{"id":527,"date":"2023-07-29T15:03:25","date_gmt":"2023-07-29T15:03:25","guid":{"rendered":"https:\/\/statorials.org\/tr\/guven-araligi-f-dagilimi\/"},"modified":"2023-07-29T15:03:25","modified_gmt":"2023-07-29T15:03:25","slug":"guven-araligi-f-dagilimi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/guven-araligi-f-dagilimi\/","title":{"rendered":"F da\u011f\u0131l\u0131m\u0131n\u0131 kullanarak g\u00fcven aral\u0131\u011f\u0131 nas\u0131l olu\u015fturulur"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">\u0130ki pop\u00fclasyonun varyanslar\u0131n\u0131n e\u015fit olup olmad\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in, <strong>\u03c3 <sup>2<\/sup> <sub>1<\/sub> \/ \u03c3 <sup>2<\/sup> <sub>2<\/sub><\/strong> varyans oran\u0131n\u0131 hesaplayabiliriz; burada \u03c3 <sup>2<\/sup> <sub>1<\/sub> , pop\u00fclasyon 1&#8217;in varyans\u0131 ve \u03c3 <sup>2<\/sup> <sub>2,<\/sub> pop\u00fclasyon 2&#8217;nin varyans\u0131d\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Ger\u00e7ek pop\u00fclasyon varyans oran\u0131n\u0131 tahmin etmek i\u00e7in, genellikle her pop\u00fclasyondan <a href=\"https:\/\/statorials.org\/tr\/ornekleme-yontemleri\/\" target=\"_blank\" rel=\"noopener\">basit rastgele bir \u00f6rnek<\/a> al\u0131r\u0131z ve \u00f6rnek varyans oran\u0131n\u0131 hesaplar\u0131z, <strong>s <sub>1<\/sub> <sup>2<\/sup> \/ s <sub>2<\/sub> <sup>2<\/sup><\/strong> ; burada s <sub>1<\/sub> <sup>2<\/sup> ve s <sub>2<\/sub> <sup>2<\/sup> , \u00f6rnek 1 ve \u00f6rnek i\u00e7in \u00f6rnek varyanslard\u0131r. . s\u0131ras\u0131yla 2.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu test, <sub>s12<\/sub> ve <sub>s22&#8217;nin<\/sub> <sup>,<\/sup> her ikisi de normal da\u011f\u0131l\u0131m g\u00f6steren pop\u00fclasyonlardan <sup>olan<\/sup> , <sub>n1<\/sub> ve <sub>n2<\/sub> b\u00fcy\u00fckl\u00fc\u011f\u00fcndeki ba\u011f\u0131ms\u0131z \u00f6rneklerden hesapland\u0131\u011f\u0131n\u0131 varsayar.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu oran birden ne kadar uzakla\u015f\u0131rsa, pop\u00fclasyon i\u00e7indeki e\u015fit olmayan varyanslar\u0131n kan\u0131t\u0131 o kadar g\u00fc\u00e7l\u00fc olur.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u03c3 <sup>2<\/sup> <sub>1<\/sub> \/ \u03c3 <sup>2<\/sup> <sub>2<\/sub> i\u00e7in <strong>(1-\u03b1)%100 g\u00fcven aral\u0131\u011f\u0131<\/strong> \u015fu \u015fekilde tan\u0131mlan\u0131r:<\/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;\">burada F <sub>n <sub>2<\/sub> -1, n <sub>1<\/sub> -1, \u03b1\/2<\/sub> ve F <sub>n <sub>1<\/sub> -1, n <sub>2<\/sub> -1,<\/sub> <sub>\u03b1\/2<\/sub> <sub>&nbsp;<\/sub> se\u00e7ilen \u00f6nem seviyesi \u03b1 i\u00e7in F da\u011f\u0131l\u0131m\u0131n\u0131n kritik de\u011ferleridir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki \u00f6rnekler, \u00fc\u00e7 farkl\u0131 y\u00f6ntem kullan\u0131larak \u03c3 <sup>2<\/sup> <sub>1<\/sub> \/ \u03c3 <sup>2<\/sup> <sub>2<\/sub> i\u00e7in bir g\u00fcven aral\u0131\u011f\u0131n\u0131n nas\u0131l olu\u015fturulaca\u011f\u0131n\u0131 g\u00f6stermektedir:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">El ile<\/span><\/li>\n<li> <span style=\"color: #000000;\">Microsoft Excel&#8217;i kullan\u0131n<\/span><\/li>\n<li> <span style=\"color: #000000;\"><em>R<\/em> istatistik yaz\u0131l\u0131m\u0131n\u0131n kullan\u0131m\u0131<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki \u00f6rneklerin her biri i\u00e7in a\u015fa\u011f\u0131daki bilgileri kullanaca\u011f\u0131z:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>a<\/strong> = 0,05<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong><sub>n1<\/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>Manuel olarak bir g\u00fcven aral\u0131\u011f\u0131 olu\u015fturma<\/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> i\u00e7in bir g\u00fcven aral\u0131\u011f\u0131n\u0131 manuel olarak hesaplamak i\u00e7in elimizdeki say\u0131lar\u0131 g\u00fcven aral\u0131\u011f\u0131 form\u00fcl\u00fcne yerle\u015ftirece\u011fiz:<\/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>a\/2<\/sub><\/span><\/p>\n<p> <span style=\"color: #000000;\">Eksik oldu\u011fumuz tek rakamlar kritik de\u011ferlerdir.<\/span> <span style=\"color: #000000;\">Neyse ki bu kritik de\u011ferleri <a href=\"https:\/\/statorials.org\/tr\/f-dagitim-tablosu\/\" target=\"_blank\" rel=\"noopener\">F da\u011f\u0131t\u0131m tablosunda<\/a> bulabiliriz:<\/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>(Tabloyu yak\u0131nla\u015ft\u0131rmak i\u00e7in t\u0131klay\u0131n)<\/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=\"Alfa i\u00e7in F da\u011f\u0131l\u0131m tablosu = 0,025.\" width=\"1361\" height=\"829\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Art\u0131k t\u00fcm say\u0131lar\u0131 g\u00fcven form\u00fcl\u00fc aral\u0131\u011f\u0131na yerle\u015ftirebiliriz:<\/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>a\/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;\">Dolay\u0131s\u0131yla ana k\u00fctle varyanslar\u0131n\u0131n oran\u0131 i\u00e7in %95 g\u00fcven aral\u0131\u011f\u0131 <strong>(0,4148, 4,4714)&#8217;<\/strong> tir.<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>Excel Kullanarak G\u00fcven Aral\u0131\u011f\u0131 Olu\u015fturma<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki g\u00f6r\u00fcnt\u00fc, Excel&#8217;de pop\u00fclasyon varyans oran\u0131 i\u00e7in %95 g\u00fcven aral\u0131\u011f\u0131n\u0131n nas\u0131l hesaplanaca\u011f\u0131n\u0131 g\u00f6sterir. G\u00fcven aral\u0131\u011f\u0131n\u0131n alt ve \u00fcst s\u0131n\u0131rlar\u0131 E s\u00fctununda, alt ve \u00fcst s\u0131n\u0131rlar\u0131 bulmak i\u00e7in kullan\u0131lan form\u00fcl ise F s\u00fctununda g\u00f6sterilmi\u015ftir:<\/span><\/p>\n<p> <span style=\"color: #000000;\">Dolay\u0131s\u0131yla ana k\u00fctle varyanslar\u0131n\u0131n oran\u0131 i\u00e7in %95 g\u00fcven aral\u0131\u011f\u0131 <strong>(0,4148, 4,4714)&#8217;<\/strong> tir. Bu, g\u00fcven aral\u0131\u011f\u0131n\u0131 manuel olarak hesaplad\u0131\u011f\u0131m\u0131zda elde etti\u011fimiz sonu\u00e7la e\u015fle\u015fiyor.<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>R Kullanarak G\u00fcven Aral\u0131\u011f\u0131 Olu\u015fturma<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki kod, R&#8217;deki pop\u00fclasyon varyanslar\u0131n\u0131n oran\u0131 i\u00e7in %95 g\u00fcven aral\u0131\u011f\u0131n\u0131n nas\u0131l hesaplanaca\u011f\u0131n\u0131 g\u00f6sterir:<\/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;\">Dolay\u0131s\u0131yla ana k\u00fctle varyanslar\u0131n\u0131n oran\u0131 i\u00e7in %95 g\u00fcven aral\u0131\u011f\u0131 <strong>(0,4148, 4,4714)&#8217;<\/strong> tir. Bu, g\u00fcven aral\u0131\u011f\u0131n\u0131 manuel olarak hesaplad\u0131\u011f\u0131m\u0131zda elde etti\u011fimiz sonu\u00e7la e\u015fle\u015fiyor.<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>Ek kaynaklar<\/strong><\/span><\/h2>\n<p> <strong><a href=\"https:\/\/statorials.org\/tr\/dagitim-tablosu-f-nasil-okunur\/\" target=\"_blank\" rel=\"noopener\">F da\u011f\u0131t\u0131m panosu nas\u0131l okunur<\/a><br \/> Excel&#8217;de kritik F de\u011feri nas\u0131l bulunur?<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0130ki pop\u00fclasyonun varyanslar\u0131n\u0131n e\u015fit olup olmad\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in, \u03c3 2 1 \/ \u03c3 2 2 varyans oran\u0131n\u0131 hesaplayabiliriz; burada \u03c3 2 1 , pop\u00fclasyon 1&#8217;in varyans\u0131 ve \u03c3 2 2, pop\u00fclasyon 2&#8217;nin varyans\u0131d\u0131r. Ger\u00e7ek pop\u00fclasyon varyans oran\u0131n\u0131 tahmin etmek i\u00e7in, genellikle her pop\u00fclasyondan basit rastgele bir \u00f6rnek al\u0131r\u0131z ve \u00f6rnek varyans oran\u0131n\u0131 hesaplar\u0131z, s 1 [&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-rehber"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.3 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>F Da\u011f\u0131l\u0131m\u0131 Kullan\u0131larak G\u00fcven Aral\u0131\u011f\u0131 Nas\u0131l Olu\u015fturulur - Statorials<\/title>\n<meta name=\"description\" content=\"Bu e\u011fitimde, iki varyans\u0131n oran\u0131 i\u00e7in bir g\u00fcven aral\u0131\u011f\u0131 olu\u015fturmak amac\u0131yla F da\u011f\u0131l\u0131m\u0131n\u0131n nas\u0131l kullan\u0131laca\u011f\u0131 a\u00e7\u0131klanmaktad\u0131r.\" \/>\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\/tr\/guven-araligi-f-dagilimi\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"F Da\u011f\u0131l\u0131m\u0131 Kullan\u0131larak G\u00fcven Aral\u0131\u011f\u0131 Nas\u0131l Olu\u015fturulur - 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