{"id":245,"date":"2023-08-03T17:04:50","date_gmt":"2023-08-03T17:04:50","guid":{"rendered":"https:\/\/statorials.org\/tr\/ornek-boyut\/"},"modified":"2023-08-03T17:04:50","modified_gmt":"2023-08-03T17:04:50","slug":"ornek-boyut","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/ornek-boyut\/","title":{"rendered":"\u00d6rnek boyut"},"content":{"rendered":"<p>Bu makalede \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fcn\u00fcn ne oldu\u011fu ve istatistikte neden \u00f6nemli oldu\u011fu a\u00e7\u0131klanmaktad\u0131r. Ek olarak, uygun \u00f6rneklem boyutunun nas\u0131l hesaplanaca\u011f\u0131n\u0131 ve \u00e7\u00f6z\u00fclm\u00fc\u015f bir al\u0131\u015ft\u0131rmay\u0131 ke\u015ffederek bunun nas\u0131l yap\u0131ld\u0131\u011f\u0131n\u0131 g\u00f6rebilirsiniz. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-el-tamano-de-la-muestra\"><\/span> \u00d6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc nedir?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>\u00d6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc<\/strong> (veya <strong>\u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc<\/strong> ), bir \u00e7al\u0131\u015fman\u0131n \u00f6rne\u011fini olu\u015fturan bireylerin say\u0131s\u0131d\u0131r. \u0130statistiklerde \u00f6rneklemin t\u00fcm pop\u00fclasyonu temsil edebilmesi i\u00e7in \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc \u00f6nemlidir.<\/p>\n<p> Bu nedenle istatistiksel bir \u00e7al\u0131\u015fman\u0131n \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fcn\u00fcn, evrenin tamam\u0131n\u0131n \u00f6zelliklerini temsil edecek kadar b\u00fcy\u00fck olmas\u0131 gerekir. \u00d6te yandan, \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc a\u015f\u0131r\u0131 b\u00fcy\u00fck olamaz \u00e7\u00fcnk\u00fc ara\u015ft\u0131rma daha pahal\u0131 hale gelir. Sonu\u00e7 olarak \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc yeterli olmal\u0131, ne \u00e7ok b\u00fcy\u00fck ne de \u00e7ok k\u00fc\u00e7\u00fck olmal\u0131d\u0131r.<\/p>\n<p> \u00d6rne\u011fin bir \u00fclkenin boy uzunlu\u011funa ili\u015fkin bir analiz yapmak istiyorsak, o \u00fclkede ya\u015fayan herkesin boyunu isteyemeyiz \u00e7\u00fcnk\u00fc ara\u015ft\u0131rma uzun zaman al\u0131r ve \u00e7ok pahal\u0131 olur. Bu nedenle rastgele \u00f6rnekleme yap\u0131lmas\u0131 ve pop\u00fclasyonun yaln\u0131zca temsili bir \u00f6rne\u011fiyle r\u00f6portaj yap\u0131lmas\u0131 gereklidir. <\/p>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 20px; padding-left: 30px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Bak\u0131n\u0131z:<\/strong> <a href=\"https:\/\/statorials.org\/tr\/ornekleme-turleri\/\">\u00d6rnekleme t\u00fcrleri<\/a><\/div>\n<p> Peki uygun \u00f6rnek boyutunu nas\u0131l bilebiliriz? Bir sonraki b\u00f6l\u00fcmde ara\u015ft\u0131rma gereksinimlerine g\u00f6re uygun \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fcn\u00fcn nas\u0131l belirlenece\u011fini g\u00f6rece\u011fiz. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"como-calcular-el-tamano-de-la-muestra\"><\/span> \u00d6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc nas\u0131l hesaplan\u0131r<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Bir ortalamay\u0131 tahmin etmek i\u00e7in gerekli numune boyutu, Z <sub>\u03b1\/2&#8217;nin<\/sub> karesinin standart sapma (\u03c3) ile istenen hata marj\u0131na (e) b\u00f6l\u00fcnmesine e\u015fittir. Bu nedenle <strong>\u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fcn\u00fc hesaplama form\u00fcl\u00fc<\/strong> \u015fu \u015fekildedir:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-ddd725a5b2cefc85de7e4ca67694863a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle n=\\left(\\frac{Z_{\\alpha\/2}\\cdot\\sigma}{e}\\right)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"47\" width=\"130\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:7px\"> Alt\u0131n:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:7px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-ec4217f4fa5fcd92a9edceba0e708cf7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fcd\u00fcr.<\/li>\n<li style=\"margin-bottom:7px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-5f44d9bbc8046069be4aa2989bff19aa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\alpha\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> istenilen anlaml\u0131l\u0131k d\u00fczeyidir. Bunu dikkate alarak<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-5280f4c3615553fc7f5a96263d8db651_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"1-\\alpha\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"41\" style=\"vertical-align: 0px;\"><\/p>\n<p> istenilen g\u00fcven d\u00fczeyidir.<\/li>\n<li style=\"margin-bottom:7px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-6f8ee37ecf97c2a7c7d6dbe8fddddc27_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Z_{\\alpha\/2}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"34\" style=\"vertical-align: -8px;\"><\/p>\n<p> \u03b1\/2 olas\u0131l\u0131\u011f\u0131na kar\u015f\u0131l\u0131k gelen standart normal da\u011f\u0131l\u0131m\u0131n niceli\u011fidir. B\u00fcy\u00fck \u00f6rneklem b\u00fcy\u00fckl\u00fckleri ve %95 g\u00fcven d\u00fczeyi i\u00e7in genellikle 1,96&#8217;ya, %99 g\u00fcven d\u00fczeyi i\u00e7in ise genellikle 2,576&#8217;ya yak\u0131nd\u0131r.<\/li>\n<li style=\"margin-bottom:7px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-eaaf379fee5e67946f3fedf5631047b1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sigma\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> standart sapmad\u0131r.<\/li>\n<\/ul>\n<p> Bu form\u00fclde pop\u00fclasyon b\u00fcy\u00fckl\u00fc\u011f\u00fcn\u00fcn sonsuz oldu\u011fu, yani pop\u00fclasyon b\u00fcy\u00fckl\u00fc\u011f\u00fcn\u00fcn \u00e7ok b\u00fcy\u00fck oldu\u011fu veya bilinmedi\u011fi varsay\u0131ld\u0131\u011f\u0131n\u0131 unutmay\u0131n.<\/p>\n<p> <strong>Not:<\/strong> Yukar\u0131daki form\u00fcl <a href=\"https:\/\/statorials.org\/tr\/ortalama-icin-guven-araligi\/\">ortalama i\u00e7in g\u00fcven form\u00fcl\u00fc aral\u0131\u011f\u0131ndan<\/a> t\u00fcretilmi\u015ftir. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-del-calculo-del-tamano-de-una-muestra\"><\/span> \u00d6rnek b\u00fcy\u00fckl\u00fc\u011f\u00fc hesaplama \u00f6rne\u011fi<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Bu b\u00f6l\u00fcmde \u00f6rnek olarak istatistiksel bir ara\u015ft\u0131rma i\u00e7in uygun \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fcn\u00fc hesaplayaca\u011f\u0131z.<\/p>\n<ul>\n<li> Bir pop\u00fclasyonun standart sapmas\u0131n\u0131n 15 civar\u0131nda oldu\u011funu biliyoruz ancak ortalamas\u0131n\u0131 bilmiyoruz, bu nedenle ortalamay\u0131 tahmin etmek i\u00e7in bir \u00e7al\u0131\u015fma yapmak istiyoruz. %95 g\u00fcven d\u00fczeyinde \u00b12 hata pay\u0131 istiyorsak hangi \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fcne ihtiyac\u0131m\u0131z var?<\/li>\n<\/ul>\n<p> Yukar\u0131da g\u00f6rd\u00fc\u011f\u00fcm\u00fcz gibi \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fcn\u00fc hesaplama form\u00fcl\u00fc \u015fu \u015fekildedir:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-ddd725a5b2cefc85de7e4ca67694863a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle n=\\left(\\frac{Z_{\\alpha\/2}\\cdot\\sigma}{e}\\right)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"47\" width=\"130\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> Bu durumda istenen g\u00fcven d\u00fczeyi %95&#8217;tir, dolay\u0131s\u0131yla kar\u015f\u0131l\u0131k gelen Z <sub>\u03b1\/2<\/sub> de\u011feri 1,96&#8217;d\u0131r. <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-776a555edd1d064cf29a3a354caa5325_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"1-\\alpha=0,95 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\alpha=0,05 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black}\\ \\alpha\/2=0,025\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"534\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-54dda39d0da5b29f2d25728b89565859_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}Z_{\\alpha\/2}= \\ \\color{orange}\\bm{?}\\\\[4ex]Z_{0,025}=1,96\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"71\" width=\"127\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 20px; padding-left: 30px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Bak\u0131n\u0131z:<\/strong> <a href=\"https:\/\/statorials.org\/tr\/bir-guven-seviyesi\/\">G\u00fcven d\u00fczeyi de\u011ferlerini i\u00e7eren tablo<\/a><\/div>\n<p> Son olarak, art\u0131k t\u00fcm parametrelerin ne kadar de\u011ferli oldu\u011funu bildi\u011fimize g\u00f6re, de\u011ferlerini form\u00fclde yerine koyar\u0131z ve \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fcn\u00fc hesaplar\u0131z:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-dd8e2d30042f759051fb52c5c55ade44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\displaystyle n&amp;=\\left(\\frac{Z_{\\alpha\/2}\\cdot\\sigma}{e}\\right)^2\\\\[2ex] n&amp;=\\left(\\frac{1,96\\cdot 15}{2}\\right)^2\\\\[2ex] n&amp;=216,09 \\approx 217 \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"155\" width=\"137\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> K\u0131sacas\u0131, istenen gereksinimlere sahip pop\u00fclasyon ortalamas\u0131n\u0131 tahmin etmek i\u00e7in en az 217 ki\u015fiden olu\u015fan bir \u00f6rne\u011fe ihtiyac\u0131m\u0131z var. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"tamano-de-la-muestra-nivel-de-confianza-y-margen-de-error\"><\/span> \u00d6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc, g\u00fcven d\u00fczeyi ve hata pay\u0131<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> G\u00fcven d\u00fczeyine ve gerekli hata pay\u0131na ba\u011fl\u0131 olarak gerekli \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc de\u011fi\u015fecektir. Dolay\u0131s\u0131yla \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc, g\u00fcven d\u00fczeyi ve hata pay\u0131 \u015fu \u015fekilde ili\u015fkilidir:<\/p>\n<ol style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">\u00d6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc ve g\u00fcven d\u00fczeyi do\u011fru orant\u0131l\u0131d\u0131r. Yani g\u00fcven d\u00fczeyi artt\u0131k\u00e7a \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc de artacakt\u0131r.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">\u00d6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc ile hata pay\u0131 ters orant\u0131l\u0131d\u0131r. Yani hata pay\u0131 artarsa \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc azalacakt\u0131r.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">Bu nedenle \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fcn\u00fc art\u0131rmak g\u00fcven d\u00fczeyini art\u0131rabilir veya hata pay\u0131n\u0131 azaltabilir.<\/span> <\/li>\n<\/ol>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"otras-formulas-del-tamano-de-una-muestra\"><\/span> Di\u011fer numune b\u00fcy\u00fckl\u00fc\u011f\u00fc form\u00fclleri<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Tahmin edilecek parametreye ba\u011fl\u0131 olarak gerekli \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc form\u00fcl\u00fc biraz de\u011fi\u015fir. Bu nedenle bu b\u00f6l\u00fcmde baz\u0131 \u00f6zel durumlarda \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fcn\u00fcn hesaplanmas\u0131nda faydal\u0131 olabilecek di\u011fer form\u00fclleri g\u00f6rece\u011fiz. <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"tamano-de-la-muestra-de-una-proporcion\"><\/span> bir oran\u0131n \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> Bir oran\u0131 (p) tahmin etmek i\u00e7in gereken \u00f6rnek boyutunu hesaplama form\u00fcl\u00fc \u015f\u00f6yledir: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-b9c850fbd64ce3f5024b580699beeea6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n=\\cfrac{N\\cdot Z_{\\alpha\/2}^2\\cdot p\\cdot (1-p)}{e^2\\cdot (N-1)+Z_{\\alpha\/2}^2\\cdot p\\cdot (1-p)}\" title=\"Rendered by QuickLaTeX.com\" height=\"55\" width=\"271\" style=\"vertical-align: -23px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"tamano-de-la-muestra-de-una-probabilidad\"><\/span> Bir olas\u0131l\u0131\u011f\u0131n \u00f6rnek b\u00fcy\u00fckl\u00fc\u011f\u00fc<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> Bir olas\u0131l\u0131\u011f\u0131 tahmin etmek istedi\u011finizde gerekli \u00f6rnek boyutunu belirlemek i\u00e7in a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullanman\u0131z \u00f6nerilir: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-7326a4beac1d233ca698f7dad2a2bc2f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle n=\\left(\\frac{Z_{\\alpha\/2}}{2\\cdot e}\\right)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"47\" width=\"107\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"tamano-de-la-muestra-para-la-comparacion-de-dos-medias-independientes\"><\/span> \u0130ki ba\u011f\u0131ms\u0131z ortalamay\u0131 kar\u015f\u0131la\u015ft\u0131rmak i\u00e7in \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> \u0130ki ba\u011f\u0131ms\u0131z ortalamay\u0131 belirli bir \u03b1 riski ve \u03b2 riskiyle kar\u015f\u0131la\u015ft\u0131r\u0131rken \u00f6rneklem boyutunu hesaplama form\u00fcl\u00fc a\u015fa\u011f\u0131daki gibidir:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-d4be37582bdec1aa6b75b35e4d937114_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n=\\cfrac{2\\cdot \\sigma^2 \\cdot \\left(Z_{\\alpha\/2}+Z_\\beta\\right)}{\\Delta^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"184\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Alt\u0131n<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-b7305a6cb6d013542b2aa8af4e001985_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\Delta\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"14\" style=\"vertical-align: 0px;\"><\/p>\n<p> alternatif hipotezin iki arac\u0131 aras\u0131ndaki farkt\u0131r. <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"tamano-de-la-muestra-para-la-comparacion-de-dos-medias-apareadas\"><\/span> \u0130ki e\u015fle\u015ftirilmi\u015f ortalamay\u0131 kar\u015f\u0131la\u015ft\u0131rmak i\u00e7in \u00f6rnek boyutu<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> Sabit hata \u03b1 ve hata \u03b2 ile iki e\u015fle\u015ftirilmi\u015f ortalamay\u0131 kar\u015f\u0131la\u015ft\u0131rmak istiyorsan\u0131z, \u00f6rnekteki g\u00f6zlem say\u0131s\u0131n\u0131 bulmak i\u00e7in kullan\u0131lacak form\u00fcl \u015f\u00f6yledir:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-113aea01351fbe5454666ea2e00f7ec0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n=\\cfrac{2\\cdot \\sigma_d^2 \\cdot \\left(Z_{\\alpha\/2}+Z_\\beta\\right)}{\\Delta^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"184\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Alt\u0131n<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-b7305a6cb6d013542b2aa8af4e001985_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\Delta\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"14\" style=\"vertical-align: 0px;\"><\/p>\n<p> alternatif hipotezin iki e\u015fle\u015ftirilmi\u015f arac\u0131 aras\u0131ndaki farkt\u0131r ve<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-d352962e030563a6172d0afe4491b991_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sigma_d^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"18\" style=\"vertical-align: -5px;\"><\/p>\n<p> Ayn\u0131 bireyin iki \u00f6l\u00e7\u00fcm\u00fc aras\u0131ndaki farklar\u0131n varyans\u0131d\u0131r.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Bu makalede \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fcn\u00fcn ne oldu\u011fu ve istatistikte neden \u00f6nemli oldu\u011fu a\u00e7\u0131klanmaktad\u0131r. Ek olarak, uygun \u00f6rneklem boyutunun nas\u0131l hesaplanaca\u011f\u0131n\u0131 ve \u00e7\u00f6z\u00fclm\u00fc\u015f bir al\u0131\u015ft\u0131rmay\u0131 ke\u015ffederek bunun nas\u0131l yap\u0131ld\u0131\u011f\u0131n\u0131 g\u00f6rebilirsiniz. \u00d6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc nedir? \u00d6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc (veya \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc ), bir \u00e7al\u0131\u015fman\u0131n \u00f6rne\u011fini olu\u015fturan bireylerin say\u0131s\u0131d\u0131r. \u0130statistiklerde \u00f6rneklemin t\u00fcm pop\u00fclasyonu temsil edebilmesi i\u00e7in \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc \u00f6nemlidir. Bu nedenle [&hellip;]<\/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-245","post","type-post","status-publish","format-standard","hentry","category-istatistik"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.3 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u25b7 \u00d6rnek boyutunu hesaplay\u0131n (form\u00fcl ve \u00f6rnek)<\/title>\n<meta name=\"description\" content=\"Burada \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fcn\u00fcn ne oldu\u011funu, istatistikteki \u00f6nemini, nas\u0131l hesapland\u0131\u011f\u0131n\u0131 (form\u00fcl) ve somut bir \u00f6rne\u011fi bulacaks\u0131n\u0131z.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" 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