{"id":527,"date":"2023-07-29T15:03:25","date_gmt":"2023-07-29T15:03:25","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e7%bd%ae%e4%bf%a1%e5%8c%ba%e9%97%b4-f-%e5%88%86%e5%b8%83\/"},"modified":"2023-07-29T15:03:25","modified_gmt":"2023-07-29T15:03:25","slug":"%e7%bd%ae%e4%bf%a1%e5%8c%ba%e9%97%b4-f-%e5%88%86%e5%b8%83","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e7%bd%ae%e4%bf%a1%e5%8c%ba%e9%97%b4-f-%e5%88%86%e5%b8%83\/","title":{"rendered":"\u5982\u4f55\u4f7f\u7528 f \u5206\u5e03\u521b\u5efa\u7f6e\u4fe1\u533a\u95f4"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">\u4e3a\u4e86\u786e\u5b9a\u4e24\u4e2a\u603b\u4f53\u7684\u65b9\u5dee\u662f\u5426\u76f8\u7b49\uff0c\u6211\u4eec\u53ef\u4ee5\u8ba1\u7b97\u65b9\u5dee\u6bd4<strong>\u03c3 <sup>2<\/sup> <sub>1<\/sub> \/ \u03c3 <sup>2<\/sup> <sub>2<\/sub><\/strong> \uff0c\u5176\u4e2d \u03c3 <sup>2<\/sup> <sub>1<\/sub>\u662f\u603b\u4f53 1 \u7684\u65b9\u5dee\uff0c\u03c3 <sup>2<\/sup> <sub>2<\/sub>\u662f\u603b\u4f53 2 \u7684\u65b9\u5dee\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4e3a\u4e86\u4f30\u8ba1\u771f\u5b9e\u7684\u603b\u4f53\u65b9\u5dee\u6bd4\uff0c\u6211\u4eec\u901a\u5e38\u4ece\u6bcf\u4e2a\u603b\u4f53\u4e2d\u62bd\u53d6\u4e00\u4e2a<a href=\"https:\/\/statorials.org\/cn\/\u62bd\u6837\u65b9\u6cd5\/\" target=\"_blank\" rel=\"noopener\">\u7b80\u5355\u7684\u968f\u673a\u6837\u672c<\/a>\uff0c\u5e76\u8ba1\u7b97\u6837\u672c\u65b9\u5dee\u6bd4<strong>s <sub>1<\/sub> <sup>2<\/sup> \/ s <sub>2<\/sub> <sup>2<\/sup><\/strong> \uff0c\u5176\u4e2d s <sub>1<\/sub> <sup>2<\/sup>\u548c s <sub>2<\/sub> <sup>2<\/sup>\u662f\u6837\u672c 1 \u548c\u6837\u672c\u7684\u6837\u672c\u65b9\u5dee\u3002\u5206\u522b\u4e3a2\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u8be5\u68c0\u9a8c\u5047\u8bbe s <sub>1<\/sub> <sup>2<\/sup>\u548c s <sub>2<\/sub> <sup>2<\/sup>\u662f\u6839\u636e\u5927\u5c0f\u4e3a n <sub>1<\/sub>\u548c n <sub>2<\/sub>\u7684\u72ec\u7acb\u6837\u672c\u8ba1\u7b97\u5f97\u51fa\u7684\uff0c\u8fd9\u4e24\u4e2a\u6837\u672c\u90fd\u6765\u81ea\u6b63\u6001\u5206\u5e03\u603b\u4f53\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u8be5\u6bd4\u7387\u8ddd\u79bb 1 \u8d8a\u8fdc\uff0c\u7fa4\u4f53\u5185\u5dee\u5f02\u4e0d\u5e73\u7b49\u7684\u8bc1\u636e\u5c31\u8d8a\u6709\u529b\u3002<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u03c3 <sup>2<\/sup> <sub>1<\/sub> \/ \u03c3 <sup>2<\/sup> <sub>2<\/sub>\u7684<strong>(1-\u03b1)100% \u7f6e\u4fe1\u533a\u95f4<\/strong>\u5b9a\u4e49\u4e3a\uff1a<\/span><\/p>\n<p style=\"text-align: center;\"> <span style=\"color: #000000;\">(s <sub>1<\/sub> <sup>2<\/sup> \/ s <sub>2<\/sub> <sup>2<\/sup> ) * F <sub>n <sub>1<\/sub> -1, n <sub>2<\/sub> -1, \u03b1\/2<\/sub> \u2264 \u03c3 <sup>2<\/sup> <sub>1<\/sub> \/ \u03c3 <sup>2<\/sup> <sub>2<\/sub> \u2264 (s <sub>1<\/sub> <sup>2<\/sup> \/ s <sub>2<\/sub> <sup>2<\/sup> ) * F <sub>n <sub>2<\/sub> -1, n <sub>1<\/sub> -1,<\/sub> <sub>\u03b1\/2<\/sub><\/span><\/p>\n<p><span style=\"color: #000000;\">\u5176\u4e2d F <sub>n <sub>2<\/sub> -1\u3001n <sub>1<\/sub> -1\u3001\u03b1\/2<\/sub>\u548c F <sub>n <sub>1<\/sub> -1\u3001n <sub>2<\/sub> -1\u3001<\/sub> <sub>\u03b1\/2<\/sub> <sub>&nbsp;<\/sub>\u662f\u6240\u9009\u663e\u7740\u6027\u6c34\u5e73 \u03b1 \u7684\u5206\u5e03 F \u7684\u4e34\u754c\u503c\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4ee5\u4e0b\u793a\u4f8b\u8bf4\u660e\u5982\u4f55\u4f7f\u7528\u4e09\u79cd\u4e0d\u540c\u7684\u65b9\u6cd5\u521b\u5efa \u03c3 <sup>2<\/sup> <sub>1<\/sub> \/ \u03c3 <sup>2<\/sup> <sub>2<\/sub>\u7684\u7f6e\u4fe1\u533a\u95f4\uff1a<\/span><\/p>\n<ul>\n<li><span style=\"color: #000000;\">\u7528\u624b<\/span><\/li>\n<li><span style=\"color: #000000;\">\u4f7f\u7528\u5fae\u8f6fExcel<\/span><\/li>\n<li> <span style=\"color: #000000;\"><em>R<\/em>\u7edf\u8ba1\u8f6f\u4ef6\u7684\u4f7f\u7528<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u5bf9\u4e8e\u4ee5\u4e0b\u6bcf\u4e2a\u793a\u4f8b\uff0c\u6211\u4eec\u5c06\u4f7f\u7528\u4ee5\u4e0b\u4fe1\u606f\uff1a<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>\u03b1<\/strong> = 0.05<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>n <sub>1<\/sub><\/strong> = 16<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong><sub>n2<\/sub><\/strong> = 11<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>s <sub>1<\/sub> <sup>2<\/sup><\/strong> =28.2<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>s <sub>2<\/sub> <sup>2<\/sup><\/strong> = 19.3<\/span><\/li>\n<\/ul>\n<h2><span style=\"color: #000000;\"><strong>\u624b\u52a8\u521b\u5efa\u7f6e\u4fe1\u533a\u95f4<\/strong><\/span><\/h2>\n<p><span style=\"color: #000000;\">\u8981\u624b\u52a8\u8ba1\u7b97<strong>\u03c3 <sup>2<\/sup> <sub>1<\/sub> \/ \u03c3 <sup>2<\/sup> <sub>2<\/sub><\/strong>\u7684\u7f6e\u4fe1\u533a\u95f4\uff0c\u6211\u4eec\u53ea\u9700\u5c06\u6211\u4eec\u62e5\u6709\u7684\u6570\u5b57\u4ee3\u5165\u7f6e\u4fe1\u533a\u95f4\u516c\u5f0f\uff1a<\/span><\/p>\n<p style=\"text-align: center;\"> <span style=\"color: #000000;\">(s <sub>1<\/sub> <sup>2<\/sup> \/ s <sub>2<\/sub> <sup>2<\/sup> ) * F <sub>n1-1, n2-1,\u03b1\/2<\/sub> \u2264 \u03c3 <sup>2<\/sup> <sub>1<\/sub> \/ \u03c3 <sup>2<\/sup> <sub>2<\/sub> \u2264 (s <sub>1<\/sub> <sup>2<\/sup> \/ s <sub>2<\/sub> <sup>2<\/sup> ) * F <sub>n2-1, n1-1,<\/sub> <sub>\u03b1\/2<\/sub><\/span><\/p>\n<p><span style=\"color: #000000;\">\u6211\u4eec\u552f\u4e00\u7f3a\u5c11\u7684\u6570\u5b57\u662f\u4e34\u754c\u503c\u3002<\/span><span style=\"color: #000000;\">\u5e78\u8fd0\u7684\u662f\uff0c\u6211\u4eec\u53ef\u4ee5\u5728<a href=\"https:\/\/statorials.org\/cn\/f\u5206\u5e03\u8868\/\" target=\"_blank\" rel=\"noopener\">\u5206\u5e03\u8868 F<\/a>\u4e2d\u627e\u5230\u8fd9\u4e9b\u4e34\u754c\u503c\uff1a<\/span><\/p>\n<p> <span style=\"color: #000000;\">F <sub>n2-1, n1-1, \u03b1\/2<\/sub> = F <sub>10, 15, 0.025<\/sub> = <strong>3.0602<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">F <sub>n1-1, n2-1,<\/sub> <sub>\u03b1\/2<\/sub> = 1\/ F <sub>15, 10, 0.025<\/sub> = 1 \/ 3.5217 = <strong>0.2839<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><em>\uff08\u70b9\u51fb\u53ef\u653e\u5927\u8868\u683c\uff09<\/em><\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-489 size-full\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/f2.5.png\" alt=\"alpha = 0.025 \u7684 F \u5206\u5e03\u8868\u3002\" width=\"1361\" height=\"829\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p><span style=\"color: #000000;\">\u6211\u4eec\u73b0\u5728\u53ef\u4ee5\u5c06\u6240\u6709\u6570\u5b57\u4ee3\u5165\u7f6e\u4fe1\u516c\u5f0f\u533a\u95f4\uff1a<\/span><\/p>\n<p style=\"text-align: center;\"> <span style=\"color: #000000;\">(s <sub>1<\/sub> <sup>2<\/sup> \/ s <sub>2<\/sub> <sup>2<\/sup> ) * F <sub>n1-1, n2-1,\u03b1\/2<\/sub> \u2264 \u03c3 <sup>2<\/sup> <sub>1<\/sub> \/ \u03c3 <sup>2<\/sup> <sub>2<\/sub> \u2264 (s <sub>1<\/sub> <sup>2<\/sup> \/ s <sub>2<\/sub> <sup>2<\/sup> ) * F <sub>n2-1, n1-1,<\/sub> <sub>\u03b1\/2<\/sub><\/span><\/p>\n<p style=\"text-align: center;\"> <span style=\"color: #000000;\">(28.2 \/ 19.3) * (0.2839) \u2264 \u03c3 <sup>2<\/sup> <sub>1<\/sub> \/ \u03c3 <sup>2<\/sup> <sub>2<\/sub> \u2264 (28.2 \/ 19.3) * (3.0602)<\/span><\/p>\n<p style=\"text-align: center;\"> <span style=\"color: #000000;\">0.4148 \u2264 \u03c3 <sup>2<\/sup> <sub>1<\/sub> \/ \u03c3 <sup>2<\/sup> <sub>2<\/sub> \u2264 4.4714<\/span><\/p>\n<p><span style=\"color: #000000;\">\u56e0\u6b64\uff0c\u603b\u4f53\u65b9\u5dee\u6bd4\u7387\u7684 95% \u7f6e\u4fe1\u533a\u95f4\u4e3a<strong>(0.4148, 4.4714)<\/strong> \u3002<\/span><\/p>\n<h2><span style=\"color: #000000;\"><strong>\u4f7f\u7528 Excel \u521b\u5efa\u7f6e\u4fe1\u533a\u95f4<\/strong><\/span><\/h2>\n<p><span style=\"color: #000000;\">\u4e0b\u56fe\u663e\u793a\u4e86\u5982\u4f55\u5728 Excel \u4e2d\u8ba1\u7b97\u603b\u4f53\u65b9\u5dee\u6bd4\u7684 95% \u7f6e\u4fe1\u533a\u95f4\u3002\u7f6e\u4fe1\u533a\u95f4\u7684\u4e0b\u9650\u548c\u4e0a\u9650\u663e\u793a\u5728 E \u5217\u4e2d\uff0c\u7528\u4e8e\u67e5\u627e\u4e0b\u9650\u548c\u4e0a\u9650\u7684\u516c\u5f0f\u663e\u793a\u5728 F \u5217\u4e2d\uff1a<\/span><\/p>\n<p><span style=\"color: #000000;\">\u56e0\u6b64\uff0c\u603b\u4f53\u65b9\u5dee\u6bd4\u7387\u7684 95% \u7f6e\u4fe1\u533a\u95f4\u4e3a<strong>(0.4148, 4.4714)<\/strong> \u3002\u8fd9\u4e0e\u6211\u4eec\u624b\u52a8\u8ba1\u7b97\u7f6e\u4fe1\u533a\u95f4\u65f6\u5f97\u5230\u7684\u7ed3\u679c\u76f8\u7b26\u3002<\/span><\/p>\n<h2><span style=\"color: #000000;\"><strong>\u4f7f\u7528 R \u521b\u5efa\u7f6e\u4fe1\u533a\u95f4<\/strong><\/span><\/h2>\n<p><span style=\"color: #000000;\">\u4ee5\u4e0b\u4ee3\u7801\u8bf4\u660e\u4e86\u5982\u4f55\u8ba1\u7b97 R \u4e2d\u603b\u4f53\u65b9\u5dee\u6bd4\u7387\u7684 95% \u7f6e\u4fe1\u533a\u95f4\uff1a<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#define significance level, sample sizes, and sample variances\n<\/span>alpha &lt;- .05\nn1 &lt;- 16\nn2 &lt;- 11\nvar1 &lt;- 28.2\nvar2 &lt;- 19.3\n\n<span style=\"color: #008080;\">#define F critical values\n<\/span>upper_crit &lt;- 1\/qf(alpha\/2, n1-1, n2-1)\nlower_crit &lt;- qf(alpha\/2, n2-1, n1-1)\n\n<span style=\"color: #008080;\">#find confidence interval\n<\/span>lower_bound &lt;- (var1\/var2) * lower_crit\nupper_bound &lt;- (var1\/var2) * upper_crit\n\n<span style=\"color: #008080;\">#output confidence interval\n<\/span>paste0(\"(\", lower_bound, \", \", upper_bound, \" )\")\n\n#[1] \"(0.414899337980266, 4.47137571035219 )\"\n<\/strong><\/pre>\n<p><span style=\"color: #000000;\">\u56e0\u6b64\uff0c\u603b\u4f53\u65b9\u5dee\u6bd4\u7387\u7684 95% \u7f6e\u4fe1\u533a\u95f4\u4e3a<strong>(0.4148, 4.4714)<\/strong> \u3002\u8fd9\u4e0e\u6211\u4eec\u624b\u52a8\u8ba1\u7b97\u7f6e\u4fe1\u533a\u95f4\u65f6\u5f97\u5230\u7684\u7ed3\u679c\u76f8\u7b26\u3002<\/span><\/p>\n<h2><span style=\"color: #000000;\"><strong>\u5176\u4ed6\u8d44\u6e90<\/strong><\/span><\/h2>\n<p> <strong><a href=\"https:\/\/statorials.org\/cn\/\u5982\u4f55\u9605\u8bfb\u5206\u5e03\u8868f\/\" target=\"_blank\" rel=\"noopener\">\u5982\u4f55\u8bfb\u53d6F\u914d\u7535\u76d8<\/a><br \/><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\">Excel\u4e2d\u5982\u4f55\u6c42\u4e34\u754c\u503cF<\/a><\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u4e3a\u4e86\u786e\u5b9a\u4e24\u4e2a\u603b\u4f53\u7684\u65b9\u5dee\u662f\u5426\u76f8\u7b49\uff0c\u6211\u4eec\u53ef\u4ee5\u8ba1\u7b97\u65b9\u5dee\u6bd4\u03c3 2 1 \/ \u03c3 2 2 \uff0c\u5176\u4e2d \u03c3 2 1\u662f\u603b\u4f53 1 \u7684 [&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-527","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>\u5982\u4f55\u4f7f\u7528 F \u5206\u5e03\u521b\u5efa\u7f6e\u4fe1\u533a\u95f4 - Statorials<\/title>\n<meta name=\"description\" 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