{"id":3427,"date":"2023-07-17T13:21:12","date_gmt":"2023-07-17T13:21:12","guid":{"rendered":"https:\/\/statorials.org\/tr\/t-esit-olmayan-orneklem-boyutunu-test-edin\/"},"modified":"2023-07-17T13:21:12","modified_gmt":"2023-07-17T13:21:12","slug":"t-esit-olmayan-orneklem-boyutunu-test-edin","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/t-esit-olmayan-orneklem-boyutunu-test-edin\/","title":{"rendered":"E\u015fit olmayan \u00f6rneklem boyutlar\u0131yla t testi nas\u0131l yap\u0131l\u0131r?"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">\u0130statistik s\u00f6z konusu oldu\u011funda \u00f6\u011frencilerin s\u0131kl\u0131kla sordu\u011fu bir soru \u015fudur:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong><em>Her grubun \u00f6rneklem b\u00fcy\u00fckl\u00fckleri e\u015fit olmad\u0131\u011f\u0131nda t testi yapmak m\u00fcmk\u00fcn m\u00fcd\u00fcr?<\/em><\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">K\u0131sa cevap:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Evet, \u00f6rneklem b\u00fcy\u00fckl\u00fckleri e\u015fit olmad\u0131\u011f\u0131nda t testi yapabilirsiniz. E\u015fit \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc, t-testinde yap\u0131lan <a href=\"https:\/\/statorials.org\/tr\/hipotezleri-test-etmek\/\" target=\"_blank\" rel=\"noopener\">varsay\u0131mlardan biri<\/a> de\u011fildir.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Ger\u00e7ek problemler, t-testinde yap\u0131lan varsay\u0131mlardan biri <em>olan<\/em> iki numunenin varyanslar\u0131 e\u015fit olmad\u0131\u011f\u0131nda ortaya \u00e7\u0131kar.<\/span><\/p>\n<p> <span style=\"color: #000000;\">B\u00f6yle bir durum meydana geldi\u011finde, e\u015fit varyanslar\u0131 varsaymayan <a href=\"https:\/\/statorials.org\/tr\/welchs-t-testi\/\" target=\"_blank\" rel=\"noopener\">Welch t testinin<\/a> kullan\u0131lmas\u0131 \u00f6nerilir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki \u00f6rnekler, varyanslar\u0131n e\u015fit oldu\u011fu ve olmad\u0131\u011f\u0131 durumlarda e\u015fit olmayan \u00f6rneklem b\u00fcy\u00fckl\u00fckleriyle T testlerinin nas\u0131l ger\u00e7ekle\u015ftirilece\u011fini g\u00f6stermektedir.<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>\u00d6rnek 1: E\u015fit olmayan \u00f6rneklem boyutlar\u0131 ve e\u015fit varyanslar<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">\u00d6\u011frencilerin belirli s\u0131navlarda daha iyi performans g\u00f6stermelerine yard\u0131mc\u0131 olmak i\u00e7in tasarlanm\u0131\u015f iki program y\u00f6netti\u011fimizi varsayal\u0131m.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Sonu\u00e7lar a\u015fa\u011f\u0131daki gibidir:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Program 1:<\/strong><\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>n<\/strong> (\u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc): 500<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong><span style=\"border-top: 1px solid black;\">x<\/span><\/strong> (\u00f6rnek ortalama): 80<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>s<\/strong> (\u00f6rnek standart sapmas\u0131): 5<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><strong>Program 2:<\/strong><\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>n<\/strong> (\u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc): 20<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong><span style=\"border-top: 1px solid black;\">x<\/span><\/strong> (\u00f6rnek ortalama): 85<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>s<\/strong> (\u00f6rnek standart sapmas\u0131): 5<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki kod, her program i\u00e7in s\u0131nav puanlar\u0131n\u0131n da\u011f\u0131l\u0131m\u0131n\u0131 g\u00f6rselle\u015ftirmek i\u00e7in R&#8217;de bir kutu grafi\u011finin nas\u0131l olu\u015fturulaca\u011f\u0131n\u0131 g\u00f6sterir:<\/span> <\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#make this example reproducible\n<\/span>set. <span style=\"color: #3366ff;\">seeds<\/span> (1)\n\n<span style=\"color: #008080;\">#create vectors to hold exam scores\n<\/span>program1 &lt;- rnorm(500, mean=80, sd=5)\nprogram2 &lt;- rnorm(20, mean=85, sd=5)\n\n<span style=\"color: #008080;\">#create boxplots to visualize distribution of exam scores\n<\/span>boxplot(program1, program2, names=c(\" <span style=\"color: #ff0000;\">Program 1<\/span> \",\" <span style=\"color: #ff0000;\">Program 2<\/span> \"))\n<\/strong><\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-28705 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/inegal1.jpg\" alt=\"\" width=\"446\" height=\"399\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Program 2&#8217;nin ortalama s\u0131nav puan\u0131 daha y\u00fcksek g\u00f6r\u00fcnmektedir ancak iki program aras\u0131ndaki s\u0131nav puanlar\u0131 aras\u0131ndaki fark yakla\u015f\u0131k olarak e\u015fittir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki kod, Welch t testiyle ba\u011f\u0131ms\u0131z \u00f6rnekler t testinin nas\u0131l ger\u00e7ekle\u015ftirilece\u011fini g\u00f6sterir:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#perform independent samples t-test\n<\/span>t. <span style=\"color: #3366ff;\">test<\/span> (program1, program2, var. <span style=\"color: #3366ff;\">equal<\/span> = <span style=\"color: #008000;\">TRUE<\/span> )\n\n\tTwo Sample t-test\n\ndata: program1 and program2\nt = -3.3348, df = 518, p-value = 0.0009148\nalternative hypothesis: true difference in means is not equal to 0\n95 percent confidence interval:\n -6.111504 -1.580245\nsample estimates:\nmean of x mean of y \n 80.11322 83.95910\n\n<span style=\"color: #008080;\">#perform Welch's two sample t-test\n<\/span>t. <span style=\"color: #3366ff;\">test<\/span> (program1, program2, var. <span style=\"color: #3366ff;\">equal<\/span> = <span style=\"color: #008000;\">FALSE<\/span> )\n\n\tWelch Two Sample t-test\n\ndata: program1 and program2\nt = -3.3735, df = 20.589, p-value = 0.00293\nalternative hypothesis: true difference in means is not equal to 0\n95 percent confidence interval:\n -6.219551 -1.472199\nsample estimates:\nmean of x mean of y \n 80.11322 83.95910 \n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Ba\u011f\u0131ms\u0131z \u00f6rnekler t-testi <strong>0,0009&#8217;luk<\/strong> bir p-de\u011feri d\u00f6nd\u00fcr\u00fcr ve Welch&#8217;in t-testi <strong>0,0029&#8217;luk<\/strong> bir p-de\u011feri d\u00f6nd\u00fcr\u00fcr.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Her testin p de\u011feri 0,05&#8217;ten k\u00fc\u00e7\u00fck oldu\u011fundan, her testteki s\u0131f\u0131r hipotezini reddeder ve iki program aras\u0131nda ortalama s\u0131nav puanlar\u0131nda istatistiksel olarak anlaml\u0131 bir fark oldu\u011fu sonucuna var\u0131r\u0131z.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong><span style=\"color: #000000;\">\u00d6rneklem boyutlar\u0131 e\u015fit olmasa da, ba\u011f\u0131ms\u0131z \u00f6rnekler t-testi ve Welch t-testi, iki \u00f6rne\u011fin e\u015fit varyanslara sahip olmas\u0131 nedeniyle benzer sonu\u00e7lar vermektedir.<\/span><\/strong><\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>\u00d6rnek 2: E\u015fit olmayan \u00f6rneklem boyutlar\u0131 ve e\u015fit olmayan varyanslar<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">\u00d6\u011frencilerin belirli s\u0131navlarda daha iyi performans g\u00f6stermelerine yard\u0131mc\u0131 olmak i\u00e7in tasarlanm\u0131\u015f iki program y\u00f6netti\u011fimizi varsayal\u0131m.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Sonu\u00e7lar a\u015fa\u011f\u0131daki gibidir:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Program 1:<\/strong><\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>n<\/strong> (\u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc): 500<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong><span style=\"border-top: 1px solid black;\">x<\/span><\/strong> (\u00f6rnek ortalama): 80<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>s<\/strong> (\u00f6rnek standart sapmas\u0131): 25<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><strong>Program 2:<\/strong><\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>n<\/strong> (\u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc): 20<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong><span style=\"border-top: 1px solid black;\">x<\/span><\/strong> (\u00f6rnek ortalama): 85<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>s<\/strong> (\u00f6rnek standart sapmas\u0131): 5<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki kod, her program i\u00e7in s\u0131nav puanlar\u0131n\u0131n da\u011f\u0131l\u0131m\u0131n\u0131 g\u00f6rselle\u015ftirmek i\u00e7in R&#8217;de bir kutu grafi\u011finin nas\u0131l olu\u015fturulaca\u011f\u0131n\u0131 g\u00f6sterir:<\/span> <\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#make this example reproducible\n<\/span>set. <span style=\"color: #3366ff;\">seeds<\/span> (1)\n\n<span style=\"color: #008080;\">#create vectors to hold exam scores\n<\/span>program1 &lt;- rnorm(500, mean=80, sd=25)\nprogram2 &lt;- rnorm(20, mean=85, sd=5)\n\n<span style=\"color: #008080;\">#create boxplots to visualize distribution of exam scores\n<\/span>boxplot(program1, program2, names=c(\" <span style=\"color: #ff0000;\">Program 1<\/span> \",\" <span style=\"color: #ff0000;\">Program 2<\/span> \"))\n<\/strong><\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-28706 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/inegal2.jpg\" alt=\"\" width=\"447\" height=\"404\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Program 2&#8217;nin ortalama s\u0131nav puan\u0131 daha y\u00fcksek g\u00f6r\u00fcnmektedir, ancak Program 1&#8217;in s\u0131nav puanlar\u0131n\u0131n varyans\u0131 Program 2&#8217;den \u00e7ok daha y\u00fcksektir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki kod, Welch t testiyle ba\u011f\u0131ms\u0131z \u00f6rnekler t testinin nas\u0131l ger\u00e7ekle\u015ftirilece\u011fini g\u00f6sterir:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#perform independent samples t-test\n<\/span>t. <span style=\"color: #3366ff;\">test<\/span> (program1, program2, var. <span style=\"color: #3366ff;\">equal<\/span> = <span style=\"color: #008000;\">TRUE<\/span> )\n\n\tTwo Sample t-test\n\ndata: program1 and program2\nt = -0.5988, df = 518, p-value = 0.5496\nalternative hypothesis: true difference in means is not equal to 0\n95 percent confidence interval:\n -14.52474 7.73875\nsample estimates:\nmean of x mean of y \n  80.5661 83.9591\n\n<span style=\"color: #008080;\">#perform Welch's two sample t-test\n<\/span>t. <span style=\"color: #3366ff;\">test<\/span> (program1, program2, var. <span style=\"color: #3366ff;\">equal<\/span> = <span style=\"color: #008000;\">FALSE<\/span> )\n\n\tWelch Two Sample t-test\n\ndata: program1 and program2\nt = -2.1338, df = 74.934, p-value = 0.03613\nalternative hypothesis: true difference in means is not equal to 0\n95 percent confidence interval:\n -6.560690 -0.225296\nsample estimates:\nmean of x mean of y \n  80.5661 83.9591 \n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Ba\u011f\u0131ms\u0131z \u00f6rnekler t-testi <strong>0,5496&#8217;l\u0131k<\/strong> bir p-de\u011feri verir ve Welch&#8217;in t-testi <strong>0,0361&#8217;lik<\/strong> bir p-de\u011feri verir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Ba\u011f\u0131ms\u0131z \u00f6rnekler t testi ortalama s\u0131nav puanlar\u0131ndaki fark\u0131 tespit edemez ancak Welch t testi istatistiksel olarak anlaml\u0131 bir fark tespit edebilir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0130ki numunenin varyanslar\u0131 e\u015fit olmad\u0131\u011f\u0131ndan, bu test <span style=\"color: #000000;\"><b>numuneler<\/b><\/span> <b>aras\u0131ndaki varyanslar\u0131n e\u015fit oldu\u011funu varsaymad\u0131\u011f\u0131ndan yaln\u0131zca Welch&#8217;in t testi ortalama s\u0131nav puanlar\u0131ndaki istatistiksel olarak anlaml\u0131 fark\u0131 tespit edebildi<\/b> <b>.<\/b><\/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\u011fitimler t testleri hakk\u0131nda ek bilgi sa\u011flar:<\/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><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0130statistik s\u00f6z konusu oldu\u011funda \u00f6\u011frencilerin s\u0131kl\u0131kla sordu\u011fu bir soru \u015fudur: Her grubun \u00f6rneklem b\u00fcy\u00fckl\u00fckleri e\u015fit olmad\u0131\u011f\u0131nda t testi yapmak m\u00fcmk\u00fcn m\u00fcd\u00fcr? K\u0131sa cevap: Evet, \u00f6rneklem b\u00fcy\u00fckl\u00fckleri e\u015fit olmad\u0131\u011f\u0131nda t testi yapabilirsiniz. E\u015fit \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc, t-testinde yap\u0131lan varsay\u0131mlardan biri de\u011fildir. Ger\u00e7ek problemler, t-testinde yap\u0131lan varsay\u0131mlardan biri olan iki numunenin varyanslar\u0131 e\u015fit olmad\u0131\u011f\u0131nda ortaya \u00e7\u0131kar. B\u00f6yle 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-3427","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>E\u015fit Olmayan \u00d6rneklem Boyutlar\u0131nda T-Testi Nas\u0131l Yap\u0131l\u0131r - Statorials<\/title>\n<meta name=\"description\" content=\"Bu e\u011fitimde, e\u015fit olmayan \u00f6rnek boyutlar\u0131yla T testinin nas\u0131l ger\u00e7ekle\u015ftirilece\u011fi bir \u00f6rnekle a\u00e7\u0131klanmaktad\u0131r. 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