{"id":80,"date":"2026-07-08T11:11:05","date_gmt":"2026-07-08T11:11:05","guid":{"rendered":"https:\/\/hocabul.net\/?p=80"},"modified":"2026-07-08T11:11:05","modified_gmt":"2026-07-08T11:11:05","slug":"guven-araligi-nedir-yuzde-95-guven-aslinda-ne-anlama-geliyor","status":"publish","type":"post","link":"https:\/\/hocabul.net\/?p=80","title":{"rendered":"G\u00fcven Aral\u0131\u011f\u0131 Nedir? “Y\u00fczde 95 G\u00fcven” Asl\u0131nda Ne Anlama Geliyor?"},"content":{"rendered":"\n

Bir ara\u015ft\u0131rma sonucunu okuyorsunuz: “Yeni ilac\u0131n etkinli\u011fi y\u00fczde 68 (%95 g\u00fcven aral\u0131\u011f\u0131: %61\u2013%75).” Ya da bir se\u00e7im anketi: “Aday y\u00fczde 52 deste\u011fe sahip, hata pay\u0131 \u00b13 puan.” Bu say\u0131lar ne anlama geliyor? “Y\u00fczde 95 g\u00fcven” tam olarak neyi ifade ediyor? Ve bu kavram\u0131n neden bu kadar s\u0131k yanl\u0131\u015f anla\u015f\u0131ld\u0131\u011f\u0131n\u0131 bilmek, istatistik okuryazarl\u0131\u011f\u0131n\u0131n en kritik ad\u0131mlar\u0131ndan biri.<\/p>\n\n\n\n

Bu yaz\u0131da g\u00fcven aral\u0131\u011f\u0131n\u0131 s\u0131f\u0131rdan, somut \u00f6rneklerle ve en \u00f6nemlisi yayg\u0131n yan\u0131lg\u0131lardan ka\u00e7\u0131narak ele al\u0131yoruz.<\/p>\n\n\n\n

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\u00d6nce Temel Sorun: Neden \u00d6rneklemeden \u00c7\u0131kar\u0131m Yap\u0131yoruz?<\/h2>\n\n\n\n

Bir \u015fehirdeki t\u00fcm bireylerin ortalama uyku s\u00fcresini \u00f6\u011frenmek istiyorsunuz. Ama o \u015fehirde 5 milyon ki\u015fi var. Herkesi \u00f6l\u00e7mek imk\u00e2ns\u0131z \u2014 hem zaman hem maliyet a\u00e7\u0131s\u0131ndan. Bu y\u00fczden \u00f6rnekleme yap\u0131yoruz: 1000 ki\u015fiyi rastgele se\u00e7iyor, uyku s\u00fcrelerini \u00f6l\u00e7\u00fcyor ve bu 1000 ki\u015fiden elde etti\u011fimiz sonucu t\u00fcm pop\u00fclasyon i\u00e7in genellemeye \u00e7al\u0131\u015f\u0131yoruz.<\/p>\n\n\n\n

Ama bu genelleme bir belirsizlik ta\u015f\u0131yor. Se\u00e7ti\u011fimiz 1000 ki\u015fi pop\u00fclasyonu tam yans\u0131t\u0131yor mu? Rastgele se\u00e7im, \u015fans eseri biraz daha az ya da biraz daha fazla uyuyan bir grubu m\u0131 yakalad\u0131? Bu belirsizli\u011fi \u00f6l\u00e7mek ve ifade etmek i\u00e7in g\u00fcven aral\u0131\u011f\u0131 devreye giriyor.<\/p>\n\n\n\n

Ortalamalar her zaman yalan s\u00f6ylemez ama \u00e7o\u011fu zaman eksik s\u00f6yler<\/a> \u2014 medyan ve standart sapma yaz\u0131m\u0131zda anlatt\u0131\u011f\u0131m\u0131z bu fikrin bir uzant\u0131s\u0131 bu. G\u00fcven aral\u0131\u011f\u0131 da “bir nokta tahmini yetmez, etraf\u0131ndaki belirsizli\u011fi de g\u00f6ster” mant\u0131\u011f\u0131ndan do\u011fuyor.<\/p>\n\n\n\n

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G\u00fcven Aral\u0131\u011f\u0131 Nedir? Teknik Tan\u0131m<\/h2>\n\n\n\n

G\u00fcven aral\u0131\u011f\u0131, bir pop\u00fclasyon parametresinin (\u00f6rne\u011fin ortalama ya da oran) b\u00fcy\u00fck ihtimalle i\u00e7inde bulundu\u011fu de\u011fer aral\u0131\u011f\u0131n\u0131 g\u00f6steriyor. Hesaplan\u0131\u015f \u015f\u00f6yle \u00f6zetlenebilir:<\/p>\n\n\n\n

G\u00fcven Aral\u0131\u011f\u0131 = Nokta Tahmini \u00b1 Hata Pay\u0131<\/code><\/pre>\n\n\n\n
Hata pay\u0131 ise \u00fc\u00e7 fakt\u00f6re ba\u011fl\u0131:<\/p>\n\n\n\n
    \n
  1. G\u00fcven d\u00fczeyi<\/strong> (genellikle %95 ya da %99)<\/li>\n\n\n\n
  2. \u00d6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc<\/strong> (b\u00fcy\u00fck \u00f6rneklem \u2192 dar aral\u0131k)<\/li>\n\n\n\n
  3. Pop\u00fclasyondaki de\u011fi\u015fkenlik<\/strong> (y\u00fcksek varyans \u2192 geni\u015f aral\u0131k)<\/li>\n<\/ol>\n\n\n\n
    Matematiksel olarak %95 g\u00fcven aral\u0131\u011f\u0131 \u015fu \u015fekilde hesaplan\u0131r:<\/p>\n\n\n\n
    X\u0304 \u00b1 (z \u00d7 \u03c3\/\u221an)<\/code><\/pre>\n\n\n\n
    Burada X\u0304 \u00f6rneklem ortalamas\u0131, z %95 i\u00e7in 1.96, \u03c3 standart sapma, n \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc.<\/p>\n\n\n\n
    Ama form\u00fcldaki say\u0131lardan daha \u00f6nemli olan, bu form\u00fcl\u00fcn ne s\u00f6yledi\u011fini do\u011fru anlamak.<\/p>\n\n\n\n
    \n\n\n\n
    “Y\u00fczde 95 G\u00fcven” Ne Demek De\u011fil?<\/h2>\n\n\n\n
    G\u00fcven aral\u0131\u011f\u0131 istatistikte en s\u0131k yanl\u0131\u015f anla\u015f\u0131lan kavramlardan biri. p-de\u011feri yaz\u0131m\u0131zda<\/a> istatistiksel anlaml\u0131l\u0131\u011f\u0131n nas\u0131l yanl\u0131\u015f yorumland\u0131\u011f\u0131n\u0131 anlatt\u0131k \u2014 g\u00fcven aral\u0131\u011f\u0131 da benzer yan\u0131lg\u0131lara sahne oluyor.<\/p>\n\n\n\n
    Yanl\u0131\u015f yorum 1:<\/strong> “%95 g\u00fcven aral\u0131\u011f\u0131 [61, 75] demek, ger\u00e7ek de\u011ferin y\u00fczde 95 ihtimalle bu aral\u0131kta oldu\u011fu anlam\u0131na gelir.”<\/p>\n\n\n\n
    Bu kula\u011fa \u00e7ok mant\u0131kl\u0131 geliyor ama teknik olarak yanl\u0131\u015f. Ger\u00e7ek pop\u00fclasyon parametresi sabit bir de\u011fer \u2014 o de\u011fer ya bu aral\u0131kta ya da de\u011fil. Bir olay\u0131n “y\u00fczde 95 ihtimalle bu aral\u0131kta” olmas\u0131 diye bir \u015fey yok \u00e7\u00fcnk\u00fc o de\u011fer de\u011fi\u015fmiyor.<\/p>\n\n\n\n
    Do\u011fru yorum:<\/strong> “%95 g\u00fcven aral\u0131\u011f\u0131, bu y\u00f6ntemi (ayn\u0131 pop\u00fclasyondan ayn\u0131 b\u00fcy\u00fckl\u00fckte \u00f6rneklem al\u0131p ayn\u0131 hesab\u0131 yaparak) 100 kez tekrarlasayd\u0131k, hesaplanan 100 aral\u0131\u011f\u0131n yakla\u015f\u0131k 95 tanesinin ger\u00e7ek pop\u00fclasyon parametresini i\u00e7erdi\u011fi anlam\u0131na gelir.”<\/p>\n\n\n\n
    Bu ince ama kritik fark, istatistiksel \u00e7\u0131kar\u0131m\u0131n felsefi temelini olu\u015fturuyor. American Statistical Association (amstat.org<\/a>) g\u00fcven aral\u0131klar\u0131n\u0131n yorumlanmas\u0131na ili\u015fkin kapsaml\u0131 rehber belgeler yay\u0131mlam\u0131\u015f; bu konuyu derinlemesine incelemek isteyenler i\u00e7in de\u011ferli bir kaynak.<\/p>\n\n\n\n
    Yanl\u0131\u015f yorum 2:<\/strong> “%95 g\u00fcven aral\u0131\u011f\u0131 dar ise tahmin g\u00fcvenilirdir.”<\/p>\n\n\n\n
    G\u00fcven aral\u0131\u011f\u0131n\u0131n darl\u0131\u011f\u0131, tahmininin do\u011frulu\u011funu de\u011fil hassasiyetini g\u00f6sterir. \u00d6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fcn\u00fc art\u0131rarak dar bir aral\u0131k elde edebilirsiniz ama \u00f6rneklem se\u00e7imi hatal\u0131ysa (\u00f6rne\u011fin \u00f6nyarg\u0131l\u0131 bir \u00f6rnekleme) dar aral\u0131k sizi yan\u0131lt\u0131r. Yan\u0131lt\u0131c\u0131 grafikleri tan\u0131ma yaz\u0131m\u0131zda<\/a> g\u00f6rselle\u015ftirmelerin nas\u0131l yan\u0131ltabilece\u011fini ele ald\u0131k; g\u00fcven aral\u0131\u011f\u0131 da yanl\u0131\u015f ba\u011flamda sunuldu\u011funda benzer bir yan\u0131ltma potansiyeli ta\u015f\u0131yor.<\/p>\n\n\n\n
    \n\n\n\n
    Somut \u00d6rnek: Se\u00e7im Anketi<\/h2>\n\n\n\n
    “Aday A y\u00fczde 52 oran\u0131nda destek g\u00f6r\u00fcyor, hata pay\u0131 \u00b13 puan” haberini okudu\u011funuzda ne anl\u0131yorsunuz?<\/p>\n\n\n\n
    Bu, \u015fu anlama geliyor: Bu anketi ayn\u0131 y\u00f6ntemle 100 kez yaparsak, hesaplanan aral\u0131\u011f\u0131n (bu \u00f6rnekte [49, 55]) yakla\u015f\u0131k 95 tanesi ger\u00e7ek pop\u00fclasyon de\u011ferini i\u00e7eriyor. Bu, se\u00e7menin %52’sinin o aday\u0131 destekledi\u011fini s\u00f6ylemez; bu verinin %95 g\u00fcven aral\u0131\u011f\u0131n\u0131n 49 ile 55 aras\u0131nda oldu\u011funu s\u00f6yler.<\/p>\n\n\n\n
    Pratikte ne anlama geliyor? Rakibin de bu aral\u0131kta oldu\u011funu d\u00fc\u015f\u00fcn\u00fcrsek (%50 e\u015fi\u011fine \u00e7ok yak\u0131n), bu anket ger\u00e7ekte iki aday aras\u0131nda anlaml\u0131 bir fark oldu\u011funu s\u00f6yleyemiyor. Se\u00e7im hakk\u0131nda kesin bir \u00f6ng\u00f6r\u00fc yapmak i\u00e7in bu tek anket yeterli de\u011fil.<\/p>\n\n\n\n
    B\u00fcy\u00fck say\u0131lar yasas\u0131 yaz\u0131m\u0131zda<\/a> \u00f6rneklem b\u00fcy\u00fcd\u00fck\u00e7e tahminin nas\u0131l kararl\u0131l\u0131k kazand\u0131\u011f\u0131n\u0131 anlatt\u0131k. G\u00fcven aral\u0131\u011f\u0131 bu ili\u015fkinin somut matematiksel ifadesi: daha b\u00fcy\u00fck \u00f6rneklem \u2192 daha dar aral\u0131k \u2192 daha hassas tahmin.<\/p>\n\n\n\n
    \n\n\n\n
    G\u00fcven D\u00fczeyi Nas\u0131l Se\u00e7ilir?<\/h2>\n\n\n\n
    Neden hep %95 kullan\u0131yoruz? Bu kural m\u0131, gelenek mi?<\/p>\n\n\n\n
    B\u00fcy\u00fck \u00f6l\u00e7\u00fcde gelenek. %95, t\u0131p ve sosyal bilimlerde onlarca y\u0131ld\u0131r standart olarak kabul g\u00f6rd\u00fc. Ama bu mutlak bir kural de\u011fil.<\/p>\n\n\n\n
    %99 g\u00fcven aral\u0131\u011f\u0131:<\/strong> Daha geni\u015f bir aral\u0131k verir ama “yan\u0131lma riskini” %1’e d\u00fc\u015f\u00fcr\u00fcr. Hata maliyetinin \u00e7ok y\u00fcksek oldu\u011fu durumlarda (t\u0131bbi tedavi, u\u00e7ak g\u00fcvenli\u011fi) tercih edilir.<\/p>\n\n\n\n
    %90 g\u00fcven aral\u0131\u011f\u0131:<\/strong> Daha dar aral\u0131k ama %10 yan\u0131lma riski. Ke\u015fif ama\u00e7l\u0131 ara\u015ft\u0131rmalarda bazen tercih edilir.<\/p>\n\n\n\n
    G\u00fcven d\u00fczeyi ile hassasiyet aras\u0131nda ka\u00e7\u0131n\u0131lmaz bir de\u011fi\u015f toku\u015f (trade-off) var: Ne kadar g\u00fcvenli olmak istiyorsan\u0131z, aral\u0131\u011f\u0131 o kadar geni\u015fletmek zorunda kal\u0131rs\u0131n\u0131z. Ortalamaya d\u00f6n\u00fc\u015f yaz\u0131m\u0131zda<\/a> g\u00f6zlem say\u0131s\u0131 ile g\u00fcvenilirlik aras\u0131ndaki dengeyi ele ald\u0131k \u2014 g\u00fcven aral\u0131\u011f\u0131 da bu dengenin matematiksel y\u00fcz\u00fc.<\/p>\n\n\n\n
    \n\n\n\n
    \u00d6rneklem B\u00fcy\u00fckl\u00fc\u011f\u00fc: G\u00fcven Aral\u0131\u011f\u0131n\u0131 Kim Daralt\u0131r?<\/h2>\n\n\n\n
    G\u00fcven aral\u0131\u011f\u0131n\u0131 etkileyen en pratik fakt\u00f6r \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc. 100 ki\u015filik \u00f6rneklemden hesaplanan %95 g\u00fcven aral\u0131\u011f\u0131 ile 10.000 ki\u015filik \u00f6rneklemden hesaplanan\u0131 k\u0131yaslad\u0131\u011f\u0131n\u0131zda, ikincisi \u00e7ok daha dar.<\/p>\n\n\n\n
    Form\u00fcle bakarsak: Hata pay\u0131 = z \u00d7 \u03c3\/\u221an. n (\u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc) 4 kat\u0131na \u00e7\u0131kt\u0131\u011f\u0131nda, aral\u0131k 2 kat daral\u0131yor. Yani aral\u0131\u011f\u0131 yar\u0131ya indirmek i\u00e7in \u00f6rneklemi 4 kat b\u00fcy\u00fctmek gerekiyor \u2014 ve bu, ara\u015ft\u0131rma maliyetleri a\u00e7\u0131s\u0131ndan \u00f6nemli bir pratik k\u0131s\u0131t.<\/p>\n\n\n\n
    Bu ili\u015fkiyi Simpson Paradoksu yaz\u0131m\u0131zdaki<\/a> gruplama mant\u0131\u011f\u0131yla birle\u015ftirerek d\u00fc\u015f\u00fcn\u00fcrsek, alt gruplar i\u00e7in ayr\u0131 ayr\u0131 hesaplanan g\u00fcven aral\u0131klar\u0131 \u00e7ok daha geni\u015f olabilir \u2014 \u00e7\u00fcnk\u00fc her alt grupun \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc k\u00fc\u00e7\u00fcl\u00fcyor. Bu, alt grup analizlerinin neden genellikle daha dikkatli yorumlanmas\u0131 gerekti\u011fini a\u00e7\u0131kl\u0131yor.<\/p>\n\n\n\n
    \n\n\n\n
    G\u00fcven Aral\u0131\u011f\u0131 vs. Tahmin Aral\u0131\u011f\u0131<\/h2>\n\n\n\n
    S\u0131k\u00e7a kar\u0131\u015ft\u0131r\u0131lan iki kavram: g\u00fcven aral\u0131\u011f\u0131 (confidence interval) ve tahmin aral\u0131\u011f\u0131 (prediction interval).<\/p>\n\n\n\n
    G\u00fcven aral\u0131\u011f\u0131<\/strong>, bir pop\u00fclasyon parametresini (\u00f6rne\u011fin ortalama) tahmin eder.<\/p>\n\n\n\n
    Tahmin aral\u0131\u011f\u0131<\/strong>, bireysel bir g\u00f6zlemin nerede olabilece\u011fini tahmin eder.<\/p>\n\n\n\n
    \u00d6rnek: Bir s\u0131n\u0131f\u0131n ortalama boyunu tahmin ediyorsunuz. G\u00fcven aral\u0131\u011f\u0131 size ortalamay\u0131 verir. Ama “bu s\u0131n\u0131fa kat\u0131lacak yeni bir \u00f6\u011frencinin boyu nerede olur?” sorusu i\u00e7in tahmin aral\u0131\u011f\u0131 gerekiyor \u2014 ve bu \u00e7ok daha geni\u015f bir aral\u0131k verir, \u00e7\u00fcnk\u00fc bireysel de\u011fi\u015fkenlik ortalaman\u0131n de\u011fi\u015fkenli\u011finden \u00e7ok daha b\u00fcy\u00fck.<\/p>\n\n\n\n
    Bu fark\u0131 bilmeden yap\u0131lan yorumlar, \u00f6zellikle t\u0131bbi ve psikolojik ara\u015ft\u0131rmalarda ciddi \u00e7\u0131kar\u0131m hatalar\u0131na yol a\u00e7\u0131yor.<\/p>\n\n\n\n
    \n\n\n\n
    Bayes Yakla\u015f\u0131m\u0131: Alternatif Perspektif<\/h2>\n\n\n\n
    “G\u00fcven aral\u0131\u011f\u0131 yanl\u0131\u015f yorumlan\u0131yorsa, neden farkl\u0131 bir \u015fey kullanm\u0131yoruz?” sorusu istatistik metodolojisinde me\u015fru bir tart\u0131\u015fma a\u00e7\u0131yor. Bu sorunun cevaplar\u0131ndan biri Bayes\u00e7i istatistik.<\/p>\n\n\n\n
    Bayes Teoremi yaz\u0131m\u0131zda<\/a> \u00f6nceki bilgiyi yeni kan\u0131tla g\u00fcncelleme mant\u0131\u011f\u0131n\u0131 anlatt\u0131k. Bayes\u00e7i yakla\u015f\u0131mda “g\u00fcven aral\u0131\u011f\u0131”n\u0131n kar\u015f\u0131l\u0131\u011f\u0131 olan “credible interval” (g\u00fcvenilir aral\u0131k), \u00e7ok daha do\u011fal bir yoruma sahip: “Bu aral\u0131\u011f\u0131n ger\u00e7ek de\u011feri i\u00e7erme olas\u0131l\u0131\u011f\u0131 %95.” Ama bu yorum, \u00f6nceki bilgi (prior) tan\u0131mlanmas\u0131n\u0131 gerektiriyor ve bu da kendi metodolojik tart\u0131\u015fmalar\u0131n\u0131 beraberinde getiriyor.<\/p>\n\n\n\n
    \n\n\n\n
    Sonu\u00e7: Belirsizli\u011fi G\u00f6r\u00fcn\u00fcr K\u0131lmak<\/h2>\n\n\n\n
    G\u00fcven aral\u0131\u011f\u0131, istatisti\u011fin belki de en d\u00fcr\u00fcst arac\u0131. \u00c7\u00fcnk\u00fc belirsizli\u011fi saklam\u0131yor; onu say\u0131sal olarak ifade ediyor. “Tahminim \u015fu ama yan\u0131labilece\u011fim aral\u0131k bu” demek, hem bilimsel d\u00fcr\u00fcstl\u00fck hem de pratik karar verme a\u00e7\u0131s\u0131ndan \u00e7ok de\u011ferli bir tutum.<\/p>\n","protected":false},"excerpt":{"rendered":"
    Bir ara\u015ft\u0131rma sonucunu okuyorsunuz: “Yeni ilac\u0131n etkinli\u011fi y\u00fczde 68 (%95 g\u00fcven aral\u0131\u011f\u0131: %61\u2013%75).” Ya da bir se\u00e7im anketi: “Aday y\u00fczde 52 deste\u011fe sahip, hata pay\u0131 \u00b13 puan.” Bu say\u0131lar ne anlama geliyor? “Y\u00fczde 95 g\u00fcven” tam olarak neyi ifade ediyor? Ve bu kavram\u0131n neden bu kadar s\u0131k yanl\u0131\u015f anla\u015f\u0131ld\u0131\u011f\u0131n\u0131 bilmek, istatistik okuryazarl\u0131\u011f\u0131n\u0131n en kritik ad\u0131mlar\u0131ndan … Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[],"class_list":["post-80","post","type-post","status-publish","format-standard","hentry","category-istatistik-olasilik"],"_links":{"self":[{"href":"https:\/\/hocabul.net\/index.php?rest_route=\/wp\/v2\/posts\/80","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/hocabul.net\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/hocabul.net\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/hocabul.net\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/hocabul.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=80"}],"version-history":[{"count":1,"href":"https:\/\/hocabul.net\/index.php?rest_route=\/wp\/v2\/posts\/80\/revisions"}],"predecessor-version":[{"id":81,"href":"https:\/\/hocabul.net\/index.php?rest_route=\/wp\/v2\/posts\/80\/revisions\/81"}],"wp:attachment":[{"href":"https:\/\/hocabul.net\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=80"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/hocabul.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=80"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/hocabul.net\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=80"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}