{"id":293,"date":"2023-08-03T00:39:59","date_gmt":"2023-08-03T00:39:59","guid":{"rendered":"https:\/\/statorials.org\/tr\/ogrenci-t-testi\/"},"modified":"2023-08-03T00:39:59","modified_gmt":"2023-08-03T00:39:59","slug":"ogrenci-t-testi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/ogrenci-t-testi\/","title":{"rendered":"\u00d6\u011frenci t testi"},"content":{"rendered":"<p>Bu makalede, \u00d6\u011frenci t testinin ne oldu\u011fu ve istatistikte ne i\u00e7in kullan\u0131ld\u0131\u011f\u0131 a\u00e7\u0131klanmaktad\u0131r. B\u00f6ylece, \u00d6\u011frenci t testinin nas\u0131l yap\u0131ld\u0131\u011f\u0131n\u0131, farkl\u0131 \u00d6\u011frenci t testi t\u00fcrlerinin neler oldu\u011funu ve her birinin form\u00fcl\u00fcn\u00fc ke\u015ffedeceksiniz. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-prueba-t-de-student\"><\/span> \u00d6\u011frenci t testi nedir?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Ayn\u0131 zamanda <strong>T testi<\/strong> veya basit\u00e7e <strong>t testi<\/strong> olarak da adland\u0131r\u0131lan <strong>\u00d6\u011frenci t testi<\/strong> , test istatisti\u011finin <a href=\"https:\/\/statorials.org\/tr\/ogrenci-dagilimi\/\">\u00d6\u011frencinin t da\u011f\u0131l\u0131m\u0131n\u0131<\/a> takip etti\u011fi istatistiksel bir testtir. Bu nedenle istatistikte, \u00d6\u011frenci t testi bir hipotez testinin s\u0131f\u0131r hipotezini reddetmek veya kabul etmek i\u00e7in kullan\u0131l\u0131r.<\/p>\n<p> Spesifik olarak, \u00d6\u011frenci t testi, incelenen pop\u00fclasyonun normal bir da\u011f\u0131l\u0131m izledi\u011fi ancak \u00f6rneklem boyutunun pop\u00fclasyon varyans\u0131n\u0131 bilmek i\u00e7in \u00e7ok k\u00fc\u00e7\u00fck oldu\u011fu <a href=\"https:\/\/statorials.org\/tr\/hipotez-testi-1\/\">hipotez testlerinde<\/a> kullan\u0131l\u0131r.<\/p>\n<p> K\u0131sacas\u0131, \u00d6\u011frenci t testi belirli hipotez testlerinin \u00e7al\u0131\u015fma hipotezini reddetmek veya kabul etmek i\u00e7in kullan\u0131l\u0131r. \u00d6rne\u011fin, \u00d6\u011frenci t testi bir \u00f6rnek, ba\u011f\u0131ms\u0131z \u00f6rnekler veya ilgili \u00f6rnekler i\u00e7in hipotezleri test etmek i\u00e7in kullan\u0131l\u0131r. Daha sonra her durumda \u00d6\u011frenci t testinin nas\u0131l hesapland\u0131\u011f\u0131n\u0131 g\u00f6rece\u011fiz. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"tipos-de-pruebas-t-de-student\"><\/span>\u00d6\u011frenci t-testi t\u00fcrleri<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u00dc\u00e7 <strong>t\u00fcr \u00d6\u011frenci t testi<\/strong> vard\u0131r:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:20px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Tek \u00f6rnekli \u00d6\u011frenci t testi<\/strong> \u2013 \u00f6rnek ortalaman\u0131n de\u011feri hakk\u0131ndaki hipotezi test etmek i\u00e7in kullan\u0131l\u0131r.<\/span><\/li>\n<li style=\"margin-bottom:20px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>\u0130ki ba\u011f\u0131ms\u0131z \u00f6rnek i\u00e7in \u00d6\u011frenci t testi<\/strong> : iki ba\u011f\u0131ms\u0131z \u00f6rne\u011fin ortalamalar\u0131 aras\u0131ndaki farka ili\u015fkin hipotezi test etmenize olanak tan\u0131r.<\/span><\/li>\n<li style=\"margin-bottom:20px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>\u0130ki e\u015fle\u015ftirilmi\u015f \u00f6rnek (veya ilgili \u00f6rnek) i\u00e7in \u00d6\u011frenci t testi<\/strong> \u2013 iki kez test edilen bir \u00f6rne\u011fin ortalamas\u0131 hakk\u0131ndaki hipotezi ara\u015ft\u0131rmak i\u00e7in kullan\u0131l\u0131r.<\/span> <\/li>\n<\/ul>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"prueba-t-de-student-para-una-muestra\"><\/span> \u00d6\u011frenci t testi \u00f6rne\u011fi<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> \u00d6rnek ortalamaya y\u00f6nelik hipotez testleri, testin s\u0131f\u0131r hipotezinin ve alternatif hipotezinin pop\u00fclasyon ortalamas\u0131n\u0131n de\u011feri hakk\u0131nda bir \u015feyler s\u00f6yledi\u011fi testlerdir.<\/p>\n<p> <strong>Tek \u00f6rnekli \u00d6\u011frenci t testinin form\u00fcl\u00fc<\/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-f8277d83b2d28325f25f5d118486200f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle t=\\frac{\\overline{x}-\\mu}{\\displaystyle \\frac{s}{\\sqrt{n}}} \" title=\"Rendered by QuickLaTeX.com\" height=\"57\" width=\"75\" style=\"vertical-align: -34px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\"> Alt\u0131n:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-fd9cb27edab3f0a8a249bc80cc9c6ee2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00d6\u011frenci t da\u011f\u0131l\u0131m\u0131 ile tan\u0131mlanan ortalamaya ili\u015fkin hipotez testi istatisti\u011fidir.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-a39858a792fb4fe9a3173e004701f2a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00f6rnek anlam\u0131na gelir.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-05d9eae892416bd34247a25207f8b718_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\mu\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"11\" style=\"vertical-align: -4px;\"><\/p>\n<p> hipotez testinde \u00f6nerilen ortalaman\u0131n de\u011feridir.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-1edc883862ceed1a21913f60358e31d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00f6rnek standart sapmas\u0131d\u0131r.<\/li>\n<li>\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<\/ul>\n<p> \u00d6\u011frenci t testinin de\u011feri hesapland\u0131ktan sonra, kritik de\u011fere sahip istatistiksel testin sonucu, s\u0131f\u0131r hipotezinin reddedilip reddedilmeyece\u011fi \u015feklinde yorumlanmal\u0131d\u0131r:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">Ortalama i\u00e7in hipotez testi iki tarafl\u0131 ise, \u00d6\u011frenci t testinin mutlak de\u011feri <sub>t\u03b1\/2|n-1<\/sub> kritik de\u011ferinden b\u00fcy\u00fckse s\u0131f\u0131r hipotezi reddedilir.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">Ortalama i\u00e7in hipotez testi sa\u011f kuyrukla e\u015fle\u015fiyorsa, \u00d6\u011frencinin t-testi de\u011feri t\u03b1 <sub>|n-1<\/sub> kritik de\u011ferinden b\u00fcy\u00fckse s\u0131f\u0131r hipotezi reddedilir.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">Ortalama i\u00e7in hipotez testi sol kuyrukla e\u015fle\u015fiyorsa, \u00d6\u011frencinin t-testi de\u011feri -t <sub>\u03b1|n-1<\/sub> kritik de\u011ferinden k\u00fc\u00e7\u00fckse s\u0131f\u0131r hipotezi reddedilir.<\/span><\/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-31fb206b75a47181c7c673f54ba28ee8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{l}H_1: \\mu\\neq \\mu_0 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Si } |t|>t_{\\alpha\/2|n-1} \\text{ se rechaza } H_0\\\\[3ex]H_1: \\mu> \\mu_0 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Si } t>t_{\\alpha|n-1} \\text{ se rechaza } H_0\\\\[3ex]H_1: \\mu< \\mu_0 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Si } t<-t_{\\alpha|n-1} \\text{ se rechaza } H_0\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"112\" width=\"457\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Kritik test de\u011ferlerinin \u00d6\u011frenci da\u011f\u0131l\u0131m tablosundan elde edildi\u011fini unutmay\u0131n. <\/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-hipotez-testi\/\">Ortalama i\u00e7in hipotez testinin somut \u00f6rne\u011fi<\/a> <\/div>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"prueba-t-de-student-para-muestras-independientes\"><\/span> Ba\u011f\u0131ms\u0131z \u00f6rnekler i\u00e7in student&#8217;s t testi<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> Ba\u011f\u0131ms\u0131z \u00f6rnekler i\u00e7in \u00d6\u011frenci t testi, iki pop\u00fclasyonun ortalamalar\u0131 aras\u0131ndaki bir ili\u015fkinin hipotezini reddetmek veya kabul etmek i\u00e7in kullan\u0131l\u0131r; \u00f6rne\u011fin, iki pop\u00fclasyonun ortalamalar\u0131 farkl\u0131d\u0131r veya A pop\u00fclasyonunun ortalamas\u0131, ortalamadan daha b\u00fcy\u00fckt\u00fcr. . n\u00fcfus B.<\/p>\n<p> Ancak bu durumda \u00d6\u011frenci t-testi form\u00fcl\u00fc pop\u00fclasyon varyanslar\u0131n\u0131n e\u015fit olup olmad\u0131\u011f\u0131na ba\u011fl\u0131 olarak de\u011fi\u015fir. Daha sonra iki olas\u0131 durumu g\u00f6rece\u011fiz.<\/p>\n<h4 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"varianzas-desconocidas-e-iguales\"><\/span> Bilinmeyen ve e\u015fit sapmalar<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p> <strong>Pop\u00fclasyon varyanslar\u0131n\u0131n bilinmedi\u011fi ancak e\u015fit oldu\u011fu varsay\u0131ld\u0131\u011f\u0131nda ba\u011f\u0131ms\u0131z \u00f6rnekler i\u00e7in \u00d6\u011frenci t testinin hesaplanmas\u0131na 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-b879974c3d05ebcb049125dbaf9f0a48_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle t=\\frac{\\displaystyle (\\overline{x_1}-\\overline{x_2})-(\\mu_1-\\mu_2)}{\\displaystyle s_p\\sqrt{\\frac{1}{n_1}+\\frac{1}{n_2}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"67\" width=\"197\" style=\"vertical-align: -41px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\"> Alt\u0131n:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-fd9cb27edab3f0a8a249bc80cc9c6ee2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"><\/p>\n<p> n <sub>1<\/sub> + n <sub>2<\/sub> -2 serbestlik derecesine sahip bir \u00d6\u011frenci t da\u011f\u0131l\u0131m\u0131n\u0131 takip eden, bilinmeyen varyanslara sahip ortalamalar\u0131n fark\u0131na y\u00f6nelik hipotez test istatisti\u011fidir.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-776e8d37515f607d16b6ea33cf27cb8e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\mu_1\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"17\" style=\"vertical-align: -4px;\"><\/p>\n<p> n\u00fcfus 1&#8217;in ortalamas\u0131d\u0131r.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-eed6e51baac07f2aaf1c82b4b328ded8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\mu_2\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: -4px;\"><\/p>\n<p> n\u00fcfus 2&#8217;nin ortalamas\u0131d\u0131r.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-1436bb55d331d1efe559fd1e55245851_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{x_1}\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"18\" style=\"vertical-align: -3px;\"><\/p>\n<p> \u00f6rnek 1&#8217;in ortalamas\u0131d\u0131r.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-f06b28a75570ecb4df1371dea2d9f2b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{x_2}\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"18\" style=\"vertical-align: -3px;\"><\/p>\n<p> \u00f6rnek 2&#8217;nin ortalamas\u0131d\u0131r.<\/li>\n<li>\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> birle\u015ftirilmi\u015f standart sapmad\u0131r.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-cebc0a013985f2695aeb53ded9e7afb1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n_1\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"17\" style=\"vertical-align: -3px;\"><\/p>\n<p> \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc 1&#8217;dir.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-bf1e42c248eee22a0911c24c95fe28f0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n_2\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"18\" style=\"vertical-align: -3px;\"><\/p>\n<p> \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc 2&#8217;dir.<\/li>\n<\/ul>\n<p> \u0130ki numunenin birle\u015fik standart sapmas\u0131 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-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<h4 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><\/h4>\n<p> <strong>Pop\u00fclasyon varyanslar\u0131 bilinmedi\u011finde ve ayr\u0131ca farkl\u0131 oldu\u011fu varsay\u0131ld\u0131\u011f\u0131nda, ba\u011f\u0131ms\u0131z \u00f6rnekler i\u00e7in \u00d6\u011frenci t testinin hesaplanmas\u0131na y\u00f6nelik form\u00fcl a\u015fa\u011f\u0131daki<\/strong> 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-01c79415ff9c173fa4517d4b1a859a8c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle t=\\frac{\\displaystyle (\\overline{x_1}-\\overline{x_2})-(\\mu_1-\\mu_2)}{\\displaystyle \\sqrt{\\frac{s_1^2}{n_1}+\\frac{s_2^2}{n_2}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"78\" width=\"197\" style=\"vertical-align: -52px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\"> Alt\u0131n:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-fd9cb27edab3f0a8a249bc80cc9c6ee2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00d6\u011frenci t da\u011f\u0131l\u0131m\u0131n\u0131 takip eden, bilinmeyen varyanslara sahip ortalamalar\u0131n fark\u0131na y\u00f6nelik hipotez test istatisti\u011fidir.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-776e8d37515f607d16b6ea33cf27cb8e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\mu_1\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"17\" style=\"vertical-align: -4px;\"><\/p>\n<p> n\u00fcfus 1&#8217;in ortalamas\u0131d\u0131r.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-eed6e51baac07f2aaf1c82b4b328ded8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\mu_2\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: -4px;\"><\/p>\n<p> n\u00fcfus 2&#8217;nin ortalamas\u0131d\u0131r.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-1436bb55d331d1efe559fd1e55245851_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{x_1}\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"18\" style=\"vertical-align: -3px;\"><\/p>\n<p> \u00f6rnek 1&#8217;in ortalamas\u0131d\u0131r.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-f06b28a75570ecb4df1371dea2d9f2b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{x_2}\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"18\" style=\"vertical-align: -3px;\"><\/p>\n<p> \u00f6rnek 2&#8217;nin ortalamas\u0131d\u0131r.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-802bfc799b8f222d7b47270e1569770b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sigma_1\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"16\" style=\"vertical-align: -3px;\"><\/p>\n<p> pop\u00fclasyon 1&#8217;in standart sapmas\u0131d\u0131r.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-063ad2fadbc81bd1df35589566b0bd16_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sigma_2\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"17\" style=\"vertical-align: -3px;\"><\/p>\n<p> pop\u00fclasyon 2&#8217;nin standart sapmas\u0131d\u0131r.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-cebc0a013985f2695aeb53ded9e7afb1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n_1\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"17\" style=\"vertical-align: -3px;\"><\/p>\n<p> \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc 1&#8217;dir.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-bf1e42c248eee22a0911c24c95fe28f0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n_2\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"18\" style=\"vertical-align: -3px;\"><\/p>\n<p> \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc 2&#8217;dir.<\/li>\n<\/ul>\n<p> Ancak bu durumda \u00d6\u011frenci t da\u011f\u0131l\u0131m\u0131n\u0131n serbestlik dereceleri 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<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 y\u00f6nelik hipotez testinin somut \u00f6rne\u011fi<\/a> <\/div>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"prueba-t-de-student-para-muestras-pareadas-o-relacionadas\"><\/span> E\u015fle\u015ftirilmi\u015f veya ilgili \u00f6rnekler i\u00e7in \u00d6\u011frenci t testi<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> Bu test, \u00fczerinde \u00e7al\u0131\u015f\u0131lan iki numune birbiriyle ili\u015fkili oldu\u011funda kullan\u0131l\u0131r; dolay\u0131s\u0131yla bu, asl\u0131nda iki kez (her seferinde farkl\u0131 ko\u015fullar alt\u0131nda) analiz edilen tek bir birey numunesidir.<\/p>\n<p> \u00d6rne\u011fin, bir matematik ve istatistik dersindeki \u00f6\u011frenci notlar\u0131n\u0131 analiz ederek iki dersin ortalamalar\u0131 aras\u0131nda anlaml\u0131 bir fark olup olmad\u0131\u011f\u0131n\u0131 g\u00f6rebilirsiniz. Bu durumda her \u00f6\u011frencinin matematik notu ayn\u0131 \u00f6\u011frencinin istatistik notuna ba\u011flan\u0131r.<\/p>\n<p> <strong>E\u015fle\u015ftirilmi\u015f veya ilgili \u00f6rnekler i\u00e7in \u00d6\u011frenci t-testi form\u00fcl\u00fc<\/strong> \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-8dd7c22ea301c71dac72ee39ce2e1972_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle t=\\frac{\\overline{x_D}-\\mu_D}{\\displaystyle \\frac{s_D}{\\sqrt{n}}} \" title=\"Rendered by QuickLaTeX.com\" height=\"57\" width=\"100\" style=\"vertical-align: -34px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\"> Alt\u0131n:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-fd9cb27edab3f0a8a249bc80cc9c6ee2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00d6\u011frenci t da\u011f\u0131l\u0131m\u0131 ile tan\u0131mlanan e\u015fle\u015ftirilmi\u015f ortalamalar i\u00e7in hipotez test istatisti\u011fidir.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-aa774a67ebe93af6717679d0fca9e8b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{x_D}\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"23\" style=\"vertical-align: -3px;\"><\/p>\n<p> veriler aras\u0131ndaki fark\u0131n olu\u015fturdu\u011fu \u00f6rneklemin ortalamas\u0131d\u0131r.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-2df477ea5937645e4858aa3fdc9d699a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\mu_D\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: -4px;\"><\/p>\n<p> hipotez testinde \u00f6nerilen ortalaman\u0131n de\u011feridir.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-67e59a42de9fb7b544e3bbd8030feba5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s_D\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"19\" style=\"vertical-align: -3px;\"><\/p>\n<p> verilerdeki fark\u0131n olu\u015fturdu\u011fu numunenin standart sapmas\u0131d\u0131r.<\/li>\n<li>\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<\/ul>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"asunciones-de-la-prueba-t-de-student\"><\/span> \u00d6\u011frencinin t-testi varsay\u0131mlar\u0131<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u00d6\u011frenci t testini ger\u00e7ekle\u015ftirmek i\u00e7in a\u015fa\u011f\u0131daki ko\u015fullar\u0131n kar\u015f\u0131lanmas\u0131 gerekir:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:20px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>S\u00fcreklilik<\/strong> \u2013 \u00d6rnek veriler s\u00fcreklidir.<\/span><\/li>\n<li style=\"margin-bottom:20px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Rastgelelik<\/strong> : Veri \u00f6rnekleri rastgele se\u00e7ilmi\u015ftir.<\/span><\/li>\n<li style=\"margin-bottom:20px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Homojenlik<\/strong> : Veri \u00f6rne\u011finin varyans\u0131 homojendir.<\/span><\/li>\n<li style=\"margin-bottom:20px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Normallik<\/strong> \u2013 Veri \u00f6rne\u011fini tan\u0131mlayan da\u011f\u0131l\u0131m yakla\u015f\u0131k olarak normaldir.<\/span> <\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"como-hacer-una-prueba-t-de-student\"><\/span> \u00d6\u011frenci t testi nas\u0131l yap\u0131l\u0131r<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Son olarak, \u00f6zet olarak, \u00d6\u011frenci t testini ger\u00e7ekle\u015ftirmek i\u00e7in izlenecek ad\u0131mlar ayr\u0131nt\u0131l\u0131 olarak a\u00e7\u0131klanm\u0131\u015ft\u0131r.<\/p>\n<ol style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:20px\"> <span style=\"color:#101010;font-weight: normal;\">Hipotez testinin <a href=\"https:\/\/statorials.org\/tr\/bos-ve-alternatif-hipotez\/\">bo\u015f ve alternatif hipotezlerini<\/a> tan\u0131mlay\u0131n.<\/span><\/li>\n<li style=\"margin-bottom:20px\"> <span style=\"color:#101010;font-weight: normal;\">Hipotez testinin <a href=\"https:\/\/statorials.org\/tr\/onem-duzeyi\/\">anlaml\u0131l\u0131k d\u00fczeyini (\u03b1)<\/a> belirleyin.<\/span><\/li>\n<li style=\"margin-bottom:20px\"> <span style=\"color:#101010;font-weight: normal;\">\u00d6\u011frenci t testinin varsay\u0131mlar\u0131n\u0131n kar\u015f\u0131land\u0131\u011f\u0131n\u0131 do\u011frulay\u0131n.<\/span><\/li>\n<li style=\"margin-bottom:20px\"> <span style=\"color:#101010;font-weight: normal;\">\u0130lgili \u00d6\u011frenci t-testi form\u00fcl\u00fcn\u00fc uygulay\u0131n ve test istatisti\u011fini hesaplay\u0131n.<\/span><\/li>\n<li style=\"margin-bottom:20px\"> <span style=\"color:#101010;font-weight: normal;\">\u00d6\u011frenci t testinin sonucunu testin kritik de\u011feriyle kar\u015f\u0131la\u015ft\u0131rarak yorumlay\u0131n.<\/span><\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>Bu makalede, \u00d6\u011frenci t testinin ne oldu\u011fu ve istatistikte ne i\u00e7in kullan\u0131ld\u0131\u011f\u0131 a\u00e7\u0131klanmaktad\u0131r. B\u00f6ylece, \u00d6\u011frenci t testinin nas\u0131l yap\u0131ld\u0131\u011f\u0131n\u0131, farkl\u0131 \u00d6\u011frenci t testi t\u00fcrlerinin neler oldu\u011funu ve her birinin form\u00fcl\u00fcn\u00fc ke\u015ffedeceksiniz. \u00d6\u011frenci t testi nedir? Ayn\u0131 zamanda T testi veya basit\u00e7e t testi olarak da adland\u0131r\u0131lan \u00d6\u011frenci t testi , test istatisti\u011finin \u00d6\u011frencinin t da\u011f\u0131l\u0131m\u0131n\u0131 [&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-293","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 \u00d6\u011frenci t-testi<\/title>\n<meta name=\"description\" content=\"Burada \u00d6\u011frenci t testinin ne oldu\u011funu, nas\u0131l yap\u0131ld\u0131\u011f\u0131n\u0131, farkl\u0131 \u00d6\u011frenci t testi t\u00fcrlerini (form\u00fcllerini) ve \u00e7\u00f6z\u00fclm\u00fc\u015f al\u0131\u015ft\u0131rmalar\u0131 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