{"id":1022,"date":"2023-07-27T23:19:13","date_gmt":"2023-07-27T23:19:13","guid":{"rendered":"https:\/\/statorials.org\/tr\/sonlu-populasyon-duzeltme-faktoru\/"},"modified":"2023-07-27T23:19:13","modified_gmt":"2023-07-27T23:19:13","slug":"sonlu-populasyon-duzeltme-faktoru","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/sonlu-populasyon-duzeltme-faktoru\/","title":{"rendered":"Sonlu pop\u00fclasyon d\u00fczeltme fakt\u00f6r\u00fc nedir?"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>Standart hatalar\u0131<\/strong> hesaplamak i\u00e7in kullan\u0131lan form\u00fcllerin \u00e7o\u011fu, (1) numunelerin de\u011fi\u015ftirilerek se\u00e7ilmesi veya (2) <a href=\"https:\/\/statorials.org\/tr\/populasyon-ve-ornek\/\" target=\"_blank\" rel=\"noopener noreferrer\">numunelerin<\/a> sonsuz bir pop\u00fclasyondan se\u00e7ilmesi fikrine dayanmaktad\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Ger\u00e7ek ara\u015ft\u0131rmalarda bu fikirlerin hi\u00e7biri do\u011fru de\u011fildir. Neyse ki, \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc toplam pop\u00fclasyon b\u00fcy\u00fckl\u00fc\u011f\u00fcn\u00fcn %5&#8217;inden azsa bu genellikle bir sorun de\u011fildir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bununla birlikte, \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc toplam pop\u00fclasyonun %5&#8217;inden b\u00fcy\u00fck oldu\u011funda, a\u015fa\u011f\u0131daki \u015fekilde hesaplanan <strong>sonlu bir pop\u00fclasyon d\u00fczeltmesinin<\/strong> (genellikle <em>FPC<\/em> olarak k\u0131salt\u0131l\u0131r) uygulanmas\u0131 tercih edilir:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>FPC = \u221a <span style=\"text-decoration: overline;\">(Nn) \/ (N-1)<\/span><\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Alt\u0131n:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>N:<\/strong> N\u00fcfus b\u00fcy\u00fckl\u00fc\u011f\u00fc<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>n:<\/strong> \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc<\/span><\/li>\n<\/ul>\n<h3> <span style=\"color: #000000;\"><strong>Sonlu pop\u00fclasyon d\u00fczeltme fakt\u00f6r\u00fc nas\u0131l kullan\u0131l\u0131r?<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Sonlu bir pop\u00fclasyon d\u00fczeltmesi uygulamak i\u00e7in bunu ba\u015flang\u0131\u00e7ta kullanaca\u011f\u0131n\u0131z standart hatayla \u00e7arpman\u0131z yeterlidir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin bir ortalaman\u0131n standart hatas\u0131 \u015fu \u015fekilde hesaplan\u0131r:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Ortalaman\u0131n standart hatas\u0131:<\/strong> s \/ \u221a <span style=\"text-decoration: overline;\">n<\/span><\/span><\/p>\n<p> <span style=\"color: #000000;\">Sonlu pop\u00fclasyon d\u00fczeltmesi uyguland\u0131\u011f\u0131nda form\u00fcl \u015fu \u015fekilde olur:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Ortalaman\u0131n standart hatas\u0131:<\/strong> s \/ \u221a <span style=\"text-decoration: overline;\">n<\/span> * \u221a <span style=\"text-decoration: overline;\">(Nn) \/ (N-1)<\/span><\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki \u00f6rnekler, sonlu pop\u00fclasyon d\u00fczeltmesinin farkl\u0131 senaryolarda nas\u0131l kullan\u0131laca\u011f\u0131n\u0131 g\u00f6stermektedir.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u00d6rnek 1: Bir orant\u0131 i\u00e7in g\u00fcven aral\u0131\u011f\u0131<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Ara\u015ft\u0131rmac\u0131lar, 1.300 n\u00fcfuslu bir il\u00e7ede belirli bir yasay\u0131 destekleyen sakinlerin oran\u0131n\u0131 tahmin etmek istiyor. 100 sakinden olu\u015fan<a href=\"https:\/\/statorials.org\/tr\/ornekleme-yontemleri\/\" target=\"_blank\" rel=\"noopener noreferrer\">rastgele bir \u00f6rneklem<\/a> se\u00e7iyorlar ve onlara yasadaki konumlar\u0131n\u0131 soruyorlar. 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;\">Genel olarak n\u00fcfus oran\u0131 i\u00e7in %95 g\u00fcven aral\u0131\u011f\u0131n\u0131 hesaplama form\u00fcl\u00fc a\u015fa\u011f\u0131daki gibidir:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>%95 GA = p +\/- z*(\u221a <span style=\"text-decoration: overline;\">p(1-p) \/ n<\/span> )<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Ancak bu \u00f6rnekteki \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fcm\u00fcz 100\/1300 = pop\u00fclasyonun %7,7&#8217;sidir, bu da %5&#8217;i a\u015fmaktad\u0131r. Bu nedenle g\u00fcven aral\u0131\u011f\u0131 form\u00fcl\u00fcm\u00fcze sonlu bir pop\u00fclasyon d\u00fczeltmesi uygulamam\u0131z gerekir:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>%95 GA = p +\/- z*(\u221a <span style=\"text-decoration: overline;\">p(1-p)\/n<\/span> ) * \u221a <span style=\"text-decoration: overline;\">(Nn) \/ (N-1)<\/span><\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">B\u00f6ylece %95 g\u00fcven aral\u0131\u011f\u0131m\u0131z \u015fu \u015fekilde hesaplanabilir:<\/span><\/p>\n<p data-slot-rendered-dynamic=\"true\"> <span style=\"color: #000000;\"><strong>%95 GA =<\/strong> 0,56 +\/- 1,96*(\u221a <span style=\"text-decoration: overline;\">0,56(1-0,56) \/ 100<\/span> ) * \u221a <span style=\"text-decoration: overline;\">(1300-100) \/ (1300-1)<\/span> = <strong>[0,4665, 0,6535]<\/strong><\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u00d6rnek 2: Bir ortalama i\u00e7in g\u00fcven aral\u0131\u011f\u0131<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Ara\u015ft\u0131rmac\u0131lar, 500 kaplumba\u011fa aras\u0131ndan belirli bir t\u00fcr\u00fcn ortalama a\u011f\u0131rl\u0131\u011f\u0131n\u0131 tahmin etmek istiyor. B\u00f6ylece 40 kaplumba\u011fadan rastgele bir \u00f6rnek se\u00e7iyorlar ve her birini tart\u0131yorlar. Sonu\u00e7lar burada:<\/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;\">Genel olarak pop\u00fclasyon ortalamas\u0131 i\u00e7in %95 g\u00fcven aral\u0131\u011f\u0131n\u0131 hesaplama form\u00fcl\u00fc \u015f\u00f6yledir:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>%95 GA = <span style=\"text-decoration: overline;\">x<\/span> +\/- t <sub>\u03b1\/2<\/sub> *(s\/\u221an)<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Ancak bu \u00f6rnekte \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fcm\u00fcz 40\/500 = pop\u00fclasyonun %8&#8217;idir, bu da %5&#8217;i a\u015fmaktad\u0131r. Bu nedenle g\u00fcven aral\u0131\u011f\u0131 form\u00fcl\u00fcm\u00fcze sonlu bir pop\u00fclasyon d\u00fczeltmesi uygulamam\u0131z gerekir:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>%95 GA = <span style=\"text-decoration: overline;\">x<\/span> +\/- t <sub>\u03b1\/2<\/sub> *(s\/\u221an) * \u221a <span style=\"text-decoration: overline;\">(Nn) \/ (N-1)<\/span><\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">B\u00f6ylece %95 g\u00fcven aral\u0131\u011f\u0131m\u0131z \u015fu \u015fekilde hesaplanabilir:<\/span><\/p>\n<p data-slot-rendered-dynamic=\"true\"> <span style=\"color: #000000;\"><strong>%95 GA =<\/strong> 300 +\/- 2,0227*(18,5\/\u221a <span style=\"text-decoration: overline;\">40<\/span> ) * \u221a <span style=\"text-decoration: overline;\">(500-40) \/ (500-1)<\/span> = <strong>[294,32, 305,69]<\/strong><\/span><\/p>\n<h3> <strong>Ek kaynaklar<\/strong><\/h3>\n<p><a href=\"https:\/\/statorials.org\/tr\/guvenilirlik-araligi\/\" target=\"_blank\" rel=\"noopener noreferrer\">G\u00fcven aral\u0131klar\u0131 nedir?<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/hata-payi-ve-standart-hata-arasindaki-fark-nedir\/\" target=\"_blank\" rel=\"noopener noreferrer\">Hata pay\u0131 ve standart hata: fark nedir?<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/standart-sapma-ve-standart-hata\/\" target=\"_blank\" rel=\"noopener noreferrer\">Standart sapma ve standart hata: fark nedir?<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Standart hatalar\u0131 hesaplamak i\u00e7in kullan\u0131lan form\u00fcllerin \u00e7o\u011fu, (1) numunelerin de\u011fi\u015ftirilerek se\u00e7ilmesi veya (2) numunelerin sonsuz bir pop\u00fclasyondan se\u00e7ilmesi fikrine dayanmaktad\u0131r. Ger\u00e7ek ara\u015ft\u0131rmalarda bu fikirlerin hi\u00e7biri do\u011fru de\u011fildir. Neyse ki, \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc toplam pop\u00fclasyon b\u00fcy\u00fckl\u00fc\u011f\u00fcn\u00fcn %5&#8217;inden azsa bu genellikle bir sorun de\u011fildir. Bununla birlikte, \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc toplam pop\u00fclasyonun %5&#8217;inden b\u00fcy\u00fck oldu\u011funda, a\u015fa\u011f\u0131daki \u015fekilde hesaplanan sonlu bir [&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-1022","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>Sonlu pop\u00fclasyon d\u00fczeltme fakt\u00f6r\u00fc nedir? - Statoryaller<\/title>\n<meta name=\"description\" content=\"Bir tan\u0131m ve birka\u00e7 \u00f6rnek i\u00e7eren, sonlu pop\u00fclasyon d\u00fczeltme fakt\u00f6r\u00fcn\u00fcn basit bir a\u00e7\u0131klamas\u0131.\" \/>\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\/sonlu-populasyon-duzeltme-faktoru\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Sonlu pop\u00fclasyon d\u00fczeltme fakt\u00f6r\u00fc nedir? 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