{"id":51,"date":"2023-08-06T02:06:13","date_gmt":"2023-08-06T02:06:13","guid":{"rendered":"https:\/\/statorials.org\/tr\/basit-rastgele-ornekleme\/"},"modified":"2023-08-06T02:06:13","modified_gmt":"2023-08-06T02:06:13","slug":"basit-rastgele-ornekleme","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/basit-rastgele-ornekleme\/","title":{"rendered":"Basit rastgele \u00f6rnekleme"},"content":{"rendered":"

Bu makalede basit rastgele numunenin ne oldu\u011funu ve ne t\u00fcr basit rastgele numunelerin bulundu\u011funu \u00f6\u011freneceksiniz. Ayr\u0131ca basit rastgele \u00f6rneklemenin nas\u0131l yap\u0131ld\u0131\u011f\u0131n\u0131 bir \u00f6rnek \u00fczerinden a\u00e7\u0131kl\u0131yoruz. Son olarak basit rastgele \u00f6rneklemenin avantaj ve dezavantajlar\u0131n\u0131n neler oldu\u011funu g\u00f6rebileceksiniz. <\/p>\n

<\/span> Basit rastgele \u00f6rnekleme nedir?<\/span><\/h2>\n

\u0130statistikte basit rastgele \u00f6rnekleme<\/strong> , bir \u00e7al\u0131\u015fma i\u00e7in \u00f6rneklemi se\u00e7mek i\u00e7in kullan\u0131lan olas\u0131l\u0131ksal bir y\u00f6ntemdir. Basit rastgele \u00f6rneklemenin temel \u00f6zelli\u011fi, istatistiksel pop\u00fclasyonun her bir eleman\u0131na, incelenen numuneye dahil edilme olas\u0131l\u0131\u011f\u0131n\u0131n ayn\u0131 olmas\u0131d\u0131r.<\/p>\n

Basit rastgele \u00f6rneklemede, \u00f6rnek \u00f6\u011feler rastgele se\u00e7ilir, dolay\u0131s\u0131yla ortaya \u00e7\u0131kan \u00f6rnek tamamen rastgele olur.<\/p>\n

Bu nedenle, basit rastgele \u00f6rnekleme kullan\u0131ld\u0131\u011f\u0131nda, belirli bir numuneyi elde etme olas\u0131l\u0131\u011f\u0131, herhangi bir ba\u015fka numuneyi elde etme olas\u0131l\u0131\u011f\u0131na e\u015fittir. A\u015fa\u011f\u0131da bu olas\u0131l\u0131\u011f\u0131n nas\u0131l hesapland\u0131\u011f\u0131n\u0131 g\u00f6rece\u011fiz.<\/p>\n

Bir \u00f6rnekten bireyleri se\u00e7menin ba\u015fka yollar\u0131n\u0131n da oldu\u011funu unutmay\u0131n. En \u00e7ok kullan\u0131lan \u00f6rnekleme t\u00fcrleri ba\u015fl\u0131ca \u015funlard\u0131r:<\/p>\n

    \n
  • Basit rastgele \u00f6rnekleme<\/li>\n
  • Tabakal\u0131 \u00f6rnekleme<\/li>\n
  • Sistematik \u00f6rnekleme<\/li>\n
  • K\u00fcme \u00f6rneklemesi<\/li>\n<\/ul>\n

    Basit rastgele \u00f6rnekleme kavram\u0131 kesinlikle anla\u015f\u0131lmas\u0131 en kolay t\u00fcrd\u00fcr, ancak bazen tam da rastgele do\u011fas\u0131ndan dolay\u0131 uygulanmas\u0131 en karma\u015f\u0131k olan\u0131 haline gelir. <\/p>\n

    <\/span> Basit rastgele \u00f6rnekleme nas\u0131l yap\u0131l\u0131r?<\/span><\/h2>\n

    Basit rastgele \u00f6rnekleme ger\u00e7ekle\u015ftirme ad\u0131mlar\u0131 a\u015fa\u011f\u0131daki gibidir:<\/p>\n

      \n
    1. N\u00fcfusun t\u00fcm unsurlar\u0131n\u0131 i\u00e7eren bir liste yap\u0131n.<\/span><\/li>\n
    2. Pop\u00fclasyondaki her \u00f6\u011feye s\u0131ral\u0131 bir say\u0131 (1, 2, 3,\u2026, n) atay\u0131n<\/strong> .<\/span><\/li>\n
    3. \u0130stedi\u011finiz numune boyutunu<\/strong> ayarlay\u0131n.<\/span><\/li>\n
    4. Se\u00e7ilen \u00f6rnek boyutu kadar say\u0131 \u00fcretmek i\u00e7in rastgele say\u0131 \u00fcreteci<\/strong> kullan\u0131n.<\/span><\/li>\n
    5. Olu\u015fturulan numaralara atanan bireyler,<\/strong> \u00f6rneklemin par\u00e7as\u0131 olmak \u00fczere se\u00e7ilen ki\u015filerdir.<\/span><\/li>\n<\/ol>\n

      Rastgele say\u0131lar \u00fcretmek i\u00e7in \u00e7e\u015fitli y\u00f6ntemler vard\u0131r; en geleneksel olanlar\u0131 piyango y\u00f6ntemi ve say\u0131 tablosu y\u00f6ntemidir:<\/p>\n

        \n
      • Piyango y\u00f6ntemi,<\/strong> t\u00fcm say\u0131lar\u0131 bir kutuya koymay\u0131, kar\u0131\u015ft\u0131rmay\u0131 ve ard\u0131ndan rastgele say\u0131lar\u0131 \u00e7ekmeyi i\u00e7erir.<\/li>\n
      • Say\u0131 tablosu y\u00f6ntemi,<\/strong> t\u00fcm olas\u0131 say\u0131lar\u0131 i\u00e7eren bir tablodan say\u0131lar\u0131n rastgele se\u00e7ilmesini i\u00e7erir.<\/li>\n<\/ul>\n

        \u00d6nceki iki y\u00f6ntemden birini de kullanabilseniz de, bunlar daha fazla zaman gerektirir ve daha k\u00fc\u00e7\u00fck \u00f6rneklem boyutlar\u0131na daha uygundur. \u015eu anda rastgele say\u0131lar\u0131 daha h\u0131zl\u0131 \u00fcretmek i\u00e7in bilgisayar programlar\u0131<\/strong> kullan\u0131l\u0131yor, \u00f6rne\u011fin Excel program\u0131n\u0131 kullanabilirsiniz.<\/p>\n

        \u00d6te yandan \u00f6rnekleme hatas\u0131n\u0131n minimum d\u00fczeyde olmas\u0131 i\u00e7in \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fcn\u00fcn yeterli olmas\u0131 gerekti\u011fini de dikkate almal\u0131s\u0131n\u0131z. \u0130deal \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fcn\u00fc bulmak \u00f6nemsiz de\u011fildir; E\u011fer bu konuda \u015f\u00fcpheleriniz varsa bunun nas\u0131l yap\u0131laca\u011f\u0131n\u0131 anlatt\u0131\u011f\u0131m\u0131z yaz\u0131m\u0131z\u0131 sitemizde ara\u015ft\u0131rabilirsiniz. <\/p>\n

        <\/span> Basit Rastgele \u00d6rnekleme \u00d6rne\u011fi<\/span><\/h2>\n

        Basit rastgele \u00f6rneklemenin tan\u0131m\u0131n\u0131 g\u00f6rd\u00fckten sonra, bu t\u00fcr \u00f6rneklemenin nas\u0131l yap\u0131ld\u0131\u011f\u0131na dair \u00e7\u00f6z\u00fcmlenmi\u015f bir \u00f6rnek g\u00f6rece\u011fiz.<\/p>\n

        \u00d6rne\u011fin bir \u015firkette 2000 i\u015f\u00e7i varsa ve 400 i\u015f\u00e7iden olu\u015fan bir \u00f6rneklemle istatistiksel bir \u00e7al\u0131\u015fma yapmak istiyorsak, basit tesad\u00fcfi \u00f6rneklemeyle \u00f6rneklemde yer alacak bireyleri se\u00e7mek i\u00e7in ilk yapmam\u0131z gereken \u015fey; Her \u00e7al\u0131\u015fana 1’den 2000’e kadar bir say\u0131 atan\u0131r.<\/p>\n

        Numaralar atand\u0131ktan sonra rastgele 400 numara se\u00e7memiz gerekiyor. Bu durumda \u00f6rneklem boyutu olduk\u00e7a b\u00fcy\u00fck oldu\u011fundan Excel gibi bilgisayar yaz\u0131l\u0131mlar\u0131n\u0131 kullanmak en iyisidir.<\/p>\n

        Daha sonra \u00e7al\u0131\u015fmaya kat\u0131lmak \u00fczere se\u00e7ilen 400 i\u015f\u00e7i, bir \u00f6nceki ad\u0131mda atanan say\u0131s\u0131 belirlenen i\u015f\u00e7iler olacakt\u0131r.<\/p>\n

        Bu \u00f6rnekte 400 \u00f6\u011fenin yeterince temsili bir \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc oldu\u011fu kabul edildi, ancak mant\u0131ksal olarak bu say\u0131 denemeye ba\u011fl\u0131 olarak de\u011fi\u015fecektir. <\/p>\n

        <\/span> Basit Rastgele \u00d6rnekleme T\u00fcrleri<\/span><\/h2>\n

        \u0130ki t\u00fcr basit rastgele \u00f6rnekleme vard\u0131r:<\/p>\n

          \n
        • De\u011fi\u015ftirmeli basit rastgele \u00f6rnekleme<\/strong> : \u00f6rnekleme \u00e7er\u00e7evesinin se\u00e7ilen \u00f6\u011fesi d\u00f6nd\u00fcr\u00fcl\u00fcr ve tekrar se\u00e7ilebilir.<\/li>\n
        • De\u011fi\u015ftirmeden basit rastgele \u00f6rnekleme<\/strong> : \u00d6rne\u011fin par\u00e7as\u0131 olarak se\u00e7ilen \u00f6\u011fe silinir ve art\u0131k se\u00e7ilemez.<\/li>\n<\/ul>\n

          De\u011fi\u015ftirmeli basit rastgele \u00f6rnekleme, numuneden bir \u00f6\u011feyi se\u00e7mek i\u00e7in tamamen ayn\u0131 i\u015flem her zaman tekrarland\u0131\u011f\u0131ndan, en basit \u00f6rnekleme t\u00fcr\u00fcd\u00fcr. Bununla birlikte, yerine koymadan basit rastgele \u00f6rnekleme daha kesin oldu\u011fu i\u00e7in daha yayg\u0131n olarak kullan\u0131lmaktad\u0131r. Her iki t\u00fcr de a\u015fa\u011f\u0131da daha ayr\u0131nt\u0131l\u0131 olarak a\u00e7\u0131klanmaktad\u0131r. <\/p>\n

          <\/span> De\u011fi\u015ftirme ile basit rastgele \u00f6rnekleme<\/span><\/h3>\n

          De\u011fi\u015ftirmeli basit rastgele \u00f6rnekleme,<\/strong> se\u00e7ilen her \u00f6\u011fenin \u00f6rnekleme \u00e7er\u00e7evesine geri g\u00f6nderilmesini ve b\u00f6ylece onu tekrar se\u00e7me olas\u0131l\u0131\u011f\u0131n\u0131n ortaya \u00e7\u0131kmas\u0131n\u0131 i\u00e7erir.<\/p>\n

          Bu nedenle, tek bir \u00f6\u011fenin birden \u00e7ok kez se\u00e7ilmesiyle bir \u00f6rnek elde etmek m\u00fcmk\u00fcnd\u00fcr, ancak bu \u00e7ok d\u00fc\u015f\u00fck bir ihtimaldir.<\/p>\n

          Matematiksel olarak bu \u00e7ok basit bir \u00f6rnekleme t\u00fcr\u00fcd\u00fcr \u00e7\u00fcnk\u00fc her bir \u00e7\u0131karman\u0131n olas\u0131l\u0131\u011f\u0131 ayn\u0131d\u0131r. Bu \u00f6rnekleme tekni\u011fini di\u011ferlerinden \u00f6nce \u00e7al\u0131\u015fmaya ba\u015flaman\u0131n nedeni budur.<\/p>\n

          De\u011fi\u015ftirmeli basit rastgele \u00f6rneklemede, belirli bir s\u0131rayla numune alma olas\u0131l\u0131\u011f\u0131 a\u015fa\u011f\u0131daki form\u00fcl kullan\u0131larak hesaplanabilir:<\/p>\n<\/p>\n

          \"P=\\cfrac{1}{N^n}\"<\/p>\n<\/p>\n

          Olmak<\/p>\n<\/p>\n

          \"N\"<\/p>\n

          pop\u00fclasyonun toplam element say\u0131s\u0131 ve<\/p>\n

          \"n\"<\/p>\n

          Ger\u00e7ekle\u015ftirilecek ba\u011f\u0131ms\u0131z ekstraksiyonlar\u0131n say\u0131s\u0131.<\/p>\n

          S\u0131ra \u00f6nemli olmad\u0131\u011f\u0131nda ise numune alma olas\u0131l\u0131\u011f\u0131 a\u015fa\u011f\u0131daki ifade kullan\u0131larak hesaplan\u0131r:<\/p>\n<\/p>\n

          \"P=\\cfrac{n!}{\\displaystyle<\/p>\n<\/p>\n

          Alt\u0131n<\/p>\n<\/p>\n

          \"n\"<\/p>\n

          ba\u011f\u0131ms\u0131z ekstraksiyonlar\u0131n say\u0131s\u0131d\u0131r,<\/p>\n

          \"z\"<\/p>\n

          \u00d6rnekteki farkl\u0131 elementlerin say\u0131s\u0131 ve<\/p>\n

          \"k_i\"<\/p>\n

          \u00f6\u011fenin ka\u00e7 kez g\u00f6r\u00fcnmesini istiyorsunuz?<\/p>\n

          \"i\"<\/p>\n

          \u00f6rnekte.<\/p>\n

          Son olarak eleman\u0131n dahil olma olas\u0131l\u0131\u011f\u0131n\u0131 bulmak i\u00e7in<\/p>\n<\/p>\n

          \"i\"<\/p>\n

          yani \u00f6\u011fenin dahil edilme olas\u0131l\u0131\u011f\u0131<\/p>\n

          \"i\"<\/p>\n

          \u00d6rnekte a\u015fa\u011f\u0131daki form\u00fcl kullan\u0131lmal\u0131d\u0131r: <\/p>\n<\/p>\n

          \"\\displaystyle<\/p>\n<\/p>\n

          <\/span> De\u011fi\u015ftirilmeden basit rastgele \u00f6rnekleme<\/span><\/h3>\n

          De\u011fi\u015ftirmeden basit rastgele \u00f6rnekleme,<\/strong> bir \u00f6rnekten istenen \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fcn\u00fcn g\u00f6sterdi\u011fi kadar \u00e7ok bireyin se\u00e7ilmesini i\u00e7erir, b\u00f6ylece her birey se\u00e7ildikten sonra tekrar se\u00e7ilemez. Bu nedenle se\u00e7ilen her \u00f6\u011fe silinir ve de\u011fi\u015ftirilmez.<\/p>\n

          Basit tesad\u00fcfi \u00f6rneklemeden bahsetti\u011fimizde, pratikte en \u00e7ok kullan\u0131lan y\u00f6ntem oldu\u011fundan normalde bireylerin de\u011fi\u015ftirilmedi\u011fi \u00f6rneklemeyi kastediyoruz.<\/p>\n

          Basit rastgele \u00f6rneklemede de\u011fi\u015ftirme ile belirli bir s\u0131rayla numune alma olas\u0131l\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in a\u015fa\u011f\u0131daki form\u00fcl kullan\u0131l\u0131r:<\/p>\n<\/p>\n

          \"P=\\cfrac{1}{n!\\begin{pmatrix}N\\\\n\\end{pmatrix}}\"<\/p>\n<\/p>\n

          Olmak<\/p>\n<\/p>\n

          \"N\"<\/p>\n

          Pop\u00fclasyondaki toplam element say\u0131s\u0131 ve<\/p>\n

          \"n\"<\/p>\n

          Ger\u00e7ekle\u015ftirilecek ba\u011f\u0131ml\u0131 ekstraksiyonlar\u0131n say\u0131s\u0131.<\/p>\n

          \u00d6te yandan, ekstraksiyon s\u0131ras\u0131n\u0131n dikkate al\u0131nmamas\u0131 gerekiyorsa numune alma olas\u0131l\u0131\u011f\u0131 \u015funa e\u015fittir:<\/p>\n<\/p>\n

          \"P=\\cfrac{1}{\\begin{pmatrix}N\\\\n\\end{pmatrix}}\"<\/p>\n<\/p>\n

          Son olarak, bir \u00f6\u011fenin de\u011fi\u015ftirilmeden basit rastgele \u00f6rneklemeye dahil edilme olas\u0131l\u0131\u011f\u0131 Laplace kural\u0131 uygulanarak hesaplan\u0131r: <\/p>\n<\/p>\n

          \"\\displaystyle<\/p>\n<\/p>\n

          <\/span> Basit Rastgele \u00d6rneklemenin Avantajlar\u0131 ve Dezavantajlar\u0131<\/span><\/h2>\n

          Basit rastgele \u00f6rneklemenin a\u015fa\u011f\u0131daki avantaj ve dezavantajlar\u0131 vard\u0131r: <\/p>\n

          \n\n\n\n\n\n\n\n\n\n\n
          avantaj<\/th>\n Dezavantajlar\u0131<\/th>\n<\/tr>\n<\/thead>\n
          Anlamas\u0131 kolay.<\/td>\n N\u00fcfusun t\u00fcm unsurlar\u0131n\u0131n bir listesi gereklidir.<\/td>\n<\/tr>\n
          Olas\u0131 t\u00fcm numuneler e\u015fit olas\u0131l\u0131kl\u0131d\u0131r.<\/td>\n B\u00fcy\u00fck \u00f6rneklem boyutlar\u0131nda bu \u00e7ok pahal\u0131 olabilir.<\/td>\n<\/tr>\n
          Temsili numuneler genellikle elde edilir.<\/td>\n Daha b\u00fcy\u00fck \u00f6rnekleme hatalar\u0131na sahip olma e\u011filimindedir.<\/td>\n<\/tr>\n
          Numune alma i\u015flemini ger\u00e7ekle\u015ftirmek i\u00e7in herhangi bir teknik bilgiye gerek yoktur.<\/td>\n Ara\u015ft\u0131rmac\u0131n\u0131n \u00e7al\u0131\u015f\u0131lan alanda sahip olabilece\u011fi bilgiden yararlan\u0131lmaz.<\/td>\n<\/tr>\n
          Ortalamalar\u0131 ve sapmalar\u0131 h\u0131zl\u0131 bir \u015fekilde hesaplaman\u0131za olanak tan\u0131r.<\/td>\n \u00d6rnek \u00e7ok k\u00fc\u00e7\u00fckse temsili olmayabilir.<\/td>\n<\/tr>\n
          Verileri analiz etmek i\u00e7in istatistiksel yaz\u0131l\u0131m var.<\/td>\n Bireysel g\u00f6r\u00fc\u015fme gerektiren \u00e7al\u0131\u015fmalar i\u00e7in uygun de\u011fildir.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\n

          G\u00f6r\u00fcld\u00fc\u011f\u00fc gibi basit rastgele \u00f6rneklemenin temel \u00f6zelliklerinden biri anla\u015f\u0131lmas\u0131n\u0131n ve a\u00e7\u0131klanmas\u0131n\u0131n kolay olmas\u0131d\u0131r. Asl\u0131nda \u00f6rneklemeyi yapan ki\u015finin analiz alan\u0131nda uzman olmas\u0131na gerek yoktur. Ancak bu hem g\u00fc\u00e7l\u00fc hem de zay\u0131f bir noktad\u0131r \u00e7\u00fcnk\u00fc di\u011fer \u00f6rnekleme t\u00fcrlerinde analistin bilgisinden daha iyi \u00f6rnekleme elde etmek i\u00e7in yararlan\u0131labilir.<\/p>\n

          Benzer \u015fekilde, \u00f6rnekleme rastgele oldu\u011fundan, incelenen \u00f6rne\u011fi olu\u015fturacak \u015fu veya bu unsuru alma olas\u0131l\u0131klar\u0131, di\u011fer \u00f6rnekleme t\u00fcrlerinden farkl\u0131 olarak e\u015fit olas\u0131l\u0131kl\u0131d\u0131r.<\/p>\n

          Genellikle pop\u00fclasyonu temsil eden \u00f6rnekler elde edilmesine ra\u011fmen, basit rastgele \u00f6rneklemede \u00f6rnekleme hatas\u0131 di\u011fer \u00f6rnekleme t\u00fcrlerine g\u00f6re b\u00fcy\u00fckt\u00fcr. Ayr\u0131ca bireylerin b\u00fcy\u00fckl\u00fc\u011f\u00fc k\u00fc\u00e7\u00fckse \u00f6rneklem temsili bile olmayabilir.<\/p>\n

          Basit rastgele \u00f6rneklemenin \u00e7ok \u00e7ekici bir \u00f6zelli\u011fi, istatistiksel hesaplamalar\u0131n h\u0131zl\u0131 bir \u015fekilde yap\u0131lmas\u0131na olanak tan\u0131yan bilgisayar programlar\u0131 kullan\u0131larak ger\u00e7ekle\u015ftirilebilmesidir.<\/p>\n

          Son olarak, basit rastgele \u00f6rneklemenin, \u00f6zellikle geni\u015f bir alana yay\u0131lm\u0131\u015f pop\u00fclasyonlarda, di\u011fer \u00f6rnekleme t\u00fcrlerinden daha pahal\u0131 olabilece\u011fi, \u00e7\u00fcnk\u00fc ara\u015ft\u0131rma i\u00e7in daha fazla kaynak kullan\u0131lmas\u0131n\u0131 gerektirebilece\u011fi unutulmamal\u0131d\u0131r. \u00d6rne\u011fin, rastgele \u00f6rnekleme oldu\u011fu i\u00e7in, \u00e7al\u0131\u015fmay\u0131 y\u00fcr\u00fctmek \u00fczere se\u00e7ilen ki\u015filer co\u011frafi olarak \u00e7ok geni\u015f bir alana da\u011f\u0131lm\u0131\u015f olabilir ve bu nedenle y\u00fcz y\u00fcze g\u00f6r\u00fc\u015fme yapmak \u00e7ok daha pahal\u0131 olabilir.<\/p>\n","protected":false},"excerpt":{"rendered":"

          Bu makalede basit rastgele numunenin ne oldu\u011funu ve ne t\u00fcr basit rastgele numunelerin bulundu\u011funu \u00f6\u011freneceksiniz. Ayr\u0131ca basit rastgele \u00f6rneklemenin nas\u0131l yap\u0131ld\u0131\u011f\u0131n\u0131 bir \u00f6rnek \u00fczerinden a\u00e7\u0131kl\u0131yoruz. Son olarak basit rastgele \u00f6rneklemenin avantaj ve dezavantajlar\u0131n\u0131n neler oldu\u011funu g\u00f6rebileceksiniz. Basit rastgele \u00f6rnekleme nedir? \u0130statistikte basit rastgele \u00f6rnekleme , bir \u00e7al\u0131\u015fma i\u00e7in \u00f6rneklemi se\u00e7mek i\u00e7in kullan\u0131lan olas\u0131l\u0131ksal bir y\u00f6ntemdir. […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[14],"tags":[],"class_list":["post-51","post","type-post","status-publish","format-standard","hentry","category-istatistik"],"yoast_head":"\n\u25b7 Basit rastgele \u00f6rnekleme nedir? 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