{"id":85,"date":"2006-01-25T17:37:49","date_gmt":"2006-01-25T15:37:49","guid":{"rendered":"http:\/\/www.muratakyildiz.com\/wordpress\/?p=85"},"modified":"2006-01-25T17:37:49","modified_gmt":"2006-01-25T15:37:49","slug":"ancova","status":"publish","type":"post","link":"https:\/\/www.istatistik.gen.tr\/?p=85","title":{"rendered":"Kovaryans Analizi (Ancova)"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\" size-full wp-image-84\" src=\"http:\/\/www.muratakyildiz.com\/wordpress\/wp-content\/uploads\/2006\/01\/bread.jpg\" border=\"0\" alt=\"Image\" title=\"Image\" hspace=\"6\" width=\"150\" height=\"159\" \/>Alper \u00c7uhadaro\u00f0lu, Eylem G\u00f6k\u00e7e Cengiz, Hicran \u00c7etin, Nejat Akfirat Ve Ramin Aliyev&#8217;in haz\u0131rlam\u0131\u015f oldu\u011fu Ancova konusunu yaz\u0131n\u0131n devam\u0131nda okuyabilirsiniz. <!--more-->     Untitled Document  <\/p>\n<p>ANCOVA<\/p>\n<p>   (KOVARYANS ANAL\u0130Z\u0130)<\/p>\n<p>   Yazarlar:  Alper \u00c7uhadaro\u011flu, Eylem G\u00f6k\u00e7e Cengiz, Hicran \u00c7etin, Nejat  Akfirat ve Ramin Aliyev<\/p>\n<p>Kovaryans analizi bir ara\u015ft\u0131rmada, etkisi test edilen  ba\u011f\u0131ms\u0131z de\u011fi\u015fkenin d\u0131\u015f\u0131nda ba\u011f\u0131ml\u0131 de\u011fi\u015fken ile ili\u015fkisi bulunan ve ortak  de\u011fi\u015fken olarak isimlendirilen bir ba\u015fka de\u011fi\u015fkenin ya da  de\u011fi\u015fkenlerin istatistiksel olarak kontrol edilmesini sa\u011flayan bir teknik  olarak tan\u0131mlanabilir. <\/p>\n<p>Kovaryans analizine genellikle \u00f6n-test son  test kontrol gruplu desenlerde, deney ve kontrol grubunun son test \u00f6l\u00e7\u00fcmleri  aras\u0131nda anlaml\u0131 bir fark\u0131n olup olmad\u0131\u011f\u0131n\u0131 test etmek i\u00e7in ba\u015fvurulmaktad\u0131r.  Burada \u00f6n-test \u00f6l\u00e7\u00fcmleri ortak de\u011fi\u015fken olarak tan\u0131mlanmaktad\u0131r (B\u00fcy\u00fck\u00f6zt\u00fcrk,  1998). <\/p>\n<p>Kovaryans analizinin  mant\u0131\u011f\u0131 ba\u011f\u0131ml\u0131 de\u011fi\u015fkenden, ortak de\u011fi\u015fkenden kaynakl\u0131 de\u011fi\u015fmeleri \u00e7ekip  \u00e7\u0131karmak ve sonra da ba\u011f\u0131ml\u0131 de\u011fi\u015fkendeki de\u011fi\u015fmenin ba\u011f\u0131ms\u0131z de\u011fi\u015fkenden  kaynaklan\u0131p kaynaklanmad\u0131\u011f\u0131n\u0131 anlamakt\u0131r. ANCOVA analizdeki bir de\u011fi\u015fkeni  denetlemek yani, etkisini ortadan kald\u0131rmak i\u00e7in kullan\u0131lan yollardan en  genelidir (Punch, 2005<\/p>\n<p>ANCOVA\u2019n\u0131n 3 amac\u0131:<\/p>\n<p>Deneysel desenlerde, randomize edilemeyen ama bir aral\u0131k \u00f6l\u00e7e\u011fi  ile \u00f6l\u00e7\u00fclebilen fakt\u00f6rleri kontrol etmek i\u00e7in,<br \/>   G\u00f6zlemsel desenlerde; kategorik ba\u011f\u0131ms\u0131z de\u011fi\u015fkenlerin aral\u0131kl\u0131  ba\u011f\u0131ml\u0131 de\u011fi\u015fkenlere olan ili\u015fkisini de\u011fi\u015ftiren de\u011fi\u015fkenlerin etkisini \u00e7\u0131karmak  i\u00e7in, <br \/>   Regresyon modellerinde, hem kategorik hem de aral\u0131kl\u0131 ba\u011f\u0131ms\u0131z  de\u011fi\u015fken oldu\u011funda regresyona uymas\u0131 (fit) i\u00e7in.<\/p>\n<p>Kovaryans analizi  s\u0131ras\u0131nda grup ortalamalar\u0131 aras\u0131ndaki fark \u00f6l\u00e7\u00fcl\u00fcrken, regresyon analizi ve  varyans analizi  birlikte kullan\u0131l\u0131r, yani kovaryans analizi varyans  analizi ile regresyon analizinin kombinasyonudur. <\/p>\n<p>\u00d6ncelikle regresyon  prosed\u00fcr\u00fc uygulan\u0131r, daha sonra da d\u00fczeltilmi\u015f de\u011ferler \u00fczerinden normal  varyans analizi y\u00f6ntemi uygulan\u0131r. B\u00f6ylelikle, ba\u011f\u0131ml\u0131 de\u011fi\u015fken ile ortak  de\u011fi\u015fken aras\u0131ndaki do\u011frusal ili\u015fki i\u00e7in bir d\u00fczeltme yap\u0131lm\u0131\u015f olur ve  sonucunda hata varyans\u0131 d\u00fc\u015fer, veriler aras\u0131ndaki di\u011fer farkl\u0131l\u0131klar g\u00f6z \u00f6n\u00fcne  al\u0131narak grup farkl\u0131l\u0131klar\u0131 ortaya konulabilir (Ed.Kalayc\u0131, 2005). <\/p>\n<p> Ryan ve Hess (1991) ANCOVA\u2019y\u0131 ko\u015fullar\u0131  sa\u011fland\u0131\u011f\u0131nda varyans analizini kullan\u0131ld\u0131\u011f\u0131 ara\u015ft\u0131rma desenlerinin hemen  t\u00fcm\u00fcnde kullabilen g\u00fc\u00e7l\u00fc bir istatistik olarak tan\u0131mlamaktad\u0131r. Howitt ve  Cramer\u2019e g\u00f6re (1997), varyans analiziyle kovaryans analizi aras\u0131ndaki temel  fark, ANCOVA\u2019n\u0131n analizde ba\u011f\u0131ml\u0131 de\u011fi\u015fken ile ili\u015fkili olan ve ANOVA deseninde  belirlenen ba\u011f\u0131ms\u0131z de\u011fi\u015fkenlerden farkl\u0131 olarak bir ya da daha fazla  de\u011fi\u015fkenin analize kat\u0131lmas\u0131na olanak sa\u011flamas\u0131d\u0131r (akt. B\u00fcy\u00fck\u00f6zt\u00fcrk, 1998).<\/p>\n<p>E\u011fer gruplar bir sebepten  dolay\u0131 e\u015fit de\u011filse bunlar\u0131 e\u015fitlemek amac\u0131yla da ANCOVA kullan\u0131labilir.  \u00d6rne\u011fin, rasgele se\u00e7ilmeyen \u00f6\u011frencilerin kullan\u0131ld\u0131\u011f\u0131 de\u011fi\u015fik \u00f6\u011fretim  metotlar\u0131n\u0131n kar\u015f\u0131la\u015ft\u0131r\u0131lmas\u0131 \u00e7al\u0131\u015fmas\u0131nda gruplar aras\u0131nda ba\u015flang\u0131\u00e7ta zek\u00e2  gibi bir farkl\u0131l\u0131k bulunabilir. E\u011fer gruplar\u0131n farkl\u0131 oldu\u011fu kanaati varsa  ANCOVA bunlar\u0131 e\u015fitlemek amac\u0131yla kullan\u0131labilir. B\u00f6ylece grup ortalamalar\u0131  ba\u011f\u0131ml\u0131 de\u011fi\u015fken \u00fczerinde kar\u015f\u0131la\u015ft\u0131r\u0131lmadan \u00f6nce zekan\u0131n etkisi ortadan  kald\u0131r\u0131l\u0131r. <\/p>\n<p>ANCOVA ayn\u0131 zamanda  rasgele \u00f6rneklemenin ba\u015far\u0131l\u0131 olmad\u0131\u011f\u0131 durumda uygulanabilir. \u00d6zellikle k\u00fc\u00e7\u00fck  \u00f6rneklemlerde rasgele \u00f6rneklem yap\u0131lm\u0131\u015f olmas\u0131na ra\u011fmen gruplar  e\u015fitlenemeyebilir. Gruplar bir ba\u015fka de\u011fi\u015fkenden dolay\u0131 farkl\u0131 olabilirler.  ANCOVA gruplar\u0131 e\u015fitlemek amac\u0131yla kullan\u0131labilir. Bu ama\u00e7la yayg\u0131n olarak  kullan\u0131lmas\u0131na ra\u011fmen, b\u00fct\u00fcn \u00f6rneklere \u00e7\u00f6z\u00fcm getirememekte olup, dikkatli  olarak kullan\u0131lmal\u0131d\u0131r. <\/p>\n<p>ANCOVA\u2019da ba\u015fvurulan bir alanda  test \u00f6ncesi temel de\u011fi\u015fiklikleri kontrol etmektir. Grup test \u00f6ncesinde  farkl\u0131la\u015f\u0131yorsa ANCOVA bu farkl\u0131l\u0131klar\u0131 kontrol etmede kullan\u0131l\u0131r. Bunu  ANCOVA\u2019da yapman\u0131n al\u0131\u015f\u0131lm\u0131\u015f yolu test sonras\u0131 puanlar\u0131n\u0131n ba\u011f\u0131ms\u0131z de\u011fi\u015fken olarak  ve test \u00f6ncesi puanlar\u0131 ortak de\u011fi\u015fken olarak kullan\u0131lmas\u0131d\u0131r. <\/p>\n<p>Grup random olarak atand\u0131\u011f\u0131nda ANCOVA iki grup aras\u0131ndaki de\u011fi\u015fiklikleri  kar\u015f\u0131la\u015ft\u0131rmada \u00e7ok iyi bir y\u00f6ntemdir. Bununla birlikte, grup do\u011fal olarak  olu\u015ftu\u011funda (k\u0131z ve erkek gibi) test \u00f6ncesi temel farkl\u0131l\u0131klar \u015fanstan  kaynaklanmamaktad\u0131r (Jamieson, 2004). <\/p>\n<p> Her hangi bir s\u00fcrekli de\u011fi\u015fken bir  ortak de\u011fi\u015fken olarak kullan\u0131labilir ama en iyisi genellikle \u00f6n testtir. \u00c7\u00fcnk\u00fc  \u00e7o\u011funlukla son test ile en y\u00fcksek korelasyon g\u00f6steren de\u011fi\u015fken \u00f6n testtir. \u00d6n  test y\u00fcksek koelasyon g\u00f6sterdi\u011fi i\u00e7in \u00f6n test \u00e7\u0131kar\u0131ld\u0131\u011f\u0131nda son testten konu  d\u0131\u015f\u0131- yabanc\u0131 de\u011fi\u015fkende \u00e7ekilmi\u015f olur. Ortak de\u011fi\u015fkenleri se\u00e7medeki kural,  sonu\u00e7 ile en y\u00fcksek korelasyonu g\u00f6steren \u00f6l\u00e7\u00fcm\u00fc ya da \u00f6l\u00e7\u00fcmleri se\u00e7mektir.  \u00c7oklu Kovaryans analizi i\u00e7inde aralar\u0131ndaki korelasyonun\u00a0 en d\u00fc\u015f\u00fck oldu\u011fu \u00f6l\u00e7\u00fcmleri se\u00e7mek gerekir.  Yoksa gereksiz ortak de\u011fi\u015fken eklemi\u015f ve kesinli\u011fi kaybetmi\u015f oluruz. \u00d6rne\u011fin  net ve br\u00fct geliri iki ortak de\u011fi\u015fken olarak kullanmak gibi (www.socialresearchmethods.net). <\/p>\n<p>ANCOVA, ba\u011f\u0131ml\u0131 de\u011fi\u015fken  \u00fczerindeki ortak de\u011fi\u015fkenin etkisini \u00e7ekmek i\u00e7in iki y\u00f6ntem kullan\u0131r:<\/p>\n<p>\u0130lk y\u00f6ntem,  her bir grubun i\u00e7ine odaklan\u0131r ve her bir grup i\u00e7in ortak de\u011fi\u015fkenden ba\u011f\u0131ml\u0131  de\u011fi\u015fkeni yordamak i\u00e7in regresyon do\u011frular\u0131n\u0131 hesaplar. Bu regresyon do\u011frular\u0131  ortak de\u011fi\u015fken puanlar\u0131na dayanan her bir durum i\u00e7in, yordanan ba\u011f\u0131ml\u0131 de\u011fi\u015fken  puanlar\u0131n\u0131 bulmak i\u00e7in kullan\u0131l\u0131r. Her bir durum i\u00e7in fazladan\/gereksiz puanlar  (ba\u011f\u0131ml\u0131 de\u011fi\u015fkenin g\u00f6zlenen puan\u0131 eksi yordanan ba\u011f\u0131ml\u0131 de\u011fi\u015fkenin puan\u0131) bir  hata terimini hesaplamak i\u00e7in toplan\u0131r. Regresyonun bu grup i\u00e7i kullan\u0131m\u0131 ortak  de\u011fi\u015fkenin etkisini hata varyans\u0131ndan ay\u0131rmak i\u00e7in m\u00fckemmel bir y\u00f6ntemdir.<\/p>\n<p> ANCOVA&#8217;da d\u00fczeltmenin ikinci y\u00f6ntemi ise daha sorunludur. Tek bir regresyon katsay\u0131s\u0131 (b)  elde etmek i\u00e7in her gruptan regresyon do\u011frular\u0131 toplan\u0131r (regresyonun  homojenli\u011fi varsay\u0131m\u0131ndan kaynakl\u0131) bu toplanan (pooled)regresyon katsay\u0131s\u0131  daha sonra her grup i\u00e7in ba\u011f\u0131ml\u0131 de\u011fi\u015fkenin ortalamas\u0131n\u0131 d\u00fczeltmek i\u00e7in bir  form\u00fcl i\u00e7inde kullan\u0131l\u0131r. Kolayla\u015ft\u0131rmak i\u00e7in rakam kullanmak yerine Lord&#8217;un  paradoksu \u00f6rnek verilebilir (Lord, 1978); <\/p>\n<p><strong>Kovaryans Analizinin \u00d6zellikleri ve Varsay\u0131mlar\u0131<\/strong><br \/> ANCOVA deseni fakt\u00f6r (Ba\u011f\u0131ms\u0131z de\u011fi\u015fken) ve ba\u011f\u0131ml\u0131 de\u011fi\u015fkene  ek olarak, ba\u011f\u0131ml\u0131 de\u011fi\u015fken ile ili\u015fkisi olan, onu etkileyen ve hata kontrol\u00fc  ile gruplar\u0131n ba\u011f\u0131ml\u0131 de\u011fi\u015fkendeki ortalamalar\u0131n\u0131 ayarlamak i\u00e7in kullan\u0131lan ba\u015fka  de\u011fi\u015fkenlerin varl\u0131\u011f\u0131n\u0131 gerektirir. S\u00f6z konusu bu de\u011fi\u015fkenlere ortak de\u011fi\u015fkenler  (covariates ya da concomitants) ad\u0131 verilmektedir. Deneysel desen ile kontrol  alt\u0131na al\u0131namayan d\u0131\u015f etkenler, do\u011frusal bir regresyon y\u00f6ntemiyle ortadan kald\u0131r\u0131labilir.  ANCOVA, varyans analizi ve regresyon analizini birlikte kullanarak deneydeki i\u015flemin  ger\u00e7ek etkisini belirleyebilmektedir. <\/p>\n<p>ANCOVA, ANOVA\u2019da oldu\u011fu gibi temelde ilgilenilen fakt\u00f6r ya  da fakt\u00f6rlerin ba\u011f\u0131ml\u0131 de\u011fi\u015fken \u00fczerinde etkilerinin olup olmad\u0131\u011f\u0131n\u0131 test eder.  Ancak bunu yaparken, ANOVA\u2019dan farkl\u0131 olarak, ba\u011f\u0131ml\u0131 de\u011fi\u015fken \u00fczerinde etkisi  g\u00f6zlenen d\u0131\u015f etkenlerin yol a\u00e7t\u0131\u011f\u0131 varyans\u0131 kontrol ederek sonu\u00e7ta testin g\u00fcc\u00fcn\u00fc  daha da artmas\u0131n\u0131 sa\u011flar.<\/p>\n<p>Gren, Salkind ve Akey\u2019e  g\u00f6re (1997), ANCOVA deseninde denekler ba\u011f\u0131ml\u0131 de\u011fi\u015fken, ba\u011f\u0131ms\u0131z de\u011fi\u015fken-fakt\u00f6r  ve ortak de\u011fi\u015fkene ili\u015fkin birer de\u011fere sahiptir. Denekler, ba\u011f\u0131ms\u0131z de\u011fi\u015fkenin  d\u00fczeyine g\u00f6re iki ya da daha fazla gruba ayr\u0131l\u0131rken, di\u011fer iki de\u011fi\u015fkene ili\u015fkin  s\u00fcreklilik \u00f6zelli\u011fi olan say\u0131sal de\u011ferlere sahiptir (B\u00fcy\u00fck\u00f6zt\u00fcrk, 1998).<\/p>\n<p>Kovaryans analizi; tek y\u00f6nl\u00fc, iki y\u00f6nl\u00fc ve \u00e7ok de\u011fi\u015fkenli  varyans analizi tekniklerinin bir par\u00e7as\u0131 olarak kullan\u0131labilir. Tek y\u00f6nl\u00fc ve  iki y\u00f6nl\u00fc varyans analizinde kullan\u0131lan de\u011fi\u015fken say\u0131lar\u0131 \u015fu \u015fekildedir:<\/p>\n<p>Tek y\u00f6nl\u00fc ANCOVA: Bir ba\u011f\u0131ms\u0131z de\u011fi\u015fken, bir ba\u011f\u0131ml\u0131 de\u011fi\u015fken,  bir ya da daha fazla ortak de\u011fi\u015fken.<\/p>\n<p>\u0130ki y\u00f6nl\u00fc ANCOVA: \u0130ki ba\u011f\u0131ms\u0131z de\u011fi\u015fken, bir ba\u011f\u0131ml\u0131 de\u011fi\u015fken,  bir ya da daha fazla ortak de\u011fi\u015fken (Kalayc\u0131, 2005).<\/p>\n<p><strong>ANCOVA\u2019n\u0131n varsay\u0131mlar\u0131 \u015funlard\u0131r: <\/strong><\/p>\n<ul>\n<li>Gruplar\u0131n ba\u011f\u0131ml\u0131 de\u011fi\u015fkene ili\u015fkin puanlar\u0131 normal da\u011f\u0131lmal\u0131d\u0131r.  Normallik say\u0131lt\u0131s\u0131, e\u015fit ve  makul bir b\u00fcy\u00fckl\u00fckteki (Ni\u226515 ) gruplarda ihmal edilebilir.<\/li>\n<li>Ba\u011f\u0131ml\u0131 de\u011fi\u015fken aral\u0131kl\u0131 veya oransal olmal\u0131d\u0131r (B\u00fcy\u00fck\u00f6zt\u00fcrk, 2001,\u00a0 Kalayc\u0131, 2005). <\/li>\n<li> Gruplar\u0131n varyans\u0131 e\u015fit olmal\u0131d\u0131r. Ba\u015fka bir ifadeyle  varyanslar\u0131n homojenli\u011fi sa\u011flanmal\u0131d\u0131r. <\/li>\n<li>Gruplar i\u00e7i regresyon katsay\u0131lar\u0131 e\u015fit olmal\u0131d\u0131r.<\/li>\n<li>Gruplar birbirinden ba\u011f\u0131ms\u0131z olmal\u0131d\u0131r (Kalayc\u0131, 2005). <\/li>\n<li>Ortak de\u011fi\u015fken, aral\u0131kl\u0131 veya oransal veri bi\u00e7iminde olmal\u0131d\u0131r.  Nominal (kategorik)de\u011fi\u015fkenler ortak de\u011fi\u015fken olarak kullan\u0131lamaz ayr\u0131ca, se\u00e7ilecek olan  ortak de\u011fi\u015fken dikkatli se\u00e7ilmelidir. \u00d6ncelikle ortak de\u011fi\u015fkenin modele dahil  edilmesi gerekti\u011finden emin olunmal\u0131d\u0131r. <\/li>\n<li>Se\u00e7ilen ortak de\u011fi\u015fken ya da de\u011fi\u015fkenler, g\u00fcvenilir olmal\u0131  yani hatas\u0131z bir \u015fekilde \u00f6l\u00e7\u00fclm\u00fc\u015f olmal\u0131d\u0131r. \u00c7\u00fcnk\u00fc ANCOVA, ortak de\u011fi\u015fkenin  hatas\u0131z ve do\u011fru \u00f6l\u00e7t\u00fc\u011f\u00fcn\u00fc varsayar.<\/li>\n<li>Birden fazla ortak de\u011fi\u015fken kullan\u0131lacaksa se\u00e7ilen ortak de\u011fi\u015fkenler  aras\u0131nda g\u00fc\u00e7l\u00fc bir korelasyon olmamal\u0131d\u0131r. E\u011fer y\u00fcksek derecede bir korelasyon (r=0,8 ve  daha fazla) varsa, ortak de\u011fi\u015fkenlerden biri ya da birka\u00e7\u0131 \u00e7\u0131kar\u0131lmal\u0131d\u0131r. <\/li>\n<li>Ortak de\u011fi\u015fken ve ba\u011f\u0131ml\u0131 de\u011fi\u015fken do\u011frusal bir ili\u015fki i\u00e7inde  olmal\u0131d\u0131r. E\u011fer  ortak de\u011fi\u015fken ve ba\u011f\u0131ml\u0131 de\u011fi\u015fken aras\u0131nda do\u011frusal ili\u015fki yoksa analizden  istenilen verim al\u0131namaz. Bir ba\u015fka deyi\u015fle, bu varsay\u0131m\u0131n ihlali testin g\u00fcc\u00fcn\u00fc  azalt\u0131r. \u00c7\u00fcnk\u00fc b\u00f6yle bir durumda hata varyans\u0131 \u00e7ok az azalt\u0131labilecektir. Bu  test, ortak de\u011fi\u015fken ve ba\u011f\u0131ml\u0131 de\u011fi\u015fken aras\u0131ndaki korelasyonun 0,30\u2019dan y\u00fcksek  oldu\u011fu durumlarda etkili olur. Daha g\u00fc\u00e7l\u00fc do\u011frusal ili\u015fki daha g\u00fc\u00e7l\u00fc ANCOVA  sonu\u00e7lar\u0131n\u0131n elde edilmesini sa\u011flar. Ortak de\u011fi\u015fken ile ba\u011f\u0131ml\u0131 de\u011fi\u015fken aras\u0131ndaki ili\u015fki do\u011frusal  de\u011filse ortak de\u011fi\u015fkenin ba\u011f\u0131ms\u0131z de\u011fi\u015fken oldu\u011fu ANOVA testi uygulanabilir. Ba\u015fka  bir se\u00e7enek ise, do\u011frusal ili\u015fkiyi sa\u011flamak i\u00e7in de\u011fi\u015fkenlerin matematiksel d\u00f6n\u00fc\u015f\u00fcmlerini  ger\u00e7ekle\u015ftirilmesidir. D\u00f6n\u00fc\u015ft\u00fcr\u00fclen de\u011fi\u015fkenlerde daha sonra ANCOVA kullan\u0131labilir.<\/li>\n<li>Ortak de\u011fi\u015fken ve ba\u011f\u0131ml\u0131 de\u011fi\u015fken aras\u0131ndaki ili\u015fkinin g\u00fcc\u00fc  ve y\u00f6n\u00fc her grupta benzer olmal\u0131d\u0131r. Bu durum gruplarda regresyon homojenli\u011fi  olarak ifade edilmektedir. Ba\u015fka bir de\u011fi\u015fle ortak de\u011fi\u015fken ile ba\u011f\u0131ml\u0131 de\u011fi\u015fken  aras\u0131ndaki ili\u015fki \u00fczerinde ba\u011f\u0131ml\u0131 de\u011fi\u015fkenin etkisi olmamal\u0131d\u0131r. Yani ortak de\u011fi\u015fken  gruplardaki ba\u011f\u0131ml\u0131 de\u011fi\u015fken \u00fczerinde ayn\u0131 etkiye sahip olmal\u0131d\u0131r.<\/li>\n<\/ul>\n<p>(Konu ile ilgili powerpoint sunusundan uyarlanm\u0131\u015ft\u0131r) <\/p>\n","protected":false},"excerpt":{"rendered":"<p>Alper \u00c7uhadaro\u00f0lu, Eylem G\u00f6k\u00e7e Cengiz, Hicran \u00c7etin, Nejat Akfirat Ve Ramin Aliyev&#8217;in haz\u0131rlam\u0131\u015f oldu\u011fu Ancova konusunu yaz\u0131n\u0131n devam\u0131nda okuyabilirsiniz.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_kad_post_transparent":"","_kad_post_title":"","_kad_post_layout":"","_kad_post_sidebar_id":"","_kad_post_content_style":"","_kad_post_vertical_padding":"","_kad_post_feature":"","_kad_post_feature_position":"","_kad_post_header":false,"_kad_post_footer":false,"_kad_post_classname":"","footnotes":""},"categories":[],"tags":[],"class_list":["post-85","post","type-post","status-publish","format-standard","hentry"],"_links":{"self":[{"href":"https:\/\/www.istatistik.gen.tr\/index.php?rest_route=\/wp\/v2\/posts\/85","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.istatistik.gen.tr\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.istatistik.gen.tr\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.istatistik.gen.tr\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.istatistik.gen.tr\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=85"}],"version-history":[{"count":0,"href":"https:\/\/www.istatistik.gen.tr\/index.php?rest_route=\/wp\/v2\/posts\/85\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.istatistik.gen.tr\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=85"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.istatistik.gen.tr\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=85"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.istatistik.gen.tr\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=85"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}