f4\u5bf9\u7684\u8ba1\u7b97\" width=\"316\" height=\"280\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p><span style=\"color: #000000;\">\u4e00\u65e6\u6211\u4eec\u627e\u5230\u4e00\u4e2a\u6392\u540d<em>\u4f4e\u4e8e<\/em>\u4ed6\u4e4b\u524d\u7684\u73a9\u5bb6\u7684\u73a9\u5bb6\uff0c\u4ed6\u5c31\u4f1a\u88ab\u7b80\u5355\u5730\u5206\u914d\u4e0e\u4ed6\u4e4b\u524d\u7684\u73a9\u5bb6\u76f8\u540c\u7684\u503c\u3002\u4f8b\u5982\uff0c\u57c3\u5229\u5965\u7279\u7684\u6392\u540d\u4e3a\u201c4\u201d\uff0c\u4f4e\u4e8e\u524d\u4e00\u4e2a\u73a9\u5bb6\u7684\u6392\u540d\u201c5\u201d\uff0c\u56e0\u6b64\u4ed6\u53ea\u662f\u88ab\u5206\u914d\u4e0e\u4ed6\u4e4b\u524d\u7684\u73a9\u5bb6\u76f8\u540c\u7684\u503c\uff1a<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-5445 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/kendall4.png\" alt=\"\u80af\u5fb7\u5c14\u7684\u5934\" width=\"321\" height=\"286\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p><span style=\"color: #000000;\">\u5bf9\u6240\u6709\u73a9\u5bb6\u91cd\u590d\u6b64\u8fc7\u7a0b\uff1a<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-5446 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/kendall5.png\" alt=\"\u80af\u5fb7\u5c14\u7684\u5934\" width=\"321\" height=\"288\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p><span style=\"color: #000000;\"><strong>\u6b65\u9aa42\uff1a\u8ba1\u7b97\u4e0d\u4e00\u81f4\u5bf9\u7684\u6570\u91cf\u3002<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u518d\u6b21\u5f3a\u8c03\uff0c\u53ea\u770b\u6559\u7ec3 #2 \u7684\u6392\u540d\u3002\u5bf9\u4e8e\u6bcf\u4e2a\u73a9\u5bb6\uff0c\u8ba1\u7b97\u4ed6\u6216\u5979\u4e0b\u9762\u6709\u591a\u5c11\u4e2a\u7b49\u7ea7<em>\u8f83\u5c0f<\/em>\u3002\u4f8b\u5982\uff0c2 \u53f7\u6559\u7ec3\u4e3a AJ \u5206\u914d\u4e86\u6392\u540d\u201c1\u201d\uff0c\u5e76\u4e14\u5728\u4ed6\u4e4b\u4e0b\u7684\u7403\u5458\u6ca1\u6709\u66f4\u4f4e\u7684\u6392\u540d\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u5c06\u5176\u8d4b\u503c\u4e3a 0\uff1a<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-5447 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/kendall6.png\" alt=\"\u8ba1\u7b97\u4e0d\u4e00\u81f4\u5bf9\u7684 Kendall tau\" width=\"396\" height=\"283\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p><span style=\"color: #000000;\">\u5bf9\u6bcf\u4e2a\u73a9\u5bb6\u91cd\u590d\u6b64\u8fc7\u7a0b\uff1a<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-5448 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/kendall7.png\" alt=\"\u80af\u5fb7\u5c14\u7684 tau \u4f8b\u5b50\" width=\"397\" height=\"282\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p><span style=\"color: #000000;\"><strong>\u6b65\u9aa4 3\uff1a\u8ba1\u7b97\u6bcf\u5217\u7684\u603b\u548c\u5e76\u627e\u5230 Kendall \u7684 Tau\u3002<\/strong><\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-5449 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/kendall8.png\" alt=\"Kendall tau \u7684\u8ba1\u7b97\" width=\"401\" height=\"308\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p><span style=\"color: #000000;\">\u80af\u5fb7\u5c14\u7684 Tau = (CD) \/ (C+D) = (63-3) \/ (63+3) = (60\/66) = <strong>0.909<\/strong> \u3002<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>Kendall&#8217;s Tau \u7684\u7edf\u8ba1\u91cd\u8981\u6027<\/strong><\/span><\/h2>\n<p>\u5f53 n=10 \u5bf9\u4ee5\u4e0a\u65f6\uff0cKendall \u7684 Tau \u901a\u5e38\u9075\u5faa\u6b63\u6001\u5206\u5e03\u3002\u60a8\u53ef\u4ee5\u4f7f\u7528\u4ee5\u4e0b\u516c\u5f0f\u8ba1\u7b97 Kendall&#8217;s Tau \u7684 z \u5206\u6570\uff1a<\/p>\n<p> <span style=\"color: #000000;\">z = 3\u03c4*\u221a <span style=\"text-decoration: overline;\">n(n-1)<\/span> \/ \u221a <span style=\"text-decoration: overline;\">2(2n+5)<\/span><\/span><\/p>\n<p><span style=\"color: #000000;\">\u91d1\u5b50\uff1a<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u03c4 = \u60a8\u4e3a Kendall \u7684 Tau \u8ba1\u7b97\u7684\u503c<\/span><\/p>\n<p><span style=\"color: #000000;\">n = \u5bf9\u6570<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4ee5\u4e0b\u662f\u8ba1\u7b97\u4e0a\u4e00\u4e2a\u793a\u4f8b\u7684<em>z<\/em>\u7684\u65b9\u6cd5\uff1a<\/span><\/p>\n<p> <span style=\"color: #000000;\">z = 3(.909)*\u221a <span style=\"text-decoration: overline;\">12(12-1)<\/span> \/ \u221a <span style=\"text-decoration: overline;\">2(2*12+5)<\/span> = <strong>4.11<\/strong> \u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4f7f\u7528 P \u503c Z \u5f97\u5206\u8ba1\u7b97\u5668\uff0c\u6211\u4eec\u770b\u5230\u8be5 z \u5f97\u5206\u7684 p \u503c\u4e3a<strong>0.00004<\/strong> \uff0c\u8fd9\u5728 0.05 alpha \u6c34\u5e73\u4e0a\u5177\u6709\u7edf\u8ba1\u663e\u7740\u6027\u3002\u56e0\u6b64\uff0c\u4e24\u4f4d\u6559\u7ec3\u5206\u914d\u7ed9\u7403\u5458\u7684\u6392\u540d\u4e4b\u95f4\u5b58\u5728\u7edf\u8ba1\u4e0a\u663e\u7740\u7684\u76f8\u5173\u6027\u3002<\/span><\/p>\n<h2><span style=\"color: #000000;\"><strong>\u9644\u8d60\uff1a\u5982\u4f55\u5728 R \u4e2d\u8ba1\u7b97 Kendall \u7684 Tau<\/strong><\/span><\/h2>\n<p><span style=\"color: #000000;\">\u5728 R \u7edf\u8ba1\u8f6f\u4ef6\u4e2d\uff0c\u60a8\u53ef\u4ee5\u4f7f\u7528 VGAM \u5e93\u4e2d\u7684<strong>kendall.tau()<\/strong>\u51fd\u6570\u6765\u8ba1\u7b97\u4e24\u4e2a\u5411\u91cf\u7684 Kendall&#8217;s Tau\uff0c\u5176\u8bed\u6cd5\u5982\u4e0b\uff1a<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>\u80af\u5fb7\u5c14.tau(x, y)<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u5176\u4e2d<em>x<\/em>\u548c<em>y<\/em>\u662f\u4e24\u4e2a\u957f\u5ea6\u76f8\u7b49\u7684\u6570\u5b57\u5411\u91cf\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4ee5\u4e0b\u4ee3\u7801\u8bf4\u660e\u4e86\u5982\u4f55\u8ba1\u7b97\u6211\u4eec\u5728\u4e0a\u4e00\u4e2a\u793a\u4f8b\u4e2d\u4f7f\u7528\u7684\u786e\u5207\u6570\u636e\u7684 Kendall&#8217;s Tau\uff1a<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#load <em>VGAM\n<\/em><\/span>library(VGAM)\n\n<span style=\"color: #008080;\">#create vector for each coach's rankings<\/span>\ncoach_1 &lt;- c(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12)\ncoach_2 &lt;- c(1, 2, 3, 5, 4, 7, 6, 8, 10, 9, 11, 12)\n\n<span style=\"color: #008080;\">#calculate Kendall's Tau\n<\/span>kendall.tau(coach_1, coach_2)\n\n#[1] 0.9090909<\/strong><\/pre>\n<p><span style=\"color: #000000;\">\u8bf7\u6ce8\u610f Kendall \u7684 Tau \u503c\u4e0e\u6211\u4eec\u624b\u52a8\u8ba1\u7b97\u7684\u503c\u5982\u4f55\u5339\u914d\u3002<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5728\u7edf\u8ba1\u5b66\u4e2d\uff0c\u76f8\u5173\u6027\u662f\u6307\u4e24\u4e2a\u53d8\u91cf\u4e4b\u95f4\u5173\u7cfb\u7684\u5f3a\u5ea6\u548c\u65b9\u5411\u3002\u76f8\u5173\u7cfb\u6570\u7684\u503c\u8303\u56f4\u4e3a -1 \u5230 1\uff0c\u5176\u4e2d -1 \u8868\u793a\u5b8c\u5168\u8d1f\u5173 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[],"class_list":["post-593","post","type-post","status-publish","format-standard","hentry","category-11"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Kendall \u7684 Tau\uff1a\u5b9a\u4e49 + \u793a\u4f8b - Statorials<\/title>\n<meta name=\"description\" content=\"Kendall \u7684 Tau \u7b49\u7ea7\u76f8\u5173\u7cfb\u6570\u7684\u7b80\u5355\u8bf4\u660e\uff0c\u5305\u62ec\u5b9a\u4e49\u548c\u8ba1\u7b97\u65b9\u6cd5\u7684\u793a\u4f8b\u3002\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/statorials.org\/cn\/\u80af\u5fb7\u5c14\u65af\u5934\/\" \/>\n<meta property=\"og:locale\" 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