{"id":934,"date":"2023-07-28T06:40:51","date_gmt":"2023-07-28T06:40:51","guid":{"rendered":"https:\/\/statorials.org\/tr\/standart-sapma-ve-standart-hata\/"},"modified":"2023-07-28T06:40:51","modified_gmt":"2023-07-28T06:40:51","slug":"standart-sapma-ve-standart-hata","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/standart-sapma-ve-standart-hata\/","title":{"rendered":"Standart sapma ve standart hata: fark nedir?"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">\u00d6\u011frencilerin istatistikte s\u0131kl\u0131kla kar\u0131\u015ft\u0131rd\u0131\u011f\u0131 iki terim <strong>standart sapma<\/strong> ve <strong>standart hatad\u0131r<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Standart sapma,<\/strong> bir veri setindeki de\u011ferlerin da\u011f\u0131l\u0131m\u0131n\u0131 \u00f6l\u00e7er.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Standart hata,<\/strong> bir pop\u00fclasyondan tekrarlanan \u00f6rneklerin ortalamas\u0131n\u0131n standart sapmas\u0131d\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu fikri a\u00e7\u0131k\u00e7a g\u00f6stermek i\u00e7in bir \u00f6rne\u011fe bakal\u0131m.<\/span><\/p>\n<h2> <strong>\u00d6rnek: standart sapmaya kar\u015f\u0131 standart hata<\/strong><\/h2>\n<p> <span style=\"color: #000000;\">10 farkl\u0131 kaplumba\u011fan\u0131n a\u011f\u0131rl\u0131\u011f\u0131n\u0131 \u00f6l\u00e7t\u00fc\u011f\u00fcm\u00fcz\u00fc varsayal\u0131m.<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-9896 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/standard_dev_vs_standard_error1.png\" alt=\"\" width=\"492\" height=\"122\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">10 kaplumba\u011fadan olu\u015fan bu \u00f6rnek i\u00e7in \u00f6rnek ortalamas\u0131n\u0131 ve \u00f6rnek standart sapmas\u0131n\u0131 hesaplayabiliriz:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-9899 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/standard_dev_vs_standard_error2-1.png\" alt=\"\" width=\"492\" height=\"129\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Standart sapman\u0131n 8,68 oldu\u011funu varsayal\u0131m. Bu da bize bu kaplumba\u011falar\u0131n a\u011f\u0131rl\u0131k da\u011f\u0131l\u0131m\u0131 hakk\u0131nda fikir veriyor.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Ancak, 10 kaplumba\u011fadan olu\u015fan ba\u015fka bir<a href=\"https:\/\/statorials.org\/tr\/ornekleme-yontemleri\/\" target=\"_blank\" rel=\"noopener noreferrer\">basit rastgele \u00f6rnek<\/a> toplad\u0131\u011f\u0131m\u0131z\u0131 ve onlar\u0131n \u00f6l\u00e7\u00fcmlerini de ald\u0131\u011f\u0131m\u0131z\u0131 varsayal\u0131m.<\/span><\/p>\n<p> <span style=\"color: #000000;\">10 kaplumba\u011fadan olu\u015fan bu numunenin, ayn\u0131 pop\u00fclasyondan gelmelerine ra\u011fmen biraz farkl\u0131 bir ortalamaya ve standart sapmaya sahip olmas\u0131 muhtemeldir:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-9900 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/standard_dev_vs_standard_error3.png\" alt=\"\" width=\"498\" height=\"132\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">\u015eimdi, ayn\u0131 pop\u00fclasyondan tekrarlanan \u00f6rnekler ald\u0131\u011f\u0131m\u0131z\u0131 ve her \u00f6rnek i\u00e7in \u00f6rnek ortalamas\u0131n\u0131 ve \u00f6rnek standart sapmas\u0131n\u0131 kaydetti\u011fimizi hayal edersek:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-9901 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/standard_dev_vs_standard_error4.png\" alt=\"\" width=\"492\" height=\"144\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">\u015eimdi \u00f6rnek ortalamalar\u0131n her birini ayn\u0131 sat\u0131ra \u00e7izdi\u011fimizi hayal edin:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-9902 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/standard_dev_vs_standard_error5.png\" alt=\"\" width=\"480\" height=\"126\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\"><strong>Bu ortalamalar\u0131n standart sapmas\u0131na standart hata denir.<\/strong><\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-9903 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/standard_dev_vs_standard_error6.png\" alt=\"\" width=\"490\" height=\"117\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Standart hatay\u0131 ger\u00e7ekte hesaplamak i\u00e7in kullan\u0131lan form\u00fcl:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Standart hata = s\/ \u221a <span style=\"border-top: 1px solid black;\">n<\/span><\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Alt\u0131n:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>s:<\/strong> numune standart sapmas\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>n:<\/strong> \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc<\/span><\/li>\n<\/ul>\n<h2> <span style=\"color: #000000;\"><strong>Standart hatay\u0131 kullanman\u0131n amac\u0131 nedir?<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Belirli bir \u00f6rne\u011fin ortalamas\u0131n\u0131 hesaplad\u0131\u011f\u0131m\u0131zda, asl\u0131nda o belirli \u00f6rne\u011fin ortalamas\u0131n\u0131 de\u011fil, \u00f6rne\u011fin geldi\u011fi daha b\u00fcy\u00fck pop\u00fclasyonun ortalamas\u0131n\u0131 bilmek istiyoruz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Ancak \u00f6rnekleri kullan\u0131yoruz \u00e7\u00fcnk\u00fc bunlar i\u00e7in veri toplamak, t\u00fcm pop\u00fclasyondan \u00e7ok daha kolay.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Ve elbette, numune ortalamas\u0131 numuneden numuneye de\u011fi\u015fir, dolay\u0131s\u0131yla ortalama tahminimizin kesinli\u011fini \u00f6l\u00e7menin bir yolu olarak <strong>ortalaman\u0131n standart hatas\u0131n\u0131<\/strong> kullan\u0131r\u0131z.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Standart hatay\u0131 hesaplama form\u00fcl\u00fcnde, \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc (n) artt\u0131k\u00e7a standart hatan\u0131n azald\u0131\u011f\u0131n\u0131 g\u00f6receksiniz:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Standart hata = s\/ \u221a <span style=\"border-top: 1px solid black;\">n<\/span><\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu mant\u0131kl\u0131 olmal\u0131 \u00e7\u00fcnk\u00fc daha b\u00fcy\u00fck \u00f6rnekler de\u011fi\u015fkenli\u011fi azalt\u0131r ve \u00f6rnek ortalamam\u0131z\u0131n ger\u00e7ek pop\u00fclasyon ortalamas\u0131na daha yak\u0131n olma \u015fans\u0131n\u0131 art\u0131r\u0131r.<\/span><\/p>\n<h2> <strong><span style=\"color: #000000;\">Standart sapmaya kar\u015f\u0131 standart hata ne zaman kullan\u0131l\u0131r?<\/span><\/strong><\/h2>\n<p> <span style=\"color: #000000;\">Bir veri setindeki de\u011ferlerin da\u011f\u0131l\u0131m\u0131n\u0131 basit\u00e7e \u00f6l\u00e7mek istiyorsak <strong>standart sapmay\u0131<\/strong> kullanabiliriz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Ancak ortalama tahmini etraf\u0131ndaki belirsizli\u011fi \u00f6l\u00e7mek istiyorsak <strong>ortalaman\u0131n standart hatas\u0131n\u0131<\/strong> kullanabiliriz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6zel senaryonuza ve neyi ba\u015farmaya \u00e7al\u0131\u015ft\u0131\u011f\u0131n\u0131za ba\u011fl\u0131 olarak standart sapmay\u0131 veya standart hatay\u0131 kullanmay\u0131 se\u00e7ebilirsiniz.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u00d6\u011frencilerin istatistikte s\u0131kl\u0131kla kar\u0131\u015ft\u0131rd\u0131\u011f\u0131 iki terim standart sapma ve standart hatad\u0131r . Standart sapma, bir veri setindeki de\u011ferlerin da\u011f\u0131l\u0131m\u0131n\u0131 \u00f6l\u00e7er. Standart hata, bir pop\u00fclasyondan tekrarlanan \u00f6rneklerin ortalamas\u0131n\u0131n standart sapmas\u0131d\u0131r. Bu fikri a\u00e7\u0131k\u00e7a g\u00f6stermek i\u00e7in bir \u00f6rne\u011fe bakal\u0131m. \u00d6rnek: standart sapmaya kar\u015f\u0131 standart hata 10 farkl\u0131 kaplumba\u011fan\u0131n a\u011f\u0131rl\u0131\u011f\u0131n\u0131 \u00f6l\u00e7t\u00fc\u011f\u00fcm\u00fcz\u00fc varsayal\u0131m. 10 kaplumba\u011fadan olu\u015fan bu \u00f6rnek i\u00e7in [&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-934","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 sapma ve standart hata: fark nedir?<\/title>\n<meta name=\"description\" content=\"Standart sapma ile standart hata aras\u0131ndaki fark\u0131n bir \u00f6rnekle basit bir 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