{"id":1349,"date":"2023-07-26T18:42:57","date_gmt":"2023-07-26T18:42:57","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e6%9f%b1%e5%ad%90%e7%9a%84%e7%97%95%e8%bf%b9\/"},"modified":"2023-07-26T18:42:57","modified_gmt":"2023-07-26T18:42:57","slug":"%e6%9f%b1%e5%ad%90%e7%9a%84%e7%97%95%e8%bf%b9","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e6%9f%b1%e5%ad%90%e7%9a%84%e7%97%95%e8%bf%b9\/","title":{"rendered":"\u76ae\u83b1\u7684\u8e2a\u8ff9\u662f\u4ec0\u4e48\uff1f \uff08\u5b9a\u4e49&amp;#038\uff1b\u793a\u4f8b\uff09"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/cn\/\u5355\u56e0\u7d20\u65b9\u5dee\u5206\u6790\u7edf\u8ba1\/\" target=\"_blank\" rel=\"noopener\">\u5355\u5411\u65b9\u5dee\u5206\u6790<\/a>\u7528\u4e8e\u786e\u5b9a\u89e3\u91ca\u53d8\u91cf\u7684\u4e0d\u540c\u6c34\u5e73\u662f\u5426\u4f1a\u5bfc\u81f4\u67d0\u4e9b<a href=\"https:\/\/statorials.org\/cn\/\u53d8\u91cf\u89e3\u91ca\u6027\u53cd\u5e94\/\" target=\"_blank\" rel=\"noopener\">\u54cd\u5e94\u53d8\u91cf<\/a>\u51fa\u73b0\u7edf\u8ba1\u4e0a\u4e0d\u540c\u7684\u7ed3\u679c\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4f8b\u5982\uff0c\u6211\u4eec\u53ef\u80fd\u6709\u5174\u8da3\u4e86\u89e3\u4e09\u4e2a\u6559\u80b2\u7ea7\u522b\uff08\u526f\u5b66\u58eb\u5b66\u4f4d\u3001\u5b66\u58eb\u5b66\u4f4d\u3001\u7855\u58eb\u5b66\u4f4d\uff09\u662f\u5426\u4f1a\u5bfc\u81f4\u5e74\u6536\u5165<a href=\"https:\/\/statorials.org\/cn\/p\u503c\u7edf\u8ba1\u663e\u7740\u6027\/\" target=\"_blank\" rel=\"noopener\">\u5728\u7edf\u8ba1\u4e0a\u6709\u6240\u4e0d\u540c<\/a>\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u6709\u4e00\u4e2a\u89e3\u91ca\u53d8\u91cf\u548c\u4e00\u4e2a\u54cd\u5e94\u53d8\u91cf\u3002<\/span><\/p>\n<p> <a href=\"https:\/\/statorials.org\/cn\/\u65b9\u5dee\u5206\u6790-ancova-\u65b9\u5dee\u5206\u6790-mancova-\u4e4b\u95f4\u7684\u5dee\u5f02\/\" target=\"_blank\" rel=\"noopener\">\u591a\u5143\u65b9\u5dee\u5206\u6790<\/a><span style=\"color: #000000;\">\u662f<\/span><span style=\"color: #000000;\">\u5355\u5411\u65b9\u5dee\u5206\u6790\u7684\u6269\u5c55\uff0c\u5176\u4e2d\u6709\u591a\u4e2a\u54cd\u5e94\u53d8\u91cf\u3002\u4f8b\u5982\uff0c\u6211\u4eec\u53ef\u80fd\u6709\u5174\u8da3\u4e86\u89e3\u6559\u80b2\u662f\u5426\u4f1a\u5bfc\u81f4\u4e0d\u540c\u7684\u5e74\u6536\u5165<em>\u548c<\/em>\u4e0d\u540c\u6570\u91cf\u7684\u5b66\u751f\u503a\u52a1\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u6709\u4e00\u4e2a\u89e3\u91ca\u53d8\u91cf\u548c\u4e24\u4e2a\u54cd\u5e94\u53d8\u91cf\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u7531\u591a\u5143\u65b9\u5dee\u5206\u6790\u4ea7\u751f\u7684\u68c0\u9a8c\u7edf\u8ba1\u91cf\u4e4b\u4e00\u662f<strong>Pillai \u8ff9\u7ebf<\/strong>\u3002<\/span><\/p>\n<h3><strong><span style=\"color: #000000;\">\u4ec0\u4e48\u662f\u76ae\u83b1\u75d5\u8ff9\uff1f<\/span><\/strong><\/h3>\n<p><span style=\"color: #000000;\"><strong>\u76ae\u83b1\u7684\u8e2a\u8ff9<em>&nbsp;<\/em><\/strong>\u662f\u591a\u5143\u65b9\u5dee\u5206\u6790\u4ea7\u751f\u7684\u68c0\u9a8c\u7edf\u8ba1\u91cf\u3002\u5b83\u662f\u4e00\u4e2a\u4ece 0 \u5230 1 \u53d8\u5316\u7684\u503c\u3002<\/span><\/p>\n<p> <span style=\"color: #000000;\">Pillai \u8ff9\u7ebf\u8d8a\u63a5\u8fd1 1\uff0c\u8bf4\u660e\u89e3\u91ca\u53d8\u91cf\u5bf9\u54cd\u5e94\u53d8\u91cf\u7684\u503c\u5177\u6709\u7edf\u8ba1\u663e\u7740\u5f71\u54cd\u7684\u8bc1\u636e\u5c31\u8d8a\u6709\u529b\u3002<\/span><\/p>\n<p> <span style=\"color: #000000;\">Pillai \u8ff9\u7ebf\uff08\u901a\u5e38\u8868\u793a\u4e3a V\uff09\u8ba1\u7b97\u5982\u4e0b\uff1a<\/span><\/p>\n<p> <span style=\"color: #000000;\">V = \u8ff9\u7ebf(H(H+E) <sup>-1<\/sup> )<\/span><\/p>\n<p><span style=\"color: #000000;\">\u91d1\u5b50\uff1a<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>H\uff1a<\/strong>\u5e73\u65b9\u548c\u4e0e\u53c9\u79ef\u77e9\u9635\u7684\u5047\u8bbe<\/span><\/li>\n<li><span style=\"color: #000000;\"><strong>E\uff1a<\/strong>\u8bef\u5dee\u5e73\u65b9\u548c\u4e0e\u5411\u91cf\u79ef\u77e9\u9635<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u8fd0\u884c\u591a\u5143\u65b9\u5dee\u5206\u6790\u65f6\uff0c\u5927\u591a\u6570\u7edf\u8ba1\u8f6f\u4ef6\u4f7f\u7528 Pillai \u8ff9\u6765\u8ba1\u7b97 F \u7edf\u8ba1\u91cf\u7684\u7c97\u7565\u8fd1\u4f3c\u503c\u4ee5\u53ca\u76f8\u5e94\u7684 p \u503c\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u5982\u679c\u8fd9\u4e2a p \u503c\u4f4e\u4e8e\u4e00\u5b9a\u7684\u663e\u7740\u6027\u6c34\u5e73\uff08\u5373 \u03b1 = 0.05\uff09\uff0c\u90a3\u4e48\u6211\u4eec\u62d2\u7edd\u591a\u5143\u65b9\u5dee\u5206\u6790\u7684\u539f\u5047\u8bbe\uff0c\u5e76\u5f97\u51fa\u7ed3\u8bba\uff1a\u89e3\u91ca\u53d8\u91cf\u5bf9\u503c\u54cd\u5e94\u53d8\u91cf\u6709\u663e\u7740\u5f71\u54cd\u3002<\/span><\/p>\n<h3><strong><span style=\"color: #000000;\">\u4f55\u65f6\u4f7f\u7528 Pillai \u8f68\u8ff9<\/span><\/strong><\/h3>\n<p><span style=\"color: #000000;\">\u8fd0\u884c\u591a\u5143\u65b9\u5dee\u5206\u6790\u65f6\uff0c\u5927\u591a\u6570\u7edf\u8ba1\u8f6f\u4ef6\u5b9e\u9645\u4e0a\u4f1a\u4ea7\u751f\u56db\u4e2a\u68c0\u9a8c\u7edf\u8ba1\u91cf\uff1a<\/span><\/p>\n<ul>\n<li><span style=\"color: #000000;\">\u76ae\u83b1\u7684\u8e2a\u8ff9<\/span><\/li>\n<li><span style=\"color: #000000;\">\u5a01\u5c14\u514b\u65af\u7684\u62c9\u59c6\u8fbe<\/span><\/li>\n<li><span style=\"color: #000000;\">\u7279\u96f7\u65af\u00b7\u52b3\u5229-\u970d\u7279\u6797<\/span><\/li>\n<li><span style=\"color: #000000;\">\u7f57\u4f0a\u6700\u5927\u7684\u6839<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u5f53\u4e0d\u6ee1\u8db3\u591a\u5143\u65b9\u5dee\u5206\u6790\u7684\u5047\u8bbe\u65f6\uff0c\u5efa\u8bae\u4f7f\u7528 Pillai \u8ff9\u4f5c\u4e3a\u68c0\u9a8c\u7edf\u8ba1\u91cf\u3002\u63d0\u9192\u4e00\u4e0b\uff0c\u591a\u5143\u65b9\u5dee\u5206\u6790\u505a\u51fa\u4ee5\u4e0b\u5047\u8bbe\uff1a<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/cn\/\u6b8b\u7559\u7269\/\" target=\"_blank\" rel=\"noopener\">\u6b8b\u5dee<\/a>\u9075\u5faa\u5747\u503c\u4e3a\u96f6\u7684\u591a\u5143\u6b63\u6001\u6982\u7387\u5206\u5e03\u3002<\/span><\/li>\n<li><span style=\"color: #000000;\">\u6bcf\u7ec4\u6b8b\u5dee\u7684\u65b9\u5dee-\u534f\u65b9\u5dee\u77e9\u9635\u76f8\u7b49\u3002<\/span><\/li>\n<li> <span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/cn\/\u7edf\u8ba1\u89c2\u5bdf\/\" target=\"_blank\" rel=\"noopener\">\u89c2\u5bdf\u7ed3\u679c<\/a>\u662f\u72ec\u7acb\u7684\u3002<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u5f53\u8fdd\u53cd\u8fd9\u4e9b\u5047\u8bbe\u4e2d\u7684\u4e00\u4e2a\u6216\u591a\u4e2a\u65f6\uff0cPillai \u8ff9\u7ebf\u5f80\u5f80\u662f\u6700\u7a33\u5065\u7684\u68c0\u9a8c\u7edf\u8ba1\u91cf\u3002<\/span><\/p>\n<h3><span style=\"color: #000000;\"><strong>\u8ba1\u7b97 Pillai \u8ff9\u7ebf\u7684\u793a\u4f8b<\/strong><\/span><\/h3>\n<p><span style=\"color: #000000;\">\u5728<a href=\"https:\/\/statorials.org\/cn\/\u65b9\u5dee\u7edf\u8ba1\/\" target=\"_blank\" rel=\"noopener\">\u672c\u6559\u7a0b<\/a>\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528\u4ee5\u4e0b\u53d8\u91cf\u5728 Stata \u4e2d\u6267\u884c\u591a\u5143\u65b9\u5dee\u5206\u6790\uff1a<\/span><\/p>\n<ul>\n<li><span style=\"color: #000000;\"><strong>\u89e3\u91ca\u53d8\u91cf\uff1a<\/strong>\u5b66\u4e60\u6c34\u5e73\uff08\u526f\u5b66\u58eb\u3001\u5b66\u58eb\u6216\u7855\u58eb\uff09<\/span><\/li>\n<li><span style=\"color: #000000;\"><strong>\u54cd\u5e94\u53d8\u91cf\uff1a<\/strong>\u5e74\u6536\u5165\u3001\u5b66\u751f\u8d37\u6b3e\u503a\u52a1\u603b\u989d<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u4ee5\u4e0b\u5c4f\u5e55\u622a\u56fe\u663e\u793a\u4e86 MANOVA \u7684\u8f93\u51fa\uff1a<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/manovastata3.png\" alt=\"Stata \u4e2d\u7684\u591a\u5143\u65b9\u5dee\u5206\u6790\u8f93\u51fa\" width=\"538\" height=\"315\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p><span style=\"color: #000000;\">\u8bf7\u6ce8\u610f\uff0c\u591a\u5143\u65b9\u5dee\u5206\u6790\u4ea7\u751f\u4e86\u56db\u4e2a\u68c0\u9a8c\u7edf\u8ba1\u91cf\uff1a<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>Wilks \u7684 lambda\uff1a<\/strong> F \u7edf\u8ba1\u91cf = 5.02\uff0cP \u503c = 0.0023\u3002<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>Pillai \u8ff9\u7ebf\uff1a<\/strong> F \u7edf\u8ba1\u91cf = 4.07\uff0cP \u503c = 0.0071\u3002<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>Lawley-Hotelling \u8ff9\u7ebf\uff1a<\/strong> F \u7edf\u8ba1\u91cf = 5.94\uff0cP \u503c = 0.0008\u3002<\/span><\/li>\n<li><span style=\"color: #000000;\"><strong>\u6700\u5927 Roy \u6839\uff1a<\/strong> F \u7edf\u8ba1\u91cf = 13.10\uff0cP \u503c = 0.0002\u3002<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u6bcf\u4e2a\u68c0\u9a8c\u7edf\u8ba1\u91cf\u7684 F \u503c\u5404\u4e0d\u76f8\u540c\uff0c\u4f46\u6bcf\u4e2a\u76f8\u5e94\u7684 p \u503c\u5747\u5c0f\u4e8e 0.05\uff0c\u56e0\u6b64\u6211\u4eec\u4f1a\u62d2\u7edd\u591a\u5143\u65b9\u5dee\u5206\u6790\u7684\u539f\u5047\u8bbe\uff0c\u5e76\u5f97\u51fa\u7ed3\u8bba\uff1a\u6559\u80b2\u6c34\u5e73\u5bf9\u5b66\u751f\u7684\u5e74\u6536\u5165\u548c\u503a\u52a1\u603b\u6570\u6709\u663e\u7740\u5f71\u54cd\u3002<\/span><\/p>\n<h3><span style=\"color: #000000;\"><strong>\u5176\u4ed6\u8d44\u6e90<\/strong><\/span><\/h3>\n<p><a href=\"https:\/\/statorials.org\/cn\/\u65b9\u5dee\u7edf\u8ba1\/\" target=\"_blank\" rel=\"noopener\">\u5982\u4f55\u5728 Stata \u4e2d\u6267\u884c\u591a\u5143\u65b9\u5dee\u5206\u6790<\/a><br \/><a href=\"https:\/\/statorials.org\/cn\/\u65b9\u5dee\u5206\u6790-1\/\" target=\"_blank\" rel=\"noopener\">\u5982\u4f55\u5728 SPSS \u4e2d\u6267\u884c\u591a\u5143\u65b9\u5dee\u5206\u6790<\/a><br \/><a href=\"https:\/\/statorials.org\/cn\/r-\u7684\u591a\u5143\u65b9\u5dee\u5206\u6790\/\" target=\"_blank\" rel=\"noopener\">\u5982\u4f55\u5728 R \u4e2d\u6267\u884c\u591a\u5143\u65b9\u5dee\u5206\u6790<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5355\u5411\u65b9\u5dee\u5206\u6790\u7528\u4e8e\u786e\u5b9a\u89e3\u91ca\u53d8\u91cf\u7684\u4e0d\u540c\u6c34\u5e73\u662f\u5426\u4f1a\u5bfc\u81f4\u67d0\u4e9b\u54cd\u5e94\u53d8\u91cf\u51fa\u73b0\u7edf\u8ba1\u4e0a\u4e0d\u540c\u7684\u7ed3\u679c\u3002 \u4f8b\u5982\uff0c\u6211\u4eec\u53ef\u80fd\u6709\u5174\u8da3\u4e86\u89e3\u4e09 [&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-1349","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\u76ae\u83b1\u75d5\u8ff9\uff1f \uff08\u5b9a\u4e49\u548c\u4f8b\u5b50\uff09<\/title>\n<meta name=\"description\" content=\"\u672c\u6559\u7a0b\u89e3\u91ca\u4e86 Pillai \u8ff9\u7ebf\uff0c\u5305\u62ec\u6b63\u5f0f\u5b9a\u4e49\u548c\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\/\u67f1\u5b50\u7684\u75d5\u8ff9\/\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta 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