{"id":524,"date":"2023-07-29T15:03:25","date_gmt":"2023-07-29T15:03:25","guid":{"rendered":"https:\/\/statorials.org\/ja\/%e4%bf%a1%e9%a0%bc%e5%8c%ba%e9%96%93-f-%e5%88%86%e5%b8%83\/"},"modified":"2023-07-29T15:03:25","modified_gmt":"2023-07-29T15:03:25","slug":"%e4%bf%a1%e9%a0%bc%e5%8c%ba%e9%96%93-f-%e5%88%86%e5%b8%83","status":"publish","type":"post","link":"https:\/\/statorials.org\/ja\/%e4%bf%a1%e9%a0%bc%e5%8c%ba%e9%96%93-f-%e5%88%86%e5%b8%83\/","title":{"rendered":"F \u5206\u5e03\u3092\u4f7f\u7528\u3057\u3066\u4fe1\u983c\u533a\u9593\u3092\u4f5c\u6210\u3059\u308b\u65b9\u6cd5"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">2 \u3064\u306e\u6bcd\u96c6\u56e3\u306e\u5206\u6563\u304c\u7b49\u3057\u3044\u304b\u3069\u3046\u304b\u3092\u5224\u65ad\u3059\u308b\u306b\u306f\u3001\u5206\u6563\u6bd4<strong>\u03c3 <sup>2<\/sup> <sub>1<\/sub> \/ \u03c3 <sup>2<\/sup> <sub>2<\/sub><\/strong>\u3092\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002\u3053\u3053\u3067\u3001\u03c3 <sup>2<\/sup> <sub>1<\/sub>\u306f\u6bcd\u96c6\u56e3 1 \u306e\u5206\u6563\u3001\u03c3 <sup>2<\/sup> <sub>2<\/sub>\u306f\u6bcd\u96c6\u56e3 2 \u306e\u5206\u6563\u3067\u3059\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u771f\u306e\u6bcd\u96c6\u56e3\u5206\u6563\u6bd4\u3092\u63a8\u5b9a\u3059\u308b\u306b\u306f\u3001\u901a\u5e38\u3001\u5404\u6bcd\u96c6\u56e3\u304b\u3089 <a href=\"https:\/\/statorials.org\/ja\/\u30b5\u30f3\u30d5\u309a\u30ea\u30f3\u30af\u3099\u65b9\u6cd5\/\" target=\"_blank\" rel=\"noopener\">\u5358\u7d14\u306a\u7121\u4f5c\u70ba\u30b5\u30f3\u30d7\u30eb<\/a>\u3092\u53d6\u5f97\u3057\u3001\u30b5\u30f3\u30d7\u30eb\u5206\u6563\u6bd4<strong>s <sub>1<\/sub> <sup>2<\/sup> \/ s <sub>2<\/sub> <sup>2<\/sup><\/strong>\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002\u3053\u3053\u3067\u3001s <sub>1<\/sub> <sup>2<\/sup>\u3068 s <sub>2<\/sub> <sup>2<\/sup>\u306f\u30b5\u30f3\u30d7\u30eb 1 \u3068\u30b5\u30f3\u30d7\u30eb\u306e\u30b5\u30f3\u30d7\u30eb\u5206\u6563\u3067\u3059\u3002 \u3002\u305d\u308c\u305e\u308c2\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u3053\u306e\u691c\u5b9a\u306f\u3001s <sub>1<\/sub> <sup>2<\/sup>\u3068 s <sub>2<\/sub> <sup>2 \u304c<\/sup>\u3001\u3069\u3061\u3089\u3082\u6b63\u898f\u5206\u5e03\u6bcd\u96c6\u56e3\u304b\u3089\u306e\u30b5\u30a4\u30ba n <sub>1<\/sub>\u3068 n <sub>2<\/sub>\u306e\u72ec\u7acb\u3057\u305f\u30b5\u30f3\u30d7\u30eb\u304b\u3089\u8a08\u7b97\u3055\u308c\u308b\u3053\u3068\u3092\u524d\u63d0\u3068\u3057\u3066\u3044\u307e\u3059\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u3053\u306e\u6bd4\u7387\u304c 1 \u304b\u3089\u9060\u3056\u304b\u308b\u307b\u3069\u3001\u6bcd\u96c6\u56e3\u5185\u306e\u5206\u6563\u304c\u4e0d\u5747\u7b49\u3067\u3042\u308b\u8a3c\u62e0\u304c\u5f37\u304f\u306a\u308a\u307e\u3059\u3002<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u03c3 <sup>2<\/sup> <sub>1<\/sub> \/ \u03c3 <sup>2<\/sup> <sub>2<\/sub>\u306e<strong>(1-\u03b1)100% \u4fe1\u983c\u533a\u9593\u306f<\/strong>\u6b21\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u3002<\/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\u3001<\/sub> <sub>\u03b1\/2<\/sub><\/span><\/p>\n<p><span style=\"color: #000000;\">\u3053\u3053\u3067\u3001F <sub>n <sub>2<\/sub> -1\u3001n <sub>1<\/sub> -1\u3001\u03b1\/2<\/sub>\u304a\u3088\u3073 F <sub>n <sub>1<\/sub> -1\u3001n <sub>2<\/sub> -1\u3001<\/sub> <sub>\u03b1\/2<\/sub> <sub>&nbsp;<\/sub>\u306f\u3001\u9078\u629e\u3055\u308c\u305f\u6709\u610f\u6c34\u6e96 \u03b1 \u306b\u5bfe\u3059\u308b\u5206\u5e03 F \u306e\u81e8\u754c\u5024\u3067\u3059\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u6b21\u306e\u4f8b\u306f\u30013 \u3064\u306e\u7570\u306a\u308b\u65b9\u6cd5\u3092\u4f7f\u7528\u3057\u3066 \u03c3 <sup>2<\/sup> <sub>1<\/sub> \/ \u03c3 <sup>2<\/sup> <sub>2<\/sub>\u306e\u4fe1\u983c\u533a\u9593\u3092\u4f5c\u6210\u3059\u308b\u65b9\u6cd5\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002<\/span><\/p>\n<ul>\n<li><span style=\"color: #000000;\">\u624b\u306b\u3088\u3063\u3066<\/span><\/li>\n<li><span style=\"color: #000000;\">Microsoft Excel\u3092\u4f7f\u7528\u3059\u308b<\/span><\/li>\n<li><span style=\"color: #000000;\"><em>R<\/em>\u7d71\u8a08\u30bd\u30d5\u30c8\u306e\u5229\u7528<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u6b21\u306e\u5404\u4f8b\u3067\u306f\u3001\u6b21\u306e\u60c5\u5831\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002<\/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>\u4fe1\u983c\u533a\u9593\u3092\u624b\u52d5\u3067\u4f5c\u6210\u3059\u308b<\/strong><\/span><\/h2>\n<p><span style=\"color: #000000;\"><strong>\u03c3 <sup>2<\/sup> <sub>1<\/sub> \/ \u03c3 <sup>2<\/sup> <sub>2<\/sub><\/strong>\u306e\u4fe1\u983c\u533a\u9593\u3092\u624b\u52d5\u3067\u8a08\u7b97\u3059\u308b\u306b\u306f\u3001\u5f97\u305f\u6570\u5024\u3092\u4fe1\u983c\u533a\u9593\u306e\u5f0f\u306b\u4ee3\u5165\u3059\u308b\u3060\u3051\u3067\u3059\u3002<\/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;\">\u6b20\u843d\u3057\u3066\u3044\u308b\u6570\u5024\u306f\u81e8\u754c\u5024\u3060\u3051\u3067\u3059\u3002<\/span><span style=\"color: #000000;\">\u5e78\u3044\u306a\u3053\u3068\u306b\u3001<a href=\"https:\/\/statorials.org\/ja\/f\u5206\u5e03\u8868\/\" target=\"_blank\" rel=\"noopener\">\u5206\u5e03\u30c6\u30fc\u30d6\u30eb F<\/a>\u3067\u3053\u308c\u3089\u306e\u91cd\u8981\u306a\u5024\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/span><\/p>\n<p> <span style=\"color: #000000;\">F <sub>n2-1\u3001n1-1\u3001\u03b1\/2<\/sub> = F <sub>10\u300115\u30010.025<\/sub> = <strong>3.0602<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">F <sub>n1-1\u3001n2-1\u3001<\/sub> <sub>\u03b1\/2<\/sub> = 1\/F <sub>15\u300110\u30010.025<\/sub> = 1 \/ 3.5217 = <strong>0.2839<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><em>(\u30af\u30ea\u30c3\u30af\u3059\u308b\u3068\u8868\u304c\u62e1\u5927\u3055\u308c\u307e\u3059)<\/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=\"\u30a2\u30eb\u30d5\u30a1\u306e F \u5206\u5e03\u8868 = 0.025\u3002\" width=\"1361\" height=\"829\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p><span style=\"color: #000000;\">\u3053\u308c\u3067\u3001\u3059\u3079\u3066\u306e\u6570\u5024\u3092\u4fe1\u983c\u5f0f\u533a\u9593\u306b\u4ee3\u5165\u3067\u304d\u307e\u3059\u3002<\/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;\">\u3057\u305f\u304c\u3063\u3066\u3001\u6bcd\u96c6\u56e3\u5206\u6563\u6bd4\u306e 95% \u4fe1\u983c\u533a\u9593\u306f<strong>(0.4148, 4.4714)<\/strong>\u3068\u306a\u308a\u307e\u3059\u3002<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>Excel \u3092\u4f7f\u7528\u3057\u305f\u4fe1\u983c\u533a\u9593\u306e\u4f5c\u6210<\/strong><\/span><\/h2>\n<p><span style=\"color: #000000;\">\u6b21\u306e\u56f3\u306f\u3001Excel \u3067\u6bcd\u96c6\u56e3\u5206\u6563\u6bd4\u306e 95% \u4fe1\u983c\u533a\u9593\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002\u4fe1\u983c\u533a\u9593\u306e\u4e0b\u9650\u3068\u4e0a\u9650\u306f\u5217 E \u306b\u793a\u3055\u308c\u3001\u4e0b\u9650\u3068\u4e0a\u9650\u3092\u6c42\u3081\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u308b\u5f0f\u306f\u5217 F \u306b\u793a\u3055\u308c\u307e\u3059\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u3057\u305f\u304c\u3063\u3066\u3001\u6bcd\u96c6\u56e3\u5206\u6563\u6bd4\u306e 95% \u4fe1\u983c\u533a\u9593\u306f<strong>(0.4148, 4.4714)<\/strong>\u3068\u306a\u308a\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u4fe1\u983c\u533a\u9593\u3092\u624b\u52d5\u3067\u8a08\u7b97\u3057\u305f\u3068\u304d\u306b\u5f97\u3089\u308c\u305f\u5024\u3068\u4e00\u81f4\u3057\u307e\u3059\u3002<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>R \u3092\u4f7f\u7528\u3057\u305f\u4fe1\u983c\u533a\u9593\u306e\u4f5c\u6210<\/strong><\/span><\/h2>\n<p><span style=\"color: #000000;\">\u6b21\u306e\u30b3\u30fc\u30c9\u306f\u3001R \u306e\u6bcd\u96c6\u56e3\u5206\u6563\u6bd4\u306e 95% \u4fe1\u983c\u533a\u9593\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002<\/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;\">\u3057\u305f\u304c\u3063\u3066\u3001\u6bcd\u96c6\u56e3\u5206\u6563\u6bd4\u306e 95% \u4fe1\u983c\u533a\u9593\u306f<strong>(0.4148, 4.4714)<\/strong>\u3068\u306a\u308a\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u4fe1\u983c\u533a\u9593\u3092\u624b\u52d5\u3067\u8a08\u7b97\u3057\u305f\u3068\u304d\u306b\u5f97\u3089\u308c\u305f\u5024\u3068\u4e00\u81f4\u3057\u307e\u3059\u3002<\/span><\/p>\n<h2><span style=\"color: #000000;\"><strong>\u8ffd\u52a0\u30ea\u30bd\u30fc\u30b9<\/strong><\/span><\/h2>\n<p><strong><a href=\"https:\/\/statorials.org\/ja\/\u5206\u5e03\u8868f\u306e\u898b\u65b9\/\" target=\"_blank\" rel=\"noopener\">F\u5206\u96fb\u76e4\u306e\u898b\u65b9<\/a><br \/><a href=\"https:\/\/statorials.org\/ja\/-10\/\" target=\"_blank\" rel=\"noopener\">Excel\u3067\u81e8\u754c\u5024F\u3092\u898b\u3064\u3051\u308b\u65b9\u6cd5<\/a><\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>2 \u3064\u306e\u6bcd\u96c6\u56e3\u306e\u5206\u6563\u304c\u7b49\u3057\u3044\u304b\u3069\u3046\u304b\u3092\u5224\u65ad\u3059\u308b\u306b\u306f\u3001\u5206\u6563\u6bd4\u03c3 2 1 \/ \u03c3 2 2\u3092\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002\u3053\u3053\u3067\u3001\u03c3 2 1\u306f\u6bcd\u96c6\u56e3 1 \u306e\u5206\u6563\u3001\u03c3 2 2\u306f\u6bcd\u96c6\u56e3 2 \u306e\u5206\u6563\u3067\u3059\u3002 \u771f\u306e\u6bcd\u96c6\u56e3\u5206\u6563\u6bd4\u3092\u63a8\u5b9a\u3059\u308b\u306b\u306f\u3001\u901a\u5e38\u3001\u5404\u6bcd [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[16],"tags":[],"class_list":["post-524","post","type-post","status-publish","format-standard","hentry","category-16"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>F \u5206\u5e03\u3092\u4f7f\u7528\u3057\u3066\u4fe1\u983c\u533a\u9593\u3092\u4f5c\u6210\u3059\u308b\u65b9\u6cd5 - Statorials<\/title>\n<meta name=\"description\" content=\"\u3053\u306e\u30c1\u30e5\u30fc\u30c8\u30ea\u30a2\u30eb\u3067\u306f\u3001F \u5206\u5e03\u3092\u4f7f\u7528\u3057\u3066 2 \u3064\u306e\u5206\u6563\u306e\u6bd4\u306e\u4fe1\u983c\u533a\u9593\u3092\u4f5c\u6210\u3059\u308b\u65b9\u6cd5\u3092\u8aac\u660e\u3057\u307e\u3059\u3002\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, 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