{"id":52,"date":"2023-08-06T01:14:35","date_gmt":"2023-08-06T01:14:35","guid":{"rendered":"https:\/\/statorials.org\/tr\/tabakali-ornekleme\/"},"modified":"2023-08-06T01:14:35","modified_gmt":"2023-08-06T01:14:35","slug":"tabakali-ornekleme","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/tabakali-ornekleme\/","title":{"rendered":"Tabakal\u0131 \u00f6rnekleme"},"content":{"rendered":"

Bu yaz\u0131m\u0131zda tabakal\u0131 \u00f6rneklemenin ne oldu\u011funu ve nas\u0131l yap\u0131ld\u0131\u011f\u0131n\u0131 anlataca\u011f\u0131z. Burada tabakal\u0131 \u00f6rneklemenin alt t\u00fcrlerinin a\u00e7\u0131klamas\u0131n\u0131 ve son olarak tabakal\u0131 \u00f6rneklemenin avantaj ve dezavantajlar\u0131n\u0131n neler oldu\u011funu bulacaks\u0131n\u0131z. <\/p>\n

<\/span> Tabakal\u0131 \u00f6rnekleme nedir?<\/span><\/h2>\n

Tabakal\u0131 \u00f6rnekleme,<\/strong> pop\u00fclasyonu gruplara (tabaka ad\u0131 verilen) b\u00f6lerek bir numunenin \u00f6\u011felerini se\u00e7mek i\u00e7in kullan\u0131lan istatistiksel bir y\u00f6ntemdir. Yani tabakal\u0131 \u00f6rneklemede evren tabakalara b\u00f6l\u00fcn\u00fcr ve her tabakadan bireyler rastgele se\u00e7ilerek \u00e7al\u0131\u015fma \u00f6rnekleminin tamam\u0131 olu\u015fturulur.<\/p>\n

Tabakalar homojen gruplard\u0131r, yani bir tabakadaki bireylerin kendilerini di\u011fer tabakalardan ay\u0131ran kendilerine has \u00f6zellikleri vard\u0131r. Bu nedenle bir birey yaln\u0131zca bir katmana ait olabilir. <\/p>\n

\n
\"tabakal\u0131<\/figure>\n<\/div>\n

Tabakal\u0131 \u00f6rnekleme, pop\u00fclasyonun birbirinden \u00e7ok farkl\u0131, \u00e7ok homojen gruplardan olu\u015ftu\u011fu durumlarda \u00e7ok faydal\u0131d\u0131r.<\/p>\n

Mant\u0131ksal olarak, t\u00fcm katmanlar\u0131n boyutlar\u0131n\u0131n toplam\u0131 istatistiksel pop\u00fclasyonun boyutunu verir:<\/p>\n<\/p>\n

\"N=N_1+N_2+N_3+\\dots+N_k\"<\/p>\n<\/p>\n

Benzer \u015fekilde, her tabakada se\u00e7ilen \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fcn\u00fcn toplam\u0131, istatistiksel \u00e7al\u0131\u015fman\u0131n toplam \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fcne e\u015fittir:<\/p>\n<\/p>\n

\"n=n_1+n_2+n_3+\\dots+n_k\"<\/p>\n<\/p>\n

S\u0131ras\u0131yla pop\u00fclasyonu veya \u00f6rne\u011fi belirtmek i\u00e7in genellikle b\u00fcy\u00fck ve k\u00fc\u00e7\u00fck harfler aras\u0131nda ayr\u0131m yapar\u0131z. <\/p>\n

<\/span> Tabakal\u0131 \u00f6rnekleme nas\u0131l yap\u0131l\u0131r<\/span><\/h2>\n

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

    \n
  1. Hedef pop\u00fclasyonu tan\u0131mlay\u0131n.<\/span><\/li>\n
  2. De\u011fi\u015fken tabakala\u015fmay\u0131<\/strong> ve ka\u00e7 tabaka olaca\u011f\u0131n\u0131 se\u00e7in.<\/span><\/li>\n
  3. N\u00fcfusun her bir unsurunun hangi tabakaya ait oldu\u011funu belirleyin.<\/strong><\/span><\/li>\n
  4. Numunenin bir par\u00e7as\u0131 olacak her tabakan\u0131n boyutunu<\/strong> hesaplay\u0131n.<\/span><\/li>\n
  5. \u00c7al\u0131\u015fma \u00f6rne\u011fine ait olacak her katmandan \u00f6\u011feleri rastgele se\u00e7in<\/strong> . Her katman i\u00e7in \u00f6nceki ad\u0131mda kararla\u015ft\u0131r\u0131ld\u0131\u011f\u0131 kadar \u00e7ok \u00f6\u011fe se\u00e7ilmelidir.<\/span><\/li>\n<\/ol>\n

    \u00d6rnekte her katman\u0131n temsil edece\u011fi boyutun yaln\u0131zca katman\u0131n boyutuna de\u011fil ayn\u0131 zamanda katmanl\u0131 \u00f6rneklemenin t\u00fcr\u00fcne de ba\u011fl\u0131 oldu\u011funu unutmay\u0131n. Daha sonra, her bir tabakal\u0131 \u00f6rnekleme t\u00fcr\u00fc a\u00e7\u0131klanmakta ve bir \u00f6rnek kullan\u0131larak her bir tabakan\u0131n \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fcn\u00fcn nas\u0131l hesapland\u0131\u011f\u0131 anlat\u0131lmaktad\u0131r. <\/p>\n

    <\/span> Tabakal\u0131 \u00d6rnekleme T\u00fcrleri<\/span><\/h2>\n

    Art\u0131k tabakal\u0131 \u00f6rneklemenin tan\u0131m\u0131n\u0131 bildi\u011finize g\u00f6re, a\u015fa\u011f\u0131daki \u015fekilde s\u0131n\u0131fland\u0131r\u0131lan \u00e7e\u015fitli tabakal\u0131 \u00f6rnekleme t\u00fcrleri oldu\u011funu bilmelisiniz:<\/p>\n

      \n
    • Orant\u0131l\u0131 tabakal\u0131 \u00f6rnekleme<\/strong><\/li>\n
    • Tekd\u00fcze Tabakal\u0131 \u00d6rnekleme<\/strong><\/li>\n
    • \u00d6rnekleme<\/span> optimaldir<\/strong><\/li>\n<\/ul>\n

      Her bir tabakal\u0131 \u00f6rnekleme t\u00fcr\u00fc, her birinin anlam\u0131n\u0131 daha iyi anlamak i\u00e7in a\u015fa\u011f\u0131da ayr\u0131nt\u0131l\u0131 olarak a\u00e7\u0131klanmaktad\u0131r. <\/p>\n

      <\/span> Orant\u0131l\u0131 tabakal\u0131 \u00f6rnekleme<\/span><\/h3>\n

      Tabakal\u0131 orant\u0131l\u0131 \u00f6rneklemede<\/strong> veya orant\u0131l\u0131 tahsis \u00f6rneklemesinde, \u00e7al\u0131\u015fma \u00f6rne\u011finin par\u00e7as\u0131 olan her tabakadan gelen \u00f6\u011felerin say\u0131s\u0131, her tabakan\u0131n boyutuyla orant\u0131l\u0131d\u0131r.<\/p>\n

      Dolay\u0131s\u0131yla, e\u011fer bir tabaka di\u011ferinden daha b\u00fcy\u00fckse, son \u00f6rnek o tabakadan daha fazla element i\u00e7erecektir. \u00d6te yandan, e\u011fer bir katman di\u011ferinden daha k\u00fc\u00e7\u00fckse istatistiksel analiz \u00f6rne\u011finde bu katmandan daha az \u00f6\u011fe bulunacakt\u0131r.<\/p>\n

      Bu t\u00fcr katmanl\u0131 \u00f6rnekleme, katmanlar farkl\u0131 boyutlarda oldu\u011funda ve \u00f6rne\u011fin daha b\u00fcy\u00fck katmanlardan daha fazla \u00f6\u011fe i\u00e7ermesini istedi\u011fimizde kullan\u0131\u015fl\u0131d\u0131r.<\/p>\n

      Numunede yer alacak her tabakadaki elementlerin say\u0131s\u0131n\u0131 hesaplamak<\/strong> i\u00e7in, her tabakan\u0131n boyutunun t\u00fcm tabakalar\u0131n boyutlar\u0131n\u0131n toplam\u0131na b\u00f6l\u00fcnmesi gerekir. Sonu\u00e7, numuneye dahil edilmesi gereken tabakan\u0131n oran\u0131 olacakt\u0131r, dolay\u0131s\u0131yla bunun istenen numune boyutuyla \u00e7arp\u0131lmas\u0131 gerekecektir.<\/p>\n<\/p>\n

      \"n_i=n\\cdot<\/p>\n<\/p>\n

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

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

      istenen toplam numune b\u00fcy\u00fckl\u00fc\u011f\u00fcd\u00fcr,<\/p>\n

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

      tabakadaki elementlerin say\u0131s\u0131<\/p>\n

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

      \u00f6rne\u011fe dahil edilecek,<\/p>\n

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

      katman boyutu<\/p>\n

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

      , Ve<\/p>\n

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

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

      \u00d6rne\u011fin 150 \u00e7al\u0131\u015fan\u0131 olan bir \u015firkette 50 ki\u015filik bir \u00f6rneklem alarak verileri \u00e7al\u0131\u015fanlar\u0131n ya\u015flar\u0131na g\u00f6re katmanland\u0131rarak bir \u00e7al\u0131\u015fma yapmak istedi\u011fimizi d\u00fc\u015f\u00fcn\u00fcn. Verileri \u015fu \u015fekilde s\u0131n\u0131fland\u0131rabiliriz:<\/p>\n

        \n
      • 20 ila 29 ya\u015f aras\u0131: 35 i\u015f\u00e7i<\/li>\n
      • 30 ila 39 ya\u015f aras\u0131: 57 \u00e7al\u0131\u015fan<\/li>\n
      • 40 ila 49 ya\u015f aras\u0131: 42 \u00e7al\u0131\u015fan<\/li>\n
      • 50 ila 59 ya\u015f aras\u0131: 16 \u00e7al\u0131\u015fan<\/li>\n<\/ul>\n

        Dolay\u0131s\u0131yla verileri orant\u0131l\u0131 olarak katmanland\u0131r\u0131rsak \u00f6rnekleme \u015fu \u015fekilde olacakt\u0131r: <\/p>\n

        \n
        \"orant\u0131l\u0131<\/figure>\n<\/div>\n

        <\/span> Tekd\u00fcze Tabakal\u0131 \u00d6rnekleme<\/span><\/h3>\n

        Tekd\u00fcze tabakal\u0131 \u00f6rneklemede<\/strong> veya tek tip ekleme \u00f6rneklemesinde, her tabakadan \u00e7al\u0131\u015fma \u00f6rne\u011finin par\u00e7as\u0131 olan \u00f6\u011felerin say\u0131s\u0131 e\u015fittir.<\/p>\n

        Dolay\u0131s\u0131yla bu t\u00fcr \u00f6rneklemede her tabaka ayn\u0131 a\u011f\u0131rl\u0131\u011fa sahiptir. Bir tabakan\u0131n di\u011fer tabakadan daha fazla ya da daha az bireyi olsun, hepsi \u00f6rnekte ayn\u0131 say\u0131da birey taraf\u0131ndan temsil edilecektir.<\/p>\n

        Bu durumda, her katmandaki elemanlar\u0131n boyutunu hesaplamak<\/strong> i\u00e7in istenen \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fcn\u00fcn mevcut katman say\u0131s\u0131na b\u00f6l\u00fcnmesi gerekir. Ba\u015fka bir deyi\u015fle a\u015fa\u011f\u0131daki form\u00fcl kullan\u0131lmal\u0131d\u0131r:<\/p>\n<\/p>\n

        \"n_i=\\cfrac{n}{k}\"<\/p>\n<\/p>\n

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

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

        istenen toplam numune b\u00fcy\u00fckl\u00fc\u011f\u00fcd\u00fcr,<\/p>\n

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

        tabakadaki elementlerin say\u0131s\u0131<\/p>\n

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

        \u00f6rne\u011fe kimlerin dahil edilece\u011fi ve<\/p>\n

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

        N\u00fcfusun b\u00f6l\u00fcnd\u00fc\u011f\u00fc katmanlar\u0131n say\u0131s\u0131.<\/p>\n

        \u00d6nceki \u00f6rne\u011fi takip edersek, 50 i\u015f\u00e7iden olu\u015fan bir \u00f6rnek istedi\u011fimizden ve toplamda 4 farkl\u0131 katman oldu\u011fundan, her katman\u0131n \u00f6rnek boyutu \u015f\u00f6yle olacakt\u0131r:<\/p>\n<\/p>\n

        \"n_i=\\cfrac{50}{4}=12,5\"<\/p>\n<\/p>\n

        Sonu\u00e7 ondal\u0131k bir say\u0131 oldu\u011fundan, 50 i\u015f\u00e7iye ula\u015fana kadar baz\u0131 katmanlarda 12, di\u011ferlerinde 13 i\u015f\u00e7i olacakt\u0131r. Yani tekd\u00fcze tabakal\u0131 \u00f6rnekleme a\u015fa\u011f\u0131daki gibidir: <\/p>\n

        \n
        \"tekd\u00fcze<\/figure>\n<\/div>\n

        G\u00f6rd\u00fc\u011f\u00fcn\u00fcz gibi her tabakan\u0131n \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc her birinin oran\u0131ndan ba\u011f\u0131ms\u0131zd\u0131r. <\/p>\n

        <\/span>Optimum katmanl\u0131 \u00f6rnekleme<\/span><\/h3>\n

        Optimal tabakal\u0131 \u00f6rneklemede<\/strong> , her tabakadaki elementlerin say\u0131s\u0131, her tabakan\u0131n de\u011fi\u015fkenli\u011fine orant\u0131l\u0131 olarak ba\u011fl\u0131d\u0131r.<\/p>\n

        Bu nedenle, daha fazla de\u011fi\u015fkenli\u011fe sahip katmanlar daha b\u00fcy\u00fck bir \u00f6rneklem boyutuna sahip olacak ve tam tersi, daha az de\u011fi\u015fkenli\u011fe sahip katmanlar daha k\u00fc\u00e7\u00fck bir \u00f6rneklem boyutuna sahip olacakt\u0131r.<\/p>\n

        Her katmandan ka\u00e7 \u00f6\u011fenin istatistiksel \u00e7al\u0131\u015fma \u00f6rne\u011finin par\u00e7as\u0131 olaca\u011f\u0131n\u0131 belirleme form\u00fcl\u00fc a\u015fa\u011f\u0131daki gibidir:<\/p>\n<\/p>\n

        \"n_i=n\\cdot<\/p>\n<\/p>\n

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

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

        istenen toplam numune b\u00fcy\u00fckl\u00fc\u011f\u00fcd\u00fcr,<\/p>\n

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

        katmandaki elementlerin say\u0131s\u0131d\u0131r<\/p>\n

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

        \u00f6rne\u011fe dahil edilecek,<\/p>\n

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

        tabakan\u0131n standart sapmas\u0131 (veya tipik sapmas\u0131)<\/p>\n

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

        , Ve<\/p>\n

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

        tabakan\u0131n b\u00fcy\u00fckl\u00fc\u011f\u00fc<\/p>\n

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

        . <\/p>\n

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

        Tabakal\u0131 \u00f6rneklemenin a\u015fa\u011f\u0131daki avantajlar\u0131 ve dezavantajlar\u0131 vard\u0131r: <\/p>\n

        \n\n\n\n\n\n\n\n\n
        avantaj<\/th>\n Dezavantajlar\u0131<\/th>\n<\/tr>\n<\/thead>\n
        Yaln\u0131zca n\u00fcfusun tamam\u0131n\u0131 de\u011fil, ayn\u0131 zamanda her bir katman\u0131 da istatistiksel olarak incelemeyi m\u00fcmk\u00fcn k\u0131lar.<\/td>\n Bu, uygulanmas\u0131 karma\u015f\u0131k bir \u00f6rnekleme y\u00f6ntemidir.<\/td>\n<\/tr>\n
        Tabakal\u0131 \u00f6rneklemenin yapt\u0131\u011f\u0131 \u00f6rnekleme hatas\u0131 her zaman basit rastgele \u00f6rneklemeninkine e\u015fit veya ondan daha azd\u0131r.<\/td>\n Bu zaman al\u0131c\u0131 ve dolay\u0131s\u0131yla pahal\u0131 bir numune alma i\u015flemidir.<\/td>\n<\/tr>\n
        Ara\u015ft\u0131rmac\u0131n\u0131n pop\u00fclasyon hakk\u0131ndaki bilgisinden yararlanman\u0131za olanak tan\u0131r.<\/td>\n Analiz edilen numuneyi katmanland\u0131rabilmek i\u00e7in \u00e7ok fazla bilgiye ihtiya\u00e7 vard\u0131r.<\/td>\n<\/tr>\n
        Tabakal\u0131 \u00f6rnekleme ile her tabakadan en az bir unsurun \u00f6rne\u011fe dahil edilmesini sa\u011fl\u0131yoruz.<\/td>\n \u00d6rnekleme yapabilmek i\u00e7in her tabakan\u0131n oran\u0131n\u0131n bilinmesi gerekir.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\n

        Tabakal\u0131 \u00f6rneklemenin temel \u00f6zelli\u011fi, pop\u00fclasyonun b\u00f6l\u00fcnd\u00fc\u011f\u00fc her grubu veya tabakay\u0131 istatistiksel olarak analiz etmek i\u00e7in kullan\u0131lmas\u0131d\u0131r. Elbette bu t\u00fcr \u00f6rneklemeyle evrenin tamam\u0131 da incelenebilir. Ek olarak, katmanlar\u0131n birbirinden farkl\u0131 olmas\u0131 durumunda veri katmanla\u015ft\u0131rman\u0131n faydalar\u0131 daha fazla olacakt\u0131r.<\/p>\n

        Tam tersine, \u00f6rneklemeyi ger\u00e7ekle\u015ftirebilmek i\u00e7in verilerin katmanla\u015ft\u0131r\u0131lmas\u0131, \u00f6rneklemenin karma\u015f\u0131kl\u0131\u011f\u0131n\u0131n artt\u0131\u011f\u0131n\u0131, katmanl\u0131 \u00f6rneklemenin ger\u00e7ekle\u015ftirilmesinin di\u011fer \u00f6rnekleme t\u00fcrlerine g\u00f6re daha karma\u015f\u0131k oldu\u011funu ima eder. Bu \u00f6zellik ayn\u0131 zamanda tabakala\u015fman\u0131n do\u011fru \u015fekilde yap\u0131lmas\u0131 zaman ald\u0131\u011f\u0131ndan, bunun yap\u0131lmas\u0131n\u0131n pahal\u0131 bir \u00f6rnek oldu\u011funu da ima eder.<\/p>\n

        Tabakal\u0131 \u00f6rneklemenin di\u011fer bir dezavantaj\u0131, \u00e7al\u0131\u015fmak istenen pop\u00fclasyon hakk\u0131nda \u00e7ok fazla bilgi gerektirmesidir; bu, basit rastgele \u00f6rnekleme gibi di\u011fer \u00f6rnekleme t\u00fcrlerinde gerekli de\u011fildir. Ancak ara\u015ft\u0131rmac\u0131n\u0131n bu alanda yeterli bilgiye sahip olmas\u0131 durumunda bu dezavantaj azalt\u0131labilir.<\/p>\n

        Son olarak, katmanl\u0131 \u00f6rneklemeyle, di\u011fer \u00f6rnekleme t\u00fcrlerine g\u00f6re pop\u00fclasyonu daha iyi temsil eden bir \u00f6rnek elde ederiz \u00e7\u00fcnk\u00fc her katmandan \u00f6\u011felerin dahil edilmesini sa\u011flar\u0131z. Bunun aksine, di\u011fer \u00f6rneklerde, elde edilen \u00f6rnek herhangi bir tabakadan herhangi bir \u00f6\u011fe i\u00e7ermeyebilir.<\/p>\n","protected":false},"excerpt":{"rendered":"

        Bu yaz\u0131m\u0131zda tabakal\u0131 \u00f6rneklemenin ne oldu\u011funu ve nas\u0131l yap\u0131ld\u0131\u011f\u0131n\u0131 anlataca\u011f\u0131z. Burada tabakal\u0131 \u00f6rneklemenin alt t\u00fcrlerinin a\u00e7\u0131klamas\u0131n\u0131 ve son olarak tabakal\u0131 \u00f6rneklemenin avantaj ve dezavantajlar\u0131n\u0131n neler oldu\u011funu bulacaks\u0131n\u0131z. Tabakal\u0131 \u00f6rnekleme nedir? Tabakal\u0131 \u00f6rnekleme, pop\u00fclasyonu gruplara (tabaka ad\u0131 verilen) b\u00f6lerek bir numunenin \u00f6\u011felerini se\u00e7mek i\u00e7in kullan\u0131lan istatistiksel bir y\u00f6ntemdir. Yani tabakal\u0131 \u00f6rneklemede evren tabakalara b\u00f6l\u00fcn\u00fcr ve her […]<\/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-52","post","type-post","status-publish","format-standard","hentry","category-istatistik"],"yoast_head":"\n\u25b7 Tabakal\u0131 \u00f6rnekleme nedir? 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