{"id":307,"date":"2023-08-02T18:50:10","date_gmt":"2023-08-02T18:50:10","guid":{"rendered":"https:\/\/statorials.org\/tr\/varyans-analizi-anova\/"},"modified":"2023-08-02T18:50:10","modified_gmt":"2023-08-02T18:50:10","slug":"varyans-analizi-anova","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/varyans-analizi-anova\/","title":{"rendered":"Varyans analizi (anova)"},"content":{"rendered":"<p>Bu makale istatistikte ANOVA olarak da bilinen varyans analizinin ne oldu\u011funu a\u00e7\u0131klamaktad\u0131r. B\u00f6ylece varyans analizinin nas\u0131l yap\u0131laca\u011f\u0131n\u0131, ANOVA tablosunun ne oldu\u011funu ve ad\u0131m ad\u0131m \u00e7\u00f6z\u00fclm\u00fc\u015f bir al\u0131\u015ft\u0131rmay\u0131 ke\u015ffedeceksiniz. Ayr\u0131ca varyans analizi ger\u00e7ekle\u015ftirmek i\u00e7in uyulmas\u0131 gereken \u00f6n varsay\u0131mlar\u0131n neler oldu\u011funu ve son olarak ANOVA analizinin avantaj ve dezavantajlar\u0131n\u0131n neler oldu\u011funu g\u00f6sterir. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-el-analisis-de-la-varianza-anova\"><\/span> Varyans analizi (ANOVA) nedir?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0130statistikte, <strong>ANOVA<\/strong> (Varyans Analizi) olarak da adland\u0131r\u0131lan <strong>varyans analizi<\/strong> , farkl\u0131 \u00f6rneklerin ortalamalar\u0131 aras\u0131ndaki varyanslar\u0131 kar\u015f\u0131la\u015ft\u0131rman\u0131za olanak tan\u0131yan bir tekniktir.<\/p>\n<p> Varyans analizi (ANOVA), ikiden fazla pop\u00fclasyonun ortalamalar\u0131 aras\u0131nda fark olup olmad\u0131\u011f\u0131n\u0131 analiz etmek i\u00e7in kullan\u0131l\u0131r. B\u00f6ylece varyans analizi, \u00f6rnek ortalamalar\u0131 aras\u0131ndaki de\u011fi\u015fkenli\u011fi analiz ederek iki veya daha fazla grubun pop\u00fclasyon ortalamalar\u0131n\u0131n farkl\u0131 olup olmad\u0131\u011f\u0131n\u0131 belirlememize olanak tan\u0131r.<\/p>\n<p> Dolay\u0131s\u0131yla varyans analizinin s\u0131f\u0131r hipotezi, analiz edilen t\u00fcm gruplar\u0131n ortalamalar\u0131n\u0131n e\u015fit oldu\u011fu y\u00f6n\u00fcndedir. Alternatif hipotez, ara\u00e7lardan en az birinin farkl\u0131 oldu\u011funu savunur.<\/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-6918550a8ad2954432ea33e07c7b83d0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{cases}H_0: \\mu_1=\\mu_2=\\ldots=\\mu_k=\\mu\\\\[2ex]H_1: \\exists \\mu_i\\neq \\mu \\quad i=1,2,\\ldots, k\\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"232\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Dolay\u0131s\u0131yla, varyans analizi \u00f6zellikle ikiden fazla grubun ortalamalar\u0131n\u0131 kar\u015f\u0131la\u015ft\u0131rmak i\u00e7in kullan\u0131\u015fl\u0131d\u0131r, \u00e7\u00fcnk\u00fc bu t\u00fcr bir analizle ortalamalar\u0131 \u00e7iftler halinde kar\u015f\u0131la\u015ft\u0131rmak yerine t\u00fcm gruplar\u0131n ortalamalar\u0131n\u0131 ayn\u0131 anda inceleyebilirsiniz. A\u015fa\u011f\u0131da varyans analizinin avantaj ve dezavantajlar\u0131n\u0131n neler oldu\u011funu g\u00f6rece\u011fiz.<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"tabla-anova\"><\/span> ANOVA tablosu<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Varyans analizi, form\u00fclleri a\u015fa\u011f\u0131daki gibi olan <strong>ANOVA tablosu<\/strong> ad\u0131 verilen bir tabloda \u00f6zetlenmi\u015ftir: <\/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\/tableau-anova-formules-.png\" alt=\"varyans analizi veya ANOVA form\u00fclleri\" class=\"wp-image-6387\" width=\"664\" height=\"397\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p style=\"margin-bottom:5px\"> Alt\u0131n:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-5f087375b50e0b49186779714206626b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n_i\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"16\" style=\"vertical-align: -3px;\"><\/p>\n<p> \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc i&#8217;dir.<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-7354bae77b50b7d1faed3e8ea7a3511a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"N\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: 0px;\"><\/p>\n<p> toplam g\u00f6zlem say\u0131s\u0131d\u0131r.<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-d42bc2203d6f76ad01b27ac9acc0bee1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> varyans analizindeki farkl\u0131 gruplar\u0131n say\u0131s\u0131d\u0131r.<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-393bb0c333649c80fe6365339bc42b38_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y_{ij}\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"20\" style=\"vertical-align: -6px;\"><\/p>\n<p> i grubunun j de\u011feridir.<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-8effb66cfe7466ba329c455ccb9289f1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{y}_{i}\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"14\" style=\"vertical-align: -4px;\"><\/p>\n<p> i grubunun ortalamas\u0131d\u0131r.<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-ed5becac4ccb36fec040f449ba9fa52d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{y}\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"10\" style=\"vertical-align: -4px;\"><\/p>\n<p> Bu, analiz edilen t\u00fcm verilerin ortalamas\u0131d\u0131r. <\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-un-analisis-de-la-varianza-anova\"><\/span> Varyans Analizi \u00d6rne\u011fi (ANOVA)<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> ANOVA kavram\u0131n\u0131 anlamay\u0131 tamamlamak i\u00e7in ad\u0131m ad\u0131m bir \u00f6rnek \u00e7\u00f6zerek varyans analizinin nas\u0131l yap\u0131ld\u0131\u011f\u0131n\u0131 g\u00f6relim.<\/p>\n<ul>\n<li> D\u00f6rt \u00f6\u011frencinin \u00fc\u00e7 farkl\u0131 dersten (A, B ve C) ald\u0131klar\u0131 puanlar\u0131 kar\u015f\u0131la\u015ft\u0131rmak i\u00e7in istatistiksel bir \u00e7al\u0131\u015fma yap\u0131l\u0131r. A\u015fa\u011f\u0131daki tablo, her \u00f6\u011frencinin maksimum 20 puana sahip bir testte ald\u0131\u011f\u0131 puanlar\u0131 detayland\u0131rmaktad\u0131r. Her \u00f6\u011frencinin her derste ald\u0131\u011f\u0131 puanlar\u0131 kar\u015f\u0131la\u015ft\u0131rmak i\u00e7in bir varyans analizi yap\u0131n. <\/li>\n<\/ul>\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/table-anova-donnees.png\" alt=\"\" class=\"wp-image-6389\" width=\"471\" height=\"205\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> Bu varyans analizinin s\u0131f\u0131r hipotezi, \u00fc\u00e7 dene\u011fin puanlar\u0131n\u0131n ortalamalar\u0131n\u0131n e\u015fit olmas\u0131d\u0131r. \u00d6te yandan s\u0131f\u0131r hipotezi bu yollardan baz\u0131lar\u0131n\u0131n farkl\u0131 oldu\u011fu y\u00f6n\u00fcndedir.<\/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-d1587da405a54d6a2bae626989b04562_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{cases}H_0: \\mu_A=\\mu_B=\\mu_C=\\mu\\\\[2ex]H_1: \\exists \\mu_i\\neq \\mu \\quad i=A, B, C\\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"215\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Varyans analizini ger\u00e7ekle\u015ftirmek i\u00e7in yap\u0131lacak ilk \u015fey, her bir konunun ortalamas\u0131n\u0131 ve verilerin toplam ortalamas\u0131n\u0131 hesaplamakt\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-792e2e662519db421d0c9c4d7f831282_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{y}_A=\\cfrac{14+12+14+10}{4}=12,5\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"239\" 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-ace3ea8d1e0ce91dafdf4b5458e9760a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{y}_B=\\cfrac{13+14+10+14}{4}=12,75\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"249\" 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-d2781ad166914d48b6d458fe8e326f7d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{y}_C=\\cfrac{19+17+16+19}{4}=17,75\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"249\" 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-26caf7f83546e9112594e6886e8dccae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{y}=\\cfrac{14+12+14+10+13+14+10+14+19+17+16+19}{12}=14,33\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"553\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Ortalamalar\u0131n de\u011ferini \u00f6\u011frendikten sonra, yukar\u0131da g\u00f6r\u00fclen varyans analizi (ANOVA) form\u00fcllerini kullanarak kareler toplamlar\u0131n\u0131 hesaplar\u0131z: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-77b3fecdc3b577841da684cd80297288_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\displaystyle SS_F&amp;=\\sum_{i=1}^k n_i(\\overline{y}_i-\\overline{y})^2\\\\[2ex] SS_F&amp;= 4\\cdot (12,5-14,33)^2+4\\cdot (12,75-14,33)^2+4\\cdot (17,75-14,33)^2\\\\[2ex] SS_F&amp;=70,17\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"138\" width=\"546\" style=\"vertical-align: 0px;\"><\/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-aa02f1b826df45c26ead3537ecc4c7e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\displaystyle SS_E=&amp;\\sum_{i=1}^k\\sum_{j=1}^{n_i} (y_{ij}-\\overline{y}_i)^2\\\\[2ex] \\displaystyle SS_E=\\ &amp;(14-12,5)^2+(12-12,5)^2+(14-12,5)^2+(10-12,5)^2+\\\\&amp;+(13-12,75)^2+(14-12,75)^2+(10-12,75)^2+(14-12,75)^2+\\\\&amp;+(19-17,75)^2+(17-17,75)^2+(16-17,75)^2+(19-17,75)^2\\\\[2ex] SS_E=\\ &amp;28,50\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"198\" width=\"575\" style=\"vertical-align: 0px;\"><\/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-2eb66d1d37653749f38916c905108a3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\displaystyle SS_T=&amp;\\sum_{i=1}^k\\sum_{j=1}^{n_i} (y_{ij}-\\overline{y})^2\\\\[2ex] \\displaystyle SS_T= \\ &amp;(14-14,33)^2+(12-14,33)^2+(14-14,33)^2+(10-14,33)^2+\\\\&amp;+(13-14,33)^2+(14-14,33)^2+(10-14,33)^2+(14-14,33)^2+\\\\&amp;+(19-14,33)^2+(17-14,33)^2+(16-14,33)^2+(19-14,33)^2\\\\[2ex] SS_T= \\ &amp;98,67\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"198\" width=\"575\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Daha sonra fakt\u00f6r\u00fcn serbestlik derecelerini, hatay\u0131 ve toplam\u0131 belirleriz: <\/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-481e16a2bd9b99bcd934aa0b6e3bdce7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"GL_F=k-1=3-1=2\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"196\" style=\"vertical-align: -3px;\"><\/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-6c71951c1e79cb2368b941b79387fe82_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"GL_E=N-k=12-3=9\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"213\" style=\"vertical-align: -3px;\"><\/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-c62813e7a06bfd423af43109bfb508d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"GL_F=N-1=12-1=11\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"220\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p> \u015eimdi, fakt\u00f6r\u00fcn ve hatan\u0131n karelerinin toplam\u0131n\u0131 ilgili serbestlik derecelerine b\u00f6lerek ortalama karesel hatalar\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-477d73197865e6166394e3d20732b237_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"MSE_F=\\cfrac{SS_F}{GL_F}=\\cfrac{70,17}{2}=35,08\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"255\" style=\"vertical-align: -15px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-a5b4e07b9ec4135498762b5dbc0f173e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"MSE_R=\\cfrac{SS_R}{GL_R}=\\cfrac{28,50}{9}=3,17\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"245\" style=\"vertical-align: -15px;\"><\/p>\n<\/p>\n<p> Ve son olarak bir \u00f6nceki ad\u0131mda hesaplad\u0131\u011f\u0131m\u0131z iki hatay\u0131 b\u00f6lerek F istatisti\u011finin de\u011ferini 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-4a30a3a61861deb9f53bd1cfcdb0b664_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"F=\\cfrac{MSE_F}{MSE_R}=\\cfrac{35,09}{3,17}=11,08\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"231\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> K\u0131saca \u00f6rnek verilere ili\u015fkin ANOVA tablosu \u015fu \u015fekilde g\u00f6r\u00fcnecektir: <\/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\/table-anova-exemple.png\" alt=\"varyans analizi \u00f6rne\u011fi (ANOVA)\" class=\"wp-image-6408\" width=\"726\" height=\"279\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> ANOVA tablosundaki t\u00fcm de\u011ferler hesapland\u0131ktan sonra geriye sadece elde edilen sonu\u00e7lar\u0131n yorumlanmas\u0131 kal\u0131yor. Bunu yapmak i\u00e7in, kar\u015f\u0131l\u0131k gelen serbestlik derecelerine sahip bir Snedecor F da\u011f\u0131l\u0131m\u0131nda F istatisti\u011finden daha b\u00fcy\u00fck bir de\u011fer elde etme olas\u0131l\u0131\u011f\u0131n\u0131 bulmam\u0131z gerekir, yani testin p de\u011ferini belirlememiz gerekir:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-b706e5d710c3919d145399dc9d8efca5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P[F>11,08]=0,004&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;18&#8243; width=&#8221;172&#8243; style=&#8221;vertical-align: -5px;&#8221;><\/p>\n<\/p>\n<p> Bu nedenle, anlaml\u0131l\u0131k d\u00fczeyini \u03b1=0,05 (en yayg\u0131n olan\u0131) al\u0131rsak, testin p de\u011feri anlaml\u0131l\u0131k d\u00fczeyinden d\u00fc\u015f\u00fck oldu\u011fundan s\u0131f\u0131r hipotezini reddetmeli ve alternatif hipotezi kabul etmeliyiz. Bu, incelenen gruplar\u0131n ara\u00e7lar\u0131n\u0131n en az\u0131ndan baz\u0131lar\u0131n\u0131n di\u011ferlerinden farkl\u0131 oldu\u011fu anlam\u0131na gelir.<\/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-df22e22716e8cfbb1ab37d5e3e74fc9d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"0,004 < 0,05 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black}\\ \\text{Se rechaza } H_0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"346\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> \u015eu anda sadece birka\u00e7 saniye i\u00e7inde varyans analizi yapabilen bir\u00e7ok bilgisayar program\u0131n\u0131n mevcut oldu\u011funu belirtmek gerekir. Ancak hesaplamalar\u0131n arkas\u0131ndaki teoriyi bilmek de \u00f6nemlidir. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"supuestos-del-analisis-de-la-varianza-anova\"><\/span> Varyans Analizi Varsay\u0131mlar\u0131 (ANOVA)<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Varyans analizi (ANOVA) 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:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Ba\u011f\u0131ms\u0131zl\u0131k<\/strong> : G\u00f6zlenen de\u011ferler birbirinden ba\u011f\u0131ms\u0131zd\u0131r. G\u00f6zlemlerin ba\u011f\u0131ms\u0131zl\u0131\u011f\u0131n\u0131 sa\u011flaman\u0131n bir yolu \u00f6rnekleme s\u00fcrecine rastgelelik eklemektir.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Homoskedastisite<\/strong> : Varyanslarda homojenlik olmal\u0131d\u0131r, yani art\u0131klar\u0131n de\u011fi\u015fkenli\u011fi sabittir.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Normallik<\/strong> : Art\u0131klar\u0131n normal da\u011f\u0131lmas\u0131, yani normal da\u011f\u0131l\u0131m izlemesi gerekmektedir.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>S\u00fcreklilik<\/strong> : Ba\u011f\u0131ml\u0131 de\u011fi\u015fken s\u00fcrekli olmal\u0131d\u0131r.<\/span> <\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"tipos-de-analisis-de-la-varianza-anova\"><\/span> Varyans Analizi T\u00fcrleri (ANOVA)<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u00dc\u00e7 <strong>t\u00fcr varyans analizi (ANOVA)<\/strong> vard\u0131r:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Tek y\u00f6nl\u00fc varyans analizi (one-way ANOVA)<\/strong> : Varyans analizinde tek fakt\u00f6r yani tek ba\u011f\u0131ms\u0131z de\u011fi\u015fken vard\u0131r.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>\u0130ki y\u00f6nl\u00fc varyans analizi (two-way ANOVA)<\/strong> : Varyans analizinde iki fakt\u00f6r bulundu\u011fundan iki ba\u011f\u0131ms\u0131z de\u011fi\u015fken ve aralar\u0131ndaki etkile\u015fim analiz edilir.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>\u00c7ok De\u011fi\u015fkenli Varyans Analizi (MANOVA)<\/strong> : Varyans analizinde birden fazla ba\u011f\u0131ml\u0131 de\u011fi\u015fken bulunur. Ama\u00e7, ba\u011f\u0131ml\u0131 de\u011fi\u015fkenler de\u011fi\u015fti\u011finde ba\u011f\u0131ms\u0131z de\u011fi\u015fkenlerin de\u011ferlerinin de\u011fi\u015fip de\u011fi\u015fmedi\u011fini belirlemektir.<\/span> <\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ventajas-y-desventajas-del-analisis-de-la-varianza-anova\"><\/span> Varyans Analizinin (ANOVA) Avantajlar\u0131 ve Dezavantajlar\u0131<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Son olarak varyans analizini ne zaman kullanmam\u0131z\u0131n uygun oldu\u011funu ve ayr\u0131ca bu t\u00fcr istatistiksel analizin s\u0131n\u0131rlar\u0131n\u0131n neler oldu\u011funu g\u00f6rece\u011fiz.<\/p>\n<p> Varyans analizinin (ANOVA) temel avantaj\u0131, ayn\u0131 anda ikiden fazla grubun kar\u015f\u0131la\u015ft\u0131r\u0131lmas\u0131na olanak sa\u011flamas\u0131d\u0131r. Yaln\u0131zca bir veya iki \u00f6rne\u011fin ortalamas\u0131n\u0131 analiz edebildi\u011finiz <a href=\"https:\/\/statorials.org\/tr\/ogrenci-t-testi\/\">t testinin<\/a> aksine, varyans analizi, birden fazla pop\u00fclasyonun ayn\u0131 ortalamaya sahip olup olmad\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in kullan\u0131l\u0131r.<\/p>\n<p> Ancak varyans analizi bize hangi \u00e7al\u0131\u015fma grubunun farkl\u0131 bir ortalamaya sahip oldu\u011funu s\u00f6ylemez; yaln\u0131zca \u00f6nemli \u00f6l\u00e7\u00fcde farkl\u0131 ortalamalar\u0131n olup olmad\u0131\u011f\u0131n\u0131 veya t\u00fcm ortalamalar\u0131n benzer olup olmad\u0131\u011f\u0131n\u0131 bilmemizi sa\u011flar.<\/p>\n<p> Benzer \u015fekilde, varyans analizinin di\u011fer bir dezavantaj\u0131, ANOVA analizini ger\u00e7ekle\u015ftirmek i\u00e7in \u00f6nceki d\u00f6rt varsay\u0131m\u0131n (yukar\u0131ya bak\u0131n) kar\u015f\u0131lanmas\u0131 gerekti\u011fidir, aksi takdirde var\u0131lan sonu\u00e7lar yanl\u0131\u015f olabilir. Bu nedenle istatistiksel veri setinin bu d\u00f6rt gereksinimi kar\u015f\u0131lad\u0131\u011f\u0131 her zaman do\u011frulanmal\u0131d\u0131r.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Bu makale istatistikte ANOVA olarak da bilinen varyans analizinin ne oldu\u011funu a\u00e7\u0131klamaktad\u0131r. B\u00f6ylece varyans analizinin nas\u0131l yap\u0131laca\u011f\u0131n\u0131, ANOVA tablosunun ne oldu\u011funu ve ad\u0131m ad\u0131m \u00e7\u00f6z\u00fclm\u00fc\u015f bir al\u0131\u015ft\u0131rmay\u0131 ke\u015ffedeceksiniz. Ayr\u0131ca varyans analizi ger\u00e7ekle\u015ftirmek i\u00e7in uyulmas\u0131 gereken \u00f6n varsay\u0131mlar\u0131n neler oldu\u011funu ve son olarak ANOVA analizinin avantaj ve dezavantajlar\u0131n\u0131n neler oldu\u011funu g\u00f6sterir. Varyans analizi (ANOVA) nedir? \u0130statistikte, [&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-307","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 Varyans analizi (ANOVA)<\/title>\n<meta name=\"description\" content=\"Burada varyans analizinin (ANOVA) ne oldu\u011funu, nas\u0131l yap\u0131ld\u0131\u011f\u0131n\u0131, somut bir \u00f6rne\u011fini ve ANOVA analizinin avantaj ve dezavantajlar\u0131n\u0131 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\" href=\"https:\/\/statorials.org\/tr\/varyans-analizi-anova\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u25b7 Varyans analizi (ANOVA)\" \/>\n<meta property=\"og:description\" content=\"Burada varyans analizinin (ANOVA) ne oldu\u011funu, nas\u0131l yap\u0131ld\u0131\u011f\u0131n\u0131, somut bir \u00f6rne\u011fini ve ANOVA analizinin avantaj ve dezavantajlar\u0131n\u0131 bulacaks\u0131n\u0131z.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/tr\/varyans-analizi-anova\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-08-02T18:50:10+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-6918550a8ad2954432ea33e07c7b83d0_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\/varyans-analizi-anova\/\",\"url\":\"https:\/\/statorials.org\/tr\/varyans-analizi-anova\/\",\"name\":\"\u25b7 Varyans analizi (ANOVA)\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/tr\/#website\"},\"datePublished\":\"2023-08-02T18:50:10+00:00\",\"dateModified\":\"2023-08-02T18:50:10+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/tr\/#\/schema\/person\/365dc158a39a7c8ae256355451e3de48\"},\"description\":\"Burada varyans analizinin (ANOVA) ne oldu\u011funu, nas\u0131l yap\u0131ld\u0131\u011f\u0131n\u0131, somut bir \u00f6rne\u011fini ve ANOVA analizinin avantaj ve dezavantajlar\u0131n\u0131 bulacaks\u0131n\u0131z.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/tr\/varyans-analizi-anova\/#breadcrumb\"},\"inLanguage\":\"tr\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/tr\/varyans-analizi-anova\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/tr\/varyans-analizi-anova\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Ev\",\"item\":\"https:\/\/statorials.org\/tr\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Varyans analizi (anova)\"}]},{\"@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. Daha fazlas\u0131n\u0131 bil\",\"sameAs\":[\"https:\/\/statorials.org\/tr\"]}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"\u25b7 Varyans analizi (ANOVA)","description":"Burada varyans analizinin (ANOVA) ne oldu\u011funu, nas\u0131l yap\u0131ld\u0131\u011f\u0131n\u0131, somut bir \u00f6rne\u011fini ve ANOVA analizinin avantaj ve dezavantajlar\u0131n\u0131 bulacaks\u0131n\u0131z.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/statorials.org\/tr\/varyans-analizi-anova\/","og_locale":"tr_TR","og_type":"article","og_title":"\u25b7 Varyans analizi (ANOVA)","og_description":"Burada varyans analizinin (ANOVA) ne oldu\u011funu, nas\u0131l yap\u0131ld\u0131\u011f\u0131n\u0131, somut bir \u00f6rne\u011fini ve ANOVA analizinin avantaj ve dezavantajlar\u0131n\u0131 bulacaks\u0131n\u0131z.","og_url":"https:\/\/statorials.org\/tr\/varyans-analizi-anova\/","og_site_name":"Statorials","article_published_time":"2023-08-02T18:50:10+00:00","og_image":[{"url":"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-6918550a8ad2954432ea33e07c7b83d0_l3.png"}],"author":"Dr.benjamin anderson","twitter_card":"summary_large_image","twitter_misc":{"Yazan:":"Dr.benjamin anderson","Tahmini okuma s\u00fcresi":"5 dakika"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/statorials.org\/tr\/varyans-analizi-anova\/","url":"https:\/\/statorials.org\/tr\/varyans-analizi-anova\/","name":"\u25b7 Varyans analizi (ANOVA)","isPartOf":{"@id":"https:\/\/statorials.org\/tr\/#website"},"datePublished":"2023-08-02T18:50:10+00:00","dateModified":"2023-08-02T18:50:10+00:00","author":{"@id":"https:\/\/statorials.org\/tr\/#\/schema\/person\/365dc158a39a7c8ae256355451e3de48"},"description":"Burada varyans analizinin (ANOVA) ne oldu\u011funu, nas\u0131l yap\u0131ld\u0131\u011f\u0131n\u0131, somut bir \u00f6rne\u011fini ve ANOVA analizinin avantaj ve dezavantajlar\u0131n\u0131 bulacaks\u0131n\u0131z.","breadcrumb":{"@id":"https:\/\/statorials.org\/tr\/varyans-analizi-anova\/#breadcrumb"},"inLanguage":"tr","potentialAction":[{"@type":"ReadAction","target":["https:\/\/statorials.org\/tr\/varyans-analizi-anova\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/statorials.org\/tr\/varyans-analizi-anova\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Ev","item":"https:\/\/statorials.org\/tr\/"},{"@type":"ListItem","position":2,"name":"Varyans analizi (anova)"}]},{"@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. Daha fazlas\u0131n\u0131 bil","sameAs":["https:\/\/statorials.org\/tr"]}]}},"yoast_meta":{"yoast_wpseo_title":"","yoast_wpseo_metadesc":"","yoast_wpseo_canonical":""},"_links":{"self":[{"href":"https:\/\/statorials.org\/tr\/wp-json\/wp\/v2\/posts\/307","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/statorials.org\/tr\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/statorials.org\/tr\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/statorials.org\/tr\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/statorials.org\/tr\/wp-json\/wp\/v2\/comments?post=307"}],"version-history":[{"count":0,"href":"https:\/\/statorials.org\/tr\/wp-json\/wp\/v2\/posts\/307\/revisions"}],"wp:attachment":[{"href":"https:\/\/statorials.org\/tr\/wp-json\/wp\/v2\/media?parent=307"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/statorials.org\/tr\/wp-json\/wp\/v2\/categories?post=307"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/statorials.org\/tr\/wp-json\/wp\/v2\/tags?post=307"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}