{"id":1223,"date":"2023-07-27T05:49:03","date_gmt":"2023-07-27T05:49:03","guid":{"rendered":"https:\/\/statorials.org\/tr\/r-cinsinden-ornekleme-dagilimi\/"},"modified":"2023-07-27T05:49:03","modified_gmt":"2023-07-27T05:49:03","slug":"r-cinsinden-ornekleme-dagilimi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/r-cinsinden-ornekleme-dagilimi\/","title":{"rendered":"R&#39;de \u00f6rnekleme da\u011f\u0131l\u0131mlar\u0131 nas\u0131l hesaplan\u0131r?"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/tr\/ornekleme-dagilimi-1\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u00d6rnekleme da\u011f\u0131l\u0131m\u0131,<\/a> belirli bir <a href=\"https:\/\/statorials.org\/tr\/istatistik-ve-parametre\/\" target=\"_blank\" rel=\"noopener noreferrer\">istatisti\u011fin<\/a> tek bir pop\u00fclasyondan bir\u00e7ok rastgele \u00f6rne\u011fe dayanan olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131d\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu e\u011fitimde R&#8217;deki \u00f6rnekleme da\u011f\u0131l\u0131mlar\u0131yla a\u015fa\u011f\u0131dakilerin nas\u0131l yap\u0131laca\u011f\u0131 a\u00e7\u0131klanmaktad\u0131r:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Bir \u00f6rnekleme da\u011f\u0131l\u0131m\u0131 olu\u015fturun.<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u00d6rnekleme da\u011f\u0131l\u0131m\u0131n\u0131 g\u00f6rselle\u015ftirin.<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u00d6rnekleme da\u011f\u0131l\u0131m\u0131n\u0131n ortalamas\u0131n\u0131 ve standart sapmas\u0131n\u0131 hesaplay\u0131n.<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u00d6rnekleme da\u011f\u0131l\u0131m\u0131na ili\u015fkin olas\u0131l\u0131klar\u0131 hesaplay\u0131n.<\/span><\/li>\n<\/ul>\n<h3> <span style=\"color: #000000;\"><strong>R&#8217;de bir \u00f6rnekleme da\u011f\u0131l\u0131m\u0131 olu\u015fturun<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki kod, R&#8217;de bir \u00f6rnekleme da\u011f\u0131l\u0131m\u0131n\u0131n nas\u0131l olu\u015fturulaca\u011f\u0131n\u0131 g\u00f6sterir:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <span style=\"color: #000000;\"><strong><span style=\"color: #008080;\">#make this example reproducible\n<\/span>set.seed(0)\n\n<span style=\"color: #008080;\">#define number of samples\n<\/span>n = 10000\n\n<span style=\"color: #008080;\">#create empty vector of length n\n<\/span>sample_means = <span style=\"color: #3366ff;\">rep<\/span> (NA, n)\n\n<span style=\"color: #008080;\">#fill empty vector with means\n<\/span><span style=\"color: #008000;\">for<\/span> (i <span style=\"color: #008000;\">in<\/span> 1:n){\n  sample_means[i] = <span style=\"color: #3366ff;\">mean<\/span> ( <span style=\"color: #3366ff;\">rnorm<\/span> (20, mean=5.3, sd=9))\n}\n\n<span style=\"color: #008080;\">#view first six sample means\n<\/span>head(sample_means)\n\n[1] 5.283992 6.304845 4.259583 3.915274 7.756386 4.532656\n<\/strong><\/span><\/pre>\n<p> <span style=\"color: #000000;\">Bu \u00f6rnekte, her \u00f6rnek boyutunun 20 oldu\u011fu ve ortalamas\u0131 5,3 ve standart sapmas\u0131 9 olan normal bir da\u011f\u0131l\u0131mdan olu\u015fturulan 10.000 \u00f6rne\u011fin ortalamas\u0131n\u0131 hesaplamak i\u00e7in <a href=\"https:\/\/statorials.org\/tr\/rde-dnorm-pnorm-rnorm-qnorm\/\" target=\"_blank\" rel=\"noopener noreferrer\">rnorm()<\/a> i\u015flevini kulland\u0131k.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0130lk numunenin ortalamas\u0131n\u0131n 5,283992 oldu\u011funu, ikinci numunenin ortalamas\u0131n\u0131n 6,304845 oldu\u011funu vb. g\u00f6rebiliriz.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u00d6rnekleme da\u011f\u0131l\u0131m\u0131n\u0131 g\u00f6rselle\u015ftirin<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki kod, \u00f6rnekleme da\u011f\u0131l\u0131m\u0131n\u0131 g\u00f6rselle\u015ftirmek i\u00e7in basit bir histogram\u0131n nas\u0131l olu\u015fturulaca\u011f\u0131n\u0131 g\u00f6sterir:<\/span> <\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <span style=\"color: #000000;\"><strong><span style=\"color: #008080;\">#create histogram to visualize the sampling distribution<\/span>\nhist(sample_means, main = \"\", xlab = \" <span style=\"color: #008000;\">Sample Means<\/span> \", col = \" <span style=\"color: #008000;\">steelblue<\/span> \")\n<\/strong><\/span><\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-12122 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/echantillonnagemoyenne1.png\" alt=\"R histogram\u0131nda \u00f6rnekleme da\u011f\u0131l\u0131m\u0131\" width=\"435\" height=\"407\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rnekleme da\u011f\u0131l\u0131m\u0131n\u0131n \u00e7an \u015feklinde oldu\u011fu ve 5 de\u011ferine yak\u0131n bir zirveye sahip oldu\u011fu g\u00f6r\u00fclebilir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Ancak da\u011f\u0131l\u0131m\u0131n kuyruklar\u0131ndan baz\u0131 \u00f6rneklerin ortalamalar\u0131n\u0131n 10&#8217;dan b\u00fcy\u00fck, baz\u0131lar\u0131n\u0131n ise 0&#8217;dan k\u00fc\u00e7\u00fck ortalamalara sahip oldu\u011funu g\u00f6rebiliriz.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Ortalamay\u0131 ve standart sapmay\u0131 bulun<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki kod \u00f6rnekleme da\u011f\u0131l\u0131m\u0131n\u0131n ortalama ve standart sapmas\u0131n\u0131n nas\u0131l hesaplanaca\u011f\u0131n\u0131 g\u00f6sterir:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <span style=\"color: #000000;\"><strong><span style=\"color: #008080;\">#mean of sampling distribution<\/span>\nmean(sample_means)\n\n[1] 5.287195\n\n<span style=\"color: #008080;\">#standard deviation of sampling distribution\n<\/span>sd(sample_means)\n\n[1] 2.00224<\/strong><\/span><\/pre>\n<p> <span style=\"color: #000000;\">Teorik olarak \u00f6rnekleme da\u011f\u0131l\u0131m\u0131n\u0131n ortalamas\u0131 5,3 olmal\u0131d\u0131r. Bu \u00f6rnekte ger\u00e7ek \u00f6rnek ortalaman\u0131n 5,3&#8217;e yak\u0131n olan <strong>5,287195<\/strong> oldu\u011funu g\u00f6rebiliriz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Ve teorik olarak \u00f6rnekleme da\u011f\u0131l\u0131m\u0131n\u0131n standart sapmas\u0131 s\/\u221an&#8217;ye e\u015fit olmal\u0131d\u0131r, bu da 9 \/ \u221a20 = 2,012 olacakt\u0131r. \u00d6rnekleme da\u011f\u0131l\u0131m\u0131n\u0131n ger\u00e7ek standart sapmas\u0131n\u0131n 2,012&#8217;ye yak\u0131n olan <strong>2,00224<\/strong> oldu\u011funu g\u00f6rebiliriz.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Olas\u0131l\u0131klar\u0131 hesaplay\u0131n<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki kod, pop\u00fclasyon ortalamas\u0131, pop\u00fclasyon standart sapmas\u0131 ve \u00f6rnek boyutu g\u00f6z \u00f6n\u00fcne al\u0131nd\u0131\u011f\u0131nda, \u00f6rnek ortalamas\u0131 i\u00e7in belirli bir de\u011fer elde etme olas\u0131l\u0131\u011f\u0131n\u0131n nas\u0131l hesaplanaca\u011f\u0131n\u0131 g\u00f6sterir.<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <span style=\"color: #000000;\"><strong><span style=\"color: #008080;\">#calculate probability that sample mean is less than or equal to 6<\/span>\nsum(sample_means &lt;= 6) \/ length(sample_means)\n<\/strong><\/span><\/pre>\n<p> <span style=\"color: #000000;\">Bu \u00f6zel \u00f6rnekte, pop\u00fclasyon ortalamas\u0131n\u0131n 5,3, pop\u00fclasyon standart sapmas\u0131n\u0131n 9 ve 20&#8217;lik numune boyutunun <strong>0,6417<\/strong> oldu\u011fu g\u00f6z \u00f6n\u00fcne al\u0131nd\u0131\u011f\u0131nda, numune ortalamas\u0131n\u0131n 6&#8217;dan k\u00fc\u00e7\u00fck veya 6&#8217;ya e\u015fit olma olas\u0131l\u0131\u011f\u0131n\u0131 buluyoruz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu, <a href=\"https:\/\/statorials.org\/tr\/ornekleme-dagitim-hesaplayicisi\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u00d6rnekleme Da\u011f\u0131t\u0131m\u0131 Hesaplay\u0131c\u0131s\u0131<\/a> taraf\u0131ndan hesaplanan olas\u0131l\u0131\u011fa \u00e7ok yak\u0131nd\u0131r:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-12123 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/echantillonnagemoyenne2.png\" alt=\"\u00d6rnekleme da\u011f\u0131l\u0131m\u0131n\u0131n hesaplanmas\u0131\" width=\"358\" height=\"550\" srcset=\"\" sizes=\"auto, \"><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Kodun tamam\u0131<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Bu \u00f6rnekte kullan\u0131lan R kodunun tamam\u0131 a\u015fa\u011f\u0131da g\u00f6sterilmi\u015ftir:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <span style=\"color: #000000;\"><strong><span style=\"color: #008080;\">#make this example reproducible\n<\/span>set.seed(0)\n\n<span style=\"color: #008080;\">#define number of samples\n<\/span>n = 10000\n\n<span style=\"color: #008080;\">#create empty vector of length n\n<\/span>sample_means = <span style=\"color: #3366ff;\">rep<\/span> (NA, n)\n\n<span style=\"color: #008080;\">#fill empty vector with means\n<\/span><span style=\"color: #008000;\">for<\/span> (i <span style=\"color: #008000;\">in<\/span> 1:n){\n  sample_means[i] = <span style=\"color: #3366ff;\">mean<\/span> ( <span style=\"color: #3366ff;\">rnorm<\/span> (20, mean=5.3, sd=9))\n}\n\n<span style=\"color: #008080;\">#view first six sample means\n<\/span>head(sample_means)\n\n<span style=\"color: #008080;\">#create histogram to visualize the sampling distribution\n<\/span>hist(sample_means, main = \"\", xlab = \" <span style=\"color: #008000;\">Sample Means<\/span> \", col = \" <span style=\"color: #008000;\">steelblue<\/span> \")\n\n<span style=\"color: #008080;\">#mean of sampling distribution\n<\/span>mean(sample_means)\n\n<span style=\"color: #008080;\">#standard deviation of sampling distribution\n<\/span>sd(sample_means)\n\n<span style=\"color: #008080;\">#calculate probability that sample mean is less than or equal to 6<\/span>\nsum(sample_means &lt;= 6) \/ length(sample_means)\n<\/strong><\/span><\/pre>\n<h3> <span style=\"color: #000000;\"><strong>Ek kaynaklar<\/strong><\/span><\/h3>\n<p><a href=\"https:\/\/statorials.org\/tr\/ornekleme-dagilimi-1\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u00d6rnekleme Da\u011f\u0131l\u0131mlar\u0131na Giri\u015f<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/ornekleme-dagitim-hesaplayicisi\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u00d6rnekleme Da\u011f\u0131t\u0131m\u0131 Hesaplay\u0131c\u0131<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/merkezi-limit-teoremi\/\" target=\"_blank\" rel=\"noopener noreferrer\">Merkezi Limit Teoremine Giri\u015f<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u00d6rnekleme da\u011f\u0131l\u0131m\u0131, belirli bir istatisti\u011fin tek bir pop\u00fclasyondan bir\u00e7ok rastgele \u00f6rne\u011fe dayanan olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131d\u0131r. Bu e\u011fitimde R&#8217;deki \u00f6rnekleme da\u011f\u0131l\u0131mlar\u0131yla a\u015fa\u011f\u0131dakilerin nas\u0131l yap\u0131laca\u011f\u0131 a\u00e7\u0131klanmaktad\u0131r: Bir \u00f6rnekleme da\u011f\u0131l\u0131m\u0131 olu\u015fturun. \u00d6rnekleme da\u011f\u0131l\u0131m\u0131n\u0131 g\u00f6rselle\u015ftirin. \u00d6rnekleme da\u011f\u0131l\u0131m\u0131n\u0131n ortalamas\u0131n\u0131 ve standart sapmas\u0131n\u0131 hesaplay\u0131n. \u00d6rnekleme da\u011f\u0131l\u0131m\u0131na ili\u015fkin olas\u0131l\u0131klar\u0131 hesaplay\u0131n. R&#8217;de bir \u00f6rnekleme da\u011f\u0131l\u0131m\u0131 olu\u015fturun A\u015fa\u011f\u0131daki kod, R&#8217;de bir \u00f6rnekleme da\u011f\u0131l\u0131m\u0131n\u0131n nas\u0131l olu\u015fturulaca\u011f\u0131n\u0131 [&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-1223","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&#039;de \u00f6rnekleme da\u011f\u0131l\u0131mlar\u0131 nas\u0131l hesaplan\u0131r?<\/title>\n<meta name=\"description\" content=\"Bu e\u011fitimde, belirli bir parametre k\u00fcmesi i\u00e7in R&#039;de \u00f6rnekleme da\u011f\u0131l\u0131mlar\u0131n\u0131n nas\u0131l hesaplanaca\u011f\u0131 ve 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