{"id":3641,"date":"2023-07-16T09:29:02","date_gmt":"2023-07-16T09:29:02","guid":{"rendered":"https:\/\/statorials.org\/tr\/z-puani-sas\/"},"modified":"2023-07-16T09:29:02","modified_gmt":"2023-07-16T09:29:02","slug":"z-puani-sas","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/z-puani-sas\/","title":{"rendered":"Sas&#39;ta z puanlar\u0131 nas\u0131l hesaplan\u0131r?"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">\u0130statistiklerde <strong>z-puan\u0131<\/strong> bize bir de\u011ferin <a href=\"https:\/\/statorials.org\/tr\/merkezi-egilimi-olcer\/\" target=\"_blank\" rel=\"noopener\">ortalamadan<\/a> ka\u00e7 standart sapma oldu\u011funu s\u00f6yler.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Z-puan\u0131n\u0131 hesaplamak i\u00e7in a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullan\u0131r\u0131z:<\/span><\/p>\n<p style=\"text-align: center;\"> <span style=\"color: #000000;\"><strong>z<\/strong> = (X \u2013 \u03bc) \/ \u03c3<\/span><\/p>\n<p> <span style=\"color: #000000;\">Alt\u0131n:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">X tek bir ham veri de\u011feridir<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u03bc veri k\u00fcmesinin ortalamas\u0131d\u0131r<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u03c3 veri k\u00fcmesinin standart sapmas\u0131d\u0131r<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki \u00f6rnek, SAS&#8217;taki ham veri de\u011ferleri i\u00e7in z puanlar\u0131n\u0131n nas\u0131l hesaplanaca\u011f\u0131n\u0131 g\u00f6sterir.<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>\u00d6rnek: SAS&#8217;ta Z puanlar\u0131n\u0131 hesaplama<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">SAS&#8217;ta a\u015fa\u011f\u0131daki veri k\u00fcmesini olu\u015fturdu\u011fumuzu varsayal\u0131m:<\/span> <\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008000;\">\/*create dataset*\/\n<\/span><span style=\"color: #800080;\">data<\/span> original_data;\n    <span style=\"color: #3366ff;\">input<\/span> values;\n    <span style=\"color: #3366ff;\">datalines<\/span> ;\n7\n12\n14\n12\n16\n18\n6\n7\n14\n17\n19\n22\n24\n13\n17\n12\n;\n<span style=\"color: #800080;\">run<\/span> ;\n\n<span style=\"color: #008000;\">\/*view dataset*\/\n<\/span><span style=\"color: #800080;\">proc print<\/span> <span style=\"color: #3366ff;\">data<\/span> = original_data;\n<\/strong><\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-29896 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/zsas1-1.jpg\" alt=\"\" width=\"107\" height=\"433\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">\u015eimdi veri k\u00fcmesindeki her de\u011fer i\u00e7in z-puan\u0131n\u0131 hesaplamak istedi\u011fimizi varsayal\u0131m.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bunu yapmak i\u00e7in <strong>proc sql&#8217;yi<\/strong> kullanabiliriz:<\/span> <\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <span style=\"color: #000000;\"><strong><span style=\"color: #008000;\">\/*create new variable that shows z-scores for each raw data value*\/\n<\/span><span style=\"color: #800080;\">proc sql<\/span> ;\n    <span style=\"color: #3366ff;\">select<\/span> values, (values - mean(values)) \/ std(values) <span style=\"color: #3366ff;\">as<\/span> z_scores\n    <span style=\"color: #3366ff;\">from<\/span> original_data;\n<span style=\"color: #800080;\">quit<\/span> ;<\/strong><\/span> <\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-29897\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/zsas2-1.jpg\" alt=\"SAS'ta z puanlar\u0131\" width=\"154\" height=\"480\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\"><strong>De\u011ferler<\/strong> s\u00fctunu orijinal veri de\u011ferlerini, <strong>z_scores<\/strong> s\u00fctunu ise her de\u011fer i\u00e7in z puan\u0131n\u0131 g\u00f6r\u00fcnt\u00fcler.<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>SAS&#8217;ta Z puanlar\u0131 nas\u0131l yorumlan\u0131r?<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\"><strong>Z-puan\u0131<\/strong> bize bir de\u011ferin ortalamadan ka\u00e7 standart sapma oldu\u011funu g\u00f6sterir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Z puan\u0131 pozitif, negatif veya s\u0131f\u0131r olabilir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Pozitif z puan\u0131 belirli bir de\u011ferin ortalaman\u0131n \u00fczerinde oldu\u011funu, negatif z puan\u0131 belirli bir de\u011ferin ortalaman\u0131n alt\u0131nda oldu\u011funu ve az s\u0131f\u0131r puan\u0131 belirli bir de\u011ferin ortalamaya e\u015fit oldu\u011funu g\u00f6sterir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Veri setimizin ortalamas\u0131n\u0131 ve standart sapmas\u0131n\u0131 hesaplarsak ortalaman\u0131n <strong>14.375<\/strong> , standart sapman\u0131n ise <strong>5.162<\/strong> oldu\u011funu buluruz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Yani veri setimizdeki ilk de\u011fer 7 idi ve bunun z puan\u0131 (7-14.375) \/ 5.162 = <strong>-1.428&#8217;di<\/strong> . Bu da \u201c7\u201d de\u011ferinin ortalaman\u0131n 1.428 standart sapma <em>alt\u0131nda<\/em> oldu\u011fu anlam\u0131na geliyor.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Verilerimizdeki bir sonraki de\u011fer olan 12&#8217;nin z puan\u0131 (12-14,375) \/ 5,162 = <strong>-0,46&#8217;yd\u0131<\/strong> . Bu, \u201c12\u201d de\u011ferinin ortalaman\u0131n 0,46 standart sapma <em>alt\u0131nda<\/em> oldu\u011fu anlam\u0131na gelir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bir de\u011fer ortalamadan ne kadar uzaksa, o de\u011fer i\u00e7in z puan\u0131n\u0131n mutlak de\u011feri o kadar y\u00fcksek olacakt\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin, 7 de\u011feri ortalamadan (14,375) 12 de\u011ferinden daha uzaktad\u0131r; bu da 7&#8217;nin neden daha b\u00fcy\u00fck mutlak de\u011fere sahip bir z puan\u0131na sahip oldu\u011funu a\u00e7\u0131klamaktad\u0131r.<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>Ek kaynaklar<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki makalelerde SAS&#8217;ta di\u011fer ortak g\u00f6revlerin nas\u0131l ger\u00e7ekle\u015ftirilece\u011fi a\u00e7\u0131klanmaktad\u0131r:<\/span><\/p>\n<p> <a href=\"https:\/\/statorials.org\/tr\/sas-aykiri-degerleri\/\" target=\"_blank\" rel=\"noopener\">SAS&#8217;ta ayk\u0131r\u0131 de\u011ferler nas\u0131l belirlenir<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/sas-yuzdelikleri\/\" target=\"_blank\" rel=\"noopener\">SAS&#8217;ta y\u00fczdelikler nas\u0131l hesaplan\u0131r?<\/a><br \/><a href=\"https:\/\/statorials.org\/tr\/hava-kilidinde-orta-medyan-modu\/\" target=\"_blank\" rel=\"noopener\">SAS&#8217;ta ortalama, medyan ve mod nas\u0131l hesaplan\u0131r?<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0130statistiklerde z-puan\u0131 bize bir de\u011ferin ortalamadan ka\u00e7 standart sapma oldu\u011funu s\u00f6yler. Z-puan\u0131n\u0131 hesaplamak i\u00e7in a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullan\u0131r\u0131z: z = (X \u2013 \u03bc) \/ \u03c3 Alt\u0131n: X tek bir ham veri de\u011feridir \u03bc veri k\u00fcmesinin ortalamas\u0131d\u0131r \u03c3 veri k\u00fcmesinin standart sapmas\u0131d\u0131r A\u015fa\u011f\u0131daki \u00f6rnek, SAS&#8217;taki ham veri de\u011ferleri i\u00e7in z puanlar\u0131n\u0131n nas\u0131l hesaplanaca\u011f\u0131n\u0131 g\u00f6sterir. \u00d6rnek: SAS&#8217;ta Z [&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-3641","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>SAS \u2013 Statorialsde Z Puanlar\u0131 Nas\u0131l 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