{"id":433,"date":"2023-07-29T23:15:25","date_gmt":"2023-07-29T23:15:25","guid":{"rendered":"https:\/\/statorials.org\/tr\/pearson-korelasyon-katsayisi\/"},"modified":"2023-07-29T23:15:25","modified_gmt":"2023-07-29T23:15:25","slug":"pearson-korelasyon-katsayisi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/pearson-korelasyon-katsayisi\/","title":{"rendered":"Pearson korelasyon katsay\u0131s\u0131"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>Pearson korelasyon katsay\u0131s\u0131<\/strong> (\u201c\u00e7arp\u0131m-moment korelasyon katsay\u0131s\u0131\u201d olarak da bilinir) iki de\u011fi\u015fken <em>X<\/em> ve <em>Y<\/em> aras\u0131ndaki do\u011frusal ili\u015fkinin bir \u00f6l\u00e7\u00fcs\u00fcd\u00fcr. -1 ile 1 aras\u0131nda bir de\u011fere sahiptir; burada:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">-1, iki de\u011fi\u015fken aras\u0131nda tamamen negatif bir do\u011frusal korelasyonu g\u00f6sterir<\/span><\/li>\n<li> <span style=\"color: #000000;\">0, iki de\u011fi\u015fken aras\u0131nda do\u011frusal bir korelasyon olmad\u0131\u011f\u0131n\u0131 g\u00f6sterir<\/span><\/li>\n<li> <span style=\"color: #000000;\">1, iki de\u011fi\u015fken aras\u0131nda m\u00fckemmel pozitif do\u011frusal bir korelasyonu g\u00f6sterir<\/span><\/li>\n<\/ul>\n<h2> <strong><span style=\"color: #000000;\">Pearson korelasyon katsay\u0131s\u0131n\u0131 bulma form\u00fcl\u00fc<\/span><\/strong><\/h2>\n<p> <span style=\"color: #000000;\">Bir veri \u00f6rne\u011fi i\u00e7in <em>r<\/em> ile g\u00f6sterilen Pearson korelasyon katsay\u0131s\u0131n\u0131 bulma form\u00fcl\u00fc ( <a href=\"https:\/\/en.wikipedia.org\/wiki\/Pearson_correlation_coefficient\" target=\"_blank\" rel=\"noopener\">Wikipedia arac\u0131l\u0131\u011f\u0131yla<\/a> ):<\/span><\/p>\n<p> <span style=\"color: #000000;\">Muhtemelen bu form\u00fcl\u00fc hi\u00e7bir zaman elle hesaplamak zorunda kalmayacaks\u0131n\u0131z \u00e7\u00fcnk\u00fc bunu sizin yerinize yapacak bir yaz\u0131l\u0131m kullanabilirsiniz, ancak bir \u00f6rnek \u00fczerinden ge\u00e7erek bu form\u00fcl\u00fcn tam olarak ne i\u015fe yarad\u0131\u011f\u0131n\u0131 anlamak yararl\u0131 olacakt\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki veri setine sahip oldu\u011fumuzu varsayal\u0131m:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-4985 size-full\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/correlationexemple.jpg\" alt=\"\" width=\"135\" height=\"154\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Bu \u00e7iftleri (X, Y) bir da\u011f\u0131l\u0131m grafi\u011fine \u00e7izersek, \u015f\u00f6yle g\u00f6r\u00fcnecektir:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-1532 size-full\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/correl1-1.jpg\" alt=\"Da\u011f\u0131l\u0131m grafi\u011finde Pearson korelasyonu \u00f6rne\u011fi\" width=\"455\" height=\"362\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Sadece bu da\u011f\u0131l\u0131m grafi\u011fine bakarak, X ve Y de\u011fi\u015fkenleri aras\u0131nda pozitif bir ili\u015fki oldu\u011funu g\u00f6rebiliriz: X artt\u0131k\u00e7a Y de artma e\u011filimindedir.<\/span> <span style=\"color: #000000;\">Ancak bu iki de\u011fi\u015fkenin tam olarak ne kadar pozitif ili\u015fkili oldu\u011funu \u00f6l\u00e7mek i\u00e7in Pearson korelasyon katsay\u0131s\u0131n\u0131 bulmam\u0131z gerekiyor.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Form\u00fcl\u00fcn pay\u0131na odaklanal\u0131m:<\/span><\/p>\n<p> <span style=\"color: #000000;\">Veri setimizdeki her bir (X, Y) \u00e7ifti i\u00e7in x de\u011feri ile ortalama x de\u011feri aras\u0131ndaki fark\u0131, y de\u011feri ile ortalama y de\u011feri aras\u0131ndaki fark\u0131 bulmam\u0131z ve daha sonra bu iki say\u0131y\u0131 \u00e7arpmam\u0131z gerekiyor.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin ilk \u00e7iftimiz (X, Y) (2, 2)&#8217;dir. Bu veri setinde x&#8217;in ortalama de\u011feri 5 ve y&#8217;nin bu veri setinde ortalama de\u011feri 7&#8217;dir. Yani bu \u00e7iftin x de\u011feri ile x&#8217;in ortalama de\u011feri aras\u0131ndaki fark 2 \u2013 5 = -3 olur. Bu \u00e7iftin y de\u011feri ile ortalama y de\u011feri aras\u0131ndaki fark 2 \u2013 7 = -5\u2019tir. Daha sonra bu iki say\u0131y\u0131 \u00e7arpt\u0131\u011f\u0131m\u0131zda -3 * -5 = 15 elde ederiz.<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-1528 size-full\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/correl3.jpg\" alt=\"Pearson korelasyonu elle\" width=\"409\" height=\"157\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">\u0130\u015fte az \u00f6nce yapt\u0131klar\u0131m\u0131z\u0131n g\u00f6rsel bir \u00f6zeti:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-1533 size-full\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/correl3-1.jpg\" alt=\"Pearson Korelasyonu \u00d6rne\u011fi\" width=\"457\" height=\"356\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Daha sonra her \u00e7ift i\u00e7in bunu yap\u0131n:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-1534 size-full\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/correl5.jpg\" alt=\"Pearson Korelasyonu \u00d6rne\u011fi\" width=\"414\" height=\"156\" srcset=\"\" sizes=\"auto, \"><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-1535 size-full\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/correl6.jpg\" alt=\"Da\u011f\u0131l\u0131m grafi\u011finde Pearson korelasyonu \u00f6rne\u011fi\" width=\"447\" height=\"352\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Form\u00fcl\u00fcn pay\u0131n\u0131 elde etmenin son ad\u0131m\u0131, t\u00fcm bu de\u011ferleri bir araya toplamakt\u0131r:<\/span><\/p>\n<p style=\"text-align: center;\"> <span style=\"color: #000000;\">15 + 3 +3 + 15 = <strong>36<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Daha sonra form\u00fcl\u00fcn paydas\u0131 bize x ve y&#8217;nin t\u00fcm kare farklar\u0131n\u0131n toplam\u0131n\u0131 bulmam\u0131z\u0131, ard\u0131ndan bu iki say\u0131y\u0131 \u00e7arpmam\u0131z\u0131 ve ard\u0131ndan karek\u00f6k almam\u0131z\u0131 s\u00f6yler:<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6ncelikle x ve y farklar\u0131n\u0131n karelerinin toplam\u0131n\u0131 bulaca\u011f\u0131z:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-1537 size-full\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/correl7.jpg\" alt=\"\" width=\"529\" height=\"137\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Daha sonra bu iki say\u0131y\u0131 birbiriyle \u00e7arpaca\u011f\u0131z: 20 * 68 = 1.360.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Son olarak karek\u00f6k\u00fcn\u00fc alaca\u011f\u0131z: \u221a <span style=\"text-decoration: overline;\">1,360<\/span> = <strong>36,88<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">B\u00f6ylece form\u00fcl\u00fcn pay\u0131n\u0131n 36, paydas\u0131n\u0131n ise 36,88 oldu\u011funu bulduk. Bu, Pearson korelasyon katsay\u0131m\u0131z\u0131n r = 36 \/ 36,88 = <strong>0,976<\/strong> oldu\u011fu anlam\u0131na gelir<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu say\u0131n\u0131n 1&#8217;e yak\u0131n olmas\u0131, <em>X<\/em> ve <em>Y<\/em> de\u011fi\u015fkenlerimiz aras\u0131nda g\u00fc\u00e7l\u00fc bir pozitif do\u011frusal ili\u015fki oldu\u011funu g\u00f6sterir. Bu, da\u011f\u0131l\u0131m grafi\u011finde g\u00f6zlemledi\u011fimiz ili\u015fkiyi do\u011frular.<\/span><\/p>\n<h2> <strong><span style=\"color: #000000;\">Korelasyonlar\u0131 g\u00f6r\u00fcnt\u00fcle<\/span><\/strong><\/h2>\n<p> <span style=\"color: #000000;\">Pearson korelasyon katsay\u0131s\u0131n\u0131n bize iki de\u011fi\u015fken aras\u0131ndaki do\u011frusal ili\u015fkinin <strong>t\u00fcr\u00fcn\u00fc<\/strong> (pozitif, negatif, yok) ve bu ili\u015fkinin <strong>g\u00fcc\u00fcn\u00fc<\/strong> (zay\u0131f, orta, g\u00fc\u00e7l\u00fc) s\u00f6yledi\u011fini unutmay\u0131n.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0130ki de\u011fi\u015fkenin da\u011f\u0131l\u0131m grafi\u011fini olu\u015fturdu\u011fumuzda iki de\u011fi\u015fken aras\u0131ndaki ger\u00e7ek ili\u015fkiyi <em>g\u00f6rebiliriz<\/em> . G\u00f6zlemleyebilece\u011fimiz bir\u00e7ok do\u011frusal ili\u015fki t\u00fcr\u00fc \u015funlard\u0131r:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>G\u00fc\u00e7l\u00fc, pozitif ili\u015fki:<\/strong> X eksenindeki de\u011fi\u015fken artt\u0131k\u00e7a y eksenindeki de\u011fi\u015fken de artar. Noktalar\u0131n yak\u0131ndan k\u00fcmelenmesi g\u00fc\u00e7l\u00fc bir ili\u015fkiyi g\u00f6sterir.<\/span> <span style=\"color: #000000;\"><img decoding=\"async\" loading=\"lazy\" class=\"wp-image-616 size-full aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/pos_strong.jpg\" alt=\"\" width=\"323\" height=\"301\" srcset=\"\" sizes=\"auto, \"><\/span><\/p>\n<p style=\"text-align: center;\"> <span style=\"color: #000000;\">Pearson korelasyon katsay\u0131s\u0131: <strong>0,94<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Zay\u0131f ve pozitif ili\u015fki:<\/strong> X eksenindeki de\u011fi\u015fken artt\u0131k\u00e7a y eksenindeki de\u011fi\u015fken de artar. Noktalar\u0131n olduk\u00e7a da\u011f\u0131n\u0131k olmas\u0131 zay\u0131f bir ili\u015fkiye i\u015faret etmektedir.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-618 size-full\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/pos_faible.jpg\" alt=\"\" width=\"323\" height=\"297\" srcset=\"\" sizes=\"auto, \"><\/span><\/p>\n<p style=\"text-align: center;\"> <span style=\"color: #000000;\">Pearson korelasyon katsay\u0131s\u0131: <strong>0,44<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u0130li\u015fki yok:<\/strong> De\u011fi\u015fkenler aras\u0131nda a\u00e7\u0131k (olumlu veya olumsuz) bir ili\u015fki yoktur.<\/span> <\/p>\n<p style=\"text-align: center;\"><img decoding=\"async\" loading=\"lazy\" class=\"wp-image-621 size-full aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/aucun.jpg\" alt=\"\" width=\"324\" height=\"296\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p style=\"text-align: center;\"> <span style=\"color: #000000;\">Pearson korelasyon katsay\u0131s\u0131: <strong>0,03<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>G\u00fc\u00e7l\u00fc, negatif ili\u015fki:<\/strong> X eksenindeki de\u011fi\u015fken artt\u0131k\u00e7a y eksenindeki de\u011fi\u015fken azal\u0131r. Noktalar s\u0131k\u0131 bir \u015fekilde bir araya toplanm\u0131\u015ft\u0131r, bu da g\u00fc\u00e7l\u00fc bir ili\u015fkiyi g\u00f6sterir.<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-622 size-full\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/neg_strong.jpg\" alt=\"\" width=\"321\" height=\"297\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p style=\"text-align: center;\"> <span style=\"color: #000000;\">Pearson korelasyon katsay\u0131s\u0131: <strong>-0,87<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Zay\u0131f ve negatif ili\u015fki:<\/strong> X eksenindeki de\u011fi\u015fken artt\u0131k\u00e7a y eksenindeki de\u011fi\u015fken azal\u0131r. Noktalar\u0131n olduk\u00e7a da\u011f\u0131n\u0131k olmas\u0131 zay\u0131f bir ili\u015fkiye i\u015faret etmektedir.<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-625 size-full\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/negatif_faible.jpg\" alt=\"\" width=\"324\" height=\"296\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p style=\"text-align: center;\"> <span style=\"color: #000000;\">Pearson korelasyon katsay\u0131s\u0131: \u2013 <strong>0,46<\/strong><\/span><\/p>\n<h2> <strong>Pearson korelasyon katsay\u0131s\u0131n\u0131n \u00f6neminin test edilmesi<\/strong><\/h2>\n<p> <span style=\"color: #000000;\">Bir veri k\u00fcmesi i\u00e7in Pearson korelasyon katsay\u0131s\u0131n\u0131 buldu\u011fumuzda genellikle daha b\u00fcy\u00fck bir <em>pop\u00fclasyondan<\/em> al\u0131nan bir veri <em>\u00f6rne\u011fiyle<\/em> \u00e7al\u0131\u015f\u0131yoruz. Bu, genel pop\u00fclasyonda asl\u0131nda korelasyonsuz olsalar bile iki de\u011fi\u015fken i\u00e7in s\u0131f\u0131rdan farkl\u0131 bir korelasyon bulman\u0131n m\u00fcmk\u00fcn oldu\u011fu anlam\u0131na gelir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin, t\u00fcm pop\u00fclasyondaki her veri noktas\u0131 i\u00e7in <em>X<\/em> ve <em>Y<\/em> de\u011fi\u015fkenlerine y\u00f6nelik bir da\u011f\u0131l\u0131m grafi\u011fi olu\u015fturdu\u011fumuzu ve bunun \u015f\u00f6yle g\u00f6r\u00fcnd\u00fc\u011f\u00fcn\u00fc varsayal\u0131m:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-1543 size-full\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/correl12.jpg\" alt=\"S\u0131f\u0131r korelasyon \u00f6rne\u011fi\" width=\"466\" height=\"251\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Bu iki de\u011fi\u015fkenin birbiriyle ili\u015fkili olmad\u0131\u011f\u0131 a\u00e7\u0131kt\u0131r. Ancak evrenden 10 puanl\u0131k bir \u00f6rneklem ald\u0131\u011f\u0131m\u0131zda a\u015fa\u011f\u0131daki noktalar\u0131 se\u00e7memiz m\u00fcmk\u00fcnd\u00fcr:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-1544 size-full\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/correl13.jpg\" alt=\"Korelasyon \u00d6rne\u011fi\" width=\"460\" height=\"244\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Bu puan \u00f6rne\u011fi i\u00e7in Pearson korelasyon katsay\u0131s\u0131n\u0131n 0,93 oldu\u011funu g\u00f6rebiliriz; bu da pop\u00fclasyon korelasyonu s\u0131f\u0131r olmas\u0131na ra\u011fmen g\u00fc\u00e7l\u00fc bir pozitif korelasyona i\u015faret eder.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0130ki de\u011fi\u015fken aras\u0131ndaki ili\u015fkinin istatistiksel olarak anlaml\u0131 olup olmad\u0131\u011f\u0131n\u0131 test etmek i\u00e7in a\u015fa\u011f\u0131daki test istatisti\u011fini bulabiliriz:<\/span><\/p>\n<p> <span style=\"color: #000000;\">Test istatisti\u011fi T = r * \u221a <span style=\"text-decoration: overline;\">(n-2) \/ (1-r <sup>2<\/sup> )<\/span><\/span><\/p>\n<p> <span style=\"color: #000000;\">burada <em>n<\/em> , \u00f6rne\u011fimizdeki \u00e7iftlerin say\u0131s\u0131d\u0131r, <em>r<\/em> , Pearson korelasyon katsay\u0131s\u0131d\u0131r ve T testi istatisti\u011fi, n-2 serbestlik derecesine sahip bir da\u011f\u0131l\u0131m izler.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Pearson korelasyon katsay\u0131s\u0131n\u0131n \u00f6neminin nas\u0131l test edilece\u011fine dair bir \u00f6rne\u011fi inceleyelim.<\/span><\/p>\n<h3> <strong><span style=\"color: #000000;\">\u00d6rnek<\/span><\/strong><\/h3>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki veri seti 12 ki\u015finin boy ve kilosunu g\u00f6stermektedir:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-4986 size-full\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/correlationexemple2.jpg\" alt=\"\" width=\"193\" height=\"266\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki da\u011f\u0131l\u0131m grafi\u011fi bu iki de\u011fi\u015fkenin de\u011ferini g\u00f6stermektedir:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-1547 size-full\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/correl15.jpg\" alt=\"Korelasyon Da\u011f\u0131l\u0131m Grafi\u011fi\" width=\"461\" height=\"335\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Bu iki de\u011fi\u015fken i\u00e7in Pearson korelasyon katsay\u0131s\u0131 r = 0,836&#8217;d\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Test istatisti\u011fi T = 0,836 * \u221a <span style=\"text-decoration: overline;\"><span style=\"color: #000000; text-decoration: overline;\">(12<\/span> -2) \/ (1-0,836 <sup>2<\/sup> )<\/span> = 4,804.<\/span><\/p>\n<p> <span style=\"color: #000000;\">T da\u011f\u0131l\u0131m\u0131 hesaplay\u0131c\u0131m\u0131za g\u00f6re, 10 serbestlik derecesine sahip 4,804 puan\u0131n\u0131n p de\u011feri 0,0007&#8217;dir. 0,0007 &lt; 0,05 oldu\u011fundan, bu \u00f6rnekte a\u011f\u0131rl\u0131k ve boy aras\u0131ndaki korelasyonun alfa = 0,05&#8217;te istatistiksel olarak anlaml\u0131 oldu\u011fu sonucuna varabiliriz.<\/span><\/p>\n<h2> <strong><span style=\"color: #000000;\">\u00d6nlemler<\/span><\/strong><\/h2>\n<p> <span style=\"color: #000000;\">Pearson korelasyon katsay\u0131s\u0131 bize iki de\u011fi\u015fkenin do\u011frusal bir ili\u015fkiye sahip olup olmad\u0131\u011f\u0131n\u0131 s\u00f6ylemede yararl\u0131 olsa da, Pearson korelasyon katsay\u0131s\u0131n\u0131 yorumlarken \u00fc\u00e7 \u015feyi akl\u0131m\u0131zda tutmam\u0131z gerekir:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1. Korelasyon nedensellik anlam\u0131na gelmez.<\/strong> \u0130ki de\u011fi\u015fkenin birbiriyle ili\u015fkili olmas\u0131, birinin zorunlu olarak di\u011ferinin daha fazla veya daha az s\u0131kl\u0131kta ortaya \u00e7\u0131kmas\u0131na <em>neden olmas\u0131<\/em> de\u011fildir. Bunun klasik bir \u00f6rne\u011fi, dondurma sat\u0131\u015flar\u0131 ile k\u00f6pekbal\u0131\u011f\u0131 sald\u0131r\u0131lar\u0131 aras\u0131ndaki pozitif korelasyondur. Y\u0131l\u0131n belirli zamanlar\u0131nda dondurma sat\u0131\u015flar\u0131 artt\u0131\u011f\u0131nda k\u00f6pekbal\u0131\u011f\u0131 sald\u0131r\u0131lar\u0131 da artma e\u011filimindedir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu, dondurma yemenin k\u00f6pekbal\u0131\u011f\u0131 sald\u0131r\u0131lar\u0131na <em>neden oldu\u011fu<\/em> anlam\u0131na m\u0131 geliyor? Tabii ki de\u011fil! Bu basit\u00e7e yaz aylar\u0131nda buz t\u00fcketiminin ve k\u00f6pekbal\u0131\u011f\u0131 sald\u0131r\u0131lar\u0131n\u0131n artma e\u011filiminde oldu\u011fu anlam\u0131na gelir, \u00e7\u00fcnk\u00fc buz yaz\u0131n daha pop\u00fclerdir ve yaz aylar\u0131nda daha fazla insan okyanusa gider.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>2. Korelasyonlar ayk\u0131r\u0131 de\u011ferlere duyarl\u0131d\u0131r.<\/strong> A\u015f\u0131r\u0131 u\u00e7 de\u011ferler Pearson korelasyon katsay\u0131s\u0131n\u0131 \u00f6nemli \u00f6l\u00e7\u00fcde de\u011fi\u015ftirebilir. A\u015fa\u011f\u0131daki \u00f6rne\u011fi d\u00fc\u015f\u00fcn\u00fcn:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-1539 size-full\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/correl9.jpg\" alt=\"Korelasyon Ayk\u0131r\u0131 De\u011ferleri \u00d6rne\u011fi\" width=\"454\" height=\"306\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\"><em>X<\/em> ve <em>Y<\/em> de\u011fi\u015fkenlerinin Pearson korelasyon katsay\u0131s\u0131 <strong>0,00&#8217;d\u0131r<\/strong> . Ancak veri k\u00fcmesinde bir ayk\u0131r\u0131 de\u011ferin oldu\u011funu hayal edin:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-1540 size-full\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/correl10.jpg\" alt=\"Pearson Korelasyonu \u00d6rne\u011fi\" width=\"456\" height=\"305\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Ancak bu iki de\u011fi\u015fkene ili\u015fkin Pearson korelasyon katsay\u0131s\u0131 <strong>0,878&#8217;dir<\/strong> . Bu ayk\u0131r\u0131 durum her \u015feyi de\u011fi\u015ftirir. Bu nedenle, iki de\u011fi\u015fken i\u00e7in korelasyon hesaplan\u0131rken ayk\u0131r\u0131 de\u011ferleri kontrol etmek i\u00e7in de\u011fi\u015fkenleri bir da\u011f\u0131l\u0131m grafi\u011fi kullanarak g\u00f6rselle\u015ftirmek iyi bir fikirdir.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>3. Pearson korelasyon katsay\u0131s\u0131 iki de\u011fi\u015fken aras\u0131ndaki do\u011frusal olmayan ili\u015fkileri yans\u0131tmaz.<\/strong> A\u015fa\u011f\u0131daki ili\u015fkiye sahip iki de\u011fi\u015fkenimiz oldu\u011funu varsayal\u0131m:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-1541 size-full\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/correl11.jpg\" alt=\"Do\u011frusal olmayan bir ili\u015fki i\u00e7in korelasyon\" width=\"448\" height=\"307\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Bu iki de\u011fi\u015fkenin Pearson korelasyon katsay\u0131s\u0131 0,00&#8217;d\u0131r \u00e7\u00fcnk\u00fc do\u011frusal bir ili\u015fki yoktur. Ancak bu iki de\u011fi\u015fkenin do\u011frusal olmayan bir ili\u015fkisi vard\u0131r: y de\u011ferleri basit\u00e7e x de\u011ferlerinin karesidir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Pearson korelasyon katsay\u0131s\u0131n\u0131 kullan\u0131rken, yaln\u0131zca iki de\u011fi\u015fkenin <em>do\u011frusal olarak<\/em> ili\u015fkili olup olmad\u0131\u011f\u0131n\u0131 test etti\u011finizi unutmay\u0131n. Pearson korelasyon katsay\u0131s\u0131 bize iki de\u011fi\u015fkenin ili\u015fkili olmad\u0131\u011f\u0131n\u0131 s\u00f6ylese bile, yine de bir t\u00fcr do\u011frusal olmayan ili\u015fkiye sahip olabilirler. Bu, iki de\u011fi\u015fken aras\u0131ndaki ili\u015fkiyi analiz ederken bir da\u011f\u0131l\u0131m grafi\u011fi olu\u015fturman\u0131n yararl\u0131 olmas\u0131n\u0131n bir ba\u015fka nedenidir: do\u011frusal olmayan bir ili\u015fkiyi tespit etmenize yard\u0131mc\u0131 olabilir.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Pearson korelasyon katsay\u0131s\u0131 (\u201c\u00e7arp\u0131m-moment korelasyon katsay\u0131s\u0131\u201d olarak da bilinir) iki de\u011fi\u015fken X ve Y aras\u0131ndaki do\u011frusal ili\u015fkinin bir \u00f6l\u00e7\u00fcs\u00fcd\u00fcr. -1 ile 1 aras\u0131nda bir de\u011fere sahiptir; burada: -1, iki de\u011fi\u015fken aras\u0131nda tamamen negatif bir do\u011frusal korelasyonu g\u00f6sterir 0, iki de\u011fi\u015fken aras\u0131nda do\u011frusal bir korelasyon olmad\u0131\u011f\u0131n\u0131 g\u00f6sterir 1, iki de\u011fi\u015fken aras\u0131nda m\u00fckemmel pozitif do\u011frusal bir korelasyonu [&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-433","post","type-post","status-publish","format-standard","hentry","category-rehber"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.3 - 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