{"id":284,"date":"2023-08-03T03:28:35","date_gmt":"2023-08-03T03:28:35","guid":{"rendered":"https:\/\/statorials.org\/tr\/ortalamalardaki-fark-icin-guven-araligi\/"},"modified":"2023-08-03T03:28:35","modified_gmt":"2023-08-03T03:28:35","slug":"ortalamalardaki-fark-icin-guven-araligi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/ortalamalardaki-fark-icin-guven-araligi\/","title":{"rendered":"Ortalamalardaki fark i\u00e7in g\u00fcven aral\u0131\u011f\u0131"},"content":{"rendered":"<p>Bu makalede istatistiklerde ortalamalar aras\u0131ndaki farka ili\u015fkin g\u00fcven aral\u0131\u011f\u0131n\u0131n ne oldu\u011fu ve ne i\u00e7in kullan\u0131ld\u0131\u011f\u0131 a\u00e7\u0131klanmaktad\u0131r. B\u00f6ylece, iki ortalaman\u0131n fark\u0131 i\u00e7in g\u00fcven aral\u0131\u011f\u0131n\u0131 nas\u0131l hesaplayaca\u011f\u0131n\u0131z\u0131 ve ad\u0131m ad\u0131m \u00e7\u00f6z\u00fclen bir al\u0131\u015ft\u0131rmay\u0131 ke\u015ffedeceksiniz. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-el-intervalo-de-confianza-para-la-diferencia-de-medias\"><\/span> Ortalamalar aras\u0131ndaki fark i\u00e7in g\u00fcven aral\u0131\u011f\u0131 nedir?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Ortalamalar fark\u0131 i\u00e7in g\u00fcven aral\u0131\u011f\u0131,<\/strong> iki pop\u00fclasyonun ortalamalar\u0131 fark\u0131n\u0131n de\u011ferinin belirli bir g\u00fcven d\u00fczeyinde bulundu\u011fu bir maksimum de\u011fer ve bir minimum de\u011fer sa\u011flayan bir aral\u0131kt\u0131r.<\/p>\n<p> \u00d6rne\u011fin, %95 g\u00fcven d\u00fczeyine sahip iki pop\u00fclasyonun ortalamalar\u0131 aras\u0131ndaki fark\u0131n g\u00fcven aral\u0131\u011f\u0131 (3,5) ise bu, iki pop\u00fclasyonun ortalamalar\u0131 aras\u0131ndaki fark\u0131n 95 olas\u0131l\u0131kla 3 ile 5 aras\u0131nda olaca\u011f\u0131 anlam\u0131na gelir. %.<\/p>\n<p> Bu nedenle istatistiklerde, ortalamalar aras\u0131ndaki farka ili\u015fkin g\u00fcven aral\u0131\u011f\u0131, iki pop\u00fclasyon ortalamas\u0131 aras\u0131ndaki fark\u0131n aralar\u0131nda bulundu\u011fu iki de\u011feri tahmin etmek i\u00e7in kullan\u0131l\u0131r. B\u00f6ylece, iki \u00f6rnekten elde edilen verileri kullanarak pop\u00fclasyon ortalamalar\u0131 aras\u0131ndaki fark\u0131 yakla\u015f\u0131k olarak tahmin etmek m\u00fcmk\u00fcnd\u00fcr. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-del-intervalo-de-confianza-para-la-diferencia-de-medias\"><\/span> Ortalamalardaki fark i\u00e7in g\u00fcven aral\u0131\u011f\u0131 form\u00fcl\u00fc<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Ortalamalardaki farka ili\u015fkin g\u00fcven aral\u0131\u011f\u0131 form\u00fcl\u00fc, pop\u00fclasyon varyanslar\u0131n\u0131n bilinip bilinmedi\u011fine ve bilinmiyorsa pop\u00fclasyon varyanslar\u0131n\u0131n e\u015fit oldu\u011funun varsay\u0131l\u0131p varsay\u0131lamayaca\u011f\u0131na ba\u011fl\u0131d\u0131r. . Daha sonra her durumda ortalamalar aras\u0131ndaki farka ili\u015fkin g\u00fcven aral\u0131\u011f\u0131n\u0131n nas\u0131l hesapland\u0131\u011f\u0131n\u0131 g\u00f6rece\u011fiz.<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"varianzas-conocidas\"><\/span> bilinen sapmalar<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> <strong>\u0130ki pop\u00fclasyonun varyanslar\u0131 1-\u03b1 g\u00fcven d\u00fczeyiyle bilindi\u011finde ortalamalar aras\u0131ndaki fark i\u00e7in g\u00fcven aral\u0131\u011f\u0131n\u0131 hesaplamaya y\u00f6nelik form\u00fcl<\/strong> 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-43af3f53a009f90021521508efe8c2a1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle (\\overline{x_1}-\\overline{x_2})\\pm Z_{\\alpha\/2}\\sqrt{\\frac{\\sigma_1^2}{n_1}+\\frac{\\sigma_2^2}{n_2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"212\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\"> Alt\u0131n:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-a4071a38558726a684ed069430c89fe2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{x_i}\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"16\" style=\"vertical-align: -3px;\"><\/p>\n<p> \u00f6rnek i&#8217;nin ortalamas\u0131d\u0131r.<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-dc8c8f782c0ed8b7925012b60e174fa3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sigma_i\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"15\" style=\"vertical-align: -3px;\"><\/p>\n<p> pop\u00fclasyonun standart sapmas\u0131 i&#8217;dir.<\/li>\n<li style=\"margin-bottom:5px\">\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\u0131kla standart normal da\u011f\u0131l\u0131m\u0131n de\u011feridir.<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-5f087375b50e0b49186779714206626b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n_i\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"16\" style=\"vertical-align: -3px;\"><\/p>\n<p> \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc i&#8217;dir.<\/li>\n<\/ul>\n<p> Pop\u00fclasyon varyanslar\u0131n\u0131n de\u011feri genellikle bilinmedi\u011finden bu durum en az g\u00f6r\u00fclen durumdur.<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"varianzas-desconocidas-e-iguales\"><\/span> bilinmeyen ve e\u015fit varyanslar<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> <strong>\u0130ki pop\u00fclasyonun varyanslar\u0131 bilinmedi\u011finde ancak e\u015fit oldu\u011fu tahmin edilebildi\u011finde, 1-\u03b1 g\u00fcven d\u00fczeyine sahip ortalamalar fark\u0131 i\u00e7in g\u00fcven aral\u0131\u011f\u0131n\u0131 hesaplamaya y\u00f6nelik form\u00fcl a\u015fa\u011f\u0131daki gibidir:<\/strong><\/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-0534fc597a2d7842c41a47a907c1b185_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle (\\overline{x_1}-\\overline{x_2})\\pm t_{\\alpha\/2}s_p\\sqrt{\\frac{1}{n_1}+\\frac{1}{n_2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"222\" style=\"vertical-align: -15px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\"> Alt\u0131n:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-a4071a38558726a684ed069430c89fe2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{x_i}\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"16\" style=\"vertical-align: -3px;\"><\/p>\n<p> \u00f6rnek i&#8217;nin ortalamas\u0131d\u0131r.<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-db24109a40d5779feee64c7bccc11371_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s_p\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"15\" style=\"vertical-align: -6px;\"><\/p>\n<p> havuzlanm\u0131\u015f standart sapmad\u0131r.<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-33bd5d525ddf37600aef97b0c8c08f94_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t_{\\alpha\/2}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"29\" style=\"vertical-align: -8px;\"><\/p>\n<p> \u03b1\/2 olas\u0131l\u0131\u011f\u0131 ile n <sub>1<\/sub> + n <sub>2<\/sub> -2 serbestlik derecesinin \u00d6\u011frenci t da\u011f\u0131l\u0131m\u0131n\u0131n de\u011feridir.<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-5f087375b50e0b49186779714206626b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n_i\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"16\" style=\"vertical-align: -3px;\"><\/p>\n<p> \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc i&#8217;dir.<\/li>\n<\/ul>\n<p> Bu durumda pop\u00fclasyon varyanslar\u0131n\u0131n e\u015fde\u011fer oldu\u011fu varsay\u0131ld\u0131\u011f\u0131ndan, a\u015fa\u011f\u0131daki form\u00fclle hesaplanan g\u00fcven aral\u0131\u011f\u0131n\u0131 hesaplamak i\u00e7in birle\u015fik standart sapma kullan\u0131l\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-a8fb43d179e453d19f5781319aa9e1ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle s_p=\\sqrt{\\frac{(n_1-1)s_1^2+(n_2-1)s_2^2}{n_1+n_2-2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"240\" style=\"vertical-align: -20px;\"><\/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-2071979c45a4a9e06d8cccc739ffc771_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s_i\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"13\" style=\"vertical-align: -3px;\"><\/p>\n<p> \u00f6rnek i&#8217;nin standart sapmas\u0131d\u0131r. <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"varianzas-desconocidas-y-diferentes\"><\/span> Bilinmeyen ve farkl\u0131 varyasyonlar<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> <strong>\u0130ki pop\u00fclasyonun varyanslar\u0131 bilinmedi\u011finde ve e\u015fit oldu\u011fu varsay\u0131lamazsa, 1-\u03b1 g\u00fcven d\u00fczeyiyle ortalamalar fark\u0131 i\u00e7in g\u00fcven aral\u0131\u011f\u0131n\u0131 hesaplamaya y\u00f6nelik form\u00fcl a\u015fa\u011f\u0131daki gibidir:<\/strong><\/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-ef56281d972a143678514c47fed3690d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle (\\overline{x_1}-\\overline{x_2})\\pm t_{\\alpha\/2}\\sqrt{\\frac{s_1^2}{n_1}+\\frac{s_2^2}{n_2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"206\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\"> Alt\u0131n: <\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-a4071a38558726a684ed069430c89fe2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{x_i}\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"16\" style=\"vertical-align: -3px;\"><\/p>\n<p> \u00f6rnek i&#8217;nin ortalamas\u0131d\u0131r.<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-2071979c45a4a9e06d8cccc739ffc771_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s_i\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"13\" style=\"vertical-align: -3px;\"><\/p>\n<p> \u00f6rnek i&#8217;nin standart sapmas\u0131d\u0131r.<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-33bd5d525ddf37600aef97b0c8c08f94_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t_{\\alpha\/2}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"29\" style=\"vertical-align: -8px;\"><\/p>\n<p> \u03b1\/2 olas\u0131l\u0131kl\u0131 \u00d6\u011frenci t da\u011f\u0131l\u0131m\u0131n\u0131n de\u011feridir.<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-5f087375b50e0b49186779714206626b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n_i\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"16\" style=\"vertical-align: -3px;\"><\/p>\n<p> \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc i&#8217;dir.<\/li>\n<\/ul>\n<p> Bu durumda \u00d6\u011frenci t da\u011f\u0131l\u0131m\u0131n\u0131n serbestlik derecesi a\u015fa\u011f\u0131daki form\u00fcl kullan\u0131larak hesaplan\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-ecf1ccfa1ecb47b889c569e5faa65a78_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle GL=\\frac{\\displaystyle\\left(\\frac{s_1^2}{n_1}+\\frac{s_2^2}{n_2}\\right)^2}{\\displaystyle\\frac{\\displaystyle\\frac{s_1^2}{n_1}}{n_1-1}+\\frac{\\displaystyle\\frac{s_2^2}{n_2}}{n_2-1}}\" title=\"Rendered by QuickLaTeX.com\" height=\"115\" width=\"180\" style=\"vertical-align: -61px;\"><\/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-2071979c45a4a9e06d8cccc739ffc771_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s_i\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"13\" style=\"vertical-align: -3px;\"><\/p>\n<p> \u00f6rnek i&#8217;nin standart sapmas\u0131d\u0131r. <\/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\/ortalama-icin-guven-araligi\/\">Ortalama i\u00e7in g\u00fcven aral\u0131\u011f\u0131 form\u00fcl\u00fc<\/a> <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-resuelto-del-intervalo-de-confianza-para-la-diferencia-de-medias\"><\/span> Ortalamalardaki fark i\u00e7in g\u00fcven aral\u0131\u011f\u0131n\u0131n somut \u00f6rne\u011fi<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Ortalamalar fark\u0131 i\u00e7in g\u00fcven aral\u0131\u011f\u0131n\u0131n tan\u0131m\u0131n\u0131 ve farkl\u0131 form\u00fcllerin neler oldu\u011funu g\u00f6rd\u00fckten sonra, \u015fimdi iki ortalaman\u0131n fark\u0131 i\u00e7in g\u00fcven aral\u0131\u011f\u0131n\u0131n nas\u0131l hesapland\u0131\u011f\u0131n\u0131 \u00f6z\u00fcmsemeyi bitirmek i\u00e7in somut bir \u00f6rnek g\u00f6rece\u011fiz.<\/p>\n<ul>\n<li> T\u00fct\u00fcn\u00fcn \u00e7ocuklar\u0131n do\u011fum a\u011f\u0131rl\u0131\u011f\u0131 \u00fczerindeki etkisini ara\u015ft\u0131rmak istiyoruz. Bunu yapmak i\u00e7in iki \u00f6rnek kar\u015f\u0131la\u015ft\u0131r\u0131l\u0131r: ilk \u00f6rnek, anneleri sigara i\u00e7meyen \u00e7ocuklardan, ikinci \u00f6rnek ise anneleri sigara i\u00e7en \u00e7ocuklardan olu\u015fur (\u00f6rnek parametreleri a\u015fa\u011f\u0131da belirtilmi\u015ftir). Ortalamalar aras\u0131ndaki fark i\u00e7in g\u00fcven aral\u0131\u011f\u0131n\u0131 %95 g\u00fcven d\u00fczeyiyle hesaplay\u0131n.\n<ol>\n<li> Sigara i\u00e7meyen anneler:\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-1493306090541d3c6e01455a25d1fecc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{x_1}=3,1 \\ kg \\quad s_1=0,6 \\ kg \\quad n_1=39\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"277\" style=\"vertical-align: -4px;\"><\/p>\n<\/li>\n<li> Sigara i\u00e7en anneler:\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-8b01145787503a21957331cbe3785111_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{x_2}=3,5 \\ kg \\quad s_2=0,4 \\ kg\\quad n_2=43\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"277\" style=\"vertical-align: -4px;\"><\/p>\n<\/li>\n<\/ol>\n<\/li>\n<\/ul>\n<p> Bu durumda pop\u00fclasyon varyanslar\u0131n\u0131n de\u011ferlerini bilmiyoruz ancak pop\u00fclasyon varyanslar\u0131n\u0131n e\u015fde\u011fer oldu\u011funu varsayabiliriz \u00e7\u00fcnk\u00fc \u00e7ok benzer \u00f6zelliklere sahip iki pop\u00fclasyonla kar\u015f\u0131 kar\u015f\u0131yay\u0131z. Bu nedenle, ortalamalar aras\u0131ndaki farka ili\u015fkin g\u00fcven aral\u0131\u011f\u0131 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-0534fc597a2d7842c41a47a907c1b185_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle (\\overline{x_1}-\\overline{x_2})\\pm t_{\\alpha\/2}s_p\\sqrt{\\frac{1}{n_1}+\\frac{1}{n_2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"222\" style=\"vertical-align: -15px;\"><\/p>\n<\/p>\n<p> B\u00f6ylece, iki numunenin standart sapmalar\u0131ndan birle\u015fik standart sapmay\u0131 hesapl\u0131yoruz:<\/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-688958252e9838e7fddc2ddcb9061b01_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\displaystyle s_p&amp;=\\sqrt{\\frac{(n_1-1)s_1^2+(n_2-1)s_2^2}{n_1+n_2-2}}\\\\[2ex]\\displaystyle s_p&amp;=\\sqrt{\\frac{(39-1)\\cdot 0,6^2+(43-1)\\cdot 0,4^2}{39+43-2}}\\\\[2ex]\\displaystyle s_p&amp;=0,50\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"161\" width=\"299\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Ayn\u0131 \u015fekilde, \u00d6\u011frenci t da\u011f\u0131l\u0131m\u0131n\u0131n <a href=\"https:\/\/statorials.org\/tr\/ogrenci-t-dagilim-tablosu\/\">olas\u0131l\u0131k da\u011f\u0131l\u0131m tablosunda, 80 serbestlik derecesinin \u00d6\u011frenci t da\u011f\u0131l\u0131m\u0131n\u0131n<\/a> de\u011ferini %2,5 olas\u0131l\u0131kla bulmam\u0131z gerekir:<\/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-5e4ea90fdc33c9a3d3dab0f1d9d29af0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}t_{\\alpha\/2| n_1+n_2-2}= \\ \\color{orange}\\bm{?}\\\\[4ex]t_{0,025|80}=1,990\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"72\" width=\"184\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Son olarak, ortalamalar aras\u0131ndaki fark i\u00e7in verileri g\u00fcven aral\u0131\u011f\u0131 form\u00fcl\u00fcne yerle\u015ftiririz ve hesaplamalar\u0131 yapar\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-0534fc597a2d7842c41a47a907c1b185_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle (\\overline{x_1}-\\overline{x_2})\\pm t_{\\alpha\/2}s_p\\sqrt{\\frac{1}{n_1}+\\frac{1}{n_2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"222\" style=\"vertical-align: -15px;\"><\/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-7c0a07bffc585f3c89a19ef1de2fc441_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle (3,1-3,5)\\pm 1,990\\cdot 0,5\\cdot\\sqrt{\\frac{1}{39}+\\frac{1}{43}}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"285\" style=\"vertical-align: -14px;\"><\/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-4863b308e6ac856e407d75022a40aa23_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle -0,4\\pm 0,22\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"94\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> Dolay\u0131s\u0131yla problemin ortalamalar\u0131 aras\u0131ndaki farka ili\u015fkin g\u00fcven aral\u0131\u011f\u0131 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-8e399a671d64c87e8c9deda851850a00_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(-0,61,-0,18)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"117\" style=\"vertical-align: -5px;\"><\/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\/ortalamalar-arasindaki-farka-yonelik-hipotez-testi\/\">Ortalamalar aras\u0131ndaki farka ili\u015fkin hipotezlerin kar\u015f\u0131tl\u0131\u011f\u0131<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Bu makalede istatistiklerde ortalamalar aras\u0131ndaki farka ili\u015fkin g\u00fcven aral\u0131\u011f\u0131n\u0131n ne oldu\u011fu ve ne i\u00e7in kullan\u0131ld\u0131\u011f\u0131 a\u00e7\u0131klanmaktad\u0131r. B\u00f6ylece, iki ortalaman\u0131n fark\u0131 i\u00e7in g\u00fcven aral\u0131\u011f\u0131n\u0131 nas\u0131l hesaplayaca\u011f\u0131n\u0131z\u0131 ve ad\u0131m ad\u0131m \u00e7\u00f6z\u00fclen bir al\u0131\u015ft\u0131rmay\u0131 ke\u015ffedeceksiniz. Ortalamalar aras\u0131ndaki fark i\u00e7in g\u00fcven aral\u0131\u011f\u0131 nedir? Ortalamalar fark\u0131 i\u00e7in g\u00fcven aral\u0131\u011f\u0131, iki pop\u00fclasyonun ortalamalar\u0131 fark\u0131n\u0131n de\u011ferinin belirli bir g\u00fcven d\u00fczeyinde bulundu\u011fu bir [&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-284","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 Ortalamalar aras\u0131ndaki fark i\u00e7in g\u00fcven aral\u0131\u011f\u0131<\/title>\n<meta name=\"description\" content=\"Burada ortalamalar fark\u0131 i\u00e7in g\u00fcven aral\u0131\u011f\u0131n\u0131n ne oldu\u011funu, nas\u0131l hesapland\u0131\u011f\u0131n\u0131 (form\u00fcl) ve somut bir \u00f6rne\u011fi 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