{"id":1231,"date":"2023-07-27T05:09:32","date_gmt":"2023-07-27T05:09:32","guid":{"rendered":"https:\/\/statorials.org\/tr\/normal-dagilim-ve-t-dagilimi\/"},"modified":"2023-07-27T05:09:32","modified_gmt":"2023-07-27T05:09:32","slug":"normal-dagilim-ve-t-dagilimi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/normal-dagilim-ve-t-dagilimi\/","title":{"rendered":"Normal da\u011f\u0131l\u0131m ve t da\u011f\u0131l\u0131m\u0131: fark nedir?"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">Normal da\u011f\u0131l\u0131m t\u00fcm istatistiklerde en s\u0131k kullan\u0131lan da\u011f\u0131l\u0131md\u0131r ve simetrik ve \u00e7an \u015feklinde oldu\u011fu bilinmektedir.<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-12187 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/norm_vs_t1.png\" alt=\"\" width=\"431\" height=\"394\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Yak\u0131ndan ili\u015fkili bir da\u011f\u0131l\u0131m da simetrik ve \u00e7an \u015feklinde olan ancak normal da\u011f\u0131l\u0131mdan daha a\u011f\u0131r &#8220;kuyruklara&#8221; sahip olan <strong>t da\u011f\u0131l\u0131m\u0131d\u0131r<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Ba\u015fka bir deyi\u015fle, normal da\u011f\u0131l\u0131ma g\u00f6re da\u011f\u0131l\u0131mda daha fazla de\u011fer merkeze g\u00f6re u\u00e7larda yer al\u0131r:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-12188 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/norm_vs_t2.png\" alt=\"Normal da\u011f\u0131l\u0131m ve t da\u011f\u0131l\u0131m\u0131\" width=\"444\" height=\"408\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">\u0130statistik jargonunda, bir da\u011f\u0131l\u0131m\u0131n ne kadar &#8220;a\u011f\u0131r&#8221; oldu\u011funu \u00f6l\u00e7mek i\u00e7in <strong>bas\u0131kl\u0131k<\/strong> ad\u0131 verilen bir \u00f6l\u00e7\u00fcm kullan\u0131r\u0131z. Dolay\u0131s\u0131yla, bir t da\u011f\u0131l\u0131m\u0131n\u0131n bas\u0131kl\u0131\u011f\u0131n\u0131n normal da\u011f\u0131l\u0131mdan daha b\u00fcy\u00fck oldu\u011funu s\u00f6yleyebiliriz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Uygulamada, <a href=\"https:\/\/statorials.org\/tr\/hipotez-testi-1\/\" target=\"_blank\" rel=\"noopener noreferrer\">hipotez testi<\/a> yaparken veya<a href=\"https:\/\/statorials.org\/tr\/guvenilirlik-araligi\/\" target=\"_blank\" rel=\"noopener noreferrer\">g\u00fcven aral\u0131klar\u0131 olu\u015ftururken<\/a> \u00e7o\u011funlukla t da\u011f\u0131l\u0131m\u0131n\u0131 kullan\u0131r\u0131z.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin, pop\u00fclasyon ortalamas\u0131 i\u00e7in g\u00fcven aral\u0131\u011f\u0131n\u0131 hesaplama form\u00fcl\u00fc \u015f\u00f6yledir:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>G\u00fcven aral\u0131\u011f\u0131 =<\/strong> <strong><span style=\"text-decoration: overline;\">x<\/span> +\/- t <sub>1-\u03b1\/2, n-1<\/sub> *(s\/\u221a <span style=\"text-decoration: overline;\">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>t:<\/strong> anlaml\u0131l\u0131k d\u00fczeyi <em>\u03b1<\/em> ve \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc <em>n&#8217;ye<\/em> dayal\u0131 olarak kritik t 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;\">Bu form\u00fclde, a\u015fa\u011f\u0131daki ko\u015fullardan biri do\u011fru oldu\u011funda z tablosunun kritik de\u011feri yerine t tablosunun kritik de\u011ferini kullan\u0131r\u0131z:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Pop\u00fclasyon standart sapmas\u0131n\u0131 bilmiyoruz.<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u00d6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc 30&#8217;dan k\u00fc\u00e7\u00fck veya ona e\u015fittir.<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki ak\u0131\u015f \u015femas\u0131, kritik de\u011feri tablo t&#8217;den mi yoksa tablo z&#8217;den mi kullanman\u0131z gerekti\u011fini bilmenin yararl\u0131 bir yolunu sa\u011flar:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-4849 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/z_table_vs_t_table.jpg\" alt=\"Tablo Z ve tablo t\" width=\"432\" height=\"271\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">G\u00fcven aral\u0131klar\u0131n\u0131 olu\u015ftururken t da\u011f\u0131l\u0131m\u0131n\u0131 kullanmak ile normal da\u011f\u0131l\u0131m\u0131 kullanmak aras\u0131ndaki temel fark, t da\u011f\u0131l\u0131m\u0131n\u0131n kritik de\u011ferlerinin daha b\u00fcy\u00fck olaca\u011f\u0131 ve dolay\u0131s\u0131yla <em>daha geni\u015f<\/em> g\u00fcven aral\u0131klar\u0131na yol a\u00e7aca\u011f\u0131d\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin, a\u015fa\u011f\u0131daki bilgilerle rastgele bir kaplumba\u011fa \u00f6rne\u011fi toplamak amac\u0131yla bir kaplumba\u011fa pop\u00fclasyonunun ortalama a\u011f\u0131rl\u0131\u011f\u0131 i\u00e7in %95&#8217;lik bir g\u00fcven aral\u0131\u011f\u0131 olu\u015fturmak istedi\u011fimizi varsayal\u0131m:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">\u00d6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc <strong>n = 25<\/strong><\/span><\/li>\n<li> <span style=\"color: #000000;\">Ortalama numune a\u011f\u0131rl\u0131\u011f\u0131 <strong>x = 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;\">%95 g\u00fcven d\u00fczeyi i\u00e7in kritik z de\u011feri <strong>1,96<\/strong> iken df = 25-1 = 24 serbestlik derecesi ile %95 g\u00fcven aral\u0131\u011f\u0131 i\u00e7in kritik t de\u011feri <strong>2,0639&#8217;dur<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Dolay\u0131s\u0131yla, z-kritik de\u011feri kullan\u0131larak pop\u00fclasyon ortalamas\u0131 i\u00e7in %95 g\u00fcven aral\u0131\u011f\u0131 \u015f\u00f6yledir:<\/span><\/p>\n<p> <span style=\"color: #000000;\">%95 GA = 300 +\/- 1,96*(18,5\/\u221a <span>25<\/span> ) = <strong>[292,75, 307,25]<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Pop\u00fclasyon ortalamas\u0131 i\u00e7in %95 g\u00fcven aral\u0131\u011f\u0131 t-kritik de\u011feri kullan\u0131ld\u0131\u011f\u0131nda \u015fu \u015fekildedir:<\/span><\/p>\n<p> <span style=\"color: #000000;\">%95 GA = 300 +\/- 2,0639*(18,5\/\u221a25) = <strong>[292,36, 307,64]<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">T-kritik de\u011feri ile g\u00fcven aral\u0131\u011f\u0131n\u0131n daha geni\u015f oldu\u011funa dikkat edin.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Buradaki fikir, k\u00fc\u00e7\u00fck \u00f6rneklem boyutlar\u0131na sahip oldu\u011fumuzda, ger\u00e7ek pop\u00fclasyon ortalamas\u0131ndan daha az emin oldu\u011fumuz, bu nedenle, ger\u00e7ek pop\u00fclasyon ortalamas\u0131n\u0131 i\u00e7erme \u015fans\u0131 daha fazla olan daha geni\u015f g\u00fcven aral\u0131klar\u0131 \u00fcretmek i\u00e7in t da\u011f\u0131l\u0131m\u0131n\u0131 kullanman\u0131n yararl\u0131 oldu\u011fudur.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>T da\u011f\u0131l\u0131m\u0131 i\u00e7in serbestlik derecelerinin g\u00f6rselle\u015ftirilmesi<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Serbestlik derecesi artt\u0131k\u00e7a t da\u011f\u0131l\u0131m\u0131n\u0131n normal da\u011f\u0131l\u0131ma yakla\u015ft\u0131\u011f\u0131n\u0131 belirtmek gerekir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bunu g\u00f6stermek i\u00e7in, t da\u011f\u0131l\u0131m\u0131n\u0131n \u015feklini a\u015fa\u011f\u0131daki serbestlik dereceleriyle g\u00f6steren a\u015fa\u011f\u0131daki grafi\u011fi d\u00fc\u015f\u00fcn\u00fcn:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">sd = 3<\/span><\/li>\n<li> <span style=\"color: #000000;\">sd = 10<\/span><\/li>\n<li> <span style=\"color: #000000;\">sd = 30<\/span> <\/li>\n<\/ul>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-12193 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/norm_vs_t3.png\" alt=\"Normal veya t da\u011f\u0131l\u0131m grafikleri\" width=\"470\" height=\"427\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">30 serbestlik derecesinin \u00f6tesinde, t da\u011f\u0131l\u0131m\u0131 ve normal da\u011f\u0131l\u0131m o kadar benzer hale gelir ki, form\u00fcllerde t-kritik de\u011feri ile z-kritik de\u011feri kullan\u0131m\u0131 aras\u0131ndaki farklar ihmal edilebilir hale gelir.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Normal da\u011f\u0131l\u0131m t\u00fcm istatistiklerde en s\u0131k kullan\u0131lan da\u011f\u0131l\u0131md\u0131r ve simetrik ve \u00e7an \u015feklinde oldu\u011fu bilinmektedir. Yak\u0131ndan ili\u015fkili bir da\u011f\u0131l\u0131m da simetrik ve \u00e7an \u015feklinde olan ancak normal da\u011f\u0131l\u0131mdan daha a\u011f\u0131r &#8220;kuyruklara&#8221; sahip olan t da\u011f\u0131l\u0131m\u0131d\u0131r . Ba\u015fka bir deyi\u015fle, normal da\u011f\u0131l\u0131ma g\u00f6re da\u011f\u0131l\u0131mda daha fazla de\u011fer merkeze g\u00f6re u\u00e7larda yer al\u0131r: \u0130statistik jargonunda, bir da\u011f\u0131l\u0131m\u0131n [&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-1231","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>Normal da\u011f\u0131l\u0131m ve t da\u011f\u0131l\u0131m\u0131: fark nedir?<\/title>\n<meta name=\"description\" content=\"Bu e\u011fitimde normal da\u011f\u0131l\u0131m ile t da\u011f\u0131l\u0131m\u0131 aras\u0131ndaki fark\u0131n basit bir a\u00e7\u0131klamas\u0131 sa\u011flanmaktad\u0131r.\" \/>\n<meta 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