{"id":514,"date":"2023-07-29T16:03:36","date_gmt":"2023-07-29T16:03:36","guid":{"rendered":"https:\/\/statorials.org\/tr\/eslestirilmis-ornekler-t-testi-r\/"},"modified":"2023-07-29T16:03:36","modified_gmt":"2023-07-29T16:03:36","slug":"eslestirilmis-ornekler-t-testi-r","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/eslestirilmis-ornekler-t-testi-r\/","title":{"rendered":"R&#39;de e\u015fle\u015ftirilmi\u015f \u00f6rnekler t testi nas\u0131l yap\u0131l\u0131r"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/tr\/eslestirilmis-ornekler-t-testi\/\" target=\"_blank\" rel=\"noopener\">E\u015fle\u015ftirilmi\u015f \u00f6rnekler t-testi,<\/a> bir \u00f6rnekteki her g\u00f6zlemin di\u011fer \u00f6rnekteki bir <a href=\"https:\/\/statorials.org\/tr\/istatistikte-gozlem\/\" target=\"_blank\" rel=\"noopener\">g\u00f6zlemle<\/a> e\u015fle\u015ftirilebildi\u011fi durumlarda iki \u00f6rne\u011fin ortalamalar\u0131n\u0131 kar\u015f\u0131la\u015ft\u0131ran istatistiksel bir testtir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin, belirli bir m\u00fcfredat\u0131n \u00f6\u011frencilerin belirli bir s\u0131navdaki performans\u0131 \u00fczerinde \u00f6nemli bir etkisinin olup olmad\u0131\u011f\u0131n\u0131 bilmek istedi\u011fimizi varsayal\u0131m. Bunu test etmek i\u00e7in bir s\u0131n\u0131ftaki 20 \u00f6\u011frenciden \u00f6n test yapmalar\u0131n\u0131 istiyoruz. Daha sonra \u00f6\u011frencilerin her biri iki hafta boyunca her g\u00fcn \u00e7al\u0131\u015fma program\u0131na kat\u0131l\u0131r. Daha sonra \u00f6\u011frenciler benzer zorluktaki bir testi tekrar al\u0131rlar.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Birinci ve ikinci testteki ortalama puanlar aras\u0131ndaki fark\u0131 kar\u015f\u0131la\u015ft\u0131rmak i\u00e7in e\u015fle\u015ftirilmi\u015f t testi kullan\u0131yoruz \u00e7\u00fcnk\u00fc her \u00f6\u011frencinin ilk testteki puan\u0131, ikinci testteki puan\u0131yla ili\u015fkilendirilebilir.<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>E\u015fle\u015ftirilmi\u015f t testi nas\u0131l yap\u0131l\u0131r<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">E\u015fle\u015ftirilmi\u015f bir t testi ger\u00e7ekle\u015ftirmek i\u00e7in a\u015fa\u011f\u0131daki yakla\u015f\u0131m\u0131 kullanabiliriz:<\/span><\/p>\n<p> <strong><span style=\"color: #000000;\">Ad\u0131m 1: Bo\u015f ve alternatif hipotezleri belirtin.<\/span><\/strong><\/p>\n<p> <span style=\"color: #000000;\"><strong>H <sub>0<\/sub> : \u03bc <sub>d<\/sub> = 0<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>H <sub>a<\/sub> : \u03bc <sub>d<\/sub> \u2260 0<\/strong> (iki tarafl\u0131)<\/span><br \/> <span style=\"color: #000000;\"><strong>H <sub>a<\/sub> : \u03bc <sub>d<\/sub> &gt; 0<\/strong> (tek tarafl\u0131)<\/span><br \/> <span style=\"color: #000000;\"><strong>H <sub>a<\/sub> : \u03bc <sub>d<\/sub> &lt; 0<\/strong> (tek tarafl\u0131)<\/span><\/p>\n<p> <span style=\"color: #000000;\"><em><strong>\u03bc <sub>d<\/sub><\/strong> ortalama farkt\u0131r.<\/em><\/span><\/p>\n<p> <strong><span style=\"color: #000000;\">Ad\u0131m 2: Test istatisti\u011fini ve kar\u015f\u0131l\u0131k gelen p de\u011ferini bulun.<\/span><\/strong><\/p>\n<p> <span style=\"color: #000000;\"><em>a<\/em> = \u00f6\u011frencinin birinci testteki puan\u0131 ve <em>b<\/em> = \u00f6\u011frencinin ikinci testteki puan\u0131 olsun. Test puanlar\u0131 aras\u0131ndaki ger\u00e7ek ortalama fark\u0131n s\u0131f\u0131r oldu\u011funa ili\u015fkin bo\u015f hipotezi test etmek i\u00e7in:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Her bir puan \u00e7ifti aras\u0131ndaki fark\u0131 hesaplay\u0131n (d <sub>i<\/sub> = b <sub>i<\/sub> \u2013 a <sub>i<\/sub> )<\/span><\/li>\n<li> <span style=\"color: #000000;\">Ortalama fark\u0131 hesaplay\u0131n (d)<\/span><\/li>\n<li> <span style=\"color: #000000;\">Farklar\u0131n standart sapmas\u0131n\u0131 hesaplay\u0131n s <sub>d<\/sub><\/span><\/li>\n<li> <span style=\"color: #000000;\">T = d \/ (s <sub>d<\/sub> \/ \u221an) olan t istatisti\u011fini hesaplay\u0131n<\/span><\/li>\n<li> <span style=\"color: #000000;\"><em>n-1<\/em> serbestlik derecesine sahip t istatisti\u011fi i\u00e7in kar\u015f\u0131l\u0131k gelen p de\u011ferini bulun.<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><strong>Ad\u0131m 3: Anlaml\u0131l\u0131k d\u00fczeyine ba\u011fl\u0131 olarak bo\u015f hipotezi reddedin veya reddetmeyin.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">P de\u011feri se\u00e7ilen anlaml\u0131l\u0131k d\u00fczeyinden k\u00fc\u00e7\u00fckse, bo\u015f hipotezi reddederiz ve iki grubun ortalamalar\u0131 aras\u0131nda istatistiksel olarak anlaml\u0131 bir fark oldu\u011fu sonucuna var\u0131r\u0131z. Aksi halde s\u0131f\u0131r hipotezini reddetmede ba\u015far\u0131s\u0131z oluruz.<\/span><\/p>\n<h2> <strong><span style=\"color: #000000;\">R&#8217;de e\u015fle\u015ftirilmi\u015f t testi nas\u0131l yap\u0131l\u0131r<\/span><\/strong><\/h2>\n<p> <span style=\"color: #000000;\">R&#8217;de e\u015fle\u015ftirilmi\u015f bir t testi ger\u00e7ekle\u015ftirmek i\u00e7in yerle\u015fik <strong>t.test()<\/strong> i\u015flevini a\u015fa\u011f\u0131daki s\u00f6zdizimiyle kullanabiliriz:<\/span><\/p>\n<p style=\"text-align: center;\"> <span style=\"color: #000000;\"><strong>t.test<\/strong> (x, y, e\u015fle\u015ftirilmi\u015f = DO\u011eRU, alternatif = \u201ciki taraf\u201d)<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>x,y:<\/strong> kar\u015f\u0131la\u015ft\u0131rmak istedi\u011fimiz iki dijital vekt\u00f6r<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>e\u015fle\u015ftirilmi\u015f:<\/strong> e\u015fle\u015ftirilmi\u015f bir t testi hesaplamak istedi\u011fimizi belirten mant\u0131ksal bir de\u011fer<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>alternatif:<\/strong> alternatif hipotez. Bu, &#8220;\u00e7ift tarafl\u0131&#8221; (varsay\u0131lan), &#8220;\u00fcst&#8221; veya &#8220;alt&#8221; olarak ayarlanabilir.<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki \u00f6rnek, 20 \u00f6\u011frenci i\u00e7in \u00f6n test ve son test aras\u0131nda ortalama puanlar aras\u0131nda anlaml\u0131 bir fark olup olmad\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in e\u015fle\u015ftirilmi\u015f t testinin nas\u0131l ger\u00e7ekle\u015ftirilece\u011fini g\u00f6stermektedir.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Verileri olu\u015fturun<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u00d6ncelikle veri setimizi olu\u015fturaca\u011f\u0131z:<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#create the dataset<\/span>\ndata &lt;- data.frame(score = c(85,85, 78, 78, 92, 94, 91, 85, 72, 97,\n                             84, 95, 99, 80, 90, 88, 95, 90, 96, 89,\n                             84, 88, 88, 90, 92, 93, 91, 85, 80, 93,\n                             97, 100, 93, 91, 90, 87, 94, 83, 92, 95),\n                   group = c(rep('pre', 20), rep('post', 20)))\n\n<span style=\"color: #008080;\">#view the dataset\n<\/span>data\n\n#scoregroup\n#1 85 pre\n#2 85 pre\n#3 78 pre\n#4 78 pre\n#5 92 pre\n#6 94 pre\n#7 91 pre\n#8 85 pre\n#9 72 pre\n#10 97 pre\n#11 84 pre\n#12 95 pre\n#13 99 pre\n#14 80 pre\n#15 90 pre\n#16 88 pre\n#17 95 pre\n#18 90 pre\n#19 96 pre\n#20 89 pre\n#21 84 post\n#22 88 post\n#23 88 post\n#24 90 post\n#25 92 post\n#26 93 post\n#27 91 post\n#28 85 post\n#29 80 post\n#30 93 post\n#31 97 post\n#32 100 posts\n#33 93 post\n#34 91 post\n#35 90 post\n#36 87 post\n#37 94 post\n#38 83 post\n#39 92 post\n#40 95 post\n<\/strong><\/pre>\n<h3> <span style=\"color: #000000;\"><strong>Farkl\u0131l\u0131klar\u0131 g\u00f6rselle\u015ftirin<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Daha sonra, <strong>dplyr<\/strong> k\u00fct\u00fcphanesindeki <strong>group_by()<\/strong> ve <strong>Summary<\/strong> <strong>()<\/strong> i\u015flevlerini kullanan iki grubun \u00f6zet istatistiklerine bakaca\u011f\u0131z:<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#load <em>dplyr<\/em> library\n<span style=\"color: #000000;\">library(dplyr)<\/span>\n\n#find sample size, mean, and standard deviation for each group\n<span style=\"color: #000000;\">data %&gt;%\n<span style=\"color: #800080;\">group_by<\/span> (group) %&gt;%\n  <span style=\"color: #800080;\">summarize<\/span> (\n    count = n(),\n    mean = mean(score),\n    sd = sd(score)\n  )\n<\/span><\/span>\n# A tibble: 2 x 4\n# group count mean sd\n#     \n#1 post 20 90.3 4.88\n#2 pre 20 88.2 7.24<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Ayr\u0131ca \u00f6n ve son gruplara ait puanlar\u0131n da\u011f\u0131l\u0131m\u0131n\u0131 g\u00f6r\u00fcnt\u00fclemek i\u00e7in R&#8217;deki <strong>boxplot()<\/strong> i\u015flevini kullanarak kutu grafikleri olu\u015fturabiliriz:<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #800080;\">boxplot<\/span> (score~group,\n  data=data,\n  main=\"Test Scores by Group\",\n  xlab=\"Group\",\n  ylab=\"Score\",\n  col=\"steelblue\",\n  border=\"black\"\n)<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">\u00d6zet istatistiklerden ve kutu grafiklerinden, <em>post<\/em> gruptaki ortalama puan\u0131n, <em>\u00f6n<\/em> gruptaki ortalama puandan biraz daha y\u00fcksek oldu\u011funu g\u00f6rebiliriz. Ayr\u0131ca grup <em>sonras\u0131<\/em> puanlar\u0131n, grup <em>\u00f6ncesi<\/em> puanlara g\u00f6re daha az de\u011fi\u015fkenli\u011fe sahip oldu\u011funu da g\u00f6rebiliriz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu iki grubun ortalamalar\u0131 aras\u0131ndaki fark\u0131n istatistiksel olarak anlaml\u0131 olup olmad\u0131\u011f\u0131n\u0131 bulmak i\u00e7in e\u015fle\u015ftirilmi\u015f t testi yapabiliriz.<\/span><\/p>\n<h3> <strong><span style=\"color: #000000;\">E\u015fle\u015ftirilmi\u015f bir t testi ger\u00e7ekle\u015ftirin<\/span><\/strong><\/h3>\n<p> <span style=\"color: #000000;\">E\u015fle\u015ftirilmi\u015f t testini ger\u00e7ekle\u015ftirmeden \u00f6nce, farklar\u0131n da\u011f\u0131l\u0131m\u0131n\u0131n normal (veya yakla\u015f\u0131k olarak normal) da\u011f\u0131ld\u0131\u011f\u0131n\u0131 do\u011frulamam\u0131z gerekir. Bunu yapmak i\u00e7in \u00f6n ve son puanlar aras\u0131ndaki fark olarak tan\u0131mlanan yeni bir vekt\u00f6r olu\u015fturabilir ve bu de\u011fer vekt\u00f6r\u00fc \u00fczerinde normallik i\u00e7in bir Shapiro-Wilk testi uygulayabiliriz:<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#define new vector for difference between post and pre scores\n<\/span>differences &lt;- with(data, score[group == \"post\"] - score[group == \"pre\"])\n\n<span style=\"color: #008080;\">#perform shapiro-wilk test for normality on this vector of values\n<\/span>shapiro.test(differences)\n\n# Shapiro-Wilk normality test\n#\n#data: differences\n#W = 0.92307, p-value = 0.1135\n#<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Testin p de\u011feri 0,1135 olup alfa = 0,05&#8217;ten b\u00fcy\u00fckt\u00fcr. Bu nedenle verilerimizin normal da\u011f\u0131ld\u0131\u011f\u0131 y\u00f6n\u00fcndeki s\u0131f\u0131r hipotezini reddetmiyoruz. Bu art\u0131k e\u015fle\u015ftirilmi\u015f t-testine ge\u00e7ebilece\u011fimiz anlam\u0131na gelir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">E\u015fle\u015ftirilmi\u015f bir t testi ger\u00e7ekle\u015ftirmek i\u00e7in a\u015fa\u011f\u0131daki kodu kullanabiliriz:<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <span style=\"color: #000000;\"><strong><span style=\"color: #800080;\">t.test<\/span> (score~group, data = data, paired = TRUE)\n\n# Paired t-test\n#\n#data: score by group\n#t = 1.588, df = 19, p-value = 0.1288\n#alternative hypothesis: true difference in means is not equal to 0\n#95 percent confidence interval:\n# -0.6837307 4.9837307\n#sample estimates:\n#mean of the differences \n#2.15 \n<\/strong><\/span><\/pre>\n<p> <span style=\"color: #000000;\">Sonu\u00e7tan \u015funu g\u00f6rebiliriz:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>T-<\/strong> testi istatisti\u011fi <strong>1,588&#8217;dir<\/strong> .<\/span><\/li>\n<li> <span style=\"color: #000000;\">19 serbestlik derecesine (df) sahip bu test istatisti\u011finin p de\u011feri <strong>0,1288&#8217;dir<\/strong> .<\/span><\/li>\n<li> <span style=\"color: #000000;\">Ortalama fark i\u00e7in %95 g\u00fcven aral\u0131\u011f\u0131 <strong>(-0,6837, 4,9837)&#8217;<\/strong> dir.<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u00d6n ve son grubun puanlar\u0131 aras\u0131ndaki ortalama fark <strong>2,15&#8217;tir<\/strong> .<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Dolay\u0131s\u0131yla, p-de\u011ferimiz 0,05 anlaml\u0131l\u0131k seviyemizin alt\u0131nda oldu\u011fundan, iki grubun istatistiksel olarak anlaml\u0131 ortalamalara sahip oldu\u011fu bo\u015f hipotezini reddetmede ba\u015far\u0131s\u0131z olaca\u011f\u0131z.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Ba\u015fka bir deyi\u015fle, \u00f6ncesi ve sonras\u0131 gruplar aras\u0131ndaki ortalama puanlar\u0131n istatistiksel olarak farkl\u0131 oldu\u011funu s\u00f6yleyecek yeterli kan\u0131t\u0131m\u0131z yok. Bu, m\u00fcfredat\u0131n test puanlar\u0131 \u00fczerinde anlaml\u0131 bir etkisinin olmad\u0131\u011f\u0131 anlam\u0131na gelir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Ek olarak %95 g\u00fcven aral\u0131\u011f\u0131m\u0131z, iki grup aras\u0131ndaki ger\u00e7ek ortalama fark\u0131n <strong>-0,6837<\/strong> ile <strong>4,9837<\/strong> aras\u0131nda oldu\u011fundan &#8220;%95 emin&#8221; oldu\u011fumuzu g\u00f6sterir.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><em>S\u0131f\u0131r<\/em> de\u011feri bu g\u00fcven aral\u0131\u011f\u0131n\u0131n i\u00e7inde yer ald\u0131\u011f\u0131ndan bu, <em>s\u0131f\u0131r\u0131n<\/em> asl\u0131nda ortalama puanlar aras\u0131ndaki ger\u00e7ek fark olabilece\u011fi anlam\u0131na gelir; bu durumda s\u0131f\u0131r hipotezini reddetmemizin nedeni budur.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>E\u015fle\u015ftirilmi\u015f \u00f6rnekler t-testi, bir \u00f6rnekteki her g\u00f6zlemin di\u011fer \u00f6rnekteki bir g\u00f6zlemle e\u015fle\u015ftirilebildi\u011fi durumlarda iki \u00f6rne\u011fin ortalamalar\u0131n\u0131 kar\u015f\u0131la\u015ft\u0131ran istatistiksel bir testtir. \u00d6rne\u011fin, belirli bir m\u00fcfredat\u0131n \u00f6\u011frencilerin belirli bir s\u0131navdaki performans\u0131 \u00fczerinde \u00f6nemli bir etkisinin olup olmad\u0131\u011f\u0131n\u0131 bilmek istedi\u011fimizi varsayal\u0131m. Bunu test etmek i\u00e7in bir s\u0131n\u0131ftaki 20 \u00f6\u011frenciden \u00f6n test yapmalar\u0131n\u0131 istiyoruz. Daha sonra \u00f6\u011frencilerin her biri [&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-514","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>R - Statorials&#039;de e\u015fle\u015ftirilmi\u015f \u00f6rnekler t testi nas\u0131l yap\u0131l\u0131r?<\/title>\n<meta name=\"description\" content=\"Ad\u0131m ad\u0131m bir \u00f6rnek de dahil olmak \u00fczere, R&#039;de e\u015fle\u015ftirilmi\u015f \u00f6rnekler t-testinin nas\u0131l ger\u00e7ekle\u015ftirilece\u011fine ili\u015fkin basit bir a\u00e7\u0131klama.\" \/>\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\/eslestirilmis-ornekler-t-testi-r\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"R - 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