{"id":1377,"date":"2023-07-26T15:34:05","date_gmt":"2023-07-26T15:34:05","guid":{"rendered":"https:\/\/statorials.org\/tr\/grup-varyansi\/"},"modified":"2023-07-26T15:34:05","modified_gmt":"2023-07-26T15:34:05","slug":"grup-varyansi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/grup-varyansi\/","title":{"rendered":"K\u00fcmelenmi\u015f varyans nedir? (tan\u0131m &amp; #038; \u00f6rnek)"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">\u0130statistiklerde <strong>k\u00fcme varyans\u0131<\/strong> basit\u00e7e iki veya daha fazla k\u00fcme varyans\u0131n\u0131n ortalamas\u0131n\u0131 ifade eder.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Gruplar aras\u0131ndaki ortak varyans i\u00e7in tek bir say\u0131 elde etmek amac\u0131yla iki veya daha fazla grup varyans\u0131n\u0131 &#8220;bir araya getirdi\u011fimizi&#8221; belirtmek i\u00e7in &#8220;havuzlanm\u0131\u015f&#8221; kelimesini kullan\u0131r\u0131z.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Uygulamada, havuzlanm\u0131\u015f varyans en \u00e7ok <a href=\"https:\/\/statorials.org\/tr\/iki-orneginizi-test-edin\/\" target=\"_blank\" rel=\"noopener\">iki \u00f6rneklemli t testinde<\/a> kullan\u0131l\u0131r; bu test, iki pop\u00fclasyonun ortalamalar\u0131n\u0131n e\u015fit olup olmad\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in kullan\u0131l\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0130ki \u00f6rnek aras\u0131ndaki havuzlanm\u0131\u015f varyans genellikle <sub>sp<\/sub> <sup>2<\/sup> ile g\u00f6sterilir ve a\u015fa\u011f\u0131daki \u015fekilde hesaplan\u0131r:<\/span><\/p>\n<p> <span style=\"color: #000000;\">s <sub>p<\/sub> <sup>2<\/sup> = ( (n <sub>1<\/sub> -1)s <sub>1<\/sub> <sup>2<\/sup> + (n <sub>2<\/sub> -1)s <sub>2<\/sub> <sup>2<\/sup> ) \/ (n <sub>1<\/sub> +n <sub>2<\/sub> -2)<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0130ki \u00f6rnek boyutu (n <sub>1<\/sub> ve n <sub>2<\/sub> ) e\u015fit oldu\u011funda form\u00fcl a\u015fa\u011f\u0131daki \u015fekilde basitle\u015ftirilir:<\/span><\/p>\n<p> <span style=\"color: #000000;\">s <sub>p<\/sub> <sup>2<\/sup> = (s <sub>1<\/sub> <sup>2<\/sup> + s <sub>2<\/sub> <sup>2<\/sup> ) \/ 2<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>K\u00fcmelenmi\u015f Bo\u015fluk Ne Zaman Hesaplanmal\u0131?<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u0130ki pop\u00fclasyon ortalamas\u0131n\u0131 kar\u015f\u0131la\u015ft\u0131rmak istedi\u011fimizde potansiyel olarak iki istatistiksel test kullanabiliriz:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1.<\/strong> <a href=\"https:\/\/statorials.org\/tr\/iki-orneginizi-test-edin\/\" target=\"_blank\" rel=\"noopener\">\u0130ki \u00f6rnekli t testi<\/a> : Bu test, iki \u00f6rnek aras\u0131ndaki varyanslar\u0131n yakla\u015f\u0131k olarak e\u015fit oldu\u011funu varsayar. Bu testi kullan\u0131rsak, havuzlanm\u0131\u015f varyans\u0131 hesaplar\u0131z.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>2.<\/strong> <a href=\"https:\/\/statorials.org\/tr\/welchs-t-testi\/\" target=\"_blank\" rel=\"noopener\">Welch t testi<\/a> : Bu test, iki \u00f6rnek aras\u0131ndaki varyanslar\u0131n yakla\u015f\u0131k olarak e\u015fit oldu\u011funu <em>varsaymaz<\/em> . Bu testi kullan\u0131rsak, havuzlanm\u0131\u015f varyans\u0131 <em>hesaplamay\u0131z<\/em> . Bunun yerine farkl\u0131 bir form\u00fcl kullan\u0131yoruz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Hangi testin kullan\u0131laca\u011f\u0131n\u0131 belirlemek i\u00e7in a\u015fa\u011f\u0131daki temel kural\u0131 kullan\u0131r\u0131z:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Genel kural:<\/strong> En b\u00fcy\u00fck varyans\u0131n en k\u00fc\u00e7\u00fck varyansa oran\u0131 4&#8217;ten k\u00fc\u00e7\u00fckse varyanslar\u0131n yakla\u015f\u0131k olarak e\u015fit oldu\u011funu varsayabilir ve iki \u00f6rnekli t testini kullanabiliriz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin, 1. numunenin varyans\u0131n\u0131n 24.5 oldu\u011funu ve 2. numunenin varyans\u0131n\u0131n 15.2 oldu\u011funu varsayal\u0131m. En b\u00fcy\u00fck \u00f6rnek varyans\u0131n\u0131n en k\u00fc\u00e7\u00fck \u00f6rnek varyans\u0131na oran\u0131 \u015fu \u015fekilde hesaplanacakt\u0131r:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Oran:<\/strong> 24,5 \/ 15,2 = 1,61<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu oran\u0131n 4&#8217;ten k\u00fc\u00e7\u00fck olmas\u0131 nedeniyle iki grup aras\u0131ndaki farklar\u0131n yakla\u015f\u0131k olarak e\u015fit oldu\u011fu varsay\u0131labilir. Bu nedenle, iki \u00f6rnekli t testini kullan\u0131r\u0131z, bu da birle\u015ftirilmi\u015f varyans\u0131 hesaplayaca\u011f\u0131m\u0131z anlam\u0131na gelir.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Grupland\u0131r\u0131lm\u0131\u015f sapmay\u0131 hesaplama \u00f6rne\u011fi<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Diyelim ki iki farkl\u0131 kaplumba\u011fa t\u00fcr\u00fcn\u00fcn ortalama a\u011f\u0131rl\u0131\u011f\u0131n\u0131n e\u015fit olup olmad\u0131\u011f\u0131n\u0131 bilmek istiyoruz. Bunu test etmek i\u00e7in her pop\u00fclasyondan a\u015fa\u011f\u0131daki bilgilerle birlikte rastgele bir kaplumba\u011fa \u00f6rne\u011fi topluyoruz:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u00d6rnek 1:<\/strong><\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">\u00d6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc n <sub>1<\/sub> = 40<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u00d6rneklem varyans\u0131 s <sub>1<\/sub> <sup>2<\/sup> = 18,5<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><strong>\u00d6rnek 2:<\/strong><\/span><\/p>\n<ul data-slot-rendered-dynamic=\"true\">\n<li> <span style=\"color: #000000;\">\u00d6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc n <sub>2<\/sub> = 38<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u00d6rneklem varyans\u0131 s <sub>2<\/sub> <sup>2<\/sup> = 6,7<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u0130ki \u00f6rnek aras\u0131ndaki havuzlanm\u0131\u015f varyans\u0131n nas\u0131l hesaplanaca\u011f\u0131 a\u015fa\u011f\u0131da a\u00e7\u0131klanm\u0131\u015ft\u0131r:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">s <sub>p<\/sub> <sup>2<\/sup> = ( (n <sub>1<\/sub> -1)s <sub>1<\/sub> <sup>2<\/sup> + (n <sub>2<\/sub> -1)s <sub>2<\/sub> <sup>2<\/sup> ) \/ (n <sub>1<\/sub> +n <sub>2<\/sub> -2)<\/span><\/li>\n<li> <span style=\"color: #000000;\">s <sub>p<\/sub> <sup>2<\/sup> = ( (40-1)*18,5 + (38-1)*6,7 ) \/ (40+38-2)<\/span><\/li>\n<li> <span style=\"color: #000000;\">s <sub>p<\/sub> <sup>2<\/sup> = (39*18,5 + 37*6,7) \/ (76) = 12,755<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Birle\u015ftirilmi\u015f varyans <strong>12.755&#8217;tir<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Birle\u015ftirilmi\u015f varyans de\u011ferinin 18,5 ve 6,7 olan iki orijinal varyans aras\u0131nda oldu\u011funu unutmay\u0131n. Birle\u015ftirilmi\u015f varyans\u0131n yaln\u0131zca iki \u00f6rnek varyans\u0131n a\u011f\u0131rl\u0131kl\u0131 ortalamas\u0131 oldu\u011fu g\u00f6z \u00f6n\u00fcne al\u0131nd\u0131\u011f\u0131nda bu mant\u0131kl\u0131d\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Bonus Kayna\u011f\u0131:<\/strong> \u0130ki \u00f6rnek aras\u0131ndaki havuzlanm\u0131\u015f varyans\u0131 otomatik olarak hesaplamak i\u00e7in bu <a href=\"https:\/\/statorials.org\/tr\/grup-varyansi-hesaplayicisi\/\" target=\"_blank\" rel=\"noopener\">havuzlanm\u0131\u015f varyans hesaplay\u0131c\u0131s\u0131n\u0131<\/a> kullan\u0131n.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0130statistiklerde k\u00fcme varyans\u0131 basit\u00e7e iki veya daha fazla k\u00fcme varyans\u0131n\u0131n ortalamas\u0131n\u0131 ifade eder. Gruplar aras\u0131ndaki ortak varyans i\u00e7in tek bir say\u0131 elde etmek amac\u0131yla iki veya daha fazla grup varyans\u0131n\u0131 &#8220;bir araya getirdi\u011fimizi&#8221; belirtmek i\u00e7in &#8220;havuzlanm\u0131\u015f&#8221; kelimesini kullan\u0131r\u0131z. Uygulamada, havuzlanm\u0131\u015f varyans en \u00e7ok iki \u00f6rneklemli t testinde kullan\u0131l\u0131r; bu test, iki pop\u00fclasyonun ortalamalar\u0131n\u0131n e\u015fit olup [&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-1377","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>K\u00fcmelenmi\u015f varyans nedir? 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