{"id":286,"date":"2023-08-03T03:02:31","date_gmt":"2023-08-03T03:02:31","guid":{"rendered":"https:\/\/statorials.org\/tr\/oranlardaki-fark-icin-hipotez-testi\/"},"modified":"2023-08-03T03:02:31","modified_gmt":"2023-08-03T03:02:31","slug":"oranlardaki-fark-icin-hipotez-testi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/oranlardaki-fark-icin-hipotez-testi\/","title":{"rendered":"Oranlardaki fark i\u00e7in hipotez testi"},"content":{"rendered":"<p>Bu makale oranlardaki farka y\u00f6nelik hipotez testinin ne oldu\u011funu a\u00e7\u0131klamaktad\u0131r. Ayr\u0131ca oranlar aras\u0131ndaki farka ili\u015fkin bir hipotez testinin nas\u0131l ger\u00e7ekle\u015ftirilece\u011fini ve ad\u0131m ad\u0131m bir al\u0131\u015ft\u0131rmay\u0131 da \u00f6\u011freneceksiniz. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-prueba-de-hipotesis-para-la-diferencia-de-proporciones\"><\/span> Oranlar aras\u0131ndaki fark i\u00e7in hipotez testi nedir?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Oran fark\u0131 hipotez testi,<\/strong> iki pop\u00fclasyonun oranlar\u0131n\u0131n farkl\u0131 oldu\u011fu hipotezini reddetmek veya kabul etmek i\u00e7in kullan\u0131lan bir y\u00f6ntemdir. Yani orant\u0131 fark\u0131 hipotez testi, iki pop\u00fclasyon oran\u0131n\u0131n e\u015fit olup olmad\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in kullan\u0131l\u0131r.<\/p>\n<p> Hipotez testinde al\u0131nan kararlar\u0131n \u00f6nceden belirlenmi\u015f bir g\u00fcven d\u00fczeyine dayand\u0131\u011f\u0131n\u0131, dolay\u0131s\u0131yla bir hipotez testi sonucunun her zaman do\u011fru olaca\u011f\u0131n\u0131n garanti edilemeyece\u011fini, bunun yerine en olas\u0131 sonucun do\u011fru oldu\u011funu 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\/bir-guven-seviyesi\/\">G\u00fcven d\u00fczeyi nedir? (\u0130statistik)<\/a><\/div>\n<p> \u0130ki oran\u0131n fark\u0131 i\u00e7in hipotez testi, test istatisti\u011finin hesaplanmas\u0131n\u0131 ve bo\u015f hipotezin reddedilip reddedilmeyece\u011fini kritik de\u011ferle kar\u015f\u0131la\u015ft\u0131rmay\u0131 i\u00e7erir. A\u015fa\u011f\u0131da oranlar aras\u0131ndaki farka ili\u015fkin hipotez testinin nas\u0131l yap\u0131laca\u011f\u0131n\u0131 ayr\u0131nt\u0131l\u0131 olarak a\u00e7\u0131klayaca\u011f\u0131z.<\/p>\n<p> Son olarak, istatistikte hipotez testine hipotez kar\u015f\u0131tl\u0131klar\u0131, hipotez testi veya anlaml\u0131l\u0131k testi de denilebilece\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\/ortalamalar-arasindaki-farka-yonelik-hipotez-testi\/\">Ortalamalar aras\u0131ndaki fark i\u00e7in hipotez testi<\/a> <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-prueba-de-hipotesis-para-la-diferencia-de-proporciones\"><\/span> Oranlardaki Fark i\u00e7in Hipotez Testi Form\u00fcl\u00fc<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0130ki pop\u00fclasyonun <strong>oranlar\u0131ndaki farka ili\u015fkin 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-161267e1562535b8ded23017389e0807_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle Z=\\frac{\\displaystyle (\\widehat{p_1}-\\widehat{p_2})-(p_1-p_2)}{\\displaystyle \\sqrt{p_0(1-p_0)\\left(\\frac{1}{n_1}+\\frac{1}{n_2}\\right)}}\" title=\"Rendered by QuickLaTeX.com\" height=\"78\" width=\"229\" 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-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> oranlardaki farka ili\u015fkin 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-023bcfb3fa329ff4f481163d36b65bf9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"p_1\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: -4px;\"><\/p>\n<p> n\u00fcfus oran\u0131 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-1a0ac2d00900c29ac35c13956874c642_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"p_2\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"17\" style=\"vertical-align: -4px;\"><\/p>\n<p> n\u00fcfus oran\u0131 2&#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-a4c76b176c372799a3a3a7aa8858eecf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\widehat{p_1}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"16\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u00f6rnek 1&#8217;in 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-cd7916af5298a603fad64ab8fb2501a5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\widehat{p_2}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"17\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u00f6rnek oran\u0131 2&#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-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<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-ccd892ed2f60029f47331cf785d30482_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"p_0\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"17\" style=\"vertical-align: -4px;\"><\/p>\n<p> iki numunenin birle\u015fik oran\u0131d\u0131r.<\/li>\n<\/ul>\n<p> \u0130ki numunenin birle\u015fik oran\u0131 a\u015fa\u011f\u0131daki \u015fekilde 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-6f349422474d622468a6a14f445f2eb3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"p_0=\\cfrac{x_1+x_2}{n_1+n_2}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"102\" style=\"vertical-align: -15px;\"><\/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-dad27a9703483183e1afd245f5232b83_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x_i\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"15\" style=\"vertical-align: -3px;\"><\/p>\n<p> \u00f6rnekteki sonu\u00e7lar\u0131n say\u0131s\u0131 iy<\/p>\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. <\/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\/oranlardaki-fark-icin-guven-araligi\/\">Oranlardaki fark i\u00e7in g\u00fcven aral\u0131\u011f\u0131<\/a> <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-resuelto-de-la-prueba-de-hipotesis-para-la-diferencia-de-proporciones\"><\/span> Oranlardaki fark i\u00e7in hipotez testinin somut \u00f6rne\u011fi<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Oranlardaki farka y\u00f6nelik hipotez testinin neleri i\u00e7erdi\u011fini g\u00f6rmeyi bitirmek i\u00e7in, bu t\u00fcr hipotez testinin ad\u0131m ad\u0131m \u00e7\u00f6z\u00fclm\u00fc\u015f bir \u00f6rne\u011fi a\u015fa\u011f\u0131da g\u00f6sterilmi\u015ftir.<\/p>\n<ul>\n<li> Ayn\u0131 hastal\u0131k i\u00e7in kullan\u0131lan iki ilac\u0131n etkisinde anlaml\u0131 fark olup olmad\u0131\u011f\u0131n\u0131 analiz etmek istiyoruz. Bunun i\u00e7in 60 ki\u015filik bir \u00f6rneklem grubuna ila\u00e7lardan biri uygulan\u0131yor ve 48 ki\u015fi iyile\u015fiyor. \u00d6te yandan di\u011fer ila\u00e7 65 hastadan olu\u015fan bir \u00f6rneklemde uygulan\u0131yor ve 55&#8217;i tedavi ediliyor. Her bir ila\u00e7la iyile\u015fen ki\u015filerin y\u00fczdesinin farkl\u0131 olup olmad\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in %5 anlaml\u0131l\u0131k d\u00fczeyine sahip bir hipotez testi yap\u0131n.<\/li>\n<\/ul>\n<p> Bu problemin test hipotezi a\u015fa\u011f\u0131daki s\u0131f\u0131r hipotezi ve alternatif hipotezden olu\u015fur:<\/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-06d3762df12e74f2c5204a5e57f4e451_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{cases}H_0: p_1-p_2=0\\\\[2ex] H_1:p_1-p_2\\neq 0 \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"137\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> \u0130lk olarak, ba\u015far\u0131l\u0131 vakalar\u0131n say\u0131s\u0131n\u0131 \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fcne b\u00f6lerek her bir \u00f6rne\u011fin oran\u0131n\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-cb931a4f209ae3f6468f761d9a1978c8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\widehat{p_1}=\\cfrac{48}{60}=0,80\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"119\" style=\"vertical-align: -12px;\"><\/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-3946308ea76348e30ec338f8500ee655_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\widehat{p_1}=\\cfrac{55}{65}=0,85\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"118\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Daha sonra iki \u00f6rne\u011fin birle\u015fik oran\u0131n\u0131 buluyoruz:<\/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-e536a515c55598373f535a15de012c5d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"p_0=\\cfrac{48+55}{60+65}=0,82\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"158\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p> Daha sonra, test istatisti\u011fini hesaplamak i\u00e7in oranlar aras\u0131ndaki farka y\u00f6nelik hipotez test form\u00fcl\u00fcn\u00fc uyguluyoruz:<\/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-a9f3f8f1a427577abac02e3f6c119be8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\displaystyle Z&amp;=\\frac{\\displaystyle (\\widehat{p_1}-\\widehat{p_2})-(p_1-p_2)}{\\displaystyle \\sqrt{p_0(1-p_0)\\left(\\frac{1}{n_1}+\\frac{1}{n_2}\\right)}}\\\\[2ex]\\displaystyle Z&amp;=\\frac{\\displaystyle (0,80-0,85)-0}{\\displaystyle \\sqrt{0,82\\cdot(1-0,82)\\left(\\frac{1}{60}+\\frac{1}{65}\\right)}}\\\\[2ex]\\displaystyle Z&amp;=-0,73 \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"218\" width=\"277\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Buna kar\u015f\u0131l\u0131k <a href=\"https:\/\/statorials.org\/tr\/normal-dagilim-tablosu\/\">Tablo Z&#8217;de<\/a> hipotez testinin kritik de\u011ferini ar\u0131yoruz. Anlaml\u0131l\u0131k d\u00fczeyi 0,05 oldu\u011fundan ve bu iki y\u00f6nl\u00fc bir hipotez testi oldu\u011fundan testin kritik de\u011feri 1,96&#8217;d\u0131r.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-8154fa6e5bfee35698c6dc26928cd98c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\alpha=0,05 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black}\\ \\alpha\/2=0,025\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"300\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-54dda39d0da5b29f2d25728b89565859_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}Z_{\\alpha\/2}= \\ \\color{orange}\\bm{?}\\\\[4ex]Z_{0,025}=1,96\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"71\" width=\"127\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Test istatisti\u011finin mutlak de\u011feri kritik de\u011ferden k\u00fc\u00e7\u00fck oldu\u011fu i\u00e7in alternatif hipotez reddedilir ve testin s\u0131f\u0131r hipotezi kabul edilir. <\/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-f336118d0fd06640ec390f85b90d1086_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"|-0,73|=0,73<1,96 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Se rechaza } H_1\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"423\" 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\/oranlar-farkinin-ornekleme-dagilimi\/\">Oranlardaki Fark\u0131n \u00d6rnekleme Da\u011f\u0131l\u0131m\u0131<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Bu makale oranlardaki farka y\u00f6nelik hipotez testinin ne oldu\u011funu a\u00e7\u0131klamaktad\u0131r. Ayr\u0131ca oranlar aras\u0131ndaki farka ili\u015fkin bir hipotez testinin nas\u0131l ger\u00e7ekle\u015ftirilece\u011fini ve ad\u0131m ad\u0131m bir al\u0131\u015ft\u0131rmay\u0131 da \u00f6\u011freneceksiniz. Oranlar aras\u0131ndaki fark i\u00e7in hipotez testi nedir? Oran fark\u0131 hipotez testi, iki pop\u00fclasyonun oranlar\u0131n\u0131n farkl\u0131 oldu\u011fu hipotezini reddetmek veya kabul etmek i\u00e7in kullan\u0131lan bir y\u00f6ntemdir. Yani orant\u0131 fark\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-286","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 Oranlardaki fark i\u00e7in hipotez testi<\/title>\n<meta name=\"description\" content=\"Burada oranlar aras\u0131ndaki farka ili\u015fkin hipotez testinin ne oldu\u011funu, nas\u0131l ger\u00e7ekle\u015ftirildi\u011fini (form\u00fcl) ve somut bir \u00f6rne\u011fi bulacaks\u0131n\u0131z.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" 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