{"id":729,"date":"2023-07-28T23:15:29","date_gmt":"2023-07-28T23:15:29","guid":{"rendered":"https:\/\/statorials.org\/tr\/ortalamalar-arasindaki-guven-araligi-farki\/"},"modified":"2023-07-28T23:15:29","modified_gmt":"2023-07-28T23:15:29","slug":"ortalamalar-arasindaki-guven-araligi-farki","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/ortalamalar-arasindaki-guven-araligi-farki\/","title":{"rendered":"Ortalamalar aras\u0131ndaki fark i\u00e7in g\u00fcven aral\u0131\u011f\u0131"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>Ortalamalar aras\u0131ndaki fark i\u00e7in bir g\u00fcven aral\u0131\u011f\u0131 (CI),<\/strong> belirli bir g\u00fcven d\u00fczeyine sahip iki pop\u00fclasyon ortalamas\u0131 aras\u0131ndaki ger\u00e7ek fark\u0131 i\u00e7ermesi muhtemel bir de\u011fer aral\u0131\u011f\u0131d\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu e\u011fitimde a\u015fa\u011f\u0131dakiler a\u00e7\u0131klanmaktad\u0131r:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Bu g\u00fcven aral\u0131\u011f\u0131n\u0131 yaratma motivasyonu.<\/span><\/li>\n<li> <span style=\"color: #000000;\">Bu g\u00fcven aral\u0131\u011f\u0131n\u0131 olu\u015fturman\u0131n form\u00fcl\u00fc.<\/span><\/li>\n<li> <span style=\"color: #000000;\">Bu g\u00fcven aral\u0131\u011f\u0131n\u0131n nas\u0131l hesaplanaca\u011f\u0131na dair bir \u00f6rnek.<\/span><\/li>\n<li> <span style=\"color: #000000;\">Bu g\u00fcven aral\u0131\u011f\u0131 nas\u0131l yorumlan\u0131r?<\/span><\/li>\n<\/ul>\n<h3> <span style=\"color: #000000;\"><strong>Ara\u00e7lar aras\u0131ndaki fark i\u00e7in CI: motivasyon<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Ara\u015ft\u0131rmac\u0131lar genellikle iki pop\u00fclasyonun ortalamalar\u0131 aras\u0131ndaki fark\u0131 tahmin etmek isterler. Bu fark\u0131 tahmin etmek i\u00e7in her pop\u00fclasyondan rastgele bir \u00f6rnek toplayacak ve her \u00f6rne\u011fin ortalamas\u0131n\u0131 hesaplayacaklar. Daha sonra iki ortalama aras\u0131ndaki fark\u0131 kar\u015f\u0131la\u015ft\u0131rabilirler.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Ancak \u00f6rnek ortalamalar aras\u0131ndaki fark\u0131n pop\u00fclasyon ortalamalar\u0131 aras\u0131ndaki ger\u00e7ek farka kar\u015f\u0131l\u0131k gelip gelmedi\u011finden emin olamazlar. Bu nedenle iki ortalama aras\u0131ndaki fark i\u00e7in bir <a href=\"https:\/\/statorials.org\/tr\/guvenilirlik-araligi\/\" target=\"_blank\" rel=\"noopener\">g\u00fcven aral\u0131\u011f\u0131<\/a> olu\u015fturabilirler. Bu, pop\u00fclasyon ortalamalar\u0131 aras\u0131ndaki ger\u00e7ek fark\u0131 i\u00e7ermesi muhtemel bir de\u011fer aral\u0131\u011f\u0131 sa\u011flar.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin, iki farkl\u0131 kaplumba\u011fa t\u00fcr\u00fc aras\u0131ndaki ortalama a\u011f\u0131rl\u0131k fark\u0131n\u0131 tahmin etmek istedi\u011fimizi varsayal\u0131m. Her pop\u00fclasyonda binlerce kaplumba\u011fa bulundu\u011fundan, her kaplumba\u011fay\u0131 ayr\u0131 ayr\u0131 tartmak \u00e7ok zaman al\u0131c\u0131 ve pahal\u0131 olacakt\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bunun yerine, her pop\u00fclasyondan 15 kaplumba\u011fadan olu\u015fan <a href=\"https:\/\/statorials.org\/tr\/ornekleme-yontemleri\/\" target=\"_blank\" rel=\"noopener\">basit rastgele bir \u00f6rnek<\/a> alabilir ve iki pop\u00fclasyon aras\u0131ndaki ortalama a\u011f\u0131rl\u0131ktaki ger\u00e7ek fark\u0131 tahmin etmek i\u00e7in her \u00f6rne\u011fin ortalama a\u011f\u0131rl\u0131\u011f\u0131n\u0131 kullanabiliriz:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-7543 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/confintmeans1.png\" alt=\"\u0130ki pop\u00fclasyon ortalamas\u0131 aras\u0131ndaki fark i\u00e7in g\u00fcven aral\u0131\u011f\u0131\" width=\"674\" height=\"224\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Sorun, \u00f6rneklerimizin rastgele olmas\u0131d\u0131r, bu nedenle iki \u00f6rnek aras\u0131ndaki ortalama a\u011f\u0131rl\u0131k fark\u0131n\u0131n, iki pop\u00fclasyon aras\u0131ndaki ortalama a\u011f\u0131rl\u0131k fark\u0131yla tam olarak e\u015fle\u015fece\u011fi garanti edilmez. Dolay\u0131s\u0131yla, bu belirsizli\u011fi yakalamak i\u00e7in, iki pop\u00fclasyon aras\u0131ndaki ortalama a\u011f\u0131rl\u0131ktaki ger\u00e7ek fark\u0131 i\u00e7ermesi muhtemel bir dizi de\u011fer i\u00e7eren bir g\u00fcven aral\u0131\u011f\u0131 olu\u015fturabiliriz.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Ara\u00e7lar aras\u0131ndaki fark i\u00e7in CI:<\/strong><\/span> <span style=\"color: #000000;\"><strong>form\u00fcl<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u0130ki ortalama aras\u0131ndaki farka ili\u015fkin g\u00fcven aral\u0131\u011f\u0131n\u0131 hesaplamak i\u00e7in a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullan\u0131r\u0131z:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>G\u00fcven aral\u0131\u011f\u0131<\/strong> = ( <span style=\"text-decoration: overline;\">x<\/span> <sub>1<\/sub> \u2013 <span style=\"text-decoration: overline;\">x<\/span> <sub>2<\/sub> ) +\/- t*\u221a((s <sub>p<\/sub> <sup>2<\/sup> \/n <sub>1<\/sub> ) + (s <sub>p<\/sub> <sup>2<\/sup> \/n <sub>2<\/sub> ))<\/span><\/p>\n<p> <span style=\"color: #000000;\">Alt\u0131n:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><span style=\"text-decoration: overline;\">x<\/span> <sub>1<\/sub> , <span style=\"text-decoration: overline;\">x<\/span> <sub>2<\/sub> : \u00f6rnek 1&#8217;in ortalamas\u0131, \u00f6rnek 2&#8217;nin ortalamas\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\">t: g\u00fcven d\u00fczeyine ve (n <sub>1<\/sub> + n <sub>2<\/sub> -2) serbestlik derecesine dayal\u0131 t-kritik de\u011feri<\/span><\/li>\n<li> <span style=\"color: #000000;\"><sub>sp<\/sub> <sup>2<\/sup> : birle\u015ftirilmi\u015f varyans<\/span><\/li>\n<li> <span style=\"color: #000000;\">n <sub>1<\/sub> , n <sub>2<\/sub> : \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc 1, \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc 2<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Alt\u0131n:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Birle\u015ftirilmi\u015f varyans \u015fu \u015fekilde hesaplan\u0131r:<\/span> <strong style=\"color: #000000;\">s <sub>p<\/sub> <sup>2<\/sup><\/strong> <span style=\"color: #000000;\">= ((n<\/span> <sub style=\"color: #000000;\">1<\/sub> <span style=\"color: #000000;\">-1)s<\/span> <sub style=\"color: #000000;\">1<\/sub> <sup style=\"color: #000000;\">2<\/sup> <span style=\"color: #000000;\">+ (n<\/span> <sub style=\"color: #000000;\">2<\/sub> <span style=\"color: #000000;\">-1)s<\/span> <sub style=\"color: #000000;\">2<\/sub> <sup style=\"color: #000000;\">2<\/sup> <span style=\"color: #000000;\">) \/ (n<\/span> <sub style=\"color: #000000;\">1<\/sub> <span style=\"color: #000000;\">+n<\/span> <sub style=\"color: #000000;\">2<\/sub> <span style=\"color: #000000;\">-2)<\/span><\/li>\n<li> <span style=\"color: #000000;\">T-kritik de\u011feri <strong>t,<\/strong> ters t da\u011f\u0131l\u0131m\u0131 hesaplay\u0131c\u0131s\u0131 kullan\u0131larak bulunabilir.<\/span><\/li>\n<\/ul>\n<h3> <span style=\"color: #000000;\"><strong>Ara\u00e7lar aras\u0131ndaki fark i\u00e7in CI:<\/strong><\/span> <span style=\"color: #000000;\"><strong>\u00f6rnek<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u0130ki farkl\u0131 kaplumba\u011fa t\u00fcr\u00fc aras\u0131ndaki ortalama a\u011f\u0131rl\u0131k fark\u0131n\u0131 tahmin etmek istedi\u011fimizi varsayal\u0131m. Bu nedenle her pop\u00fclasyondan rastgele 15 kaplumba\u011fa \u00f6rne\u011fi toplayaca\u011f\u0131z. Her numunenin \u00f6zet verileri a\u015fa\u011f\u0131da verilmi\u015ftir:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u00d6rnek 1:<\/strong><\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><span style=\"text-decoration: overline;\">x1<\/span> = <sub>310<\/sub><\/span><\/li>\n<li> <span style=\"color: #000000;\"><sub>1<\/sub> = 18,5<\/span><\/li>\n<li> <span style=\"color: #000000;\"><sub>n1<\/sub> = 15<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><strong>\u00d6rnek 2:<\/strong><\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><span style=\"text-decoration: overline;\">x2<\/span> <sub>=<\/sub> 300<\/span><\/li>\n<li> <span style=\"color: #000000;\"><sub>s2<\/sub> = 16,4<\/span><\/li>\n<li> <span style=\"color: #000000;\"><sub>n2<\/sub> = 15<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Pop\u00fclasyon ortalama a\u011f\u0131rl\u0131klar\u0131ndaki ger\u00e7ek fark i\u00e7in farkl\u0131 g\u00fcven aral\u0131klar\u0131n\u0131 nas\u0131l bulaca\u011f\u0131n\u0131z a\u015fa\u011f\u0131da a\u00e7\u0131klanm\u0131\u015ft\u0131r:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>%90 g\u00fcven aral\u0131\u011f\u0131:<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">(310-300) +\/- 1,70*\u221a((305,61\/15) + (305,61\/15)) = <strong>[-0,8589, 20,8589]<br \/><\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>%95 g\u00fcven aral\u0131\u011f\u0131:<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">(310-300) +\/- 2,05*\u221a((305,61\/15) + (305,61\/15)) = <strong>[-3,0757, 23,0757]<br \/><\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>%99 g\u00fcven aral\u0131\u011f\u0131:<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">(310-300) +\/- 2,76*\u221a((305,61\/15) + (305,61\/15)) = <strong>[-7,6389, 27,6389]<br \/><\/strong><\/span><\/p>\n<p> <em><span style=\"color: #000000;\"><strong>Not:<\/strong> Bu g\u00fcven aral\u0131klar\u0131n\u0131 <a href=\"https:\/\/statorials.org\/tr\/guven-araligi-hesaplayicisi-ortalamalar-arasindaki-fark\/\" target=\"_blank\" rel=\"noopener\">Ortalamalar Aras\u0131ndaki Fark Hesaplay\u0131c\u0131s\u0131 i\u00e7in \u0130statistiksel G\u00fcven Aral\u0131\u011f\u0131&#8217;n\u0131<\/a> kullanarak da bulabilirsiniz.<\/span><\/em><\/p>\n<p> <span style=\"color: #000000;\">G\u00fcven d\u00fczeyi ne kadar y\u00fcksek olursa g\u00fcven aral\u0131\u011f\u0131n\u0131n da o kadar geni\u015f olaca\u011f\u0131n\u0131 fark edeceksiniz. Bu mant\u0131kl\u0131 olmal\u0131, \u00e7\u00fcnk\u00fc daha geni\u015f aral\u0131klar\u0131n ger\u00e7ek n\u00fcfus ortalamas\u0131n\u0131 i\u00e7erme olas\u0131l\u0131\u011f\u0131 daha y\u00fcksektir, dolay\u0131s\u0131yla aral\u0131\u011f\u0131n ger\u00e7ek n\u00fcfus ortalamas\u0131n\u0131 i\u00e7erdi\u011finden daha &#8220;eminiz&#8221;.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Ara\u00e7lar aras\u0131ndaki fark i\u00e7in CI<\/strong><\/span> <span style=\"color: #000000;\"><strong>: yorumlama<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Bir g\u00fcven aral\u0131\u011f\u0131n\u0131 yorumlama \u015feklimiz \u015fu \u015fekildedir:<\/span><\/p>\n<blockquote>\n<p> <span style=\"color: #000000;\">[-3.0757, 23.0757] g\u00fcven aral\u0131\u011f\u0131n\u0131n iki kaplumba\u011fa pop\u00fclasyonu aras\u0131ndaki ortalama a\u011f\u0131rl\u0131ktaki ger\u00e7ek fark\u0131 i\u00e7erme olas\u0131l\u0131\u011f\u0131 %95&#8217;tir.<\/span><\/p>\n<\/blockquote>\n<p> <span style=\"color: #000000;\">Bu aral\u0131k &#8220;0&#8221; de\u011ferini i\u00e7erdi\u011finden, bu iki pop\u00fclasyondaki kaplumba\u011falar aras\u0131nda ortalama a\u011f\u0131rl\u0131k fark\u0131 olmamas\u0131n\u0131n m\u00fcmk\u00fcn oldu\u011fu anlam\u0131na gelir. Ba\u015fka bir deyi\u015fle, bu iki pop\u00fclasyondaki kaplumba\u011falar aras\u0131nda ortalama a\u011f\u0131rl\u0131k a\u00e7\u0131s\u0131ndan bir fark oldu\u011funu %95 g\u00fcvenle s\u00f6yleyemeyiz.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Ortalamalar aras\u0131ndaki fark i\u00e7in bir g\u00fcven aral\u0131\u011f\u0131 (CI), belirli bir g\u00fcven d\u00fczeyine sahip iki pop\u00fclasyon ortalamas\u0131 aras\u0131ndaki ger\u00e7ek fark\u0131 i\u00e7ermesi muhtemel bir de\u011fer aral\u0131\u011f\u0131d\u0131r. Bu e\u011fitimde a\u015fa\u011f\u0131dakiler a\u00e7\u0131klanmaktad\u0131r: Bu g\u00fcven aral\u0131\u011f\u0131n\u0131 yaratma motivasyonu. Bu g\u00fcven aral\u0131\u011f\u0131n\u0131 olu\u015fturman\u0131n form\u00fcl\u00fc. Bu g\u00fcven aral\u0131\u011f\u0131n\u0131n nas\u0131l hesaplanaca\u011f\u0131na dair bir \u00f6rnek. Bu g\u00fcven aral\u0131\u011f\u0131 nas\u0131l yorumlan\u0131r? Ara\u00e7lar aras\u0131ndaki fark i\u00e7in [&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-729","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>Ortalamalar aras\u0131ndaki fark i\u00e7in g\u00fcven aral\u0131\u011f\u0131 - Statorials<\/title>\n<meta name=\"description\" content=\"Ad\u0131m ad\u0131m \u00f6rnek de dahil olmak \u00fczere, iki ortalama aras\u0131ndaki fark i\u00e7in g\u00fcven aral\u0131\u011f\u0131n\u0131n nas\u0131l hesaplanaca\u011f\u0131na dair basit bir a\u00e7\u0131klama.\" \/>\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\/ortalamalar-arasindaki-guven-araligi-farki\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Ortalamalar aras\u0131ndaki fark i\u00e7in g\u00fcven aral\u0131\u011f\u0131 - 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