{"id":2110,"date":"2023-07-23T15:52:04","date_gmt":"2023-07-23T15:52:04","guid":{"rendered":"https:\/\/statorials.org\/tr\/pearson-kalintisi\/"},"modified":"2023-07-23T15:52:04","modified_gmt":"2023-07-23T15:52:04","slug":"pearson-kalintisi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/pearson-kalintisi\/","title":{"rendered":"Pearson art\u0131klar\u0131 nedir? (tan\u0131m &amp; #038; \u00f6rnek)"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>Pearson art\u0131klar\u0131,<\/strong> bir beklenmedik durum tablosunda g\u00f6zlemlenen h\u00fccre say\u0131s\u0131 ile beklenen h\u00fccre say\u0131s\u0131 aras\u0131ndaki fark\u0131 analiz etmek i\u00e7in <a href=\"https:\/\/statorials.org\/tr\/ki-kare-bagimsizlik-testi\/\" target=\"_blank\" rel=\"noopener\">ki-kare ba\u011f\u0131ms\u0131zl\u0131k testinde<\/a> kullan\u0131l\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Pearson kal\u0131nt\u0131s\u0131n\u0131<\/strong> hesaplama form\u00fcl\u00fc \u015f\u00f6yledir:<\/span><\/p>\n<p> <span style=\"color: #000000;\">r <sub>ij<\/sub> = (O <sub>ij<\/sub> \u2013 E <sub>ij<\/sub> ) \/ \u221a <span style=\"border-top: 1px solid black;\">E <sub>ij<\/sub><\/span><\/span><\/p>\n<p> <span style=\"color: #000000;\">Alt\u0131n:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>r <sub>ij<\/sub><\/strong> : i <sup>. s\u00fctun<\/sup> ve j <sup>.<\/sup> sat\u0131rdaki h\u00fccre i\u00e7in Pearson art\u0131\u011f\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>O <sub>ij<\/sub><\/strong> : i <sup>.<\/sup> s\u00fctun ve j <sup>.<\/sup> sat\u0131rdaki h\u00fccre i\u00e7in g\u00f6zlenen de\u011fer<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>E <sub>ij<\/sub><\/strong> : i <sup>.<\/sup> s\u00fctun ve j <sup>.<\/sup> sat\u0131rdaki h\u00fccrenin beklenen de\u011feri<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Benzer bir \u00f6l\u00e7\u00fcm, a\u015fa\u011f\u0131daki \u015fekilde hesaplanan <strong>standartla\u015ft\u0131r\u0131lm\u0131\u015f (d\u00fczeltilmi\u015f) Pearson kal\u0131nt\u0131s\u0131d\u0131r<\/strong> :<\/span><\/p>\n<p> <span style=\"color: #000000;\">r <sub>ij<\/sub> = (O <sub>ij<\/sub> \u2013 E <sub>ij<\/sub> ) \/ \u221a <span style=\"border-top: 1px solid black;\">E <sub>ij<\/sub> (1-n <sub>ben+<\/sub> )(1-n <sub>+j<\/sub> )<\/span><\/span><\/p>\n<p> <span style=\"color: #000000;\">Alt\u0131n:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>r <sub>ij<\/sub><\/strong> : i <sup>. s\u00fctun<\/sup> ve j <sup>.<\/sup> sat\u0131rdaki h\u00fccre i\u00e7in Pearson art\u0131\u011f\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>O <sub>ij<\/sub><\/strong> : i <sup>.<\/sup> s\u00fctun ve j <sup>.<\/sup> sat\u0131rdaki h\u00fccre i\u00e7in g\u00f6zlenen de\u011fer<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>E <sub>ij<\/sub><\/strong> : i <sup>.<\/sup> s\u00fctun ve j <sup>.<\/sup> sat\u0131rdaki h\u00fccrenin beklenen de\u011feri<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>p <sub>i+<\/sub><\/strong> : Sat\u0131r toplam\u0131n\u0131n genel toplama b\u00f6l\u00fcnmesi<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>p <sub>+ j<\/sub><\/strong> : S\u00fctun toplam\u0131n\u0131n genel toplama b\u00f6l\u00fcnmesi<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Standartla\u015ft\u0131r\u0131lm\u0131\u015f Pearson art\u0131klar\u0131 ortalama 0 ve standart sapma 1 ile normal olarak da\u011f\u0131t\u0131l\u0131r. Mutlak de\u011feri belirli e\u015fiklerin (\u00f6rne\u011fin 2 veya 3) \u00fczerinde olan herhangi bir standartla\u015ft\u0131r\u0131lm\u0131\u015f Pearson kal\u0131nt\u0131s\u0131 uyum eksikli\u011fini g\u00f6sterir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki \u00f6rnek Pearson art\u0131klar\u0131n\u0131n pratikte nas\u0131l hesaplanaca\u011f\u0131n\u0131 g\u00f6stermektedir.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u00d6rnek: Pearson art\u0131klar\u0131n\u0131n hesaplanmas\u0131<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Ara\u015ft\u0131rmac\u0131lar\u0131n cinsiyetin siyasi parti tercihiyle ili\u015fkili olup olmad\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in ki-kare ba\u011f\u0131ms\u0131zl\u0131k testini kullanmak istediklerini varsayal\u0131m.<\/span><\/p>\n<p> <span style=\"color: #000000;\">500 se\u00e7menden olu\u015fan basit rastgele bir \u00f6rneklem almaya ve onlara siyasi parti tercihlerini sormaya karar veriyorlar.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki beklenmedik durum tablosu anketin sonu\u00e7lar\u0131n\u0131 sunmaktad\u0131r:<\/span><\/p>\n<table width=\"379\">\n<tbody>\n<tr>\n<td width=\"84\"><\/td>\n<td style=\"text-align: center;\" width=\"74\"> <span style=\"color: #000000;\"><strong>Cumhuriyet\u00e7i<\/strong><\/span><\/td>\n<td style=\"text-align: center;\" width=\"74\"> <span style=\"color: #000000;\"><strong>Demokrat<\/strong><\/span><\/td>\n<td style=\"text-align: center;\" width=\"110\"> <span style=\"color: #000000;\"><strong>Ba\u011f\u0131ms\u0131z<\/strong><\/span><\/td>\n<td width=\"37\"> <span style=\"color: #000000;\"><strong>Toplam<\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td> <span style=\"color: #000000;\"><strong>Erkek<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">120<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">90<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">40<\/span><\/td>\n<td> <span style=\"color: #000000;\">250<\/span><\/td>\n<\/tr>\n<tr>\n<td> <span style=\"color: #000000;\"><strong>Di\u015fi<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">110<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">95<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">45<\/span><\/td>\n<td> <span style=\"color: #000000;\">250<\/span><\/td>\n<\/tr>\n<tr>\n<td> <span style=\"color: #000000;\"><strong>Toplam<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">230<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">185<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">85<\/span><\/td>\n<td> <span style=\"color: #000000;\">500<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p> <span style=\"color: #000000;\">Pearson art\u0131klar\u0131n\u0131 hesaplamadan \u00f6nce, olas\u0131l\u0131k tablosundaki her bir h\u00fccre i\u00e7in beklenen say\u0131lar\u0131 hesaplamam\u0131z gerekir. Bunu yapmak i\u00e7in a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullanabiliriz:<\/span><\/p>\n<p> <span style=\"color: #000000;\">Beklenen de\u011fer = (sat\u0131rlar\u0131n toplam\u0131 * s\u00fctunlar\u0131n toplam\u0131) \/ tablonun toplam\u0131.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin Cumhuriyet\u00e7i erkekler i\u00e7in beklenen de\u011fer: (230*250) \/ 500 = <strong>115<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Her tablo h\u00fccresi i\u00e7in beklenen de\u011feri elde etmek amac\u0131yla bu form\u00fcl\u00fc tekrarlayabiliriz:<\/span><\/p>\n<table width=\"379\">\n<tbody>\n<tr>\n<td width=\"84\"><\/td>\n<td style=\"text-align: center;\" width=\"74\"> <span style=\"color: #000000;\"><strong>Cumhuriyet\u00e7i<\/strong><\/span><\/td>\n<td style=\"text-align: center;\" width=\"74\"> <span style=\"color: #000000;\"><strong>Demokrat<\/strong><\/span><\/td>\n<td style=\"text-align: center;\" width=\"110\"> <span style=\"color: #000000;\"><strong>Ba\u011f\u0131ms\u0131z<\/strong><\/span><\/td>\n<td width=\"37\"> <span style=\"color: #000000;\"><strong>Toplam<\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td> <span style=\"color: #000000;\"><strong>Erkek<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">115<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">92.5<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">42.5<\/span><\/td>\n<td> <span style=\"color: #000000;\">250<\/span><\/td>\n<\/tr>\n<tr>\n<td> <span style=\"color: #000000;\"><strong>Di\u015fi<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">115<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">92.5<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">42.5<\/span><\/td>\n<td> <span style=\"color: #000000;\">250<\/span><\/td>\n<\/tr>\n<tr>\n<td> <span style=\"color: #000000;\"><strong>Toplam<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">230<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">185<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">85<\/span><\/td>\n<td> <span style=\"color: #000000;\">500<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p> <span style=\"color: #000000;\">Daha sonra tablodaki her h\u00fccre i\u00e7in <strong>Pearson kal\u0131nt\u0131s\u0131n\u0131<\/strong> hesaplayabiliriz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin Cumhuriyet\u00e7i erkeklerin bulundu\u011fu h\u00fccre i\u00e7in Pearson art\u0131\u011f\u0131 \u015fu \u015fekilde hesaplanacakt\u0131r:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">r <sub>ij<\/sub> = (O <sub>ij<\/sub> \u2013 E <sub>ij<\/sub> ) \/ \u221a <span style=\"border-top: 1px solid black;\">E <sub>ij<\/sub><\/span><\/span><\/li>\n<li> <span style=\"color: #000000;\">r <sub>ij<\/sub> = (120 \u2013 115) \/ \u221a <span style=\"border-top: 1px solid black;\">115<\/span><\/span><\/li>\n<li> <span style=\"color: #000000;\">r <sub>ij<\/sub> = 0,466<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Tablodaki her h\u00fccre i\u00e7in Pearson kal\u0131nt\u0131s\u0131n\u0131 elde etmek i\u00e7in bu form\u00fcl\u00fc tekrarlayabiliriz:<\/span><\/p>\n<table width=\"379\">\n<tbody>\n<tr>\n<td width=\"84\"><\/td>\n<td style=\"text-align: center;\" width=\"74\"> <span style=\"color: #000000;\"><strong>Cumhuriyet\u00e7i<\/strong><\/span><\/td>\n<td style=\"text-align: center;\" width=\"74\"> <span style=\"color: #000000;\"><strong>Demokrat<\/strong><\/span><\/td>\n<td style=\"text-align: center;\" width=\"110\"> <span style=\"color: #000000;\"><strong>Ba\u011f\u0131ms\u0131z<\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td> <span style=\"color: #000000;\"><strong>Erkek<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">0,446<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">-0,259<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">-0,383<\/span><\/td>\n<\/tr>\n<tr>\n<td> <span style=\"color: #000000;\"><strong>Di\u015fi<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">-0,446<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">0,259<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">0,383<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p> <span style=\"color: #000000;\">Daha sonra tablodaki her h\u00fccre i\u00e7in <strong>standartla\u015ft\u0131r\u0131lm\u0131\u015f Pearson kal\u0131nt\u0131s\u0131n\u0131<\/strong> hesaplayabiliriz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin, Cumhuriyet\u00e7i erkeklerin bulundu\u011fu h\u00fccre i\u00e7in standartla\u015ft\u0131r\u0131lm\u0131\u015f Pearson art\u0131\u011f\u0131 \u015fu \u015fekilde hesaplanacakt\u0131r:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">r <sub>ij<\/sub> = (O <sub>ij<\/sub> \u2013 E <sub>ij<\/sub> ) \/ \u221a <span style=\"border-top: 1px solid black;\">E <sub>ij<\/sub> (1-p <sub>i+<\/sub> )(1-p <sub>+j<\/sub> )<\/span><\/span><\/li>\n<li> <span style=\"color: #000000;\">r <sub>ij<\/sub> = (120 \u2013 115) \/ \u221a <span style=\"border-top: 1px solid black;\">115(1-250\/500)(1-230\/500)<\/span><\/span><\/li>\n<li> <span style=\"color: #000000;\">r <sub>ij<\/sub> = 0,897<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Tablodaki her h\u00fccre i\u00e7in standartla\u015ft\u0131r\u0131lm\u0131\u015f Pearson kal\u0131nt\u0131s\u0131n\u0131 elde etmek i\u00e7in bu form\u00fcl\u00fc tekrarlayabiliriz:<\/span><\/p>\n<table width=\"379\">\n<tbody>\n<tr>\n<td width=\"84\"><\/td>\n<td style=\"text-align: center;\" width=\"74\"> <span style=\"color: #000000;\"><strong>Cumhuriyet\u00e7i<\/strong><\/span><\/td>\n<td style=\"text-align: center;\" width=\"74\"> <span style=\"color: #000000;\"><strong>Demokrat<\/strong><\/span><\/td>\n<td style=\"text-align: center;\" width=\"110\"> <span style=\"color: #000000;\"><strong>Ba\u011f\u0131ms\u0131z<\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td> <span style=\"color: #000000;\"><strong>Erkek<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">0,897<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">-0,463<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">-0,595<\/span><\/td>\n<\/tr>\n<tr>\n<td> <span style=\"color: #000000;\"><strong>Di\u015fi<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">-0,897<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">0,463<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">0,595<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p> <span style=\"color: #000000;\">Standartla\u015ft\u0131r\u0131lm\u0131\u015f Pearson art\u0131klar\u0131n\u0131n hi\u00e7birinin 3&#8217;ten b\u00fcy\u00fck bir mutlak de\u011fere sahip olmad\u0131\u011f\u0131n\u0131 g\u00f6rebiliriz; bu da h\u00fccrelerin hi\u00e7birinin \u00f6nemli bir uyum eksikli\u011fine katk\u0131da bulunmad\u0131\u011f\u0131n\u0131 g\u00f6sterir.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/tr\/ki-kare-bagimsizlik-testi-hesaplayicisi\/\" target=\"_blank\" rel=\"noopener\">Bu \u00e7evrimi\u00e7i hesap makinesini<\/a> ki-kare ba\u011f\u0131ms\u0131zl\u0131k testi yapmak i\u00e7in kullan\u0131rsak, testin p de\u011ferinin <strong>0,649198<\/strong> oldu\u011funu bulaca\u011f\u0131z.<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-19624 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/ence1.png\" alt=\"\" width=\"443\" height=\"447\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Bu p de\u011feri 0,05&#8217;ten k\u00fc\u00e7\u00fck olmad\u0131\u011f\u0131ndan cinsiyet ile siyasi parti tercihi aras\u0131nda bir ili\u015fki oldu\u011funu s\u00f6yleyebilecek yeterli kan\u0131ta sahip de\u011filiz.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Ek kaynaklar<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki e\u011fitimlerde farkl\u0131 istatistiksel yaz\u0131l\u0131mlar kullan\u0131larak ki-kare ba\u011f\u0131ms\u0131zl\u0131k testinin nas\u0131l ger\u00e7ekle\u015ftirilece\u011fi a\u00e7\u0131klanmaktad\u0131r:<\/span><\/p>\n<p> <a href=\"https:\/\/statorials.org\/tr\/ki-kare-bagimsizlik-testi\/\" target=\"_blank\" rel=\"noopener\">Ki-Kare Ba\u011f\u0131ms\u0131zl\u0131k Testine Giri\u015f<\/a><br \/><a href=\"https:\/\/statorials.org\/tr\/ki-kare-bagimsizlik-testi-excel\/\" target=\"_blank\" rel=\"noopener\">Excel&#8217;de Ki-Kare Ba\u011f\u0131ms\u0131zl\u0131k Testi Nas\u0131l Yap\u0131l\u0131r?<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/rde-ki-kare-bagimsizlik-testi\/\" target=\"_blank\" rel=\"noopener\">R&#8217;de ki-kare ba\u011f\u0131ms\u0131zl\u0131k testi nas\u0131l yap\u0131l\u0131r<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/ki-kare-bagimsizlik-testi-hesaplayicisi\/\" target=\"_blank\" rel=\"noopener\">Ba\u011f\u0131ms\u0131zl\u0131k hesaplay\u0131c\u0131s\u0131n\u0131n ki-kare testi<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Pearson art\u0131klar\u0131, bir beklenmedik durum tablosunda g\u00f6zlemlenen h\u00fccre say\u0131s\u0131 ile beklenen h\u00fccre say\u0131s\u0131 aras\u0131ndaki fark\u0131 analiz etmek i\u00e7in ki-kare ba\u011f\u0131ms\u0131zl\u0131k testinde kullan\u0131l\u0131r. Pearson kal\u0131nt\u0131s\u0131n\u0131 hesaplama form\u00fcl\u00fc \u015f\u00f6yledir: r ij = (O ij \u2013 E ij ) \/ \u221a E ij Alt\u0131n: r ij : i . s\u00fctun ve j . sat\u0131rdaki h\u00fccre i\u00e7in Pearson art\u0131\u011f\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-2110","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>Pearson art\u0131klar\u0131 nedir? 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