{"id":3141,"date":"2023-07-19T00:36:05","date_gmt":"2023-07-19T00:36:05","guid":{"rendered":"https:\/\/statorials.org\/tr\/hata-marjini-yorumlamak\/"},"modified":"2023-07-19T00:36:05","modified_gmt":"2023-07-19T00:36:05","slug":"hata-marjini-yorumlamak","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/hata-marjini-yorumlamak\/","title":{"rendered":"Hata pay\u0131 nas\u0131l yorumlan\u0131r: \u00f6rneklerle"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">\u0130statistiklerde <strong>hata pay\u0131<\/strong> , n\u00fcfus oran\u0131 veya n\u00fcfus ortalamas\u0131 tahmininin kesinli\u011fini de\u011ferlendirmek i\u00e7in kullan\u0131l\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/tr\/istatistik-ve-parametre\/\" target=\"_blank\" rel=\"noopener\">Pop\u00fclasyon parametreleri<\/a> i\u00e7in g\u00fcven aral\u0131klar\u0131n\u0131 hesaplarken genellikle bir hata marj\u0131 kullan\u0131r\u0131z.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki \u00f6rnekler, n\u00fcfus oran\u0131 ve n\u00fcfus ortalamas\u0131 i\u00e7in hata marj\u0131n\u0131n nas\u0131l hesaplanaca\u011f\u0131n\u0131 ve yorumlanaca\u011f\u0131n\u0131 g\u00f6stermektedir.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u00d6rnek 1: N\u00fcfus oran\u0131na ili\u015fkin hata marj\u0131n\u0131n yorumlanmas\u0131<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">N\u00fcfus oran\u0131na 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 = p<\/strong> <strong>+\/- z*(\u221a <span style=\"text-decoration: overline;\">p(1-p) \/ n<\/span> )<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Alt\u0131n:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>p:<\/strong> \u00f6rnek oran\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>z:<\/strong> se\u00e7ilen z de\u011feri<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>n:<\/strong> \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Denklemin +\/- i\u015faretinden sonra gelen k\u0131sm\u0131 hata pay\u0131n\u0131 temsil eder:<\/span><\/p>\n<p> <strong><span style=\"color: #000000;\">Hata pay\u0131 = z*(\u221a <span style=\"text-decoration: overline;\">p(1-p) \/ n<\/span> )<\/span><\/strong><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin, bir il\u00e7ede belirli bir yasay\u0131 destekleyen sakinlerin oran\u0131n\u0131 tahmin etmek istedi\u011fimizi varsayal\u0131m. 100 sakinden rastgele bir \u00f6rnek se\u00e7iyoruz ve onlara yasadaki konumlar\u0131n\u0131n ne oldu\u011funu soruyoruz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Sonu\u00e7lar burada:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">\u00d6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc <strong>n = 100<\/strong><\/span><\/li>\n<li> <span style=\"color: #000000;\">Kanun lehine oran <strong>p = 0,56<\/strong><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Yasay\u0131 destekleyen il\u00e7e sakinlerinin ger\u00e7ek oran\u0131 i\u00e7in %95&#8217;lik bir g\u00fcven aral\u0131\u011f\u0131 hesaplamak istedi\u011fimizi varsayal\u0131m.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Yukar\u0131daki form\u00fcl\u00fc kullanarak hata marj\u0131n\u0131 \u015fu \u015fekilde hesapl\u0131yoruz:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>Hata pay\u0131 = z*(\u221a <span style=\"text-decoration: overline;\">p(1-p) \/ n<\/span> )<\/strong><\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>Hata pay\u0131 = 1,96*(\u221a <span style=\"text-decoration: overline;\">0,56(1-0,56) \/ 100<\/span> )<\/strong><\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>Hata pay\u0131 = 0,0973<\/strong><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Daha sonra %95 g\u00fcven aral\u0131\u011f\u0131n\u0131 \u015fu \u015fekilde hesaplayabiliriz:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>G\u00fcven aral\u0131\u011f\u0131 = p<\/strong> <strong>+\/- z*(\u221a <span style=\"text-decoration: overline;\">p(1-p) \/ n<\/span> )<\/strong><\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>G\u00fcven aral\u0131\u011f\u0131 = 0,56<\/strong> <strong>+\/- 0,0973<\/strong><\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>G\u00fcven aral\u0131\u011f\u0131 = [.4627, .6573]<\/strong><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u0130l\u00e7ede yasaya taraftar olanlar\u0131n oran\u0131 i\u00e7in %95&#8217;lik g\u00fcven aral\u0131\u011f\u0131 <strong>[.4627, .6573]<\/strong> olarak ortaya \u00e7\u0131kmaktad\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu, yasay\u0131 destekleyen sakinlerin ger\u00e7ek oran\u0131n\u0131n %46,27 ile %65,73 aras\u0131nda oldu\u011fundan %95 emin oldu\u011fumuz anlam\u0131na geliyor.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rneklem sakinlerinin yasay\u0131 destekleyen oran\u0131 %56 idi, ancak bu \u00f6rneklem oran\u0131na hata pay\u0131n\u0131 \u00e7\u0131kar\u0131p ekleyerek bir g\u00fcven aral\u0131\u011f\u0131 olu\u015fturabiliyoruz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu g\u00fcven aral\u0131\u011f\u0131, il\u00e7e sakinlerinin yasa lehine ger\u00e7ek oran\u0131n\u0131 i\u00e7erme olas\u0131l\u0131\u011f\u0131 en y\u00fcksek olan bir de\u011fer aral\u0131\u011f\u0131n\u0131 temsil eder.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u00d6rnek 2: Pop\u00fclasyon ortalamas\u0131 i\u00e7in hata marj\u0131n\u0131n yorumlanmas\u0131<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Pop\u00fclasyon ortalamas\u0131na 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 = <span style=\"text-decoration: overline;\">x<\/span> +\/- z*(s\/\u221a <span style=\"border-top: 1px solid black;\">n<\/span> )<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Alt\u0131n:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong><span style=\"text-decoration: overline;\">x<\/span> :<\/strong> \u00f6rnek ortalama<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>z:<\/strong> z-kritik de\u011feri<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>s:<\/strong> numune standart sapmas\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>n:<\/strong> \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Denklemin +\/- i\u015faretinden sonra gelen k\u0131sm\u0131 hata pay\u0131n\u0131 temsil eder:<\/span><\/p>\n<p> <strong><span style=\"color: #000000;\">Hata pay\u0131 = z*(s\/ <span style=\"border-top: 1px solid black;\">\u221an<\/span> )<\/span><\/strong><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin, bir yunus pop\u00fclasyonunun ortalama a\u011f\u0131rl\u0131\u011f\u0131n\u0131 tahmin etmek istedi\u011fimizi varsayal\u0131m. A\u015fa\u011f\u0131daki bilgileri i\u00e7eren <a href=\"https:\/\/statorials.org\/tr\/ornekleme-yontemleri\/\" target=\"_blank\" rel=\"noopener\">rastgele bir yunus \u00f6rne\u011fi<\/a> topluyoruz:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">\u00d6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc <strong>n = 40<\/strong><\/span><\/li>\n<li> <span style=\"color: #000000;\">Ortalama numune a\u011f\u0131rl\u0131\u011f\u0131 <strong><span style=\"text-decoration: overline;\">x<\/span> = 300<\/strong><\/span><\/li>\n<li> <span style=\"color: #000000;\">\u00d6rneklem standart sapmas\u0131 <strong>s = 18,5<\/strong><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Yukar\u0131daki form\u00fcl\u00fc kullanarak hata marj\u0131n\u0131 \u015fu \u015fekilde hesapl\u0131yoruz:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>Hata pay\u0131 = z*(s\/ <span style=\"border-top: 1px solid black;\">\u221an<\/span> )<\/strong><\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>Hata pay\u0131 = 1,96*(18,5\/ <span style=\"text-decoration: overline;\">\u221a40<\/span> )<\/strong><\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>Hata pay\u0131 = 5,733<\/strong><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Daha sonra %95 g\u00fcven aral\u0131\u011f\u0131n\u0131 \u015fu \u015fekilde hesaplayabiliriz:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>G\u00fcven aral\u0131\u011f\u0131 = <span style=\"text-decoration: overline;\">x<\/span> +\/- z*(s\/\u221a <span style=\"border-top: 1px solid black;\">n<\/span> )<\/strong><\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>G\u00fcven aral\u0131\u011f\u0131 = 300 +\/- 5,733<\/strong><\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>G\u00fcven aral\u0131\u011f\u0131 =[294.267, 305.733]<\/strong><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Bu pop\u00fclasyondaki yunuslar\u0131n ortalama a\u011f\u0131rl\u0131\u011f\u0131 i\u00e7in %95 g\u00fcven aral\u0131\u011f\u0131 <strong>[294.267, 305.733]<\/strong> olarak bulunmu\u015ftur.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu, bu pop\u00fclasyondaki yunuslar\u0131n ger\u00e7ek ortalama a\u011f\u0131rl\u0131\u011f\u0131n\u0131n 294.267 pound ile 305.733 pound aras\u0131nda oldu\u011fundan %95 emin oldu\u011fumuz anlam\u0131na geliyor.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Numunedeki yunuslar\u0131n ortalama a\u011f\u0131rl\u0131\u011f\u0131 300 pounddu, ancak bu numuneden hata marj\u0131n\u0131 \u00e7\u0131kar\u0131p ekleyerek bir g\u00fcven aral\u0131\u011f\u0131 olu\u015fturabiliyoruz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu g\u00fcven aral\u0131\u011f\u0131, bu pop\u00fclasyondaki yunuslar\u0131n ger\u00e7ek ortalama a\u011f\u0131rl\u0131\u011f\u0131n\u0131 i\u00e7ermesi \u00e7ok muhtemel olan bir de\u011fer aral\u0131\u011f\u0131n\u0131 temsil eder.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Ek kaynaklar<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki e\u011fitimler hata pay\u0131 hakk\u0131nda ek bilgi sa\u011flar:<\/span><\/p>\n<p> <a href=\"https:\/\/statorials.org\/tr\/hata-payi-ve-standart-hata-arasindaki-fark-nedir\/\" target=\"_blank\" rel=\"noopener\">Hata pay\u0131 ve standart hata: fark nedir?<\/a><br \/> Excel&#8217;de hata pay\u0131 nas\u0131l bulunur?<br \/> <a href=\"https:\/\/statorials.org\/tr\/hata-payi-ti-84\/\" target=\"_blank\" rel=\"noopener\">TI-84 Hesap Makinesinde Hata Marj\u0131 Nas\u0131l Bulunur?<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0130statistiklerde hata pay\u0131 , n\u00fcfus oran\u0131 veya n\u00fcfus ortalamas\u0131 tahmininin kesinli\u011fini de\u011ferlendirmek i\u00e7in kullan\u0131l\u0131r. Pop\u00fclasyon parametreleri i\u00e7in g\u00fcven aral\u0131klar\u0131n\u0131 hesaplarken genellikle bir hata marj\u0131 kullan\u0131r\u0131z. A\u015fa\u011f\u0131daki \u00f6rnekler, n\u00fcfus oran\u0131 ve n\u00fcfus ortalamas\u0131 i\u00e7in hata marj\u0131n\u0131n nas\u0131l hesaplanaca\u011f\u0131n\u0131 ve yorumlanaca\u011f\u0131n\u0131 g\u00f6stermektedir. \u00d6rnek 1: N\u00fcfus oran\u0131na ili\u015fkin hata marj\u0131n\u0131n yorumlanmas\u0131 N\u00fcfus oran\u0131na ili\u015fkin g\u00fcven aral\u0131\u011f\u0131n\u0131 hesaplamak 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-3141","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>Hata Marj\u0131 Nas\u0131l Yorumlan\u0131r (\u00d6rneklerle) - Statorials<\/title>\n<meta name=\"description\" content=\"Bu e\u011fitimde hata pay\u0131n\u0131n nas\u0131l yorumlanaca\u011f\u0131 \u00e7e\u015fitli \u00f6rneklerle 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\/hata-marjini-yorumlamak\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Hata Marj\u0131 Nas\u0131l Yorumlan\u0131r (\u00d6rneklerle) - 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