{"id":1388,"date":"2023-07-26T14:31:40","date_gmt":"2023-07-26T14:31:40","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e7%a7%91%e5%85%8b%e4%bc%a6%e6%96%af-q-%e6%a3%80%e9%aa%8c\/"},"modified":"2023-07-26T14:31:40","modified_gmt":"2023-07-26T14:31:40","slug":"%e7%a7%91%e5%85%8b%e4%bc%a6%e6%96%af-q-%e6%a3%80%e9%aa%8c","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e7%a7%91%e5%85%8b%e4%bc%a6%e6%96%af-q-%e6%a3%80%e9%aa%8c\/","title":{"rendered":"\u4ec0\u4e48\u662f cochran&#39;s q \u68c0\u9a8c\uff1f \uff08\u5b9a\u4e49&amp;#038\uff1b\u793a\u4f8b\uff09"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>Cochran&#8217;s Q \u68c0\u9a8c<\/strong>\u662f\u4e00\u79cd\u7edf\u8ba1\u68c0\u9a8c\uff0c\u7528\u4e8e\u786e\u5b9a\u4e09\u4e2a\u6216\u66f4\u591a\u7ec4\u4e2d\u201c\u6210\u529f\u201d\u7684\u6bd4\u4f8b\u662f\u5426\u76f8\u7b49\uff0c\u5176\u4e2d\u6bcf\u4e2a\u7ec4\u4e2d\u51fa\u73b0\u76f8\u540c\u7684\u4e2a\u4f53\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4f8b\u5982\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528 Cochran \u7684 Q \u68c0\u9a8c\u6765\u786e\u5b9a\u5728\u4f7f\u7528\u4e09\u79cd\u4e0d\u540c\u7684\u5b66\u4e60\u6280\u672f\u65f6\u901a\u8fc7\u6d4b\u8bd5\u7684\u5b66\u751f\u6bd4\u4f8b\u662f\u5426\u76f8\u7b49\u3002<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-13782 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/cochranq2.png\" alt=\"\" width=\"313\" height=\"449\" srcset=\"\" sizes=\"auto, \"><\/p>\n<h3><span style=\"color: #000000;\"><strong>\u6267\u884c Cochran Q \u68c0\u9a8c\u7684\u6b65\u9aa4<\/strong><\/span><\/h3>\n<p><span style=\"color: #000000;\">Cochran \u7684 Q \u68c0\u9a8c\u4f7f\u7528\u4ee5\u4e0b\u539f\u5047\u8bbe\u548c\u5907\u62e9\u5047\u8bbe\uff1a<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>\u539f\u5047\u8bbe (H <sub>0<\/sub> )\uff1a<\/strong>\u6240\u6709\u7ec4\u4e2d\u201c\u6210\u529f\u201d\u7684\u6bd4\u4f8b\u76f8\u540c<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>\u5907\u62e9\u5047\u8bbe ( <sub>HA<\/sub> )\uff1a<\/strong>\u81f3\u5c11\u5176\u4e2d\u4e00\u7ec4\u7684\u201c\u6210\u529f\u201d\u6bd4\u4f8b\u4e0d\u540c<\/span><\/p>\n<p><span style=\"color: #000000;\">\u68c0\u9a8c\u7edf\u8ba1\u91cf\u8ba1\u7b97\u5982\u4e0b\uff1a<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-13781 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/cochranq.png\" alt=\"\" width=\"235\" height=\"105\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p><span style=\"color: #000000;\">\u91d1\u5b50\uff1a<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>k\uff1a<\/strong>\u6cbb\u7597\u6b21\u6570\uff08\u6216\u201c\u7ec4\u201d\uff09<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>Xj\uff1a<\/strong><sup>\u7b2c j \u4e2a<\/sup>\u5904\u7406\u7684\u5217\u7684\u603b\u8ba1<\/span><\/li>\n<li><span style=\"color: #000000;\"><strong>b\uff1a<\/strong>\u5757\u6570<\/span><\/li>\n<li><span style=\"color: #000000;\"><strong>\u595a\u3002 \uff1a<\/strong><sup>\u7b2c i \u4e2a<\/sup>\u5757\u7684\u884c\u603b\u6570<\/span><\/li>\n<li><span style=\"color: #000000;\"><strong>N\uff1a<\/strong>\u603b\u8ba1<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\"><em>T<\/em>\u68c0\u9a8c\u7edf\u8ba1\u91cf\u9075\u5faa\u81ea\u7531\u5ea6\u4e3a<em>k-1 \u7684<\/em>\u5361\u65b9\u5206\u5e03\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u5982\u679c\u4e0e\u68c0\u9a8c\u7edf\u8ba1\u91cf\u76f8\u5173\u7684<a href=\"https:\/\/statorials.org\/cn\/p\u503c\u7edf\u8ba1\u663e\u7740\u6027\/\" target=\"_blank\" rel=\"noopener\">p \u503c<\/a>\u4f4e\u4e8e\u4e00\u5b9a\u7684\u663e\u7740\u6027\u6c34\u5e73\uff08\u4f8b\u5982 \u03b1 = 0.05\uff09\uff0c\u6211\u4eec\u53ef\u4ee5\u62d2\u7edd\u96f6\u5047\u8bbe\u5e76\u5f97\u51fa\u7ed3\u8bba\uff0c\u6211\u4eec\u6709\u8db3\u591f\u7684\u8bc1\u636e\u8868\u660e\u201c\u6210\u529f\u201d\u7684\u6bd4\u4f8b\u5728\u81f3\u5c11\u5176\u4e2d\u4e00\u7ec4\u3002<\/span><\/p>\n<h3><span style=\"color: #000000;\"><strong>\u793a\u4f8b\uff1aCochran \u7684 Q \u68c0\u9a8c<\/strong><\/span><\/h3>\n<p><span style=\"color: #000000;\">\u5047\u8bbe\u7814\u7a76\u4eba\u5458\u60f3\u77e5\u9053\u4e09\u79cd\u4e0d\u540c\u7684\u5b66\u4e60\u6280\u5de7\u662f\u5426\u4f1a\u5bfc\u81f4\u5b66\u751f\u6210\u529f\u7387\u7684\u6bd4\u4f8b\u4e0d\u540c\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4e3a\u4e86\u6d4b\u8bd5\u8fd9\u4e00\u70b9\uff0c\u5979\u62db\u52df\u4e86 20 \u540d\u5b66\u751f\uff0c\u6bcf\u4eba\u4f7f\u7528\u4e09\u79cd\u4e0d\u540c\u7684\u5b66\u4e60\u6280\u5de7\u53c2\u52a0\u540c\u7b49\u96be\u5ea6\u7684\u8003\u8bd5\u3002\u7ed3\u679c\u5982\u4e0b\u6240\u793a\uff1a<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-13782 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/cochranq2.png\" alt=\"\" width=\"313\" height=\"449\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p><span style=\"color: #000000;\">\u4e3a\u4e86\u6267\u884c Cochran \u7684 Q \u68c0\u9a8c\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u7edf\u8ba1\u8f6f\u4ef6\uff0c\u56e0\u4e3a\u624b\u52a8\u6267\u884c\u53ef\u80fd\u5f88\u7e41\u7410\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4ee5\u4e0b\u662f\u6211\u4eec\u53ef\u4ee5\u7528\u6765\u521b\u5efa\u6b64\u6570\u636e\u96c6\u5e76\u5728 R \u7edf\u8ba1\u7f16\u7a0b\u8bed\u8a00\u4e2d\u6267\u884c Cochran&#8217;s Q \u68c0\u9a8c\u7684\u4ee3\u7801\uff1a<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#load DescTools package<\/span>\n<span style=\"color: #993300;\">library<\/span> (DescTools)\n\n<span style=\"color: #008080;\">#create dataset<\/span>\ndf &lt;- data.frame(student= <span style=\"color: #3366ff;\">rep<\/span> (1:20, <span style=\"color: #3366ff;\">each<\/span> = <span style=\"color: #008000;\">3<\/span> ),\n                 technique= <span style=\"color: #3366ff;\">rep<\/span> (c('A', 'B', 'C'), times= <span style=\"color: #008000;\">20<\/span> ),\n                 outcome=c(1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1,\n                           1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1,\n                           1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1,\n                           1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1))\n\n<span style=\"color: #008080;\">#perform Cochran's Q test<\/span>\nCochranQTest(outcome ~ technique| student, data=df)\n\n\tCochran's Q test\n\ndata: outcome and technique and student\nQ = 0.33333, df = 2, p-value = 0.8465<\/strong><\/pre>\n<p><span style=\"color: #000000;\">\u4ece\u6d4b\u8bd5\u7ed3\u679c\u6211\u4eec\u53ef\u4ee5\u89c2\u5bdf\u5230\u4ee5\u4e0b\u51e0\u70b9\uff1a<\/span><\/p>\n<ul>\n<li><span style=\"color: #000000;\">\u68c0\u9a8c\u7edf\u8ba1\u91cf\u4e3a<strong>0.333<\/strong><\/span><\/li>\n<li><span style=\"color: #000000;\">\u76f8\u5e94\u7684 p \u503c\u4e3a<strong>0.8465<\/strong><\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u7531\u4e8e\u8be5 p \u503c\u4e0d\u5c0f\u4e8e 0.05\uff0c\u56e0\u6b64\u6211\u4eec\u65e0\u6cd5\u62d2\u7edd\u539f\u5047\u8bbe\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u8fd9\u610f\u5473\u7740\u6211\u4eec\u6ca1\u6709\u8db3\u591f\u7684\u8bc1\u636e\u8868\u660e\u5b66\u751f\u4f7f\u7528\u7684\u5b66\u4e60\u6280\u5de7\u4f1a\u5bfc\u81f4\u4e0d\u540c\u6bd4\u4f8b\u7684\u6210\u529f\u7387\u3002<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Cochran&#8217;s Q \u68c0\u9a8c\u662f\u4e00\u79cd\u7edf\u8ba1\u68c0\u9a8c\uff0c\u7528\u4e8e\u786e\u5b9a\u4e09\u4e2a\u6216\u66f4\u591a\u7ec4\u4e2d\u201c\u6210\u529f\u201d\u7684\u6bd4\u4f8b\u662f\u5426\u76f8\u7b49\uff0c\u5176\u4e2d\u6bcf\u4e2a [&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-1388","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>\u4ec0\u4e48\u662f Cochran&#039;s Q \u68c0\u9a8c\uff1f \uff08\u5b9a\u4e49\u548c\u793a\u4f8b\uff09- \u9759\u6001<\/title>\n<meta name=\"description\" content=\"\u672c\u6559\u7a0b\u63d0\u4f9b\u4e86 Cochran&#039;s Q \u68c0\u9a8c\u7684\u89e3\u91ca\uff0c\u5305\u62ec\u6b63\u5f0f\u5b9a\u4e49\u548c\u793a\u4f8b\u3002\" \/>\n<meta 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