{"id":220,"date":"2023-08-04T01:16:05","date_gmt":"2023-08-04T01:16:05","guid":{"rendered":"https:\/\/statorials.org\/tr\/ogrenci-dagilimi\/"},"modified":"2023-08-04T01:16:05","modified_gmt":"2023-08-04T01:16:05","slug":"ogrenci-dagilimi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/ogrenci-dagilimi\/","title":{"rendered":"\u00d6\u011frencinin t da\u011f\u0131l\u0131m\u0131"},"content":{"rendered":"<p>Bu makalede, \u00d6\u011frenci t da\u011f\u0131l\u0131m\u0131n\u0131n ne oldu\u011fu ve ne i\u00e7in kullan\u0131ld\u0131\u011f\u0131 a\u00e7\u0131klanmaktad\u0131r. Ayr\u0131ca, \u00d6\u011frenci t da\u011f\u0131l\u0131m\u0131n\u0131n grafi\u011fi ve bu t\u00fcr olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131n\u0131n \u00f6zelliklerinin neler oldu\u011fu g\u00f6sterilmi\u015ftir. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-distribucion-t-de-student\"><\/span> \u00d6\u011frenci da\u011f\u0131l\u0131m\u0131 nedir?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>\u00d6\u011frenci t da\u011f\u0131l\u0131m\u0131<\/strong> istatistikte yayg\u0131n olarak kullan\u0131lan bir olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131d\u0131r. \u00d6zellikle, \u00d6\u011frenci t da\u011f\u0131l\u0131m\u0131, iki numunenin ortalamalar\u0131 aras\u0131ndaki fark\u0131 belirlemek ve g\u00fcven aral\u0131klar\u0131n\u0131 olu\u015fturmak i\u00e7in \u00d6\u011frenci t testinde kullan\u0131l\u0131r.<\/p>\n<p> \u00d6\u011frencinin t da\u011f\u0131l\u0131m\u0131, istatistik\u00e7i William Sealy Gosset taraf\u0131ndan 1908 y\u0131l\u0131nda &#8220;\u00d6\u011frenci&#8221; takma ad\u0131 alt\u0131nda geli\u015ftirildi.<\/p>\n<p> \u00d6\u011frencinin t da\u011f\u0131l\u0131m\u0131, toplam g\u00f6zlem say\u0131s\u0131ndan bir birimin \u00e7\u0131kar\u0131lmas\u0131yla elde edilen serbestlik derecesi say\u0131s\u0131yla tan\u0131mlan\u0131r. Bu nedenle, \u00d6\u011frenci t da\u011f\u0131l\u0131m\u0131n\u0131n serbestlik derecesini belirleme form\u00fcl\u00fc <em>\u03bd=n-1&#8217;dir<\/em> . <\/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-1c805dc2d6ca050feb70dad99de53402_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}\\nu=n-1\\\\[2ex]X\\sim t_\\nu\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"52\" width=\"74\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"grafica-de-la-distribucion-t-de-student\"><\/span> \u00d6\u011frencinin t da\u011f\u0131l\u0131m grafi\u011fi<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Art\u0131k \u00d6\u011frenci t da\u011f\u0131l\u0131m\u0131n\u0131n tan\u0131m\u0131n\u0131 bildi\u011fimize g\u00f6re grafi\u011finin ne oldu\u011funa bakal\u0131m. A\u015fa\u011f\u0131da, farkl\u0131 serbestlik derecelerine sahip \u00d6\u011frenci t da\u011f\u0131l\u0131mlar\u0131n\u0131n birka\u00e7 \u00f6rne\u011fini grafiksel olarak g\u00f6rebilirsiniz. <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/graphique-de-distribution-t-des-etudiants.png\" alt=\"\u00d6\u011frencinin t da\u011f\u0131l\u0131m grafi\u011fi\" class=\"wp-image-4266\" width=\"700\" height=\"420\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> \u00d6\u011frenci t da\u011f\u0131l\u0131m\u0131n\u0131n grafi\u011finden a\u015fa\u011f\u0131daki \u00f6zellikler \u00e7\u0131kar\u0131labilir:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:14px\"> <span style=\"color:#101010;font-weight: normal;\">\u00d6\u011frenci t da\u011f\u0131l\u0131m\u0131 0&#8217;da simetrik merkezlidir ve \u00e7an \u015feklindedir.<\/span><\/li>\n<li style=\"margin-bottom:14px\"> <span style=\"color:#101010;font-weight: normal;\">\u00d6\u011frenci t da\u011f\u0131l\u0131m\u0131 normal da\u011f\u0131l\u0131ma g\u00f6re daha da\u011f\u0131n\u0131kt\u0131r, yani \u00d6\u011frenci t da\u011f\u0131l\u0131m\u0131n\u0131n e\u011frisi daha geni\u015ftir.<\/span><\/li>\n<li style=\"margin-bottom:14px\"> <span style=\"color:#101010;font-weight: normal;\">\u00d6\u011frencinin t da\u011f\u0131l\u0131m\u0131n\u0131n serbestlik derecesi ne kadar fazlaysa, da\u011f\u0131l\u0131m\u0131 da o kadar d\u00fc\u015f\u00fck olur.<\/span><\/li>\n<\/ul>\n<p> Yukar\u0131daki grafikte, \u00d6\u011frenci t da\u011f\u0131l\u0131m\u0131n\u0131n yo\u011funluk fonksiyonu, serbestlik derecesine g\u00f6re \u00e7izilmi\u015ftir. Ancak a\u015fa\u011f\u0131da \u00d6\u011frenci t da\u011f\u0131l\u0131m\u0131n\u0131n k\u00fcm\u00fclatif olas\u0131l\u0131k fonksiyonunun nas\u0131l de\u011fi\u015fti\u011fini g\u00f6rebilirsiniz: <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/distribution-t-etudiante-cumulative.png\" alt=\"\u00d6\u011frencinin k\u00fcm\u00fclatif t da\u011f\u0131l\u0131m\u0131n\u0131n grafi\u011fi\" class=\"wp-image-4267\" width=\"700\" height=\"420\" srcset=\"\" sizes=\"auto, \"><\/figure>\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\/ogrenci-t-dagilim-tablosu\/\">\u00d6\u011frenci da\u011f\u0131l\u0131m tablosu<\/a> <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"caracteristicas-de-la-distribucion-t-de-student\"><\/span> \u00d6\u011frenci t da\u011f\u0131l\u0131m\u0131n\u0131n \u00f6zellikleri<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u00d6\u011frenci t da\u011f\u0131l\u0131m\u0131n\u0131n en \u00f6nemli \u00f6zellikleri a\u015fa\u011f\u0131da g\u00f6sterilmi\u015ftir.<\/p>\n<ul>\n<li> \u00d6\u011frenci t da\u011f\u0131l\u0131m\u0131n\u0131n alan\u0131 ger\u00e7ek say\u0131lardan olu\u015fur.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-fd8ca9914bdf447012a1a16f7950ce95_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\\in (-\\infty, +\\infty)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"116\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> Birden fazla serbestlik derecesine sahip \u00d6\u011frenci t da\u011f\u0131l\u0131mlar\u0131 i\u00e7in da\u011f\u0131l\u0131m\u0131n ortalamas\u0131 0&#8217;a e\u015fittir.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-d4fed5eadcaa1162752aeedb7f8a0906_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}X\\sim t_\\nu\\\\[2ex] E[X]=0 \\qquad \\text{para }\\nu>1\\end{array} &#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;55&#8243; width=&#8221;190&#8243; style=&#8221;vertical-align: 0px;&#8221;><\/p>\n<\/p>\n<ul>\n<li> \u00d6\u011frenci t da\u011f\u0131l\u0131m\u0131n\u0131n varyans\u0131 a\u015fa\u011f\u0131daki ifade kullan\u0131larak hesaplanabilir:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-bfdcbc8a5f071a61e091b0ef6f686a16_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}X\\sim t_\\nu\\\\[2ex] Var(X)=\\cfrac{\\nu}{\\nu-2} \\qquad \\text{para }\\nu>2\\end{array} &#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;75&#8243; width=&#8221;245&#8243; style=&#8221;vertical-align: 0px;&#8221;><\/p>\n<\/p>\n<ul>\n<li> Serbestlik derecesine bak\u0131lmaks\u0131z\u0131n \u00d6\u011frenci t da\u011f\u0131l\u0131m\u0131n\u0131n medyan\u0131 ve modu her zaman 0&#8217;d\u0131r.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-8d90790fce0c987648c0b30216c82214_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}Me=0\\\\[2ex]Mo=0\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"50\" width=\"60\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li> \u00d6\u011frenci t da\u011f\u0131l\u0131m\u0131n\u0131n yo\u011funluk fonksiyonu a\u015fa\u011f\u0131daki form\u00fclle tan\u0131mlan\u0131r:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-8c0f1e97a8e407e8b9e2b00ba93aee0e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P[X=x]=\\frac{\\Gamma((\\nu+1)\/2)} {\\sqrt{\\nu\\pi}\\,\\Gamma(\\nu\/2)} (1+x^2\/\\nu)^{-(\\nu+1)\/2}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"339\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<ul>\n<li> \u00d6\u011frenci t da\u011f\u0131l\u0131m\u0131n\u0131n k\u00fcm\u00fclatif olas\u0131l\u0131k da\u011f\u0131l\u0131m fonksiyonu a\u015fa\u011f\u0131daki form\u00fclle tan\u0131mlan\u0131r:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-da1e3bdf2d87c3a7dcc89c236958dcec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P[X\\leq x]=\\frac{1}{2} + x \\Gamma \\left( \\frac{\\nu+1}{2} \\right) \\cdot\\frac{\\,_2F_1 \\left ( \\frac{1}{2},\\frac{\\nu+1}{2};\\frac{3}{2};-\\frac{x^2}{\\nu} \\right)}{\\sqrt{\\pi\\nu}\\,\\Gamma \\left(\\frac{\\nu}{2}\\right)}\" title=\"Rendered by QuickLaTeX.com\" height=\"59\" width=\"402\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<ul>\n<li> Serbestlik derecesi 3&#8217;ten b\u00fcy\u00fck olan \u00d6\u011frenci t da\u011f\u0131l\u0131mlar\u0131 i\u00e7in asimetri katsay\u0131s\u0131 s\u0131f\u0131rd\u0131r \u00e7\u00fcnk\u00fc bu da\u011f\u0131l\u0131m simetriktir.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-6fea0ec5e37ef4db61fb44d6f5eba6fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A=0\\qquad \\text{para }\\nu>3&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;17&#8243; width=&#8221;164&#8243; style=&#8221;vertical-align: -4px;&#8221;><\/p>\n<\/p>\n<ul>\n<li> \u00d6\u011frenci t da\u011f\u0131l\u0131m\u0131n\u0131n serbestlik derecesi d\u00f6rtten b\u00fcy\u00fckse bas\u0131kl\u0131k, alt\u0131n\u0131n serbestlik derecesi eksi d\u00f6rt&#8217;e b\u00f6l\u00fcnmesiyle hesaplanabilir. <\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-0335e705ad289732dd1be59dc8388dee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle C=\\cfrac{6}{\\nu-4}\\qquad \\text{para }\\nu>4&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;38&#8243; width=&#8221;198&#8243; style=&#8221;vertical-align: -12px;&#8221;><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"aplicaciones-de-la-distribucion-t-de-student\"><\/span> \u00d6\u011frenci t da\u011f\u0131l\u0131m\u0131n\u0131n uygulamalar\u0131<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u00d6\u011frenci t da\u011f\u0131l\u0131m\u0131 istatistikte yayg\u0131n olarak kullan\u0131lan bir olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131d\u0131r. Asl\u0131nda hipotezleri ve g\u00fcven aral\u0131klar\u0131n\u0131 test etmek i\u00e7in kullan\u0131lan \u00d6\u011frenci t testi bile vard\u0131r.<\/p>\n<p> B\u00f6ylece, \u00d6\u011frenci t da\u011f\u0131l\u0131m\u0131 iki \u00f6rne\u011fin ortalamalar\u0131 aras\u0131ndaki fark\u0131 analiz etmemizi sa\u011flar; daha do\u011frusu, iki \u00f6rne\u011fin anlaml\u0131 derecede farkl\u0131 ortalamalara sahip olup olmad\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in kullan\u0131l\u0131r. Benzer \u015fekilde, do\u011frusal regresyon analizinden elde edilen do\u011frunun e\u011fimi olup olmad\u0131\u011f\u0131n\u0131n belirlenmesinde de \u00d6\u011frenci t testi kullan\u0131l\u0131r.<\/p>\n<p> K\u0131sacas\u0131, \u00d6\u011frenci t da\u011f\u0131l\u0131m\u0131n\u0131n uygulamalar\u0131 teorik olarak normal bir da\u011f\u0131l\u0131m izleyen veri setlerinin analizine dayan\u0131r ancak toplam g\u00f6zlem say\u0131s\u0131 bu t\u00fcr bir da\u011f\u0131l\u0131m\u0131 kullanmak i\u00e7in \u00e7ok k\u00fc\u00e7\u00fckt\u00fcr.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Bu makalede, \u00d6\u011frenci t da\u011f\u0131l\u0131m\u0131n\u0131n ne oldu\u011fu ve ne i\u00e7in kullan\u0131ld\u0131\u011f\u0131 a\u00e7\u0131klanmaktad\u0131r. Ayr\u0131ca, \u00d6\u011frenci t da\u011f\u0131l\u0131m\u0131n\u0131n grafi\u011fi ve bu t\u00fcr olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131n\u0131n \u00f6zelliklerinin neler oldu\u011fu g\u00f6sterilmi\u015ftir. \u00d6\u011frenci da\u011f\u0131l\u0131m\u0131 nedir? \u00d6\u011frenci t da\u011f\u0131l\u0131m\u0131 istatistikte yayg\u0131n olarak kullan\u0131lan bir olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131d\u0131r. \u00d6zellikle, \u00d6\u011frenci t da\u011f\u0131l\u0131m\u0131, iki numunenin ortalamalar\u0131 aras\u0131ndaki fark\u0131 belirlemek ve g\u00fcven aral\u0131klar\u0131n\u0131 olu\u015fturmak i\u00e7in \u00d6\u011frenci [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12],"tags":[],"class_list":["post-220","post","type-post","status-publish","format-standard","hentry","category-olasilik"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.3 - 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