{"id":2236,"date":"2023-07-23T03:32:17","date_gmt":"2023-07-23T03:32:17","guid":{"rendered":"https:\/\/statorials.org\/tr\/kategorik-degiskenler-arasindaki-korelasyon\/"},"modified":"2023-07-23T03:32:17","modified_gmt":"2023-07-23T03:32:17","slug":"kategorik-degiskenler-arasindaki-korelasyon","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/kategorik-degiskenler-arasindaki-korelasyon\/","title":{"rendered":"Kategorik de\u011fi\u015fkenler aras\u0131ndaki korelasyon nas\u0131l hesaplan\u0131r?"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">S\u00fcrekli say\u0131sal de\u011fi\u015fkenler aras\u0131ndaki korelasyonu hesaplamak i\u00e7in s\u0131kl\u0131kla <a href=\"https:\/\/statorials.org\/tr\/pearson-korelasyon-katsayisi-1\/\" target=\"_blank\" rel=\"noopener\">Pearson korelasyon katsay\u0131s\u0131n\u0131<\/a> kullan\u0131r\u0131z.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Ancak kategorik de\u011fi\u015fkenler yani a\u015fa\u011f\u0131daki gibi ad veya etiket alan de\u011fi\u015fkenler aras\u0131ndaki korelasyonu hesaplamak i\u00e7in farkl\u0131 bir metrik kullanmam\u0131z gerekir:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Medeni durum (bekar, evli, bo\u015fanm\u0131\u015f)<\/span><\/li>\n<li> <span style=\"color: #000000;\">Sigara i\u00e7me durumu (sigara i\u00e7en, i\u00e7meyen)<\/span><\/li>\n<li> <span style=\"color: #000000;\">G\u00f6z rengi (mavi, kahverengi, ye\u015fil)<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Kategorik de\u011fi\u015fkenler aras\u0131ndaki korelasyonu hesaplamak i\u00e7in yayg\u0131n olarak kullan\u0131lan \u00fc\u00e7 \u00f6l\u00e7\u00fcm vard\u0131r:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1. Tetrakorik korelasyon:<\/strong> ikili kategorik de\u011fi\u015fkenler aras\u0131ndaki korelasyonu hesaplamak i\u00e7in kullan\u0131l\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>2. Polikorik korelasyon:<\/strong> s\u0131ral\u0131 kategorik de\u011fi\u015fkenler aras\u0131ndaki korelasyonu hesaplamak i\u00e7in kullan\u0131l\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>3. Cramer V:<\/strong> Nominal kategorik de\u011fi\u015fkenler aras\u0131ndaki korelasyonu hesaplamak i\u00e7in kullan\u0131l\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki b\u00f6l\u00fcmlerde bu \u00fc\u00e7 \u00f6l\u00e7\u00fcm\u00fcn her birinin nas\u0131l hesaplanaca\u011f\u0131na dair bir \u00f6rnek verilmektedir.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Metrik 1: Tetrakorik korelasyon<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\"><strong>Tetrakorik korelasyon,<\/strong> ikili kategorik de\u011fi\u015fkenler aras\u0131ndaki korelasyonu hesaplamak i\u00e7in kullan\u0131l\u0131r. \u0130kili de\u011fi\u015fkenlerin yaln\u0131zca iki olas\u0131 de\u011ferden birini alabilen de\u011fi\u015fkenler oldu\u011funu unutmay\u0131n.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Tetrakorik korelasyon de\u011feri -1 ile 1 aras\u0131nda de\u011fi\u015fir; burada -1, g\u00fc\u00e7l\u00fc bir negatif korelasyonu, 0, korelasyon olmad\u0131\u011f\u0131n\u0131 ve 1, g\u00fc\u00e7l\u00fc bir pozitif korelasyonu belirtir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin, cinsiyetin bir siyasi parti tercihiyle ili\u015fkili olup olmad\u0131\u011f\u0131n\u0131 bilmek istedi\u011fimizi varsayal\u0131m. Bu y\u00fczden 100 se\u00e7menden olu\u015fan basit rastgele bir \u00f6rnek al\u0131yoruz ve onlara siyasi parti tercihlerini soruyoruz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki tabloda anketin sonu\u00e7lar\u0131 sunulmaktad\u0131r:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-12679 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/tetra2.png\" alt=\"Tetrakorik korelasyon\" width=\"325\" height=\"140\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Bu senaryoda tetrakorik korelasyonu kullanaca\u011f\u0131z \u00e7\u00fcnk\u00fc her kategorik de\u011fi\u015fken ikilidir, yani her de\u011fi\u015fken yaln\u0131zca iki olas\u0131 de\u011fer alabilir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0130ki de\u011fi\u015fken aras\u0131ndaki tetrakorik korelasyonu hesaplamak i\u00e7in R&#8217;de a\u015fa\u011f\u0131daki kodu kullanabiliriz:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008000;\">library<\/span> (psych)\n\n<span style=\"color: #008080;\">#create 2x2 table\n<\/span>data = matrix(c(19, 12, 30, 39), nrow= <span style=\"color: #008000;\">2<\/span> )\n\n<span style=\"color: #008080;\">#view table\n<\/span>data\n\n<span style=\"color: #008080;\">#calculate tetrachoric correlation\n<\/span>tetrachoric(data)\n\ntetrachoric correlation \n[1] 0.27<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Tetrakorik korelasyon <strong>0,27<\/strong> olarak ortaya \u00e7\u0131k\u0131yor. Bu de\u011ferin olduk\u00e7a d\u00fc\u015f\u00fck olmas\u0131, cinsiyet ile siyasi parti tercihi aras\u0131nda (varsa) zay\u0131f bir ili\u015fkinin oldu\u011funu g\u00f6stermektedir.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Metrik 2: Polikorik korelasyon<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\"><strong>Polikorik korelasyon,<\/strong> s\u0131ral\u0131 kategorik de\u011fi\u015fkenler aras\u0131ndaki korelasyonu hesaplamak i\u00e7in kullan\u0131l\u0131r. S\u0131ral\u0131 de\u011fi\u015fkenlerin olas\u0131 de\u011ferleri do\u011fal bir s\u0131raya sahip olan de\u011fi\u015fkenler oldu\u011funu hat\u0131rlay\u0131n.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Polikorik korelasyon de\u011feri -1 ila 1 aras\u0131nda de\u011fi\u015fir; burada -1, g\u00fc\u00e7l\u00fc bir negatif korelasyonu, 0, korelasyon olmad\u0131\u011f\u0131n\u0131 ve 1, g\u00fc\u00e7l\u00fc bir pozitif korelasyonu belirtir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin, iki farkl\u0131 film derecelendirme kurulu\u015funun film derecelendirmeleri aras\u0131nda y\u00fcksek bir korelasyon olup olmad\u0131\u011f\u0131n\u0131 bilmek istedi\u011finizi varsayal\u0131m.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Her ajanstan 20 farkl\u0131 filmi 1&#8217;den 3&#8217;e kadar bir \u00f6l\u00e7ekte derecelendirmesini istiyoruz; 1 &#8220;k\u00f6t\u00fc&#8221;y\u00fc, 2 &#8220;k\u00f6t\u00fc&#8221;y\u00fc ve 3 &#8220;iyi&#8221;yi g\u00f6steriyor.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki tablo sonu\u00e7lar\u0131 g\u00f6stermektedir:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-20462 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/poly11.png\" alt=\"\" width=\"283\" height=\"525\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">\u0130ki ajans\u0131n derecelendirmeleri aras\u0131ndaki polikorik korelasyonu hesaplamak i\u00e7in R&#8217;de a\u015fa\u011f\u0131daki kodu kullanabiliriz:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008000;\">library<\/span> (polycor)\n\n<span style=\"color: #008080;\">#define movie ratings\n<\/span>x &lt;- c(1, 1, 2, 2, 3, 2, 2, 3, 2, 3, 3, 2, 1, 2, 2, 1, 1, 1, 2, 2)\ny &lt;- c(1, 1, 2, 1, 3, 3, 3, 2, 2, 3, 3, 3, 2, 2, 2, 1, 2, 1, 3, 3)\n\n<span style=\"color: #008080;\">#calculate polychoric correlation between ratings\n<\/span>polychor(x, y)\n\n[1] 0.7828328\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Polikorik korelasyon <strong>0,78<\/strong> olarak ortaya \u00e7\u0131k\u0131yor. Bu de\u011fer olduk\u00e7a y\u00fcksektir ve her ajans\u0131n derecelendirmeleri aras\u0131nda g\u00fc\u00e7l\u00fc bir pozitif ili\u015fki oldu\u011funu g\u00f6stermektedir.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Metrik 3: Cramer&#8217;in V&#8217;si<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\"><strong>Cramer V,<\/strong> nominal kategorik de\u011fi\u015fkenler aras\u0131ndaki korelasyonu hesaplamak i\u00e7in kullan\u0131l\u0131r.<\/span> <span style=\"color: #000000;\">Nominal de\u011fi\u015fkenlerin kategori etiketleri ta\u015f\u0131yan ancak do\u011fal s\u0131ralamas\u0131 olmayan de\u011fi\u015fkenler oldu\u011funu unutmay\u0131n.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Cramer V&#8217;nin de\u011feri 0 ila 1 aras\u0131nda de\u011fi\u015fir; 0, de\u011fi\u015fkenler aras\u0131nda hi\u00e7bir ili\u015fkinin olmad\u0131\u011f\u0131n\u0131, 1 ise de\u011fi\u015fkenler aras\u0131nda g\u00fc\u00e7l\u00fc bir ili\u015fkinin oldu\u011funu g\u00f6sterir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin g\u00f6z rengi ile cinsiyet aras\u0131nda bir ili\u015fki olup olmad\u0131\u011f\u0131n\u0131 bilmek istedi\u011fimizi varsayal\u0131m. Bu nedenle 50 ki\u015fiyi sorguluyor ve a\u015fa\u011f\u0131daki sonu\u00e7lar\u0131 elde ediyoruz:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-20463 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/poly12.png\" alt=\"\" width=\"370\" height=\"111\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Bu iki de\u011fi\u015fken i\u00e7in Cramer&#8217;in V&#8217;sini hesaplamak amac\u0131yla R&#8217;de a\u015fa\u011f\u0131daki kodu kullanabiliriz:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008000;\">library<\/span> (rcompanion)\n\n<span style=\"color: #008080;\">#create table\n<\/span>data = matrix(c(6, 9, 8, 5, 12, 10), nrow= <span style=\"color: #008000;\">2<\/span> )\n\n<span style=\"color: #008080;\">#view table\n<\/span>data\n\n     [,1] [,2] [,3]\n[1,] 6 8 12\n[2,] 9 5 10\n\n<span style=\"color: #008080;\">#calculate Cramer's V\n<\/span>cramerV(data)\n\nCramer V \n  0.1671<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Cramer&#8217;in V&#8217;si <strong>0,1671<\/strong> olarak \u00e7\u0131k\u0131yor. Bu de\u011ferin olduk\u00e7a d\u00fc\u015f\u00fck olmas\u0131 cinsiyet ile g\u00f6z rengi aras\u0131nda zay\u0131f bir ili\u015fkinin oldu\u011funu g\u00f6stermektedir.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Ek kaynaklar<\/strong><\/span><\/h3>\n<p> <a href=\"https:\/\/statorials.org\/tr\/pearson-korelasyon-katsayisi-1\/\" target=\"_blank\" rel=\"noopener\">Pearson Korelasyon Katsay\u0131s\u0131na Giri\u015f<\/a><br \/> Tetrakorik korelasyona giri\u015f<br \/> <a href=\"https:\/\/statorials.org\/tr\/kategorik-ve-niceliksel\/\" target=\"_blank\" rel=\"noopener\">Kategorik veya niceliksel de\u011fi\u015fkenler: fark nedir?<\/a><br \/> \u00d6l\u00e7\u00fcm seviyeleri: nominal, s\u0131ral\u0131, aral\u0131k ve oran<\/p>\n","protected":false},"excerpt":{"rendered":"<p>S\u00fcrekli say\u0131sal de\u011fi\u015fkenler aras\u0131ndaki korelasyonu hesaplamak i\u00e7in s\u0131kl\u0131kla Pearson korelasyon katsay\u0131s\u0131n\u0131 kullan\u0131r\u0131z. Ancak kategorik de\u011fi\u015fkenler yani a\u015fa\u011f\u0131daki gibi ad veya etiket alan de\u011fi\u015fkenler aras\u0131ndaki korelasyonu hesaplamak i\u00e7in farkl\u0131 bir metrik kullanmam\u0131z gerekir: Medeni durum (bekar, evli, bo\u015fanm\u0131\u015f) Sigara i\u00e7me durumu (sigara i\u00e7en, i\u00e7meyen) G\u00f6z rengi (mavi, kahverengi, ye\u015fil) Kategorik de\u011fi\u015fkenler aras\u0131ndaki korelasyonu hesaplamak i\u00e7in yayg\u0131n [&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-2236","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>Kategorik de\u011fi\u015fkenler aras\u0131ndaki korelasyon nas\u0131l hesaplan\u0131r - 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