{"id":2163,"date":"2023-07-23T10:43:47","date_gmt":"2023-07-23T10:43:47","guid":{"rendered":"https:\/\/statorials.org\/tr\/t-testi-icin-minimum-orneklem-buyuklugu\/"},"modified":"2023-07-23T10:43:47","modified_gmt":"2023-07-23T10:43:47","slug":"t-testi-icin-minimum-orneklem-buyuklugu","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/t-testi-icin-minimum-orneklem-buyuklugu\/","title":{"rendered":"Bir t-testi i\u00e7in minimum \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc: a\u00e7\u0131klama ve \u00f6rnek"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">\u00d6\u011frencilerin s\u0131kl\u0131kla sordu\u011fu soru \u015fudur:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><em><strong>T testi ger\u00e7ekle\u015ftirmek i\u00e7in gereken minimum \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc var m\u0131?<\/strong><\/em><\/span><\/p>\n<p> <span style=\"color: #000000;\">K\u0131sa cevap:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Hay\u0131r. T testi ger\u00e7ekle\u015ftirmek i\u00e7in gereken minimum \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc yoktur.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Asl\u0131nda \u015fimdiye kadar kullan\u0131lan ilk t-testi yaln\u0131zca <a href=\"https:\/\/en.wikipedia.org\/wiki\/Student%27s_t-test\" target=\"_blank\" rel=\"noopener\">d\u00f6rt ki\u015fiden olu\u015fan bir \u00f6rneklemi<\/a> kulland\u0131.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Ancak t testinin varsay\u0131mlar\u0131 kar\u015f\u0131lanmazsa sonu\u00e7lar g\u00fcvenilir olmayabilir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Ayr\u0131ca \u00f6rneklem boyutu \u00e7ok k\u00fc\u00e7\u00fckse, testin g\u00fcc\u00fc verilerdeki \u00f6nemli farkl\u0131l\u0131klar\u0131 tespit edemeyecek kadar d\u00fc\u015f\u00fck olabilir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu potansiyel sorunlar\u0131n her birine daha ayr\u0131nt\u0131l\u0131 olarak bakal\u0131m.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>T testi varsay\u0131mlar\u0131n\u0131 anlama<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\"><strong>Tek \u00f6rnekli t testi,<\/strong> 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.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu test a\u015fa\u011f\u0131daki varsay\u0131mlar\u0131 yapar:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>Ba\u011f\u0131ms\u0131zl\u0131k<\/strong> : \u00d6rnek g\u00f6zlemler ba\u011f\u0131ms\u0131z olmal\u0131d\u0131r.<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>Rastgele \u00f6rnekleme<\/strong> : Numunenin ilgilenilen pop\u00fclasyonu <a href=\"https:\/\/statorials.org\/tr\/temsili-ornek-1\/\" target=\"_blank\" rel=\"noopener\">temsil etme<\/a> \u015fans\u0131n\u0131 en \u00fcst d\u00fczeye \u00e7\u0131karmak i\u00e7in g\u00f6zlemler rastgele \u00f6rnekleme y\u00f6ntemi kullan\u0131larak toplanmal\u0131d\u0131r.<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>Normallik<\/strong> : G\u00f6zlemler yakla\u015f\u0131k olarak normal \u015fekilde da\u011f\u0131lmal\u0131d\u0131r.<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u0130ki pop\u00fclasyonun ortalamalar\u0131 aras\u0131nda anlaml\u0131 bir fark olup olmad\u0131\u011f\u0131n\u0131 kontrol etmek i\u00e7in <strong>iki \u00f6rnekli t testi<\/strong> kullan\u0131l\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu test a\u015fa\u011f\u0131daki varsay\u0131mlar\u0131 yapar:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>Ba\u011f\u0131ms\u0131zl\u0131k<\/strong> : Her numunenin g\u00f6zlemleri ba\u011f\u0131ms\u0131z olmal\u0131d\u0131r.<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>Rastgele \u00d6rnekleme<\/strong> : Her \u00f6rnekteki g\u00f6zlemler, rastgele \u00f6rnekleme y\u00f6ntemi kullan\u0131larak toplanmal\u0131d\u0131r.<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>Normallik<\/strong> : Her numune yakla\u015f\u0131k olarak normal \u015fekilde da\u011f\u0131t\u0131lmal\u0131d\u0131r.<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>E\u015fit varyans<\/strong> : Her \u00f6rnek yakla\u015f\u0131k olarak ayn\u0131 varyansa sahip olmal\u0131d\u0131r.<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Her bir t-testi t\u00fcr\u00fcn\u00fc ger\u00e7ekle\u015ftirirken bu varsay\u0131mlardan bir veya birka\u00e7\u0131 kar\u015f\u0131lanmazsa test sonu\u00e7lar\u0131 g\u00fcvenilmez hale gelebilir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu durumda bu varsay\u0131mlar\u0131 yapmayan alternatif bir parametrik olmayan test kullanmak en iyisidir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Tek \u00f6rnekli t testinin parametrik olmayan alternatifi <a href=\"https:\/\/statorials.org\/tr\/wilcoxon-isaret-siralamasi-testi\/\" target=\"_blank\" rel=\"noopener\">Wilcoxon i\u015faretli s\u0131ralama testidir<\/a> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0130ki \u00f6rnekli t testinin parametrik olmayan alternatifi <a href=\"https:\/\/statorials.org\/tr\/mann-whitney-seni-test-ediyor\/\" target=\"_blank\" rel=\"noopener\">Mann-Whitney U testidir<\/a> .<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>T-testlerinin g\u00fcc\u00fcn\u00fc anlamak<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\"><strong>\u0130statistiksel g\u00fc\u00e7,<\/strong> bir testin bir etki ger\u00e7ekten var oldu\u011funda tespit etme olas\u0131l\u0131\u011f\u0131n\u0131 ifade eder.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Kullan\u0131lan \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc ne kadar k\u00fc\u00e7\u00fckse, belirli bir testin istatistiksel g\u00fcc\u00fcn\u00fcn de o kadar d\u00fc\u015f\u00fck oldu\u011fu g\u00f6sterilebilir. Bu nedenle ara\u015ft\u0131rmac\u0131lar genellikle daha y\u00fcksek g\u00fcce sahip olmak ve dolay\u0131s\u0131yla ger\u00e7ek farkl\u0131l\u0131klar\u0131 tespit etme olas\u0131l\u0131\u011f\u0131n\u0131 art\u0131rmak i\u00e7in daha b\u00fcy\u00fck \u00f6rneklem boyutlar\u0131 isterler.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin, iki pop\u00fclasyon aras\u0131ndaki <a href=\"https:\/\/statorials.org\/tr\/etki-boyutu\/\" target=\"_blank\" rel=\"noopener\">ger\u00e7ek etki b\u00fcy\u00fckl\u00fc\u011f\u00fcn\u00fcn<\/a> 0,5 oldu\u011funu varsayal\u0131m; bu \u201corta\u201d bir etki b\u00fcy\u00fckl\u00fc\u011f\u00fcd\u00fcr. Farkl\u0131 \u00f6rneklem b\u00fcy\u00fckl\u00fcklerini kullanarak iki \u00f6rnekli bir t testinin g\u00fcc\u00fcn\u00fc hesaplamak i\u00e7in a\u015fa\u011f\u0131daki R kodunu kullanabiliriz:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#sample size n=10<\/span>\npower. <span style=\"color: #3366ff;\">t<\/span> . <span style=\"color: #3366ff;\">test<\/span> (n=10, delta=.5, sd=1, sig.level=.05, type=' <span style=\"color: #ff0000;\">two.sample<\/span> ')$power\n\n[1] 0.1838375\n\n<span style=\"color: #008080;\">#sample size n=30<\/span>\npower. <span style=\"color: #3366ff;\">t<\/span> . <span style=\"color: #3366ff;\">test<\/span> (n=30, delta=.5, sd=1, sig.level=.05, type=' <span style=\"color: #ff0000;\">two.sample<\/span> ')$power\n\n[1] 0.477841\n\n<span style=\"color: #008080;\">#sample size n=50<\/span>\npower. <span style=\"color: #3366ff;\">t<\/span> . <span style=\"color: #3366ff;\">test<\/span> (n=50, delta=.5, sd=1, sig.level=.05, type=' <span style=\"color: #ff0000;\">two.sample<\/span> ')$power\n\n[1] 0.6968888\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Sonu\u00e7lar\u0131 nas\u0131l yorumlayaca\u011f\u0131n\u0131z a\u015fa\u011f\u0131da a\u00e7\u0131klanm\u0131\u015ft\u0131r:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Her numunenin boyutu n = 10 oldu\u011funda g\u00fc\u00e7 <strong>0,184<\/strong> olur.<\/span><\/li>\n<li> <span style=\"color: #000000;\">Her numunenin boyutu n = 30 oldu\u011funda g\u00fc\u00e7 <strong>0,478<\/strong> olur.<\/span><\/li>\n<li> <span style=\"color: #000000;\">Her numunenin boyutu n = 50 oldu\u011funda g\u00fc\u00e7 <strong>0,697<\/strong> olur.<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u00d6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc artt\u0131k\u00e7a testin g\u00fcc\u00fcn\u00fcn artt\u0131\u011f\u0131n\u0131 g\u00f6rebiliriz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu nedenle, bir t-testi ger\u00e7ekle\u015ftirmek i\u00e7in minimum bir \u00f6rneklem boyutuna <em>ihtiyac\u0131m\u0131z<\/em> yoktur, ancak k\u00fc\u00e7\u00fck \u00f6rneklem boyutlar\u0131 daha d\u00fc\u015f\u00fck istatistiksel g\u00fcce ve dolay\u0131s\u0131yla verilerdeki ger\u00e7ek bir fark\u0131 tespit etme yetene\u011finin azalmas\u0131na neden olur.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u00c7\u00f6z\u00fcm<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u0130\u015fte \u00f6\u011frendiklerimizin bir \u00f6zeti:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">T-testi ger\u00e7ekle\u015ftirmek i\u00e7in gerekli minimum \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc yoktur.<\/span><\/li>\n<li> <span style=\"color: #000000;\">T testinin varsay\u0131mlar\u0131 kar\u015f\u0131lanmazsa parametrik olmayan bir alternatif kullanmal\u0131y\u0131z.<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u00d6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc \u00e7ok k\u00fc\u00e7\u00fckse t testinin g\u00fcc\u00fc d\u00fc\u015f\u00fck olacak ve testin verilerdeki ger\u00e7ek farkl\u0131l\u0131klar\u0131 tespit etme yetene\u011fi d\u00fc\u015f\u00fck olacakt\u0131r.<\/span><\/li>\n<\/ul>\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 testleri hakk\u0131nda ek bilgi sunmaktad\u0131r.<\/span><\/p>\n<p> <a href=\"https:\/\/statorials.org\/tr\/ornek-t-testi\/\" target=\"_blank\" rel=\"noopener\">Tek \u00f6rnekli t-testine giri\u015f<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/iki-orneginizi-test-edin\/\" target=\"_blank\" rel=\"noopener\">\u0130ki \u00f6rnekli t testine giri\u015f<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/eslestirilmis-ornekler-t-testi\/\" target=\"_blank\" rel=\"noopener\">E\u015fle\u015ftirilmi\u015f \u00f6rnekler t-testine giri\u015f<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/hipotezleri-test-etmek\/\" target=\"_blank\" rel=\"noopener\">Bir t testinde form\u00fcle edilen d\u00f6rt hipotez<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u00d6\u011frencilerin s\u0131kl\u0131kla sordu\u011fu soru \u015fudur: T testi ger\u00e7ekle\u015ftirmek i\u00e7in gereken minimum \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc var m\u0131? K\u0131sa cevap: Hay\u0131r. T testi ger\u00e7ekle\u015ftirmek i\u00e7in gereken minimum \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc yoktur. Asl\u0131nda \u015fimdiye kadar kullan\u0131lan ilk t-testi yaln\u0131zca d\u00f6rt ki\u015fiden olu\u015fan bir \u00f6rneklemi kulland\u0131. Ancak t testinin varsay\u0131mlar\u0131 kar\u015f\u0131lanmazsa sonu\u00e7lar g\u00fcvenilir olmayabilir. Ayr\u0131ca \u00f6rneklem boyutu \u00e7ok k\u00fc\u00e7\u00fckse, testin g\u00fcc\u00fc [&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-2163","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>Bir t-testi i\u00e7in minimum \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc: a\u00e7\u0131klama ve \u00f6rnek - Statorials<\/title>\n<meta name=\"description\" content=\"Bu e\u011fitimde, birka\u00e7 \u00f6rnek de dahil olmak \u00fczere bir t-testi i\u00e7in gereken minimum \u00f6rnek boyutunun bir a\u00e7\u0131klamas\u0131 sa\u011flanmaktad\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\/t-testi-icin-minimum-orneklem-buyuklugu\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Bir t-testi i\u00e7in minimum \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc: a\u00e7\u0131klama ve \u00f6rnek - 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