{"id":2061,"date":"2023-07-23T21:25:39","date_gmt":"2023-07-23T21:25:39","guid":{"rendered":"https:\/\/statorials.org\/tr\/t-puani-vs-z-puani\/"},"modified":"2023-07-23T21:25:39","modified_gmt":"2023-07-23T21:25:39","slug":"t-puani-vs-z-puani","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/t-puani-vs-z-puani\/","title":{"rendered":"T-score ve z-score: ne zaman kullan\u0131lmal\u0131?"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">\u0130statistik derslerinde \u00f6\u011frencilerin s\u0131kl\u0131kla kafas\u0131n\u0131 kar\u0131\u015ft\u0131ran iki terim <strong>t-puanlar\u0131<\/strong> ve <strong>z-puanlar\u0131d\u0131r<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Her ikisi de <a href=\"https:\/\/statorials.org\/tr\/hipotez-testi-1\/\" target=\"_blank\" rel=\"noopener\">hipotez testi<\/a> yaparken veya <a href=\"https:\/\/statorials.org\/tr\/guvenilirlik-araligi\/\" target=\"_blank\" rel=\"noopener\">g\u00fcven aral\u0131klar\u0131<\/a> olu\u015ftururken yayg\u0131n olarak kullan\u0131l\u0131r, ancak biraz farkl\u0131d\u0131rlar.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0130\u015fte her birinin form\u00fcl\u00fc:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>puan t = ( <span style=\"border-top: 1px solid black;\">x<\/span> \u2013 \u03bc) \/ (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=\"border-top: 1px solid black;\">x<\/span><\/strong> : \u00f6rnek ortalama<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>\u03bc<\/strong> : N\u00fcfus ortalamas\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>s<\/strong> : \u00d6rneklem standart sapmas\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>n<\/strong> : \u00d6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><strong>z-puan\u0131 = ( <span style=\"border-top: 1px solid black;\">x<\/span> \u2013 \u03bc) \/ \u03c3<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Alt\u0131n:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong><span style=\"border-top: 1px solid black;\">x<\/span><\/strong> : Ham veri de\u011feri<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>\u03bc<\/strong> : N\u00fcfus ortalamas\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>\u03c3<\/strong> : N\u00fcfus standart sapmas\u0131<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Bu ak\u0131\u015f \u015femas\u0131, verilerinize g\u00f6re her birini ne zaman kullanman\u0131z gerekti\u011fini g\u00f6sterir:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-19217 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/zscore_vs_tscore1.png\" alt=\"T-Score ve Ne Zaman Kullan\u0131laca\u011f\u0131na \u0130li\u015fkin Ak\u0131\u015f \u015eemas\u0131 Z-Skoru\" width=\"561\" height=\"276\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki \u00f6rneklerde T-puan\u0131 ve Z-puan\u0131n\u0131n pratikte nas\u0131l hesaplanaca\u011f\u0131 g\u00f6sterilmektedir.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u00d6rnek 1: T-Skorunun Hesaplanmas\u0131<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Bir restoran\u0131n ortalama a\u011f\u0131rl\u0131\u011f\u0131n\u0131n \u03bc = 0,25 pound oldu\u011funu iddia ederek hamburger haz\u0131rlad\u0131\u011f\u0131n\u0131 varsayal\u0131m.<\/span><\/p>\n<p> <span style=\"color: #000000;\">N = 20 hamburgerden rastgele bir \u00f6rnek ald\u0131\u011f\u0131m\u0131z\u0131 ve \u00f6rne\u011fin ortalama a\u011f\u0131rl\u0131\u011f\u0131n\u0131n <span style=\"border-top: 1px solid black;\">x<\/span> = 0,22 pound ve standart sapmas\u0131 s = 0,05 pound oldu\u011funu buldu\u011fumuzu varsayal\u0131m. Bu restoran\u0131n \u00fcretti\u011fi t\u00fcm hamburgerlerin ger\u00e7ek ortalama a\u011f\u0131rl\u0131\u011f\u0131n\u0131n 0,25 pound olup olmad\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in bir hipotez testi yap\u0131n.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu \u00f6rnekte, a\u015fa\u011f\u0131daki iki ko\u015fulun hi\u00e7biri kar\u015f\u0131lanmad\u0131\u011f\u0131 i\u00e7in hipotez testini ger\u00e7ekle\u015ftirmek i\u00e7in bir <strong>T-puan\u0131<\/strong> kullanaca\u011f\u0131z.<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Pop\u00fclasyon standart sapmas\u0131 (\u03c3) bilinmektedir. (bu \u00f6rnekte \u03c3 sa\u011flanmam\u0131\u015ft\u0131r)<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u00d6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc 30&#8217;dan b\u00fcy\u00fck. (Bu \u00f6rnekte n=20)<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Dolay\u0131s\u0131yla t-puan\u0131n\u0131 \u015fu \u015fekilde hesaplayabiliriz:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">puan t = ( <span style=\"border-top: 1px solid black;\">x<\/span> \u2013 \u03bc) \/ (s\/\u221a <span style=\"border-top: 1px solid black;\">n<\/span> )<\/span><\/li>\n<li> <span style=\"color: #000000;\">t-puan\u0131 = (0,22 \u2013 0,25) \/ (0,05 \/ \u221a <span style=\"border-top: 1px solid black;\">20<\/span> )<\/span><\/li>\n<li> <span style=\"color: #000000;\">t-puan\u0131 = -2,68<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/tr\/t-puani-p-degeri-hesaplayicisi\/\" target=\"_blank\" rel=\"noopener\">P de\u011feri T puan\u0131 hesaplay\u0131c\u0131s\u0131na<\/a> g\u00f6re bu t puan\u0131na kar\u015f\u0131l\u0131k gelen p de\u011feri <strong>0,01481&#8217;dir<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu p de\u011feri 0,05&#8217;ten k\u00fc\u00e7\u00fck oldu\u011fundan, bu restoranda \u00fcretilen hamburgerlerin ortalama a\u011f\u0131rl\u0131\u011f\u0131n\u0131n 0,25 pound&#8217;a e\u015fit olmad\u0131\u011f\u0131n\u0131 s\u00f6ylemek i\u00e7in yeterli kan\u0131t\u0131m\u0131z var.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u00d6rnek 2: Z puan\u0131n\u0131n hesaplanmas\u0131<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Bir \u015firketin, \u00f6mr\u00fc \u03bc = 20 saat ve standart sapmas\u0131 \u03c3 = 5 saat olan normal bir da\u011f\u0131l\u0131ma uydu\u011fu bilinen piller \u00fcretti\u011fini varsayal\u0131m.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Diyelim ki n = 50 adet pilden rastgele bir \u00f6rnek al\u0131yoruz ve \u00f6rnek ortalamas\u0131n\u0131n <span style=\"border-top: 1px solid black;\">x<\/span> = 21 saat oldu\u011funu buluyoruz. Bu \u015firket taraf\u0131ndan \u00fcretilen t\u00fcm pillerin ger\u00e7ek ortalama \u00f6mr\u00fcn\u00fcn 20 saate e\u015fit olup olmad\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in bir hipotez testi yap\u0131n.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu \u00f6rnekte, a\u015fa\u011f\u0131daki ko\u015fullar\u0131n her ikisi de kar\u015f\u0131land\u0131\u011f\u0131 i\u00e7in hipotez testini ger\u00e7ekle\u015ftirmek i\u00e7in bir <strong>z-puan\u0131<\/strong> kullanaca\u011f\u0131z:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Pop\u00fclasyon standart sapmas\u0131 (\u03c3) bilinmektedir. (\u03c3 bu \u00f6rnekte 5&#8217;e e\u015fittir)<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u00d6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc 30&#8217;dan b\u00fcy\u00fck. (Bu \u00f6rnekte n=50)<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Dolay\u0131s\u0131yla z-puan\u0131n\u0131 \u015fu \u015fekilde hesaplayabiliriz:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">z-puan\u0131 = ( <span style=\"border-top: 1px solid black;\">x<\/span> \u2013 \u03bc) \/ \u03c3<\/span><\/li>\n<li> <span style=\"color: #000000;\">z-puan\u0131 = (21 \u2013 20) \/ 5<\/span><\/li>\n<li> <span style=\"color: #000000;\">z-puan\u0131 = 0,2<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">P de\u011feri Z puan\u0131 hesaplay\u0131c\u0131s\u0131na g\u00f6re bu z puan\u0131na kar\u015f\u0131l\u0131k gelen p de\u011feri <strong>0,84184&#8217;t\u00fcr<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu p de\u011feri 0,05&#8217;ten az olmad\u0131\u011f\u0131 i\u00e7in bu firman\u0131n \u00fcretti\u011fi t\u00fcm pillerin ortalama \u00f6mr\u00fcn\u00fcn 20 saatten farkl\u0131 oldu\u011funu s\u00f6yleyecek yeterli kan\u0131t\u0131m\u0131z yok.<\/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 T puanlar\u0131 ve Z puanlar\u0131 hakk\u0131nda daha fazla bilgi sunar:<\/span><\/p>\n<p> <a href=\"https:\/\/statorials.org\/tr\/normal-dagilim-ve-t-dagilimi\/\" target=\"_blank\" rel=\"noopener\">Normal da\u011f\u0131l\u0131m ve t da\u011f\u0131l\u0131m\u0131: fark nedir?<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/t-dagitim-tablosu-nasil-okunur\/\" target=\"_blank\" rel=\"noopener\">Da\u011f\u0131t\u0131m tablosu t nas\u0131l okunur<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/z-tablosu-nasil-kullanilir\/\" target=\"_blank\" rel=\"noopener\">Z tablosu nas\u0131l okunur<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0130statistik derslerinde \u00f6\u011frencilerin s\u0131kl\u0131kla kafas\u0131n\u0131 kar\u0131\u015ft\u0131ran iki terim t-puanlar\u0131 ve z-puanlar\u0131d\u0131r . Her ikisi de hipotez testi yaparken veya g\u00fcven aral\u0131klar\u0131 olu\u015ftururken yayg\u0131n olarak kullan\u0131l\u0131r, ancak biraz farkl\u0131d\u0131rlar. \u0130\u015fte her birinin form\u00fcl\u00fc: puan t = ( x \u2013 \u03bc) \/ (s\/\u221a n ) Alt\u0131n: x : \u00f6rnek ortalama \u03bc : N\u00fcfus ortalamas\u0131 s : \u00d6rneklem [&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-2061","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>T-Score ve Z-Score: Ne Zaman Kullan\u0131lmal\u0131 \u2013 Statorials<\/title>\n<meta name=\"description\" content=\"Bu e\u011fitimde istatistiklerde T puan\u0131 ve Z puan\u0131n\u0131n ne 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