{"id":1552,"date":"2023-07-25T22:20:24","date_gmt":"2023-07-25T22:20:24","guid":{"rendered":"https:\/\/statorials.org\/tr\/beta-seviyesi\/"},"modified":"2023-07-25T22:20:24","modified_gmt":"2023-07-25T22:20:24","slug":"beta-seviyesi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/beta-seviyesi\/","title":{"rendered":"I\u0307statistikte beta d\u00fczeyi nedir? (tan\u0131m &amp; #038; \u00f6rnek)"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">\u0130statistikte, bir <a href=\"https:\/\/statorials.org\/tr\/istatistik-ve-parametre\/\" target=\"_blank\" rel=\"noopener\">pop\u00fclasyon parametresi<\/a> hakk\u0131ndaki bir hipotezin do\u011fru olup olmad\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in <a href=\"https:\/\/statorials.org\/tr\/hipotez-testi-1\/\" target=\"_blank\" rel=\"noopener\">hipotez testini<\/a> kullan\u0131r\u0131z.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bir hipotez testi her zaman a\u015fa\u011f\u0131daki iki hipoteze sahiptir:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Bo\u015f hipotez (H <sub>0<\/sub> ):<\/strong> \u00d6rneklem verileri, pop\u00fclasyon parametresine ili\u015fkin bask\u0131n inan\u00e7la tutarl\u0131d\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Alternatif Hipotez ( <sub>HA<\/sub> ):<\/strong> \u00d6rnek veriler s\u0131f\u0131r hipotezinde belirtilen hipotezin do\u011fru olmad\u0131\u011f\u0131n\u0131 g\u00f6stermektedir. Ba\u015fka bir deyi\u015fle, rastgele olmayan bir neden verileri etkiler.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Ne zaman bir hipotez testi yapsak, her zaman d\u00f6rt olas\u0131 sonu\u00e7 vard\u0131r:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-15374 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/beta1.png\" alt=\"Beta vs. \u0130statistikte Hipotez Testinde Alfa\" width=\"349\" height=\"144\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Yapabilece\u011fimiz iki t\u00fcr hata vard\u0131r:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>Tip I hatas\u0131:<\/strong> Ger\u00e7ekten do\u011fru oldu\u011funda s\u0131f\u0131r hipotezini reddederiz. Bu t\u00fcr hatan\u0131n ger\u00e7ekle\u015fme olas\u0131l\u0131\u011f\u0131 <strong>\u03b1<\/strong> ile g\u00f6sterilir.<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>Tip II hata:<\/strong> Ger\u00e7ekten yanl\u0131\u015f olan s\u0131f\u0131r hipotezini reddedemeyiz. Bu t\u00fcr hatan\u0131n ger\u00e7ekle\u015fme olas\u0131l\u0131\u011f\u0131 <strong>\u03b2<\/strong> olarak belirtilir.<\/span><\/li>\n<\/ul>\n<h3> <span style=\"color: #000000;\"><strong>Alfa ve beta aras\u0131ndaki ili\u015fki<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u0130deal olarak ara\u015ft\u0131rmac\u0131lar Tip I hata yapma olas\u0131l\u0131\u011f\u0131n\u0131n <em>ve<\/em> Tip II hata yapma olas\u0131l\u0131\u011f\u0131n\u0131n d\u00fc\u015f\u00fck olmas\u0131n\u0131 isterler.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Ancak bu iki olas\u0131l\u0131k aras\u0131nda bir uzla\u015fma s\u00f6z konusudur. Alfa d\u00fczeyini d\u00fc\u015f\u00fcr\u00fcrsek, ger\u00e7ekte do\u011fru olan bir s\u0131f\u0131r hipotezini reddetme olas\u0131l\u0131\u011f\u0131m\u0131z\u0131 azaltabiliriz, ancak bu asl\u0131nda beta d\u00fczeyini, yani yanl\u0131\u015f olan s\u0131f\u0131r hipotezini reddetmede ba\u015far\u0131s\u0131z olma olas\u0131l\u0131\u011f\u0131m\u0131z\u0131 art\u0131r\u0131r.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>G\u00fc\u00e7 ve beta aras\u0131ndaki ili\u015fki<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Bir hipotez testinin <strong>g\u00fcc\u00fc<\/strong> , bir etki veya fark ger\u00e7ekten mevcut oldu\u011funda, bir etki veya farkl\u0131l\u0131\u011f\u0131n tespit edilme olas\u0131l\u0131\u011f\u0131n\u0131 ifade eder.<\/span> <span style=\"color: #000000;\">Ba\u015fka bir deyi\u015fle, yanl\u0131\u015f bir s\u0131f\u0131r hipotezinin do\u011fru \u015fekilde reddedilme olas\u0131l\u0131\u011f\u0131d\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki \u015fekilde hesaplan\u0131r:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>G\u00fc\u00e7 = 1 \u2013 \u03b2<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Genel olarak ara\u015ft\u0131rmac\u0131lar bir testin g\u00fcc\u00fcn\u00fcn y\u00fcksek olmas\u0131n\u0131 isterler ki, e\u011fer bir etki ya da farkl\u0131l\u0131k varsa test bunu tespit edebilsin.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Yukar\u0131daki denklemden bir testin g\u00fcc\u00fcn\u00fc artt\u0131rman\u0131n en iyi yolunun beta seviyesini d\u00fc\u015f\u00fcrmek oldu\u011funu g\u00f6rebiliriz. Beta d\u00fczeyini azaltman\u0131n en iyi yolu genellikle \u00f6rneklem boyutunu art\u0131rmakt\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki \u00f6rnekler bir hipotez testinin beta d\u00fczeyinin nas\u0131l hesaplanaca\u011f\u0131n\u0131 g\u00f6sterir ve \u00f6rneklem boyutunu art\u0131rman\u0131n neden beta d\u00fczeyini azaltabilece\u011fini g\u00f6sterir.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u00d6rnek 1: Bir Hipotez Testi i\u00e7in Beta Hesaplama<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Bir ara\u015ft\u0131rmac\u0131n\u0131n bir fabrikada \u00fcretilen aletlerin ortalama a\u011f\u0131rl\u0131\u011f\u0131n\u0131n 500 onstan az olup olmad\u0131\u011f\u0131n\u0131 test etmek istedi\u011fini varsayal\u0131m. A\u011f\u0131rl\u0131klar\u0131n standart sapmas\u0131n\u0131n 24 ons oldu\u011funu biliyoruz ve ara\u015ft\u0131rmac\u0131 40 par\u00e7ac\u0131ktan olu\u015fan rastgele bir \u00f6rnek toplamaya karar veriyor.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u03b1 = 0,05&#8217;te a\u015fa\u011f\u0131daki hipotezi ger\u00e7ekle\u015ftirecektir:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>H <sub>0<\/sub> :<\/strong> u = 500<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong><sub>HA<\/sub> :<\/strong> \u03bc &lt; 500<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u015eimdi \u00fcretilen aletlerin ortalama a\u011f\u0131rl\u0131\u011f\u0131n\u0131n asl\u0131nda 490 ons oldu\u011funu hayal edin. Ba\u015fka bir deyi\u015fle s\u0131f\u0131r hipotezinin reddedilmesi gerekir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Beta d\u00fczeyini (bo\u015f hipotezin asl\u0131nda reddedilmesi gerekirken reddedilmeme olas\u0131l\u0131\u011f\u0131) hesaplamak i\u00e7in a\u015fa\u011f\u0131daki ad\u0131mlar\u0131 kullanabiliriz:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Ad\u0131m 1: Reddedilemez b\u00f6lgeyi bulun.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Kritik Z de\u011feri hesaplay\u0131c\u0131s\u0131na g\u00f6re \u03b1 = 0,05&#8217;te sol kritik de\u011fer <strong>-1,645&#8217;tir<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Ad\u0131m 2: Reddedemeyece\u011fimiz minimum numuneyi bulun.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Test istatisti\u011fi \u015fu \u015fekilde hesaplan\u0131r: z = ( <span style=\"border-top: 1px solid black;\">x<\/span> \u2013 \u03bc) \/ (s\/ <span style=\"border-top: 1px solid black;\">\u221an<\/span> )<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rnek ortalama i\u00e7in bu denklemi \u00e7\u00f6zebiliriz:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><span style=\"border-top: 1px solid black;\">x<\/span> = \u00b5 \u2013 z*(s\/ <span style=\"border-top: 1px solid black;\">\u221an<\/span> )<\/span><\/li>\n<li> <span style=\"color: #000000;\"><span style=\"border-top: 1px solid black;\">x<\/span> = 500 \u2013 1,645*(24\/ <span style=\"border-top: 1px solid black;\">\u221a40<\/span> )<\/span><\/li>\n<li> <span style=\"color: #000000;\"><span style=\"border-top: 1px solid black;\">x<\/span> = <strong>493.758<\/strong><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><strong>Ad\u0131m 3: Minimum \u00f6rnek ortalamas\u0131n\u0131n ger\u00e7ekten olu\u015fma olas\u0131l\u0131\u011f\u0131n\u0131 belirleyin.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu olas\u0131l\u0131\u011f\u0131 \u015fu \u015fekilde hesaplayabiliriz:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">P(Z \u2265 (493,758 \u2013 490) \/ (24\/\u221a <span style=\"border-top: 1px solid black;\">40<\/span> ))<\/span><\/li>\n<li> <span style=\"color: #000000;\">P(Z \u2265 0,99)<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/tr\/hizli-normal-cdf-hesaplayici\/\" target=\"_blank\" rel=\"noopener\">Normal CDF hesaplay\u0131c\u0131s\u0131na<\/a> g\u00f6re Z \u2265 0,99 olma olas\u0131l\u0131\u011f\u0131 <strong>0,1611&#8217;dir<\/strong> .<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-15376 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/beta2.png\" alt=\"\" width=\"284\" height=\"405\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Dolay\u0131s\u0131yla bu testin beta d\u00fczeyi <strong>\u03b2 = 0,1611&#8217;dir.<\/strong> Bu, ger\u00e7ek ortalaman\u0131n 490 ons olmas\u0131 durumunda fark\u0131n tespit edilememesi ihtimalinin %16,11 oldu\u011fu anlam\u0131na gelir.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u00d6rnek 2: Daha B\u00fcy\u00fck \u00d6rneklem Boyutuna Sahip Bir Test i\u00e7in Beta Hesaplama<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u015eimdi ara\u015ft\u0131rmac\u0131n\u0131n tamamen ayn\u0131 hipotez testini ger\u00e7ekle\u015ftirdi\u011fini, bunun yerine n = 100 par\u00e7ac\u0131ktan olu\u015fan bir \u00f6rnek kulland\u0131\u011f\u0131n\u0131 varsayal\u0131m. Bu testin beta seviyesini hesaplamak i\u00e7in ayn\u0131 \u00fc\u00e7 ad\u0131m\u0131 tekrarlayabiliriz:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Ad\u0131m 1: Reddedilemez b\u00f6lgeyi bulun.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Kritik Z de\u011feri hesaplay\u0131c\u0131s\u0131na g\u00f6re \u03b1 = 0,05&#8217;te sol kritik de\u011fer <strong>-1,645&#8217;tir<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Ad\u0131m 2: Reddedemeyece\u011fimiz minimum numuneyi bulun.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Test istatisti\u011fi \u015fu \u015fekilde hesaplan\u0131r: z = ( <span style=\"border-top: 1px solid black;\">x<\/span> \u2013 \u03bc) \/ (s\/ <span style=\"border-top: 1px solid black;\">\u221an<\/span> )<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rnek ortalama i\u00e7in bu denklemi \u00e7\u00f6zebiliriz:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><span style=\"border-top: 1px solid black;\">x<\/span> = \u00b5 \u2013 z*(s\/ <span style=\"border-top: 1px solid black;\">\u221an<\/span> )<\/span><\/li>\n<li> <span style=\"color: #000000;\"><span style=\"border-top: 1px solid black;\">x<\/span> = 500 \u2013 1,645*(24\/\u221a <span style=\"border-top: 1px solid black;\">100<\/span> )<\/span><\/li>\n<li> <span style=\"color: #000000;\"><span style=\"border-top: 1px solid black;\">x<\/span> = <strong>496,05<\/strong><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><strong>Ad\u0131m 3: Minimum \u00f6rnek ortalamas\u0131n\u0131n ger\u00e7ekten olu\u015fma olas\u0131l\u0131\u011f\u0131n\u0131 belirleyin.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu olas\u0131l\u0131\u011f\u0131 \u015fu \u015fekilde hesaplayabiliriz:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">P(Z \u2265 (496,05 \u2013 490) \/ (24\/\u221a <span style=\"border-top: 1px solid black;\">100<\/span> ))<\/span><\/li>\n<li> <span style=\"color: #000000;\">P(Z \u2265 2,52)<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/tr\/hizli-normal-cdf-hesaplayici\/\" target=\"_blank\" rel=\"noopener\">Normal CDF hesaplay\u0131c\u0131s\u0131na<\/a> g\u00f6re Z \u2265 2,52 olma olas\u0131l\u0131\u011f\u0131 <strong>0,0059&#8217;dur.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Dolay\u0131s\u0131yla bu testin beta d\u00fczeyi <strong>\u03b2 = 0,0059&#8217;dur.<\/strong> Bu, ger\u00e7ek ortalaman\u0131n 490 ons olmas\u0131 durumunda fark\u0131n tespit edilememesi ihtimalinin yaln\u0131zca %0,59 oldu\u011fu anlam\u0131na gelir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rneklem boyutunu 40&#8217;tan 100&#8217;e \u00e7\u0131kararak ara\u015ft\u0131rmac\u0131n\u0131n beta seviyesini 0,1611&#8217;den 0,0059&#8217;a d\u00fc\u015f\u00fcrebildi\u011fini unutmay\u0131n.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Bonus:<\/strong> Bir testin beta d\u00fczeyini otomatik olarak hesaplamak i\u00e7in bu Tip II hata hesaplay\u0131c\u0131y\u0131 kullan\u0131n.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Ek kaynaklar<\/strong><\/span><\/h3>\n<p> <a href=\"https:\/\/statorials.org\/tr\/hipotez-testi-1\/\" target=\"_blank\" rel=\"noopener\">Hipotez Testine Giri\u015f<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/sifir-hipotezi-nasil-yazilir\/\" target=\"_blank\" rel=\"noopener\">S\u0131f\u0131r Hipotezi Nas\u0131l Yaz\u0131l\u0131r (5 \u00d6rnek)<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/p-degerleri-istatistiksel-anlamlilik\/\" target=\"_blank\" rel=\"noopener\">P de\u011ferlerinin ve istatistiksel anlaml\u0131l\u0131\u011f\u0131n a\u00e7\u0131klamas\u0131<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0130statistikte, bir pop\u00fclasyon parametresi hakk\u0131ndaki bir hipotezin do\u011fru olup olmad\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in hipotez testini kullan\u0131r\u0131z. Bir hipotez testi her zaman a\u015fa\u011f\u0131daki iki hipoteze sahiptir: Bo\u015f hipotez (H 0 ): \u00d6rneklem verileri, pop\u00fclasyon parametresine ili\u015fkin bask\u0131n inan\u00e7la tutarl\u0131d\u0131r. Alternatif Hipotez ( HA ): \u00d6rnek veriler s\u0131f\u0131r hipotezinde belirtilen hipotezin do\u011fru olmad\u0131\u011f\u0131n\u0131 g\u00f6stermektedir. Ba\u015fka bir deyi\u015fle, rastgele [&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-1552","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>\u0130statistikte beta d\u00fczeyi nedir? 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