{"id":1485,"date":"2023-07-26T05:10:07","date_gmt":"2023-07-26T05:10:07","guid":{"rendered":"https:\/\/statorials.org\/tr\/olcumun-standart-hatasi\/"},"modified":"2023-07-26T05:10:07","modified_gmt":"2023-07-26T05:10:07","slug":"olcumun-standart-hatasi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/olcumun-standart-hatasi\/","title":{"rendered":"Standart \u00f6l\u00e7\u00fcm hatas\u0131: tan\u0131m ve \u00f6rnek"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">\u00c7o\u011funlukla <strong>SE <sub>m<\/sub><\/strong> olarak ifade edilen <strong>standart \u00f6l\u00e7\u00fcm hatas\u0131<\/strong> , tekrarlanan \u00f6l\u00e7\u00fcmler al\u0131nd\u0131\u011f\u0131nda bir birey i\u00e7in &#8220;ger\u00e7ek&#8221; puan\u0131n etraf\u0131ndaki de\u011fi\u015fimi tahmin eder.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki \u015fekilde hesaplan\u0131r:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>SE <sub>m<\/sub><\/strong> = s\u221a <span style=\"border-top: 1px solid black;\">1-R<\/span><\/span><\/p>\n<p> <span style=\"color: #000000;\">Alt\u0131n:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>s:<\/strong> \u00f6l\u00e7\u00fcmlerin standart sapmas\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>A:<\/strong> Bir testin g\u00fcvenirlik katsay\u0131s\u0131<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/tr\/guvenilirlik-analizi\/\" target=\"_blank\" rel=\"noopener\">G\u00fcvenilirlik katsay\u0131s\u0131n\u0131n<\/a> 0 ila 1 aras\u0131nda de\u011fi\u015fti\u011fini ve bir testin birden fazla ki\u015fiye iki kez uygulanarak ve test puanlar\u0131 aras\u0131ndaki korelasyonun hesaplanmas\u0131yla hesapland\u0131\u011f\u0131n\u0131 unutmay\u0131n.<\/span><\/p>\n<p> <span style=\"color: #000000;\">G\u00fcvenirlik katsay\u0131s\u0131 ne kadar y\u00fcksek olursa, bir test o kadar s\u0131kl\u0131kla tutarl\u0131 puanlar \u00fcretir.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u00d6rnek: Standart \u00f6l\u00e7\u00fcm hatas\u0131n\u0131n hesaplanmas\u0131<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Bir ki\u015finin haftada 10 kez genel zekay\u0131 0&#8217;dan 100&#8217;e kadar \u00f6l\u00e7en bir teste girdi\u011fini varsayal\u0131m. Ki\u015fi a\u015fa\u011f\u0131daki puanlar\u0131 al\u0131r:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Derecelendirmeler:<\/strong> 88, 90, 91, 94, 86, 88, 84, 90, 90, 94<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rneklem ortalamas\u0131 89,5 ve \u00f6rnek standart sapmas\u0131 3,17&#8217;dir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Testin g\u00fcvenirlik katsay\u0131s\u0131n\u0131n 0,88 oldu\u011funu biliyorsak, \u00f6l\u00e7\u00fcm\u00fcn standart hatas\u0131n\u0131 \u015fu \u015fekilde hesaplar\u0131z:<\/span><\/p>\n<p> <span style=\"color: #000000;\">SE <sub>m<\/sub> = s\u221a <span style=\"border-top: 1px solid black;\">1-R<\/span> = 3,17\u221a <span style=\"border-top: 1px solid black;\">1-0,88<\/span> = <strong>1,098<\/strong><\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>G\u00fcven aral\u0131klar\u0131 olu\u015fturmak i\u00e7in SE <sub>m<\/sub> nas\u0131l kullan\u0131l\u0131r?<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Standart \u00f6l\u00e7\u00fcm hatas\u0131n\u0131 kullanarak, bireyin belirli bir testte belirli bir g\u00fcven derecesine sahip &#8220;ger\u00e7ek&#8221; puan\u0131n\u0131 i\u00e7ermesi muhtemel bir g\u00fcven aral\u0131\u011f\u0131 olu\u015fturabiliriz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bir ki\u015fi bir testte <em>x<\/em> puan\u0131 al\u0131rsa bu puan i\u00e7in farkl\u0131 g\u00fcven aral\u0131klar\u0131n\u0131 hesaplamak amac\u0131yla a\u015fa\u011f\u0131daki form\u00fclleri kullanabiliriz:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">%68 g\u00fcven aral\u0131\u011f\u0131 = [ <em>x<\/em> \u2013 SE <sub>m<\/sub> , <em>x<\/em> + SE <sub>m<\/sub> ]<\/span><\/li>\n<li> <span style=\"color: #000000;\">%95 g\u00fcven aral\u0131\u011f\u0131 = [ <em>x<\/em> \u2013 2*SE <sub>m<\/sub> , <em>x<\/em> + 2*SE <sub>m<\/sub> ]<\/span><\/li>\n<li> <span style=\"color: #000000;\">%99 g\u00fcven aral\u0131\u011f\u0131 = [ <em>x<\/em> \u2013 3*SE <sub>m<\/sub> , <em>x<\/em> + 3*SE <sub>m<\/sub> ]<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin, bir ki\u015finin SE <sub>m&#8217;si<\/sub> 2,5 oldu\u011fu bilinen belirli bir testten 92 puan ald\u0131\u011f\u0131n\u0131 varsayal\u0131m. %95 g\u00fcven aral\u0131\u011f\u0131n\u0131 \u015fu \u015fekilde hesaplayabiliriz:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">%95 g\u00fcven aral\u0131\u011f\u0131 = [92 \u2013 2*2,5, 92 + 2*2,5] = [87, 97]<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Bu, bir bireyin bu testteki &#8220;ger\u00e7ek&#8221; puan\u0131n\u0131n 87 ile 97 aras\u0131nda oldu\u011fundan <strong>%95 emin<\/strong> oldu\u011fumuz anlam\u0131na gelir.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>G\u00fcvenilirlik ve \u00f6l\u00e7\u00fcm\u00fcn standart hatas\u0131<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Bir testin g\u00fcvenirlik katsay\u0131s\u0131 ile \u00f6l\u00e7\u00fcm\u00fcn standart hatas\u0131 aras\u0131nda basit bir ili\u015fki vard\u0131r:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">G\u00fcvenilirlik katsay\u0131s\u0131 ne kadar y\u00fcksek olursa, \u00f6l\u00e7\u00fcm\u00fcn standart hatas\u0131 o kadar d\u00fc\u015f\u00fck olur.<\/span><\/li>\n<li> <span style=\"color: #000000;\">G\u00fcvenilirlik katsay\u0131s\u0131 ne kadar d\u00fc\u015f\u00fck olursa, \u00f6l\u00e7\u00fcm\u00fcn standart hatas\u0131 da o kadar y\u00fcksek olur.<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Bunu g\u00f6stermek i\u00e7in, bir testi 10 kez alan ve standart sapmas\u0131 <strong>2<\/strong> olan bir ki\u015fiyi d\u00fc\u015f\u00fcn\u00fcn.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Testin g\u00fcvenilirlik katsay\u0131s\u0131 <strong>0,9<\/strong> ise, \u00f6l\u00e7\u00fcm\u00fcn standart hatas\u0131 \u015fu \u015fekilde hesaplan\u0131r:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">SE <sub>m<\/sub> = s\u221a <span style=\"border-top: 1px solid black;\">1-R<\/span> = 2\u221a <span style=\"border-top: 1px solid black;\">1-.9<\/span> = <strong>0.632<\/strong><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Ancak testin g\u00fcvenirlik katsay\u0131s\u0131 <strong>0,5<\/strong> ise \u00f6l\u00e7\u00fcm\u00fcn standart hatas\u0131 \u015fu \u015fekilde hesaplan\u0131r:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">SE <sub>m<\/sub> = s\u221a <span style=\"border-top: 1px solid black;\">1-R<\/span> = 2\u221a <span style=\"border-top: 1px solid black;\">1-.5<\/span> = <strong>1.414<\/strong><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Bunun sezgisel bir anlam\u0131 olmal\u0131: Bir testin puanlar\u0131 daha az g\u00fcvenilirse, &#8220;ger\u00e7ek&#8221; puan\u0131 \u00f6l\u00e7medeki hata daha y\u00fcksek olacakt\u0131r.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u00c7o\u011funlukla SE m olarak ifade edilen standart \u00f6l\u00e7\u00fcm hatas\u0131 , tekrarlanan \u00f6l\u00e7\u00fcmler al\u0131nd\u0131\u011f\u0131nda bir birey i\u00e7in &#8220;ger\u00e7ek&#8221; puan\u0131n etraf\u0131ndaki de\u011fi\u015fimi tahmin eder. A\u015fa\u011f\u0131daki \u015fekilde hesaplan\u0131r: SE m = s\u221a 1-R Alt\u0131n: s: \u00f6l\u00e7\u00fcmlerin standart sapmas\u0131 A: Bir testin g\u00fcvenirlik katsay\u0131s\u0131 G\u00fcvenilirlik katsay\u0131s\u0131n\u0131n 0 ila 1 aras\u0131nda de\u011fi\u015fti\u011fini ve bir testin birden fazla ki\u015fiye iki kez [&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-1485","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>Standart \u00f6l\u00e7\u00fcm hatas\u0131: tan\u0131m ve \u00f6rnek<\/title>\n<meta name=\"description\" content=\"Bu e\u011fitimde, resmi bir tan\u0131m ve \u00e7e\u015fitli \u00f6rnekler de dahil olmak \u00fczere 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