{"id":268,"date":"2023-08-03T09:00:18","date_gmt":"2023-08-03T09:00:18","guid":{"rendered":"https:\/\/statorials.org\/tr\/kontrast-istatistikleri\/"},"modified":"2023-08-03T09:00:18","modified_gmt":"2023-08-03T09:00:18","slug":"kontrast-istatistikleri","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/kontrast-istatistikleri\/","title":{"rendered":"Kontrast istatistikleri"},"content":{"rendered":"<p>Bu makale kontrast istatisti\u011finin ne oldu\u011funu, kontrast istatistikleri i\u00e7in en yayg\u0131n form\u00fcllerin neler oldu\u011funu ve daha fazlas\u0131n\u0131 kontrast istatisti\u011fi, ret b\u00f6lgesi ve kabul b\u00f6lgesi aras\u0131ndaki ili\u015fkiyi a\u00e7\u0131klamaktad\u0131r. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-el-estadistico-de-contraste\"><\/span> Kontrast istatisti\u011fi nedir?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Kontrast istatisti\u011fi<\/strong> , \u00e7al\u0131\u015fma hipoteziyle ilgili olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131 bilinen bir de\u011fi\u015fkendir. Spesifik olarak, kontrast istatisti\u011fi hipotez testinde bo\u015f hipotezi reddetmek veya kabul etmek i\u00e7in kullan\u0131l\u0131r.<\/p>\n<p> Asl\u0131nda bir hipotez testinin bo\u015f hipotezinin reddedilip reddedilmeyece\u011fi karar\u0131, test istatisti\u011finin de\u011ferine ba\u011fl\u0131d\u0131r. Test istatisti\u011finin de\u011feri red b\u00f6lgesine d\u00fc\u015ferse s\u0131f\u0131r hipotezi reddedilir. oysa test istatisti\u011finin de\u011feri kabul b\u00f6lgesi i\u00e7inde kal\u0131yorsa s\u0131f\u0131r hipotezi kabul edilir. <\/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\/hipotez-kontrasti\/\">Hipotez testleri (istatistikler)<\/a> <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formulas-de-estadisticos-de-contraste\"><\/span> Kontrast \u0130statistik Form\u00fclleri<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Hipotez testinin t\u00fcr\u00fcne ba\u011fl\u0131 olarak test istatisti\u011finin da\u011f\u0131l\u0131m\u0131 farkl\u0131d\u0131r. Bu nedenle test istatisti\u011finin form\u00fcl\u00fc ayn\u0131 zamanda hipotez testinin t\u00fcr\u00fcne de ba\u011fl\u0131d\u0131r. \u015eimdi hipotez testinin t\u00fcr\u00fcne ba\u011fl\u0131 olarak test istatisti\u011finin nas\u0131l hesapland\u0131\u011f\u0131n\u0131 g\u00f6rece\u011fiz. <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"estadistico-de-contraste-para-la-media\"><\/span> Ortalama i\u00e7in kontrast istatisti\u011fi<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> <strong>Bilinen varyansl\u0131 ortalamaya ili\u015fkin hipotez test istatisti\u011finin 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-fdf1817a07bfb8c1eda9a8d8ccd8c828_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle Z=\\frac{\\overline{x}-\\mu}{\\displaystyle \\frac{\\sigma}{\\sqrt{n}}} \" title=\"Rendered by QuickLaTeX.com\" height=\"57\" width=\"81\" 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-0be116875001706f29a24434bd0d91c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Z\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\"><\/p>\n<p> ortalama i\u00e7in 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> \u00f6nerilen ortalama de\u011ferdir.<\/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-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> n\u00fcfus 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> Ortalama i\u00e7in hipotez kontrast istatisti\u011fi hesapland\u0131ktan sonra sonu\u00e7, s\u0131f\u0131r hipotezini reddedecek veya reddedecek \u015fekilde 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, istatisti\u011fin mutlak de\u011feri Z <sub>\u03b1\/2<\/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;\">Ortalamaya y\u00f6nelik hipotez testi sa\u011f kuyrukla e\u015fle\u015fiyorsa, istatisti\u011fin Z <sub>\u03b1<\/sub> kritik de\u011ferinden b\u00fcy\u00fck olmas\u0131 durumunda 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\u015firse, istatistik kritik de\u011fer -Z <sub>\u03b1&#8217;dan<\/sub> 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-0e2ccadfc369eb7543b8f86dfccc528e_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 } |Z|>Z_{\\alpha\/2} \\text{ se rechaza } H_0\\\\[3ex]H_1: \\mu> \\mu_0 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Si } Z>Z_{\\alpha} \\text{ se rechaza } H_0\\\\[3ex]H_1: \\mu< \\mu_0 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Si } Z<-Z_{\\alpha} \\text{ se rechaza } H_0\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"108\" width=\"440\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Bu durumda kritik de\u011ferler standartla\u015ft\u0131r\u0131lm\u0131\u015f normal da\u011f\u0131l\u0131m tablosundan elde edilir.<\/p>\n<p> \u00d6te yandan, <strong>bilinmeyen varyansl\u0131 ortalamaya ili\u015fkin hipotez test istatisti\u011finin 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-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> \u00f6nerilen ortalama de\u011ferdir.<\/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> Daha \u00f6nce oldu\u011fu gibi, kontrast istatisti\u011finin hesaplanan sonucu, bo\u015f hipotezin reddedilmesi veya reddedilmemesi i\u00e7in kritik de\u011ferle 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;\">Ortalamaya y\u00f6nelik hipotez testi iki tarafl\u0131 ise, istatisti\u011fin 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, istatisti\u011fin <sub>t\u03b1|n-1<\/sub> kritik de\u011ferinden b\u00fcy\u00fck olmas\u0131 durumunda 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\u015firse, istatistik kritik de\u011fer -t <sub>\u03b1|n-1&#8217;den<\/sub> 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> Varyans\u0131n bilinmedi\u011fi durumlarda kritik test de\u011ferleri \u00d6\u011frenci da\u011f\u0131l\u0131m tablosundan elde edilir. <\/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 testi<\/a> <\/div>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"estadistico-de-contraste-para-la-proporcion\"><\/span> Orant\u0131 i\u00e7in kontrast istatisti\u011fi<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> <strong>Oran i\u00e7in hipotez test istatisti\u011finin 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-e2f5ad36dae72cd89279809ab3ea6d20_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle Z=\\frac{\\widehat{p}-p}{\\displaystyle\\sqrt{\\frac{p(1-p)}{n}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"67\" width=\"123\" 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-0be116875001706f29a24434bd0d91c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Z\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\"><\/p>\n<p> orana 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-ecd29d136a62fc6b274e1181e064e20e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\widehat{p}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"12\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u00f6rnek oran\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-5faad0904f612a3fa5b27faafb8dc903_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"p\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u00f6nerilen orant\u0131 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-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>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-661a2bbf8dccd197bcf450330420cbc1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\sqrt{\\frac{p(1-p)}{n}}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"84\" style=\"vertical-align: -13px;\"><\/p>\n<p> oran\u0131n standart sapmas\u0131d\u0131r.<\/li>\n<\/ul>\n<p> Oran i\u00e7in hipotez testi istatisti\u011fini hesaplaman\u0131n yeterli olmad\u0131\u011f\u0131n\u0131, ancak sonucun yorumlanmas\u0131 gerekti\u011fini unutmay\u0131n:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">Oran i\u00e7in hipotez testi iki tarafl\u0131 ise, istatisti\u011fin mutlak de\u011feri Z <sub>\u03b1\/2<\/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;\">Oran i\u00e7in hipotez testi sa\u011f kuyrukla e\u015fle\u015firse, istatisti\u011fin Z <sub>\u03b1<\/sub> kritik de\u011ferinden b\u00fcy\u00fck olmas\u0131 durumunda s\u0131f\u0131r hipotezi reddedilir.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">Oran i\u00e7in hipotez testi sol kuyrukla e\u015fle\u015firse, istatisti\u011fin -Z <sub>\u03b1<\/sub> kritik de\u011ferinden k\u00fc\u00e7\u00fck olmas\u0131 durumunda 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-7d5bd583532769e3014286e8ffd94c9f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{l}H_1: p\\neq p_0 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Si } |Z|>Z_{\\alpha\/2} \\text{ se rechaza } H_0\\\\[3ex]H_1: p> p_0 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Si } Z>Z_{\\alpha} \\text{ se rechaza } H_0\\\\[3ex]H_1: p< p_0 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Si } Z<-Z_{\\alpha} \\text{ se rechaza } H_0\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"108\" width=\"437\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Kritik de\u011ferlerin standart normal da\u011f\u0131l\u0131m tablosundan kolayl\u0131kla elde edilebilece\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\/oranti-icin-hipotez-testi\/\">Oran i\u00e7in hipotez testi<\/a> <\/div>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"estadistico-de-contraste-para-la-varianza\"><\/span> Varyans i\u00e7in kontrast istatisti\u011fi<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> <strong>Varyans i\u00e7in hipotez testi istatisti\u011fini hesaplama 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-3917636d4c911eeaad1a005195204d08_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\chi^2=\\cfrac{(n-1)s^2}{\\sigma^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"115\" style=\"vertical-align: -12px;\"><\/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-984dc78529fc235b078a9f3b62d0f0c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\chi^2\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"18\" style=\"vertical-align: -4px;\"><\/p>\n<p> ki-kare da\u011f\u0131l\u0131m\u0131na sahip varyans 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-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>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-3ab572e85f9cb7cb6f495387f2a6ab0b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s^2\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"15\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00f6rnek varyans\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-c6d52162ef1ec2e8130fb00687aca707_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sigma^2\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"18\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00f6nerilen pop\u00fclasyonun varyans\u0131d\u0131r.<\/li>\n<\/ul>\n<p> \u0130statisti\u011fin sonucunun yorumlanabilmesi i\u00e7in elde edilen de\u011ferin testin kritik de\u011feri ile kar\u015f\u0131la\u015ft\u0131r\u0131lmas\u0131 gerekir.<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">Varyans i\u00e7in hipotez testi iki kuyruklu ise, istatistik kritik de\u011ferden b\u00fcy\u00fckse s\u0131f\u0131r hipotezi reddedilir.\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-7bd4ac2951fb286bf19797944cba6955_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\chi_{1-\\alpha\/2|n-1}^2\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"81\" style=\"vertical-align: -10px;\"><\/p>\n<p><\/span> veya kritik de\u011ferin alt\u0131ndaysa<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-931a3f10ab51df1c9003e6cb593907c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\chi_{\\alpha\/2|n-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"63\" style=\"vertical-align: -8px;\"><\/p>\n<p> .<\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">Varyans i\u00e7in hipotez testi sa\u011f kuyrukla e\u015fle\u015fiyorsa, istatistik kritik de\u011ferden b\u00fcy\u00fckse s\u0131f\u0131r hipotezi reddedilir\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-243ef3cc114070613fd8bee8c61f8c13_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\chi_{1-\\alpha|n-1}^2\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"67\" style=\"vertical-align: -10px;\"><\/p>\n<p><\/span> .<\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">Varyans i\u00e7in hipotez testi sol kuyrukla e\u015fle\u015firse, istatistik kritik de\u011ferden k\u00fc\u00e7\u00fckse s\u0131f\u0131r hipotezi reddedilir\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-0436c61e0bdff7a21f6e6ab296607c66_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\chi_{\\alpha|n-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"49\" style=\"vertical-align: -8px;\"><\/p>\n<p><\/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-ca46378c1a2ee04b5cc5bfa93002fe9c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{l}H_1: \\sigma^2\\neq \\sigma_0 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Si } \\chi^2>\\chi^2_{1-\\alpha\/2|n-1}\\text{ se rechaza } H_0\\\\[3ex]H_1: \\sigma^2\\neq \\sigma_0 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Si }\\chi^2<\\chi^2_{\\alpha\/2|n-1}\\text{ se rechaza } H_0 \\\\[3ex]H_1: \\sigma^2> \\sigma_0 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Si } \\chi^2>\\chi^2_{1-\\alpha|n-1}\\text{ se rechaza } H_0\\\\[3ex]H_1: \\sigma^2< \\sigma_0 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Si } \\chi^2<\\chi^2_{\\alpha|n-1}\\text{ se rechaza } H_0\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"160\" width=\"489\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Varyansa ili\u015fkin kritik hipotez testi de\u011ferleri ki-kare da\u011f\u0131l\u0131m tablosundan elde edilir. Ki-kare da\u011f\u0131l\u0131m\u0131n\u0131n serbestlik derecesinin \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc eksi 1 oldu\u011funa dikkat edin. <\/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\/varyans-icin-hipotez-testi\/\">Varyans hipotez testi<\/a> <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"estadistico-de-contraste-region-de-rechazo-y-region-de-aceptacion\"><\/span> Kontrast istatisti\u011fi, ret b\u00f6lgesi ve kabul b\u00f6lgesi<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Bir hipotez testinde <strong>ret b\u00f6lgesi<\/strong> , test istatisti\u011finin da\u011f\u0131l\u0131m grafi\u011finin bo\u015f hipotezin reddedildi\u011fini (ve alternatif hipotezin kabul edildi\u011fini) ima eden b\u00f6lgesidir. Di\u011fer yandan <strong>kabul b\u00f6lgesi<\/strong> , test istatisti\u011finin da\u011f\u0131l\u0131m grafi\u011finde bo\u015f hipotezin kabul edildi\u011fini (ve alternatif hipotezin reddedildi\u011fini) ima eden b\u00f6lgedir.<\/p>\n<p> Dolay\u0131s\u0131yla kontrast istatisti\u011finin de\u011feri, bir hipotez testinin sonucunu \u015fu \u015fekilde belirler:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">Test istatisti\u011fi ret b\u00f6lgesi i\u00e7inde kal\u0131yorsa s\u0131f\u0131r hipotezi reddedilir ve alternatif hipotez kabul edilir.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">Test istatisti\u011finin kabul b\u00f6lgesi i\u00e7inde kalmas\u0131 durumunda s\u0131f\u0131r hipotezi kabul edilir ve alternatif hipotez reddedilir.<\/span><\/li>\n<\/ul>\n<p> Reddetme b\u00f6lgesini kabul b\u00f6lgesinden ay\u0131ran de\u011ferlere <strong>kritik de\u011ferler<\/strong> denir. Bu nedenle ret b\u00f6lgesinin ve kabul b\u00f6lgesinin s\u0131n\u0131rlar\u0131n\u0131 bilmek ve dolay\u0131s\u0131yla s\u0131f\u0131r hipotezini ne zaman reddedece\u011fimizi ve ne zaman kabul edece\u011fimizi bilmek i\u00e7in kritik de\u011ferleri hesaplamam\u0131z gerekir. <\/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\/kritik-deger\/\">Kritik de\u011fer<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Bu makale kontrast istatisti\u011finin ne oldu\u011funu, kontrast istatistikleri i\u00e7in en yayg\u0131n form\u00fcllerin neler oldu\u011funu ve daha fazlas\u0131n\u0131 kontrast istatisti\u011fi, ret b\u00f6lgesi ve kabul b\u00f6lgesi aras\u0131ndaki ili\u015fkiyi a\u00e7\u0131klamaktad\u0131r. Kontrast istatisti\u011fi nedir? Kontrast istatisti\u011fi , \u00e7al\u0131\u015fma hipoteziyle ilgili olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131 bilinen bir de\u011fi\u015fkendir. Spesifik olarak, kontrast istatisti\u011fi hipotez testinde bo\u015f hipotezi reddetmek veya kabul etmek i\u00e7in kullan\u0131l\u0131r. [&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-268","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 Kontrast istatistikleri<\/title>\n<meta name=\"description\" content=\"Burada kontrast istatistiklerinin ne oldu\u011funu ve hipotez testlerinde en \u00e7ok hangi kontrast istatistik form\u00fcllerinin kullan\u0131ld\u0131\u011f\u0131n\u0131 \u00f6\u011freneceksiniz.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/statorials.org\/tr\/kontrast-istatistikleri\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u25b7 Kontrast istatistikleri\" \/>\n<meta property=\"og:description\" content=\"Burada kontrast istatistiklerinin ne oldu\u011funu ve hipotez testlerinde en \u00e7ok hangi kontrast istatistik form\u00fcllerinin kullan\u0131ld\u0131\u011f\u0131n\u0131 \u00f6\u011freneceksiniz.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/tr\/kontrast-istatistikleri\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-08-03T09:00:18+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-fdf1817a07bfb8c1eda9a8d8ccd8c828_l3.png\" \/>\n<meta name=\"author\" content=\"Dr.benjamin anderson\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Yazan:\" \/>\n\t<meta name=\"twitter:data1\" content=\"Dr.benjamin anderson\" \/>\n\t<meta name=\"twitter:label2\" content=\"Tahmini okuma s\u00fcresi\" \/>\n\t<meta name=\"twitter:data2\" content=\"5 dakika\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/tr\/kontrast-istatistikleri\/\",\"url\":\"https:\/\/statorials.org\/tr\/kontrast-istatistikleri\/\",\"name\":\"\u25b7 Kontrast istatistikleri\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/tr\/#website\"},\"datePublished\":\"2023-08-03T09:00:18+00:00\",\"dateModified\":\"2023-08-03T09:00:18+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/tr\/#\/schema\/person\/365dc158a39a7c8ae256355451e3de48\"},\"description\":\"Burada kontrast istatistiklerinin ne oldu\u011funu ve hipotez testlerinde en \u00e7ok hangi kontrast istatistik form\u00fcllerinin kullan\u0131ld\u0131\u011f\u0131n\u0131 \u00f6\u011freneceksiniz.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/tr\/kontrast-istatistikleri\/#breadcrumb\"},\"inLanguage\":\"tr\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/tr\/kontrast-istatistikleri\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/tr\/kontrast-istatistikleri\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Ev\",\"item\":\"https:\/\/statorials.org\/tr\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Kontrast istatistikleri\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/statorials.org\/tr\/#website\",\"url\":\"https:\/\/statorials.org\/tr\/\",\"name\":\"Statorials\",\"description\":\"\u0130statistik okuryazarl\u0131\u011f\u0131 rehberiniz!\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/statorials.org\/tr\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"tr\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/statorials.org\/tr\/#\/schema\/person\/365dc158a39a7c8ae256355451e3de48\",\"name\":\"Dr.benjamin anderson\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"tr\",\"@id\":\"https:\/\/statorials.org\/tr\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/statorials.org\/tr\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"contentUrl\":\"https:\/\/statorials.org\/tr\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"caption\":\"Dr.benjamin anderson\"},\"description\":\"Merhaba, ben Benjamin, emekli bir istatistik profes\u00f6r\u00fc ve Statorials \u00f6\u011fretmenine d\u00f6n\u00fc\u015ft\u00fcm. \u0130statistik alan\u0131ndaki kapsaml\u0131 deneyimim ve uzmanl\u0131\u011f\u0131mla, \u00f6\u011frencilerimi Statorials arac\u0131l\u0131\u011f\u0131yla g\u00fc\u00e7lendirmek i\u00e7in bilgilerimi payla\u015fmaya can at\u0131yorum. 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