{"id":1305,"date":"2023-07-26T22:57:59","date_gmt":"2023-07-26T22:57:59","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e8%90%a8%e7%89%b9%e6%80%9d%e9%9f%a6%e7%89%b9%e8%bf%91%e4%bc%bc\/"},"modified":"2023-07-26T22:57:59","modified_gmt":"2023-07-26T22:57:59","slug":"%e8%90%a8%e7%89%b9%e6%80%9d%e9%9f%a6%e7%89%b9%e8%bf%91%e4%bc%bc","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e8%90%a8%e7%89%b9%e6%80%9d%e9%9f%a6%e7%89%b9%e8%bf%91%e4%bc%bc\/","title":{"rendered":"\u8428\u7279\u601d\u97e6\u7279\u8fd1\u4f3c\uff1a\u5b9a\u4e49\u548c\u793a\u4f8b"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>Satterthwaite \u8fd1\u4f3c<\/strong>\u662f\u7528\u4e8e\u5728\u4e24\u4e2a\u6837\u672c t \u68c0\u9a8c\u4e2d\u67e5\u627e\u201c\u6709\u6548\u81ea\u7531\u5ea6\u201d\u7684\u516c\u5f0f\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u5b83\u6700\u5e38\u7528\u4e8e<a href=\"https:\/\/statorials.org\/cn\/\u97e6\u5c14\u5947t\u68c0\u9a8c\/\" target=\"_blank\" rel=\"noopener\">\u97e6\u5c14\u5947 t \u68c0\u9a8c<\/a>\uff0c\u8be5\u68c0\u9a8c\u6bd4\u8f83\u4e24\u4e2a\u72ec\u7acb\u6837\u672c\u7684\u5747\u503c\uff0c\u800c\u4e0d\u5047\u8bbe\u4ece\u4e2d\u62bd\u53d6<a href=\"https:\/\/statorials.org\/cn\/\u603b\u4f53\u4e0e\u6837\u672c\/\" target=\"_blank\" rel=\"noopener\">\u6837\u672c<\/a>\u7684\u603b\u4f53\u5177\u6709\u76f8\u7b49\u7684\u65b9\u5dee\u3002<\/span><\/p>\n<p> <span style=\"color: #000000;\">Satterthwaite \u8fd1\u4f3c\u7684\u516c\u5f0f\u5982\u4e0b\uff1a<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #000000;\">Degrees of freedom:<\/span> <span style=\"color: #000000;\">(s <sub>1<\/sub> <sup>2<\/sup> \/n <sub>1<\/sub> + s <sub>2<\/sub> <sup>2<\/sup> \/n <sub>2<\/sub> ) <sup>2<\/sup> \/ {[(s <sub>1<\/sub> <sup>2<\/sup> \/n <sub>1<\/sub> ) <sup>2<\/sup> \/(n <sub>1<\/sub> \u2013 1)] + [(s <sub>2<\/sub> <sup>2<\/sup> \/n <sub>2<\/sub> ) <sup>2<\/sup> \/(n <sub>2<\/sub> \u2013 1)]}<\/span>\n<\/strong><\/pre>\n<p><span style=\"color: #000000;\">\u91d1\u5b50\uff1a<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>s <sub>1<\/sub> <sup>2<\/sup> , s <sub>2<\/sub> <sup>2<\/sup> \uff1a<\/strong>\u5206\u522b\u662f\u7b2c\u4e00\u4e2a\u548c\u7b2c\u4e8c\u4e2a\u6837\u672c\u7684\u6837\u672c\u65b9\u5dee\u3002<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong><sub>n1<\/sub> , <sub>n2<\/sub> \uff1a<\/strong>\u5206\u522b\u662f\u7b2c\u4e00\u4e2a\u548c\u7b2c\u4e8c\u4e2a\u6837\u672c\u7684\u6837\u672c\u5927\u5c0f\u3002<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u4ee5\u4e0b\u793a\u4f8b\u6f14\u793a\u5982\u4f55\u4f7f\u7528 Satterthwaite \u8fd1\u4f3c\u6765\u8ba1\u7b97\u6709\u6548\u81ea\u7531\u5ea6\u3002<\/span><\/p>\n<h3><span style=\"color: #000000;\"><strong>\u793a\u4f8b\uff1aSatterthwaite \u8fd1\u4f3c\u7684\u8ba1\u7b97<\/strong><\/span><\/h3>\n<p><span style=\"color: #000000;\">\u5047\u8bbe\u6211\u4eec\u60f3\u77e5\u9053\u4e24\u79cd\u4e0d\u540c\u690d\u7269\u7269\u79cd\u7684\u5e73\u5747\u9ad8\u5ea6\u662f\u5426\u76f8\u7b49\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u5c06\u6536\u96c6\u6bcf\u4e2a\u7269\u79cd\u7684\u4e24\u4e2a\u7b80\u5355\u968f\u673a\u6837\u672c\uff0c\u5e76\u6d4b\u91cf\u6bcf\u4e2a\u6837\u672c\u4e2d\u690d\u7269\u7684\u9ad8\u5ea6\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4ee5\u4e0b\u503c\u8868\u793a\u6bcf\u4e2a\u6837\u672c\u7684\u9ad8\u5ea6\uff08\u4ee5\u82f1\u5bf8\u4e3a\u5355\u4f4d\uff09\uff1a<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>\u6837\u54c1 1:<\/strong> 14, 15, 15, 15, 16, 18, 22, 23, 24, 25, 25<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>\u6837\u54c1 2:<\/strong> 10, 12, 14, 15, 18, 22, 24, 27, 31, 33, 34, 34, 34<\/span><\/p>\n<p><span style=\"color: #000000;\">\u5747\u503c\u3001\u65b9\u5dee\u548c\u6837\u672c\u91cf\u5982\u4e0b\uff1a<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong><span style=\"border-top: 1px solid black;\">x1<\/span> <sub>=<\/sub><\/strong> 19.27<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong><span style=\"border-top: 1px solid black;\">x2<\/span> <sub>=<\/sub><\/strong> 23.69<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>s <sub>1<\/sub> <sup>2<\/sup><\/strong> = 20.42<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>s <sub>2<\/sub> <sup>2<\/sup><\/strong> = 83.23<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>n1<\/strong> <sub><strong>=<\/strong><\/sub> 11<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>n2<\/strong> = <sub><strong>13<\/strong><\/sub><\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u7136\u540e\u6211\u4eec\u53ef\u4ee5\u5c06\u65b9\u5dee\u548c\u6837\u672c\u5927\u5c0f\u7684\u503c\u4ee3\u5165 Satterthwaite \u8fd1\u4f3c\u516c\u5f0f\u4e2d\u6765\u627e\u5230\u6709\u6548\u81ea\u7531\u5ea6\uff1a<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #000000;\">df = (s <sub>1<\/sub> <sup>2<\/sup> \/n <sub>1<\/sub> + s <sub>2<\/sub> <sup>2<\/sup> \/n <sub>2<\/sub> ) <sup>2<\/sup> \/ {[(s <sub>1<\/sub> <sup>2<\/sup> \/n <sub>1<\/sub> ) <sup>2<\/sup> \/(n <sub>1<\/sub> \u2013 1)] + [(s <sub>2<\/sub> <sup>2<\/sup> \/n <sub>2<\/sub> ) <sup>2<\/sup> \/ (n <sub>2<\/sub> \u2013 1)]} \n\ndf = (20.42\/11 + 83.23\/13) <sup>2<\/sup> \/{[(20.42\/11) <sup>2<\/sup> \/(11 \u2013 1)] + [(83.23\/13) <sup>2<\/sup> \/(13 \u2013 1)]} = 18.137<\/span><\/strong><\/pre>\n<p><span style=\"color: #000000;\">\u6709\u6548\u81ea\u7531\u5ea6\u4e3a<strong>18,137<\/strong> \u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u901a\u5e38\uff0c\u6211\u4eec\u5c06\u6b64\u503c\u820d\u5165\u4e3a\u6700\u63a5\u8fd1\u7684\u6574\u6570\uff0c\u56e0\u6b64\u6211\u4eec\u5728 Welch t \u68c0\u9a8c\u4e2d\u4f7f\u7528\u7684\u81ea\u7531\u5ea6\u4e3a<strong>18<\/strong> \u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u6700\u540e\uff0c\u6211\u4eec\u5c06\u5728 t \u5206\u5e03\u8868\u4e2d\u627e\u5230\u4e34\u754c\u503c<em>t<\/em> \uff0c\u5b83\u5bf9\u5e94\u4e8e 18 \u4e2a\u81ea\u7531\u5ea6\u7684 alpha = 0.05 \u7684\u53cc\u5c3e\u68c0\u9a8c\uff1a<\/span> <\/p>\n<p><img decoding=\"async\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/t_dist.png\" alt=\"\u5206\u5e03\u8868T\" srcset=\"\" sizes=\"\"><\/p>\n<p><span style=\"color: #000000;\">\u4e34\u754c\u503c t \u662f<strong>2.101<\/strong> \u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u7136\u540e\u6211\u4eec\u5c06\u8ba1\u7b97\u6211\u4eec\u7684\u68c0\u9a8c\u7edf\u8ba1\u91cf\u5982\u4e0b\uff1a<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>\u68c0\u9a8c\u7edf\u8ba1\u91cf\uff1a(<\/strong> <span style=\"border-top: 1px solid black;\">x <sub>1<\/sub><\/span> \u2013 <span style=\"border-top: 1px solid black;\">x <sub>2<\/sub><\/span> ) \/ (\u221a <span style=\"border-top: 1px solid black;\">s <sub>1<\/sub> <sup>2<\/sup> \/n <sub>1<\/sub> + s <sub>2<\/sub> <sup>2<\/sup> \/n <sub>2<\/sub><\/span> )<\/span><\/p>\n<p><span style=\"color: #000000;\">\u68c0\u9a8c\u7edf\u8ba1\u91cf\uff1a(19.27 \u2013 23.69) \/ (\u221a <span style=\"border-top: 1px solid black;\">20.42\/11 + 83.23\/13<\/span> ) = -4.42 \/ 2.873 = <strong>-1.538<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u7531\u4e8e\u6211\u4eec\u7684\u68c0\u9a8c\u7edf\u8ba1\u91cf\u7684\u7edd\u5bf9\u503c (1.538) \u4e0d\u5927\u4e8e\u4e34\u754c\u503c t\uff0c\u56e0\u6b64\u6211\u4eec\u65e0\u6cd5\u62d2\u7edd\u68c0\u9a8c\u7684\u539f\u5047\u8bbe\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u6ca1\u6709\u8db3\u591f\u7684\u8bc1\u636e\u8868\u660e\u4e24\u4e2a\u4eba\u7fa4\u7684\u5747\u503c\u5b58\u5728\u663e\u7740\u5dee\u5f02\u3002<\/span><\/p>\n<h3><span style=\"color: #000000;\"><strong>\u5b9e\u8df5\u4e2d\u7684\u8428\u7279\u601d\u97e6\u7279\u8fd1\u4f3c<\/strong><\/span><\/h3>\n<p><span style=\"color: #000000;\">\u5728\u5b9e\u8df5\u4e2d\uff0c\u60a8\u5f88\u5c11\u9700\u8981\u624b\u52a8\u8ba1\u7b97 Satterthwaite \u8fd1\u4f3c\u503c\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u76f8\u53cd\uff0cR\u3001Python\u3001Excel\u3001SAS \u548c Stata \u7b49\u5e38\u89c1\u7edf\u8ba1\u8f6f\u4ef6\u90fd\u53ef\u4ee5\u4f7f\u7528 Satterthwaite \u8fd1\u4f3c\u6765\u81ea\u52a8\u4e3a\u60a8\u8ba1\u7b97\u6709\u6548\u81ea\u7531\u5ea6\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\/\u5047\u8bbe\u68c0\u9a8c1\/\" target=\"_blank\" rel=\"noopener\">\u5047\u8bbe\u68c0\u9a8c\u7b80\u4ecb<\/a><br \/><a href=\"https:\/\/statorials.org\/cn\/\u6d4b\u8bd5\u4f60\u7684\u4e24\u4e2a\u6837\u672c\/\" target=\"_blank\" rel=\"noopener\">\u4e8c\u6837\u672ct\u68c0\u9a8c\u7b80\u4ecb<\/a><br \/><a href=\"https:\/\/statorials.org\/cn\/\u97e6\u5c14\u5947t\u68c0\u9a8c\/\" target=\"_blank\" rel=\"noopener\">\u97e6\u5c14\u5947 t \u68c0\u9a8c\u7b80\u4ecb<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Satterthwaite \u8fd1\u4f3c\u662f\u7528\u4e8e\u5728\u4e24\u4e2a\u6837\u672c t \u68c0\u9a8c\u4e2d\u67e5\u627e\u201c\u6709\u6548\u81ea\u7531\u5ea6\u201d\u7684\u516c\u5f0f\u3002 \u5b83\u6700\u5e38\u7528\u4e8e\u97e6\u5c14\u5947 t  [&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-1305","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>\u8428\u7279\u601d\u97e6\u7279\u8fd1\u4f3c\uff1a\u5b9a\u4e49\u548c\u793a\u4f8b<\/title>\n<meta name=\"description\" content=\"\u672c\u6559\u7a0b\u63d0\u4f9b\u4e86 Satterthwaite 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