{"id":422,"date":"2023-07-30T01:30:00","date_gmt":"2023-07-30T01:30:00","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e6%9b%bc%e6%83%a0%e7%89%b9%e5%b0%bcu%e6%b5%8b%e8%af%95\/"},"modified":"2023-07-30T01:30:00","modified_gmt":"2023-07-30T01:30:00","slug":"%e6%9b%bc%e6%83%a0%e7%89%b9%e5%b0%bcu%e6%b5%8b%e8%af%95","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e6%9b%bc%e6%83%a0%e7%89%b9%e5%b0%bcu%e6%b5%8b%e8%af%95\/","title":{"rendered":"\u66fc-\u60e0\u7279\u5c3c u \u68c0\u9a8c"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">\u5f53\u6837\u672c\u5206\u5e03\u4e0d\u5448\u6b63\u6001\u5206\u5e03\u4e14\u6837\u672c\u91cf\u8f83\u5c0f (n &lt; 30) \u65f6\uff0c <strong>Mann-Whitney U \u68c0\u9a8c<\/strong>\uff08\u6709\u65f6\u79f0\u4e3a Wilcoxon \u79e9\u548c\u68c0\u9a8c\uff09\u7528\u4e8e\u6bd4\u8f83\u4e24\u4e2a\u72ec\u7acb\u6837\u672c\u4e4b\u95f4\u7684\u5dee\u5f02\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u5b83\u88ab\u8ba4\u4e3a<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\">\u662f\u72ec\u7acb\u53cc\u6837\u672c t \u68c0\u9a8c<\/a>\u7684\u975e\u53c2\u6570\u7b49\u6548\u9879\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4ee5\u4e0b\u662f\u4f55\u65f6\u53ef\u4ee5\u4f7f\u7528 Mann-Whitney U \u68c0\u9a8c\u7684\u4e00\u4e9b\u793a\u4f8b\uff1a<\/span><\/p>\n<ul>\n<li><span style=\"color: #000000;\">\u60a8\u60f3\u8981\u5c06 A \u5927\u5b66\u7684 5 \u540d\u6bd5\u4e1a\u751f\u7684\u5de5\u8d44\u4e0e B \u5927\u5b66\u7684 5 \u540d\u6bd5\u4e1a\u751f\u7684\u5de5\u8d44\u8fdb\u884c\u6bd4\u8f83\u3002\u5de5\u8d44\u4e0d\u662f\u6b63\u6001\u5206\u5e03\u7684\u3002<\/span><\/li>\n<li><span style=\"color: #000000;\">\u60a8\u60f3\u77e5\u9053\u4e24\u7ec4\u7684\u4f53\u91cd\u51cf\u8f7b\u662f\u5426\u5b58\u5728\u5dee\u5f02\uff1a12 \u4eba\u4f7f\u7528\u996e\u98df A\uff0c10 \u4eba\u4f7f\u7528\u996e\u98df B\u3002\u4f53\u91cd\u51cf\u8f7b\u4e0d\u5448\u6b63\u6001\u5206\u5e03\u3002<\/span><\/li>\n<li><span style=\"color: #000000;\">\u60a8\u60f3\u77e5\u9053 A \u73ed 8 \u540d\u5b66\u751f\u7684\u5206\u6570\u4e0e B \u73ed 7 \u540d\u5b66\u751f\u7684\u5206\u6570\u662f\u5426\u4e0d\u540c\u3002\u5206\u6570\u4e0d\u670d\u4ece\u6b63\u6001\u5206\u5e03\u3002<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u5728\u6bcf\u4e2a\u793a\u4f8b\u4e2d\uff0c\u60a8\u60f3\u8981\u6bd4\u8f83\u4e24\u4e2a\u7ec4\uff0c\u62bd\u6837\u5206\u5e03\u4e0d\u6b63\u6001\uff0c\u5e76\u4e14\u6837\u672c\u91cf\u5f88\u5c0f\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u56e0\u6b64\uff0c\u53ea\u8981\u6ee1\u8db3\u4ee5\u4e0b\u5047\u8bbe\uff0cMann-Whitney U \u68c0\u9a8c\u5c31\u662f\u5408\u9002\u7684\u3002<\/span><\/p>\n<h2> <strong><span style=\"color: #000000;\">Mann-Whitney U \u68c0\u9a8c\u5047\u8bbe<\/span><\/strong><\/h2>\n<p><span style=\"color: #000000;\">\u5728\u6267\u884c Mann-Whitney U \u68c0\u9a8c\u4e4b\u524d\uff0c\u60a8\u5fc5\u987b\u786e\u4fdd\u6ee1\u8db3\u4ee5\u4e0b\u56db\u4e2a\u5047\u8bbe\uff1a<\/span><\/p>\n<ul>\n<li><span style=\"color: #000000;\"><strong>\u666e\u901a\u53d8\u91cf\u6216\u8fde\u7eed\u53d8\u91cf\uff1a<\/strong>\u60a8\u6b63\u5728\u5206\u6790\u7684\u53d8\u91cf\u662f\u6709\u5e8f\u53d8\u91cf\u6216\u8fde\u7eed\u53d8\u91cf\u3002\u5e8f\u6570\u53d8\u91cf\u7684\u793a\u4f8b\u5305\u62ec\u674e\u514b\u7279\u9879\u76ee\uff08\u4f8b\u5982\uff0c\u8303\u56f4\u4ece\u201c\u5f3a\u70c8\u4e0d\u540c\u610f\u201d\u5230\u201c\u5f3a\u70c8\u540c\u610f\u201d\u7684 5 \u70b9\u91cf\u8868\uff09\u3002\u8fde\u7eed\u53d8\u91cf\u7684\u793a\u4f8b\u5305\u62ec\u8eab\u9ad8\uff08\u4ee5\u82f1\u5bf8\u4e3a\u5355\u4f4d\uff09\u3001\u4f53\u91cd\uff08\u4ee5\u78c5\u4e3a\u5355\u4f4d\uff09\u6216\u6d4b\u8bd5\u5206\u6570\uff08\u4ece 0 \u5230 100 \u8fdb\u884c\u6d4b\u91cf\uff09\u3002<\/span><\/li>\n<li><span style=\"color: #000000;\"><strong>\u72ec\u7acb\u6027\uff1a<\/strong>\u4e24\u7ec4\u7684\u6240\u6709\u89c2\u5bdf\u7ed3\u679c\u90fd\u662f\u76f8\u4e92\u72ec\u7acb\u7684\u3002<\/span><\/li>\n<li><span style=\"color: #000000;\"><strong>\u5f62\u72b6\uff1a<\/strong>\u4e24\u7ec4\u7684\u5206\u5e03\u5f62\u72b6\u5927\u81f4\u76f8\u540c\u3002<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u5982\u679c\u6ee1\u8db3\u8fd9\u4e9b\u5047\u8bbe\uff0c\u5219\u60a8\u53ef\u4ee5\u6267\u884c Mann-Whitney U \u68c0\u9a8c\u3002<\/span><\/p>\n<h2><strong><span style=\"color: #000000;\">\u5982\u4f55\u8fdb\u884c\u66fc\u60e0\u7279\u5c3c U \u68c0\u9a8c<\/span><\/strong><\/h2>\n<p><span style=\"color: #000000;\">\u4e3a\u4e86\u6267\u884c Mann-Whitney U \u68c0\u9a8c\uff0c\u6211\u4eec\u9075\u5faa<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\">\u6807\u51c6\u7684\u4e94\u6b65\u5047\u8bbe\u68c0\u9a8c\u7a0b\u5e8f<\/a>\uff1a<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1. \u9648\u8ff0\u5047\u8bbe\u3002<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u5728\u5927\u591a\u6570\u60c5\u51b5\u4e0b\uff0cMann-Whitney U \u68c0\u9a8c\u4f5c\u4e3a\u53cc\u5c3e\u68c0\u9a8c\u8fdb\u884c\u3002\u539f\u5047\u8bbe\u548c\u5907\u62e9\u5047\u8bbe\u5199\u6210\u4ee5\u4e0b\u5f62\u5f0f\uff1a<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>H <sub>0<\/sub> \uff1a<\/strong>\u4e24\u4e2a\u603b\u4f53\u76f8\u7b49<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>H <sub>a<\/sub> :<\/strong>\u4e24\u4e2a\u4eba\u53e3\u4e0d\u76f8\u7b49<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>2. \u786e\u5b9a\u7528\u4e8e\u5047\u8bbe\u7684\u663e\u7740\u6027\u6c34\u5e73\u3002<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u786e\u5b9a\u91cd\u8981\u6027\u7ea7\u522b\u3002\u5e38\u89c1\u9009\u62e9\u4e3a .01\u3001.05 \u548c .1\u3002<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>3. \u6c42\u68c0\u9a8c\u7edf\u8ba1\u91cf\u3002<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u68c0\u9a8c\u7edf\u8ba1\u91cf\u7528 U \u8868\u793a\uff0c\u662f U <sub>1<\/sub>\u548c U <sub>2<\/sub>\u4e2d\u8f83\u5c0f\u7684\u4e00\u4e2a\uff0c\u5b9a\u4e49\u5982\u4e0b\uff1a<\/span><\/p>\n<p> <span style=\"color: #000000;\">U <sub>1<\/sub> = n <sub>1<\/sub> n <sub>2<\/sub> + n <sub>1<\/sub> (n <sub>1<\/sub> +1)\/2 \u2013 R <sub>1<\/sub><\/span><\/p>\n<p> <span style=\"color: #000000;\">U <sub>2<\/sub> = n <sub>1<\/sub> n <sub>2<\/sub> + n <sub>2<\/sub> (n <sub>2<\/sub> +1)\/2 \u2013 R <sub>2<\/sub><\/span><\/p>\n<p><span style=\"color: #000000;\">\u5176\u4e2d n <sub>1<\/sub>\u548c n <sub>2<\/sub>\u5206\u522b\u662f\u6837\u672c 1 \u548c 2 \u7684\u6837\u672c\u5927\u5c0f\uff0cR <sub>1<\/sub>\u548c R <sub>2<\/sub>\u5206\u522b\u662f\u6837\u672c 1 \u548c 2 \u7684\u79e9\u4e4b\u548c\u3002<\/span><\/p>\n<p><em><span style=\"color: #000000;\">\u4e0b\u9762\u7684\u793a\u4f8b\u5c06\u8be6\u7ec6\u8bf4\u660e\u5982\u4f55\u67e5\u627e\u6b64\u68c0\u9a8c\u7edf\u8ba1\u91cf\u3002<\/span><\/em><\/p>\n<p> <span style=\"color: #000000;\"><strong>4. \u62d2\u7edd\u6216\u4e0d\u62d2\u7edd\u539f\u5047\u8bbe\u3002<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u4f7f\u7528\u68c0\u9a8c\u7edf\u8ba1\u91cf\uff0c\u6839\u636e Mann-Whitney U \u8868\u4e2d\u7684\u663e\u7740\u6027\u6c34\u5e73\u548c\u4e34\u754c\u503c\u786e\u5b9a\u662f\u5426\u53ef\u4ee5\u62d2\u7edd\u539f\u5047\u8bbe\u3002<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>5. \u89e3\u91ca\u7ed3\u679c\u3002<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u5728\u6240\u63d0\u51fa\u95ee\u9898\u7684\u80cc\u666f\u4e0b\u89e3\u91ca\u6d4b\u8bd5\u7ed3\u679c\u3002<\/span><\/p>\n<h2><strong><span style=\"color: #000000;\">\u6267\u884c Mann-Whitney U \u68c0\u9a8c\u7684\u793a\u4f8b<\/span><\/strong><\/h2>\n<p><span style=\"color: #000000;\">\u4ee5\u4e0b\u793a\u4f8b\u663e\u793a\u5982\u4f55\u6267\u884c Mann-Whitney U \u68c0\u9a8c\u3002<\/span><\/p>\n<h3><span style=\"color: #000000;\"><strong>\u5b9e\u65bd\u4f8b1<\/strong><\/span><\/h3>\n<p><span style=\"color: #000000;\">\u6211\u4eec\u60f3\u77e5\u9053\u4e00\u79cd\u65b0\u836f\u7269\u662f\u5426\u80fd\u6709\u6548\u9884\u9632\u6050\u614c\u53d1\u4f5c\u3002\u603b\u5171 12 \u540d\u60a3\u8005\u88ab\u968f\u673a\u5206\u4e3a\u4e24\u7ec4\uff0c\u6bcf\u7ec4 6 \u4eba\uff0c\u5e76\u5206\u914d\u63a5\u53d7\u65b0\u836f\u6216\u5b89\u6170\u5242\u3002\u7136\u540e\u60a3\u8005\u8bb0\u5f55\u4ed6\u4eec\u5728\u4e00\u4e2a\u6708\u5185\u7ecf\u5386\u7684\u6050\u614c\u53d1\u4f5c\u7684\u6b21\u6570\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u7ed3\u679c\u5982\u4e0b\u6240\u793a\uff1a<\/span><\/p>\n<div style=\"width: 50%;\">\n<table>\n<thead>\n<tr>\n<th style=\"text-align: center;\"><span style=\"color: #000000;\">\u65b0\u836f<\/span><\/th>\n<th style=\"text-align: center;\"><span style=\"color: #000000;\">\u5b89\u6170\u5242<\/span><\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">3<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">4<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">5<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">8<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">1<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">6<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">4<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">2<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">3<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">1<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">5<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">9<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p><span style=\"color: #000000;\"><em><strong>\u8fdb\u884c Mann-Whitney U \u68c0\u9a8c\uff0c\u770b\u770b\u5b89\u6170\u5242\u7ec4\u60a3\u8005\u4e0e\u65b0\u836f\u7ec4\u60a3\u8005\u60ca\u6050\u53d1\u4f5c\u7684\u6b21\u6570\u662f\u5426\u5b58\u5728\u5dee\u5f02\u3002\u4f7f\u7528\u663e\u7740\u6027\u6c34\u5e73 0.05\u3002<\/strong><\/em><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1. \u9648\u8ff0\u5047\u8bbe\u3002<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>H <sub>0<\/sub> \uff1a<\/strong>\u4e24\u4e2a\u603b\u4f53\u76f8\u7b49<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>H <sub>a<\/sub> :<\/strong>\u4e24\u4e2a\u4eba\u53e3\u4e0d\u76f8\u7b49<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>2. \u786e\u5b9a\u7528\u4e8e\u5047\u8bbe\u7684\u663e\u7740\u6027\u6c34\u5e73\u3002<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u8be5\u95ee\u9898\u544a\u8bc9\u6211\u4eec\u5e94\u8be5\u4f7f\u7528 0.05 \u7684\u663e\u7740\u6027\u6c34\u5e73\u3002<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>3. \u6c42\u68c0\u9a8c\u7edf\u8ba1\u91cf\u3002<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u56de\u60f3\u4e00\u4e0b\uff0c\u68c0\u9a8c\u7edf\u8ba1\u91cf\u7528 U \u8868\u793a\uff0c\u662f U <sub>1<\/sub>\u548c U <sub>2<\/sub>\u4e2d\u8f83\u5c0f\u7684\u4e00\u4e2a\uff0c\u5b9a\u4e49\u5982\u4e0b\uff1a<\/span><\/p>\n<p> <span style=\"color: #000000;\">U <sub>1<\/sub> = n <sub>1<\/sub> n <sub>2<\/sub> + n <sub>1<\/sub> (n <sub>1<\/sub> +1)\/2 \u2013 R <sub>1<\/sub><\/span><\/p>\n<p> <span style=\"color: #000000;\">U <sub>2<\/sub> = n <sub>1<\/sub> n <sub>2<\/sub> + n <sub>2<\/sub> (n <sub>2<\/sub> +1)\/2 \u2013 R <sub>2<\/sub><\/span><\/p>\n<p><span style=\"color: #000000;\">\u5176\u4e2d n <sub>1<\/sub>\u548c n <sub>2<\/sub>\u5206\u522b\u662f\u6837\u672c 1 \u548c 2 \u7684\u6837\u672c\u5927\u5c0f\uff0cR <sub>1<\/sub>\u548c R <sub>2<\/sub>\u5206\u522b\u662f\u6837\u672c 1 \u548c 2 \u7684\u79e9\u4e4b\u548c\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4e3a\u4e86\u627e\u5230<\/span><span style=\"color: #000000;\">R <sub>1<\/sub>\u548c R <sub>2<\/sub> \uff0c\u6211\u4eec\u9700\u8981\u7ed3\u5408\u4e24\u7ec4\u7684\u89c2\u5bdf\u7ed3\u679c\u5e76\u5c06\u5b83\u4eec\u4ece\u5c0f\u5230\u5927\u6392\u5e8f\uff1a<\/span><\/p>\n<div style=\"width: 50%;\">\n<table>\n<thead>\n<tr>\n<th style=\"text-align: center;\"><span style=\"color: #008080;\">\u65b0\u836f<\/span><\/th>\n<th style=\"text-align: center;\"><span style=\"color: #ff0000;\">\u5b89\u6170\u5242<\/span><\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #008080;\"><strong>3<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #ff0000;\"><strong>4<\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #008080;\"><strong>5<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #ff0000;\"><strong>8<\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #008080;\"><strong>1<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #ff0000;\"><strong>6<\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #008080;\"><strong>4<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #ff0000;\"><strong>2<\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #008080;\"><strong>3<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #ff0000;\"><strong>1<\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #008080;\"><strong>5<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #ff0000;\"><strong>9<\/strong><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p><span style=\"color: #000000;\"><strong>\u6837\u672c\u603b\u6570\uff1a <span style=\"color: #008080;\">1<\/span> , <span style=\"color: #ff0000;\">1<\/span> , <span style=\"color: #ff0000;\">2<\/span> , <span style=\"color: #008080;\">3<\/span> , <span style=\"color: #008080;\">3<\/span> , <span style=\"color: #ff0000;\">4<\/span> , <span style=\"color: #008080;\">4<\/span> , <span style=\"color: #008080;\">5<\/span> , <span style=\"color: #008080;\">5<\/span> , <span style=\"color: #ff0000;\">6<\/span> , <span style=\"color: #ff0000;\">8<\/span> , <span style=\"color: #ff0000;\">9<\/span><\/strong><\/span><\/p>\n<div>\n<p><span style=\"color: #000000;\"><strong>\u6392\u540d\uff1a <span style=\"color: #008080;\">1.5<\/span> , <span style=\"color: #ff0000;\">1.5<\/span> , <span style=\"color: #ff0000;\">3<\/span> , <span style=\"color: #008080;\">4.5<\/span> , <span style=\"color: #008080;\">4.5<\/span> , <span style=\"color: #ff0000;\">6.5<\/span> , <span style=\"color: #008080;\">6.5<\/span> , <span style=\"color: #008080;\">8.5<\/span> , <span style=\"color: #008080;\">8.5<\/span> , <span style=\"color: #ff0000;\">10<\/span> , <span style=\"color: #ff0000;\">11<\/span> , <span style=\"color: #ff0000;\">12<\/span><\/strong><\/span><\/p>\n<p> <span style=\"color: #008080;\"><strong>R <sub>1<\/sub><\/strong><\/span> <span style=\"color: #000000;\">= \u6837\u672c 1 \u7684\u7b49\u7ea7\u603b\u548c = 1.5+4.5+4.5+6.5+8.5+8.5 = 34<\/span><\/p>\n<p> <span style=\"color: #ff0000;\"><strong>R <sub>2<\/sub><\/strong><\/span> <span style=\"color: #000000;\">= \u6837\u672c 2 \u7684\u7b49\u7ea7\u603b\u548c = 1.5+3+6.5+10+11+12 = 44<\/span><\/p>\n<p><span style=\"color: #000000;\">\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u4f7f\u7528\u6837\u672c\u5927\u5c0f n <sub>1<\/sub>\u548c n <sub>2<\/sub>\u4ee5\u53ca\u79e9\u548c R <sub>1<\/sub>\u548c R <sub>2<\/sub>\u6765\u627e\u5230 U <sub>1<\/sub>\u548c U <sub>2<\/sub> \u3002<\/span><\/p>\n<p> <span style=\"color: #000000;\"><sub>U1<\/sub> = 6(6) + 6(6+1)\/2 \u2013 34 = 23<\/span><\/p>\n<p> <span style=\"color: #000000;\"><sub>U2<\/sub> = 6(6) + 6(6+1)\/2 \u2013 44 = 13<\/span><\/p>\n<p><span style=\"color: #000000;\">\u6211\u4eec\u7684\u6d4b\u8bd5\u7edf\u8ba1\u91cf\u662f<sub>U1<\/sub>\u548c<sub>U2<\/sub>\u4e2d\u8f83\u5c0f\u7684\u4e00\u4e2a\uff0c\u6070\u597d\u662f U=13\u3002<\/span><\/p>\n<p><em><span style=\"color: #000000;\">\u6ce8\u610f\uff1a\u6211\u4eec\u8fd8\u53ef\u4ee5\u4f7f\u7528<a href=\"https:\/\/statorials.org\/cn\/\u66fc\u60e0\u7279\u5c3c-u-\u6d4b\u8bd5\u8ba1\u7b97\u5668\/\" target=\"_blank\" rel=\"noopener\">Mann-Whitney U \u68c0\u9a8c\u8ba1\u7b97\u5668<\/a>\u6765\u786e\u5b9a U = 13\u3002<\/span><\/em><\/p>\n<\/div>\n<p> <span style=\"color: #000000;\"><strong>4. \u62d2\u7edd\u6216\u4e0d\u62d2\u7edd\u539f\u5047\u8bbe\u3002<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u4f7f\u7528 n <sub>1<\/sub> = 6 \u548c n <sub>2<\/sub> = 6\uff0c\u663e\u7740\u6027\u6c34\u5e73\u4e3a 0.05\uff0cMann-Whitney U \u8868\u544a\u8bc9\u6211\u4eec\u4e34\u754c\u503c\u4e3a 5\uff1a<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-1381 size-full\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/mw_ex1.png\" alt=\"\u66fc\u60e0\u7279\u5c3c U \u68c0\u9a8c\u4e34\u754c\u503c\u8868\" width=\"544\" height=\"401\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p><span style=\"color: #000000;\">\u7531\u4e8e\u6211\u4eec\u7684\u68c0\u9a8c\u7edf\u8ba1\u91cf (13) \u5927\u4e8e\u4e34\u754c\u503c (5)\uff0c\u56e0\u6b64\u6211\u4eec\u65e0\u6cd5\u62d2\u7edd\u539f\u5047\u8bbe\u3002<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>5. \u89e3\u91ca\u7ed3\u679c\u3002<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u7531\u4e8e\u6211\u4eec\u672a\u80fd\u62d2\u7edd\u96f6\u5047\u8bbe\uff0c\u56e0\u6b64\u6211\u4eec\u6ca1\u6709\u8db3\u591f\u7684\u8bc1\u636e\u8868\u660e\u5b89\u6170\u5242\u7ec4\u60a3\u8005\u7ecf\u5386\u7684\u6050\u614c\u53d1\u4f5c\u6b21\u6570\u4e0e\u65b0\u836f\u7ec4\u60a3\u8005\u4e0d\u540c\u3002<\/span><\/p>\n<h3><span style=\"color: #000000;\"><strong>\u5b9e\u65bd\u4f8b2<\/strong><\/span><\/h3>\n<p><span style=\"color: #000000;\">\u6211\u4eec\u60f3\u77e5\u9053\u6bcf\u5468\u6bcf\u5929\u5b66\u4e60 30 \u5206\u949f\u662f\u5426\u6709\u52a9\u4e8e\u5b66\u751f\u5728\u8003\u8bd5\u4e2d\u53d6\u5f97\u66f4\u597d\u7684\u6210\u7ee9\u3002\u603b\u5171 15 \u540d\u60a3\u8005\u88ab\u968f\u673a\u5206\u914d\u5230\u7814\u7a76\u7ec4\u6216\u65e0\u7814\u7a76\u7ec4\u3002\u4e00\u5468\u540e\uff0c\u6240\u6709\u5b66\u751f\u90fd\u53c2\u52a0\u76f8\u540c\u7684\u8003\u8bd5\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4e24\u7ec4\u7684\u6d4b\u8bd5\u7ed3\u679c\u5982\u4e0b\u6240\u793a\uff1a<\/span><\/p>\n<div style=\"width: 50%;\">\n<table>\n<thead>\n<tr>\n<th style=\"text-align: center;\"><span style=\"color: #000000;\">\u5b66\u4e60<\/span><\/th>\n<th style=\"text-align: center;\"><span style=\"color: #000000;\">\u6ca1\u6709\u7814\u7a76<\/span><\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">89<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">88<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">92<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">93<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">94<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">95<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">96<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">75<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">91<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">72<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">99<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">80<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">84<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">81<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">90<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p><span style=\"color: #000000;\"><em><strong>\u6267\u884c Mann-Whitney U \u6d4b\u8bd5\uff0c\u770b\u770b\u7814\u7a76\u7ec4\u4e0e\u975e\u7814\u7a76\u7ec4\u7684\u6d4b\u8bd5\u5206\u6570\u662f\u5426\u5b58\u5728\u5dee\u5f02\u3002\u4f7f\u7528\u663e\u7740\u6027\u6c34\u5e73 0.01\u3002<\/strong><\/em><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1. \u9648\u8ff0\u5047\u8bbe\u3002<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>H <sub>0<\/sub> \uff1a<\/strong>\u4e24\u4e2a\u603b\u4f53\u76f8\u7b49<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>H <sub>a<\/sub> :<\/strong>\u4e24\u4e2a\u4eba\u53e3\u4e0d\u76f8\u7b49<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>2. \u786e\u5b9a\u7528\u4e8e\u5047\u8bbe\u7684\u663e\u7740\u6027\u6c34\u5e73\u3002<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u8be5\u95ee\u9898\u544a\u8bc9\u6211\u4eec\u5e94\u8be5\u4f7f\u7528 0.01 \u7684\u663e\u7740\u6027\u6c34\u5e73\u3002<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>3. \u6c42\u68c0\u9a8c\u7edf\u8ba1\u91cf\u3002<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u56de\u60f3\u4e00\u4e0b\uff0c\u68c0\u9a8c\u7edf\u8ba1\u91cf\u7528 U \u8868\u793a\uff0c\u662f U <sub>1<\/sub>\u548c U <sub>2<\/sub>\u4e2d\u8f83\u5c0f\u7684\u4e00\u4e2a\uff0c\u5b9a\u4e49\u5982\u4e0b\uff1a<\/span><\/p>\n<p> <span style=\"color: #000000;\">U <sub>1<\/sub> = n <sub>1<\/sub> n <sub>2<\/sub> + n <sub>1<\/sub> (n <sub>1<\/sub> +1)\/2 \u2013 R <sub>1<\/sub><\/span><\/p>\n<p> <span style=\"color: #000000;\">U <sub>2<\/sub> = n <sub>1<\/sub> n <sub>2<\/sub> + n <sub>2<\/sub> (n <sub>2<\/sub> +1)\/2 \u2013 R <sub>2<\/sub><\/span><\/p>\n<p><span style=\"color: #000000;\">\u5176\u4e2d n <sub>1<\/sub>\u548c n <sub>2<\/sub>\u5206\u522b\u662f\u6837\u672c 1 \u548c 2 \u7684\u6837\u672c\u5927\u5c0f\uff0cR <sub>1<\/sub>\u548c R <sub>2<\/sub>\u5206\u522b\u662f\u6837\u672c 1 \u548c 2 \u7684\u79e9\u4e4b\u548c\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4e3a\u4e86\u627e\u5230<\/span><span style=\"color: #000000;\">R <sub>1<\/sub>\u548c R <sub>2<\/sub> \uff0c\u6211\u4eec\u9700\u8981\u7ed3\u5408\u4e24\u7ec4\u7684\u89c2\u5bdf\u7ed3\u679c\u5e76\u5c06\u5b83\u4eec\u4ece\u5c0f\u5230\u5927\u6392\u5e8f\uff1a<\/span><\/p>\n<div style=\"width: 50%;\">\n<table>\n<thead>\n<tr>\n<th style=\"text-align: center;\"><strong><span style=\"color: #008080;\">\u5b66\u4e60<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"><span style=\"color: #ff0000;\">\u6ca1\u6709\u7814\u7a76<\/span><\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #008080;\"><strong>89<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"> <strong><span style=\"color: #ff0000;\">88<\/span><\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <strong><span style=\"color: #008080;\">92<\/span><\/strong><\/td>\n<td style=\"text-align: center;\"> <strong><span style=\"color: #ff0000;\">93<\/span><\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <strong><span style=\"color: #008080;\">94<\/span><\/strong><\/td>\n<td style=\"text-align: center;\"> <strong><span style=\"color: #ff0000;\">95<\/span><\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <strong><span style=\"color: #008080;\">96<\/span><\/strong><\/td>\n<td style=\"text-align: center;\"> <strong><span style=\"color: #ff0000;\">75<\/span><\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <strong><span style=\"color: #008080;\">91<\/span><\/strong><\/td>\n<td style=\"text-align: center;\"> <strong><span style=\"color: #ff0000;\">72<\/span><\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <strong><span style=\"color: #008080;\">99<\/span><\/strong><\/td>\n<td style=\"text-align: center;\"> <strong><span style=\"color: #ff0000;\">80<\/span><\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <strong><span style=\"color: #008080;\">84<\/span><\/strong><\/td>\n<td style=\"text-align: center;\"> <strong><span style=\"color: #ff0000;\">81<\/span><\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <strong><span style=\"color: #008080;\">90<\/span><\/strong><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p> <span style=\"color: #000000;\"><strong><span style=\"color: #000000;\"><span style=\"color: #ff0000;\">\u6837\u672c<\/span><span style=\"color: #ff0000;\">\u603b\u6570<\/span><span style=\"color: #ff0000;\">\uff1a<\/span> <span style=\"color: #ff0000;\">72\u300175\u300180\u300181\u300184\u300188\u300189\u300190\u300191\u300192\u300193\u300194\u300195\u300196\u300199<\/span> <span style=\"color: #008080;\">_<\/span> <span style=\"color: #ff0000;\">_<\/span> <span style=\"color: #008080;\">_<\/span> <span style=\"color: #008080;\">_<\/span> <span style=\"color: #008080;\">_<\/span> <span style=\"color: #008080;\">_<\/span> <span style=\"color: #ff0000;\">_<\/span> <span style=\"color: #008080;\">_<\/span> <span style=\"color: #ff0000;\">_<\/span> <span style=\"color: #008080;\">_<\/span> <span style=\"color: #008080;\">_<\/span><\/span><\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\"><strong><span style=\"color: #000000;\">\u884c\uff1a <span style=\"color: #ff0000;\">1<\/span> , <span style=\"color: #ff0000;\">2<\/span> , <span style=\"color: #ff0000;\">3<\/span> , <span style=\"color: #ff0000;\">4<\/span> , <span style=\"color: #008080;\">5<\/span> , <span style=\"color: #ff0000;\">6<\/span> , <span style=\"color: #008080;\">7<\/span> , <span style=\"color: #008080;\">8<\/span> , <span style=\"color: #008080;\">9<\/span> , <span style=\"color: #008080;\">10<\/span> , <span style=\"color: #ff0000;\">11<\/span> , <span style=\"color: #008080;\">12<\/span> , <span style=\"color: #ff0000;\">13<\/span> , <span style=\"color: #008080;\">14<\/span> , <span style=\"color: #008080;\">15<\/span><\/span><\/strong><\/span><\/p>\n<p> <span style=\"color: #008080;\"><strong>R <sub>1<\/sub><\/strong><\/span> <span style=\"color: #000000;\">= \u6837\u672c 1 \u7684\u7b49\u7ea7\u603b\u548c = 5+7+8+9+10+12+14+15 = 80<\/span><\/p>\n<p> <span style=\"color: #ff0000;\"><strong>R <sub>2<\/sub><\/strong><\/span> <span style=\"color: #000000;\">= \u6837\u672c 2 \u7684\u7b49\u7ea7\u603b\u548c = 1+2+3+4+6+11+13 = 40<\/span><\/p>\n<p><span style=\"color: #000000;\">\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u4f7f\u7528\u6837\u672c\u5927\u5c0f n <sub>1<\/sub>\u548c n <sub>2<\/sub>\u4ee5\u53ca\u79e9\u548c R <sub>1<\/sub>\u548c R <sub>2<\/sub>\u6765\u627e\u5230 U <sub>1<\/sub>\u548c U <sub>2<\/sub> \u3002<\/span><\/p>\n<p> <span style=\"color: #000000;\"><sub>U1<\/sub> = 8(7) + 8(8+1)\/2 \u2013 80 = 12<\/span><\/p>\n<p> <span style=\"color: #000000;\"><sub>U2<\/sub> = 8(7) + 7(7+1)\/2 \u2013 40 = 44<\/span><\/p>\n<p><span style=\"color: #000000;\">\u6211\u4eec\u7684\u6d4b\u8bd5\u7edf\u8ba1\u91cf\u662f<sub>U1<\/sub>\u548c<sub>U2<\/sub>\u4e2d\u8f83\u5c0f\u7684\u4e00\u4e2a\uff0c\u6070\u597d\u662f U=12\u3002<\/span><\/p>\n<p><em><span style=\"color: #000000;\">\u6ce8\u610f\uff1a\u6211\u4eec\u8fd8\u53ef\u4ee5\u4f7f\u7528<a href=\"https:\/\/statorials.org\/cn\/\u66fc\u60e0\u7279\u5c3c-u-\u6d4b\u8bd5\u8ba1\u7b97\u5668\/\" target=\"_blank\" rel=\"noopener\">Mann-Whitney U \u68c0\u9a8c\u8ba1\u7b97\u5668<\/a>\u6765\u786e\u5b9a U = 12\u3002<\/span><\/em><\/p>\n<p> <span style=\"color: #000000;\"><strong>4. \u62d2\u7edd\u6216\u4e0d\u62d2\u7edd\u539f\u5047\u8bbe\u3002<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u4f7f\u7528 n <sub>1<\/sub> = 8 \u548c n <sub>2<\/sub> = 7\uff0c\u663e\u7740\u6027\u6c34\u5e73\u4e3a 0.01\uff0cMann-Whitney U \u8868\u544a\u8bc9\u6211\u4eec\u4e34\u754c\u503c\u4e3a 6\uff1a<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-1383 size-full\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/mw_ex2.png\" alt=\"\u66fc\u60e0\u7279\u5c3c U \u68c0\u9a8c\u4e34\u754c\u503c\u8868\" width=\"544\" height=\"401\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p><span style=\"color: #000000;\">\u7531\u4e8e\u6211\u4eec\u7684\u68c0\u9a8c\u7edf\u8ba1\u91cf (12) \u5927\u4e8e\u4e34\u754c\u503c (6)\uff0c\u56e0\u6b64\u6211\u4eec\u65e0\u6cd5\u62d2\u7edd\u539f\u5047\u8bbe\u3002<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>5. \u89e3\u91ca\u7ed3\u679c\u3002<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u7531\u4e8e\u6211\u4eec\u672a\u80fd\u62d2\u7edd\u96f6\u5047\u8bbe\uff0c\u56e0\u6b64\u6211\u4eec\u6ca1\u6709\u8db3\u591f\u7684\u8bc1\u636e\u8868\u660e\u5b66\u4e60\u8fc7\u7684\u5b66\u751f\u7684\u8003\u8bd5\u6210\u7ee9\u4e0e\u672a\u5b66\u4e60\u8fc7\u7684\u5b66\u751f\u4e0d\u540c\u3002<\/span><\/p>\n<h2><span style=\"color: #000000;\"><strong>\u5176\u4ed6\u8d44\u6e90<\/strong><\/span><\/h2>\n<p> <a href=\"https:\/\/statorials.org\/cn\/\u66fc\u60e0\u7279\u5c3c-u-\u6d4b\u8bd5\u8ba1\u7b97\u5668\/\" target=\"_blank\" rel=\"noopener\">\u66fc\u60e0\u7279\u5c3c U \u68c0\u9a8c\u8ba1\u7b97\u5668<\/a><br \/>\u66fc\u60e0\u7279\u5c3c U \u8868<br \/><a href=\"https:\/\/statorials.org\/cn\/\u5982\u4f55\u5728-excel-\u4e2d\u6267\u884c\u66fc\u60e0\u7279\u5c3c-u-\u68c0\u9a8c\/\" target=\"_blank\" rel=\"noopener\">\u5982\u4f55\u5728 Excel \u4e2d\u6267\u884c\u66fc-\u60e0\u7279\u5c3c U \u68c0\u9a8c<\/a><br \/><a href=\"https:\/\/statorials.org\/cn\/\u66fc\u00b7\u60e0\u7279\u5c3c-u-\u6d4b\u8bd5-r\/\" target=\"_blank\" rel=\"noopener\">\u5982\u4f55\u5728 R \u4e2d\u6267\u884c Mann-Whitney U \u68c0\u9a8c<\/a><br \/><a href=\"https:\/\/statorials.org\/cn\/\u66fc\u00b7\u60e0\u7279\u5c3c-u-\u6d4b\u8bd5-python\/\">\u5982\u4f55\u4f7f\u7528 Python \u6267\u884c Mann-Whitney U \u68c0\u9a8c<\/a><br \/><a href=\"https:\/\/statorials.org\/cn\/\u66fc\u00b7\u60e0\u7279\u5c3c-u-\u68c0\u9a8c-spss\/\" target=\"_blank\" rel=\"noopener\">\u5982\u4f55\u5728 SPSS \u4e2d\u6267\u884c Mann-Whitney U \u68c0\u9a8c<\/a><br \/> <a href=\"https:\/\/statorials.org\/cn\/\u66fc\u00b7\u60e0\u7279\u5c3c-u-\u6d4b\u8bd5-stata\/\" target=\"_blank\" rel=\"noopener\">\u5982\u4f55\u5728 Stata \u4e2d\u6267\u884c Mann-Whitney U \u68c0\u9a8c<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5f53\u6837\u672c\u5206\u5e03\u4e0d\u5448\u6b63\u6001\u5206\u5e03\u4e14\u6837\u672c\u91cf\u8f83\u5c0f (n &lt; 30) \u65f6\uff0c Mann-Whitney U \u68c0\u9a8c\uff08\u6709\u65f6\u79f0\u4e3a [&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-422","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\/ 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