{"id":743,"date":"2023-07-28T22:09:23","date_gmt":"2023-07-28T22:09:23","guid":{"rendered":"https:\/\/statorials.org\/tr\/ornek-t-testi\/"},"modified":"2023-07-28T22:09:23","modified_gmt":"2023-07-28T22:09:23","slug":"ornek-t-testi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/ornek-t-testi\/","title":{"rendered":"Tek \u00f6rnek t testi: tan\u0131m, form\u00fcl ve \u00f6rnek"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>Tek \u00f6rnekli t testi,<\/strong> bir <a href=\"https:\/\/statorials.org\/tr\/populasyon-ve-ornek\/\" target=\"_blank\" rel=\"noopener\">pop\u00fclasyonun<\/a> ortalamas\u0131n\u0131n belirli bir de\u011fere e\u015fit olup olmad\u0131\u011f\u0131n\u0131 test etmek i\u00e7in kullan\u0131l\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;\">Tek \u00f6rnekli t testi ger\u00e7ekle\u015ftirme motivasyonu.<\/span><\/li>\n<li> <span style=\"color: #000000;\">Tek \u00f6rnekli t testi ger\u00e7ekle\u015ftirme form\u00fcl\u00fc.<\/span><\/li>\n<li> <span style=\"color: #000000;\">Tek \u00f6rnekli t testi ger\u00e7ekle\u015ftirmek i\u00e7in kar\u015f\u0131lanmas\u0131 gereken varsay\u0131mlar.<\/span><\/li>\n<li> <span style=\"color: #000000;\">Tek \u00f6rnekli t testinin nas\u0131l ger\u00e7ekle\u015ftirilece\u011fine bir \u00f6rnek.<\/span><\/li>\n<\/ul>\n<h2> <span style=\"color: #000000;\"><strong>Bir t-testi \u00f6rne\u011fi: Motivasyon<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Diyelim ki Florida&#8217;daki belirli bir kaplumba\u011fa t\u00fcr\u00fcn\u00fcn ortalama a\u011f\u0131rl\u0131\u011f\u0131n\u0131n 310 pound olup olmad\u0131\u011f\u0131n\u0131 bilmek istiyoruz. Florida&#8217;da binlerce kaplumba\u011fa oldu\u011fundan, etrafta dola\u015f\u0131p her kaplumba\u011fay\u0131 ayr\u0131 ayr\u0131 tartmak son derece zaman al\u0131c\u0131 ve pahal\u0131 olacakt\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bunun yerine, 40 kaplumba\u011fadan olu\u015fan <a href=\"https:\/\/statorials.org\/tr\/ornekleme-yontemleri\/\" target=\"_blank\" rel=\"noopener\">basit bir rastgele \u00f6rnek<\/a> alabilir ve bu \u00f6rnekteki kaplumba\u011falar\u0131n ortalama a\u011f\u0131rl\u0131\u011f\u0131n\u0131 kullanarak ger\u00e7ek pop\u00fclasyon ortalamas\u0131n\u0131 tahmin edebiliriz:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-7353 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/cimoyenne1.png\" alt=\"\u00d6rnek bir pop\u00fclasyon \u00f6rne\u011fi\" width=\"405\" height=\"270\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Ancak \u00f6rne\u011fimizdeki kaplumba\u011falar\u0131n ortalama a\u011f\u0131rl\u0131\u011f\u0131n\u0131n 310 pounddan farkl\u0131 olaca\u011f\u0131 neredeyse garantidir. <strong>Soru, bu fark\u0131n istatistiksel olarak anlaml\u0131 olup olmad\u0131\u011f\u0131d\u0131r<\/strong> . Neyse ki tek \u00f6rnekli bir t testi bu soruyu yan\u0131tlamam\u0131za olanak tan\u0131yor.<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>Tek \u00f6rnek t testi:<\/strong><\/span> <span style=\"color: #000000;\"><strong>form\u00fcl<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Tek \u00f6rnekli bir t testi her zaman a\u015fa\u011f\u0131daki s\u0131f\u0131r hipotezini kullan\u0131r:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>H <sub>0<\/sub> :<\/strong> \u03bc = \u03bc <sub>0<\/sub> (pop\u00fclasyon ortalamas\u0131 varsay\u0131msal bir \u03bc <sub>0<\/sub> de\u011ferine e\u015fittir)<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Alternatif hipotez iki tarafl\u0131, sol veya sa\u011f olabilir:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>H <sub>1<\/sub> (iki kuyruklu):<\/strong> \u03bc \u2260 \u03bc <sub>0<\/sub> (pop\u00fclasyon ortalamas\u0131, varsay\u0131msal bir \u03bc <sub>0<\/sub> de\u011ferine e\u015fit de\u011fildir)<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>H <sub>1<\/sub> (sol):<\/strong> \u03bc &lt; \u03bc <sub>0<\/sub> (pop\u00fclasyon ortalamas\u0131, varsay\u0131msal bir de\u011fer olan \u03bc <sub>0&#8217;dan<\/sub> k\u00fc\u00e7\u00fckt\u00fcr)<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>H <sub>1<\/sub> (sa\u011f):<\/strong> \u03bc &gt; \u03bc <sub>0<\/sub> (pop\u00fclasyon ortalamas\u0131, varsay\u0131msal \u03bc <sub>0<\/sub> de\u011ferinden daha b\u00fcy\u00fckt\u00fcr)<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">T-testi istatisti\u011fini hesaplamak i\u00e7in a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullan\u0131r\u0131z:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>t = (<\/strong> <strong><span style=\"text-decoration: overline;\">X<\/span> \u2013 \u03bc) \/ (s\/ <span style=\"text-decoration: overline;\">\u221an<\/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>\u03bc <sub>0<\/sub> :<\/strong> varsay\u0131msal n\u00fcfus ortalamas\u0131<\/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;\">(n-1) serbestlik derecesine sahip t testi istatisti\u011fine kar\u015f\u0131l\u0131k gelen p de\u011feri, se\u00e7ilen anlaml\u0131l\u0131k seviyesinden k\u00fc\u00e7\u00fckse (ortak se\u00e7enekler 0,10, 0,05 ve 0,01&#8217;dir), o zaman s\u0131f\u0131r hipotezini reddedebilirsiniz.<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>Bir \u00f6rnek t testi: hipotezler<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Tek \u00f6rneklemli t testi sonu\u00e7lar\u0131n\u0131n ge\u00e7erli olabilmesi i\u00e7in a\u015fa\u011f\u0131daki varsay\u0131mlar\u0131n kar\u015f\u0131lanmas\u0131 gerekir:<\/span><\/p>\n<ul>\n<li> <strong><span style=\"color: #000000;\">\u0130ncelenen de\u011fi\u015fken ya bir aral\u0131k de\u011fi\u015fkeni ya da bir oran de\u011fi\u015fkeni olmal\u0131d\u0131r.<\/span><\/strong><\/li>\n<li> <span style=\"color: #000000;\"><strong>\u00d6rnekteki g\u00f6zlemler <a href=\"https:\/\/statorials.org\/tr\/bagimsizlik-hipotezi\/\" target=\"_blank\" rel=\"noopener\">ba\u011f\u0131ms\u0131z<\/a> olmal\u0131d\u0131r.<\/strong><\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>\u0130ncelenen de\u011fi\u015fkenin yakla\u015f\u0131k olarak normal da\u011f\u0131l\u0131ma sahip olmas\u0131 gerekir.<\/strong> <span style=\"color: #000000;\">Bu varsay\u0131m\u0131 bir histogram olu\u015fturarak ve da\u011f\u0131l\u0131m\u0131n kabaca &#8220;\u00e7an \u015fekline&#8221; sahip olup olmad\u0131\u011f\u0131n\u0131 g\u00f6rsel olarak kontrol ederek test edebilirsiniz.<\/span><\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>\u0130ncelenen de\u011fi\u015fken herhangi bir ayk\u0131r\u0131 de\u011fer i\u00e7ermemelidir.<\/strong> Bu hipotezi bir <a href=\"https:\/\/statorials.org\/tr\/kutu-biyiklari\/\" target=\"_blank\" rel=\"noopener\">kutu grafi\u011fi<\/a> olu\u015fturarak ve ayk\u0131r\u0131 de\u011ferleri g\u00f6rsel olarak kontrol ederek do\u011frulayabilirsiniz.<\/span><\/li>\n<\/ul>\n<h2> <span style=\"color: #000000;\"><strong>Bir \u00f6rnek t testi<\/strong><\/span> <span style=\"color: #000000;\"><strong>: \u00f6rnek<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Belirli bir kaplumba\u011fa t\u00fcr\u00fcn\u00fcn ortalama a\u011f\u0131rl\u0131\u011f\u0131n\u0131n 310 pound olup olmad\u0131\u011f\u0131n\u0131 bilmek istedi\u011fimizi varsayal\u0131m. Bunu test etmek i\u00e7in a\u015fa\u011f\u0131daki ad\u0131mlar\u0131 kullanarak \u03b1 = 0,05 anlaml\u0131l\u0131k d\u00fczeyinde tek \u00f6rnekli bir t testi ger\u00e7ekle\u015ftirece\u011fiz:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Ad\u0131m 1: \u00d6rnek verileri toplay\u0131n.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki bilgileri i\u00e7eren rastgele bir kaplumba\u011fa \u00f6rne\u011fi toplad\u0131\u011f\u0131m\u0131z\u0131<\/span> <span style=\"color: #000000;\">varsayal\u0131m<\/span> :<\/p>\n<ul>\n<li> <span style=\"color: #000000;\">\u00d6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc n = 40<\/span><\/li>\n<li> <span style=\"color: #000000;\">Ortalama numune a\u011f\u0131rl\u0131\u011f\u0131 <span style=\"text-decoration: overline;\">x<\/span> = 300<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u00d6rneklem standart sapmas\u0131 s = 18,5<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><strong>Ad\u0131m 2: Varsay\u0131mlar\u0131 tan\u0131mlay\u0131n.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Tek \u00f6rnek t-testini a\u015fa\u011f\u0131daki hipotezlerle ger\u00e7ekle\u015ftirece\u011fiz:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>H <sub>0<\/sub> :<\/strong> \u03bc = 310 (N\u00fcfus ortalamas\u0131 310 kitaba e\u015fittir)<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>H <sub>1<\/sub> :<\/strong> \u03bc \u2260 310 (pop\u00fclasyon ortalamas\u0131 310 pound&#8217;a e\u015fit de\u011fildir)<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><strong>Ad\u0131m 3: <em>t<\/em> -testi istatisti\u011fini hesaplay\u0131n.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>t<\/strong> = ( <span style=\"text-decoration: overline;\">x<\/span> \u2013 \u03bc) \/ (s\/ <span style=\"text-decoration: overline;\">\u221an<\/span> ) = (300-310) \/ (18,5\/ <span style=\"text-decoration: overline;\">\u221a40<\/span> ) = <strong>-3,4187<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Ad\u0131m 4: <em>t-<\/em> testi istatisti\u011finin p-de\u011ferini hesaplay\u0131n.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/tr\/t-puani-p-degeri-hesaplayicisi\/\" target=\"_blank\" rel=\"noopener\">P De\u011feri hesaplay\u0131c\u0131s\u0131na g\u00f6re T puan\u0131<\/a> , t = -3,4817 ve serbestlik derecesi = n-1 = 40-1 = 39 ile ili\u015fkili p de\u011feri <strong>0,00149&#8217;dur<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Ad\u0131m 5: Bir sonu\u00e7 \u00e7\u0131kar\u0131n.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu p de\u011feri bizim anlaml\u0131l\u0131k d\u00fczeyimiz olan \u03b1 = 0,05&#8217;in alt\u0131nda oldu\u011fundan s\u0131f\u0131r hipotezini reddediyoruz. Bu kaplumba\u011fa t\u00fcr\u00fcn\u00fcn ortalama a\u011f\u0131rl\u0131\u011f\u0131n\u0131n 310 pounda e\u015fit olmad\u0131\u011f\u0131n\u0131 s\u00f6yleyecek yeterli kan\u0131t\u0131m\u0131z var.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><em><strong>Not:<\/strong> Bu tek \u00f6rnekli t testinin tamam\u0131n\u0131<a href=\"https:\/\/statorials.org\/tr\/ornek-bir-t-testi-hesaplayicisi\/\" target=\"_blank\" rel=\"noopener\">tek \u00f6rnekli t testi hesaplay\u0131c\u0131s\u0131n\u0131<\/a> kullanarak da ger\u00e7ekle\u015ftirebilirsiniz.<\/em><\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>Ek kaynaklar<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki e\u011fitimlerde, farkl\u0131 istatistiksel programlar kullan\u0131larak tek \u00f6rnekli bir t testinin nas\u0131l ger\u00e7ekle\u015ftirilece\u011fi a\u00e7\u0131klanmaktad\u0131r:<\/span><\/p>\n<p> <a href=\"https:\/\/statorials.org\/tr\/ornek-bir-t-testi-excel\/\" target=\"_blank\" rel=\"noopener\">Excel&#8217;de tek \u00f6rnek t testi nas\u0131l yap\u0131l\u0131r<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/bir-ornek-t-testi-spss\/\" target=\"_blank\" rel=\"noopener\">SPSS&#8217;de tek \u00f6rnek t testi nas\u0131l yap\u0131l\u0131r<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/bir-ornek-t-testi-durumu\/\" target=\"_blank\" rel=\"noopener\">Stata&#8217;da tek \u00f6rnekli t testi nas\u0131l yap\u0131l\u0131r?<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/rde-ornek-bir-t-testi\/\" target=\"_blank\" rel=\"noopener\">R&#8217;de tek \u00f6rnekli t testi nas\u0131l yap\u0131l\u0131r<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/ornek-bir-t-testi-pitonu\/\">Python&#8217;da tek \u00f6rnek t testi nas\u0131l yap\u0131l\u0131r<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/ornek-bir-t-testi-ti-84-hesap-makinesi\/\">TI-84 Hesap Makinesinde Tek \u00d6rnekli t-Testi Nas\u0131l Ger\u00e7ekle\u015ftirilir<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tek \u00f6rnekli t testi, bir pop\u00fclasyonun ortalamas\u0131n\u0131n belirli bir de\u011fere e\u015fit olup olmad\u0131\u011f\u0131n\u0131 test etmek i\u00e7in kullan\u0131l\u0131r. Bu e\u011fitimde a\u015fa\u011f\u0131dakiler a\u00e7\u0131klanmaktad\u0131r: Tek \u00f6rnekli t testi ger\u00e7ekle\u015ftirme motivasyonu. Tek \u00f6rnekli t testi ger\u00e7ekle\u015ftirme form\u00fcl\u00fc. Tek \u00f6rnekli t testi ger\u00e7ekle\u015ftirmek i\u00e7in kar\u015f\u0131lanmas\u0131 gereken varsay\u0131mlar. Tek \u00f6rnekli t testinin nas\u0131l ger\u00e7ekle\u015ftirilece\u011fine bir \u00f6rnek. Bir t-testi \u00f6rne\u011fi: Motivasyon Diyelim [&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-743","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>Tek \u00f6rnek t-testi: tan\u0131m, form\u00fcl ve \u00f6rnek \u2013 Statorials<\/title>\n<meta name=\"description\" content=\"Ad\u0131m ad\u0131m tan\u0131m ve \u00f6rnek i\u00e7eren, tek \u00f6rnekli t-testine basit bir giri\u015f.\" \/>\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\/ornek-t-testi\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Tek \u00f6rnek t-testi: tan\u0131m, form\u00fcl ve \u00f6rnek \u2013 Statorials\" \/>\n<meta property=\"og:description\" content=\"Ad\u0131m ad\u0131m tan\u0131m ve \u00f6rnek i\u00e7eren, tek \u00f6rnekli t-testine basit bir giri\u015f.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/tr\/ornek-t-testi\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-28T22:09:23+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/cimoyenne1.png\" \/>\n<meta name=\"author\" content=\"Dr.benjamin anderson\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Yazan:\" \/>\n\t<meta name=\"twitter:data1\" content=\"Dr.benjamin anderson\" \/>\n\t<meta name=\"twitter:label2\" content=\"Tahmini okuma s\u00fcresi\" \/>\n\t<meta name=\"twitter:data2\" content=\"4 dakika\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/tr\/ornek-t-testi\/\",\"url\":\"https:\/\/statorials.org\/tr\/ornek-t-testi\/\",\"name\":\"Tek \u00f6rnek t-testi: tan\u0131m, form\u00fcl ve \u00f6rnek \u2013 Statorials\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/tr\/#website\"},\"datePublished\":\"2023-07-28T22:09:23+00:00\",\"dateModified\":\"2023-07-28T22:09:23+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/tr\/#\/schema\/person\/365dc158a39a7c8ae256355451e3de48\"},\"description\":\"Ad\u0131m ad\u0131m tan\u0131m ve \u00f6rnek i\u00e7eren, tek \u00f6rnekli t-testine basit bir giri\u015f.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/tr\/ornek-t-testi\/#breadcrumb\"},\"inLanguage\":\"tr\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/tr\/ornek-t-testi\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/tr\/ornek-t-testi\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Ev\",\"item\":\"https:\/\/statorials.org\/tr\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Tek \u00f6rnek t testi: tan\u0131m, form\u00fcl ve \u00f6rnek\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/statorials.org\/tr\/#website\",\"url\":\"https:\/\/statorials.org\/tr\/\",\"name\":\"Statorials\",\"description\":\"\u0130statistik okuryazarl\u0131\u011f\u0131 rehberiniz!\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/statorials.org\/tr\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"tr\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/statorials.org\/tr\/#\/schema\/person\/365dc158a39a7c8ae256355451e3de48\",\"name\":\"Dr.benjamin anderson\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"tr\",\"@id\":\"https:\/\/statorials.org\/tr\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/statorials.org\/tr\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"contentUrl\":\"https:\/\/statorials.org\/tr\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"caption\":\"Dr.benjamin anderson\"},\"description\":\"Merhaba, ben Benjamin, emekli bir istatistik profes\u00f6r\u00fc ve Statorials \u00f6\u011fretmenine d\u00f6n\u00fc\u015ft\u00fcm. \u0130statistik alan\u0131ndaki kapsaml\u0131 deneyimim ve uzmanl\u0131\u011f\u0131mla, \u00f6\u011frencilerimi Statorials arac\u0131l\u0131\u011f\u0131yla g\u00fc\u00e7lendirmek i\u00e7in bilgilerimi payla\u015fmaya can at\u0131yorum. 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