{"id":97,"date":"2006-02-21T11:19:06","date_gmt":"2006-02-21T09:19:06","guid":{"rendered":"http:\/\/www.muratakyildiz.com\/wordpress\/?p=97"},"modified":"2006-02-21T11:19:06","modified_gmt":"2006-02-21T09:19:06","slug":"cok-deikenli-statistiklerin-kullanm","status":"publish","type":"post","link":"https:\/\/www.istatistik.gen.tr\/?p=97","title":{"rendered":"\u00c7ok De\u011fi\u015fkenli \u0130statistiklerin Kullan\u0131m\u0131"},"content":{"rendered":"

\"Image\"T\u00fclin Acar’\u0131n \u00c7ok De\u011fi\u015fkenli \u0131statistiklerin Kullan\u0131m\u0131 konusundaki yaz\u0131s\u0131n\u0131 yaz\u0131n\u0131n devam\u0131nda bulabilirsiniz.
\u00c7OK DE\u011f\u0131\u015fKENL\u0131 \u0131STAT\u0131ST\u0131KLER\u0131N ARA\u015fTIRMALARDA KULLANIMI <\/p>\n

\n

\u00c7OK DE\u011f\u0131\u015fKENL\u0131 \u0131STAT\u0131ST\u0131KLER\u0131N ARA\u015fTIRMALARDA KULLANIMI<\/strong><\/p>\n

Ara\u015ft\u0131rmalarda incelenen olaylar g\u00f6stermektedir ki tek de\u011fi\u015fkenli istatistiklerin kullan\u0131lmas\u0131 problemi a\u00e7\u0131klamakta yetersiz ve eksik kalmaktad\u0131r. Tek de\u011fi\u015fkenli istatistiklerde \u00e7\u00f6z\u00fcmlenen olay tektir, tek de\u011fi\u015fken incelenmektedir. Bilimsel \u00e7al\u0131\u015fmalar ise tek de\u011fi\u015fkenle a\u00e7\u0131klanamayacak kadar karma\u015f\u0131kt\u0131r. Ara\u015ft\u0131rmaya konu olan bir problemin \u00e7\u00f6z\u00fcm\u00fcnde ku\u015fkusuz problemi etkileyen bir\u00e7ok fakt\u00f6r vard\u0131r ve \u00e7\u00f6z\u00fclecek problem bu bir\u00e7ok fakt\u00f6r\u00fc dikkate alarak incelenmelidir. Bu nedenle tek de\u011fi\u015fkenli istatistiklerin s\u0131n\u0131rl\u0131l\u0131\u011f\u0131, \u00e7ok de\u011fi\u015fkenli istatistiksel analizleri do\u011furmu\u015ftur. B\u00f6ylece, tek de\u011fi\u015fkenli istatistiklerde varsay\u0131lan k\u0131s\u0131tlamalar ortadan kalkt\u0131\u011f\u0131ndan ara\u015ft\u0131rmalarda daha objektif ve tutarl\u0131 sonu\u00e7lar elde edilir. Tek de\u011fi\u015fkenli istatistiksel analizlerin en \u00f6nemli k\u0131s\u0131tlay\u0131c\u0131 varsay\u0131m\u0131 ise bir\u00e7ok fakt\u00f6r\u00fcn deneysel olarak kontrol alt\u0131nda tutulmas\u0131 ve her defas\u0131nda tek bir fakt\u00f6r\u00fcn etkisinin incelenmesidir. Bu \u015fu demektir incelenen de\u011fi\u015fken \u00fczerindeki fakt\u00f6rler t\u00fcrde\u015f ya da sabit tutulmas\u0131d\u0131r. Oysaki \u00e7ok de\u011fi\u015fkenli istatistiksel analizlerde baz\u0131 kontroll\u00fc denemeler d\u0131\u015f\u0131nda b\u00f6yle bir k\u0131s\u0131tlay\u0131c\u0131dan ya da \u00f6zellikten s\u00f6z edilmez. \u00c7ok de\u011fi\u015fkenli istatistiksel analizlerin en \u00f6nemli varsay\u0131m\u0131, verilerin \u00e7ok de\u011fi\u015fkenli normal da\u011f\u0131l\u0131ml\u0131 kitleden \u00e7ekilmi\u015f oldu\u011fudur. \u00c7ok de\u011fi\u015fkenli istatistiksel analizlerde, birden \u00e7ok \u00f6zelli\u011fin analizi ile ilgilenildi\u011finden en az ikiden \u00e7ok de\u011fi\u015fken s\u00f6z konusudur.<\/p>\n\n\n\n\n\n
\n

<\/strong><\/p>\n

<\/td>\n

\n

Tek De\u011fi\u015fkenli Analizler<\/strong><\/p>\n<\/td>\n

\n

\u00c7ok De\u011fi\u015fkenli Analizler<\/strong><\/p>\n<\/td>\n<\/tr>\n

\n

De\u011fi\u015fken Say\u0131s\u0131 (P)<\/strong><\/p>\n<\/td>\n

\n

P=1<\/p>\n<\/td>\n

\n

P=2 (iki de\u011fi\u015fkenli)<\/p>\n

P>2 (\u00e7ok de\u011fi\u015fkenli)<\/p>\n<\/td>\n<\/tr>\n

\n

Varsay\u0131m\u0131<\/strong><\/p>\n<\/td>\n

\n

De\u011fi\u015fkeni etkileyen di\u011fer fakt\u00f6rler(de\u011fi\u015fkenler) t\u00fcrde\u015f ya da sabittir.<\/p>\n<\/td>\n

\n

N birimli p tane de\u011fi\u015fkenin normal da\u011f\u0131l\u0131m g\u00f6sterir.<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\u00c7ok de\u011fi\u015fkenli istatistiksel analizler, incelenen olay ve \u00e7evresindeki \u00e7ok say\u0131da i\u00e7sel ve d\u0131\u015fsal fakt\u00f6rleri dikkate alarak, problemi do\u011fas\u0131ndaki yap\u0131s\u0131na ili\u015fkin bilgilere g\u00f6re incelemek ve \u00e7\u00f6z\u00fcmlere ula\u015fmak i\u00e7in geli\u015ftirilmi\u015f y\u00f6ntemler b\u00fct\u00fcn\u00fcd\u00fcr (\u00d6zdamar,2002:1).<\/p>\n

\u00c7ok de\u011fi\u015fkenli istatistiklerin uygulanma ama\u00e7lar\u0131 ise <\/p>\n

a) <\/span>Veri \u0131ndirgeme<\/p>\n

b) <\/span>K\u00fcmeleme ve S\u0131n\u0131flama<\/p>\n

c) <\/span>\u00d6l\u00e7ekleme<\/p>\n

d) <\/span>Hipotez Testleri (Hipotez Olu\u015fturma)<\/p>\n

A) <\/span><\/strong>Veri \u0131ndirgeme<\/strong><\/p>\n

Veri indirgemenin amac\u0131, P say\u0131da de\u011fi\u015fken i\u00e7eren veri setinin varyasyonunu a\u00e7\u0131klayan ve aralar\u0131nda ili\u015fki bulunmayan daha az say\u0131da de\u011fi\u015fkenle (k<p) veri yap\u0131s\u0131n\u0131 a\u00e7\u0131klamakt\u0131r. <\/p>\n

B) <\/span><\/strong>K\u00fcmeleme ve S\u0131n\u0131flama<\/strong><\/p>\n

Ama\u00e7, pop\u00fclasyon \u00f6zellikleri bilinmeyen yap\u0131lar hakk\u0131nda prototip k\u00fcmeler (grup, s\u0131n\u0131f) belirleme \u00e7al\u0131\u015fmalar\u0131na yard\u0131mc\u0131 olup daha \u00f6nceden belirlenmi\u015f gruplara yeni birimlerin atanmas\u0131n\u0131 sa\u011flamakt\u0131r.<\/p>\n

C) <\/span><\/strong>\u00d6l\u00e7ekleme<\/strong><\/p>\n

P say\u0131da de\u011fi\u015fken i\u00e7eren p boyutlu \u00f6l\u00e7\u00fcmlerden daha az say\u0131da de\u011fi\u015fken kullanarak birimlerin g\u00f6sterilmesini, tan\u0131mlanmas\u0131n\u0131 sa\u011flamak ve birimlerin birbirleri ile k<p boyutlu \u00f6l\u00e7ekte benzerlik ve farkl\u0131l\u0131klar\u0131n\u0131 incelemektir.<\/p>\n

D) <\/span><\/strong>\u00c7ok de\u011fi\u015fkenli hipotezlerin test edilmesi<\/strong><\/p>\n

K toplumun \u00e7ok de\u011fi\u015fkenli ortalamalar vekt\u00f6r\u00fcn\u00fcn e\u015fitli\u011fi \/ farkl\u0131l\u0131\u011f\u0131 \u00fczerine kurulacak hipotezleri test etmede \u00c7D\u0131A y\u00f6ntemleri kullan\u0131l\u0131r.<\/p>\n

\u00c7OK DE\u011f\u0131\u015fKENL\u0131 \u0131STAT\u0131ST\u0131KSEL ANAL\u0131ZLER<\/strong> <\/strong><\/p>\n

Setleraras\u0131 Korel\u00e2syon Analizi:<\/span><\/strong> <\/strong>P1<\/sub>>2 ve P2<\/sub>>2 olmak \u00fczere \u00e7ok de\u011fi\u015fkenli iki ya da daha fazla de\u011fi\u015fkenler seti(grup) aras\u0131ndaki korel\u00e2syonlar\u0131 a\u00e7\u0131klamak i\u00e7in kullan\u0131lan bu y\u00f6ntem P1<\/sub>>2 de\u011fi\u015fkenler setinin do\u011frusal bile\u015fenleri ile di\u011fer (P2<\/sub>>2) de\u011fi\u015fkenler setinin do\u011frusal bile\u015fenleri aras\u0131ndaki korelasyonlar\u0131 inceleyen bir y\u00f6ntemdir.<\/p>\n

\u00d6rne\u011fin, bir \u00f6\u011fretmen \u00f6\u011frenme yetene\u011fini \u00f6l\u00e7en 3 \u00f6l\u00e7ek (de\u011fi\u015fken) ile okuldaki ba\u015far\u0131y\u0131 \u00f6l\u00e7en 4 \u00f6l\u00e7ek (de\u011fi\u015fken) seti aras\u0131ndaki ili\u015fkiyi hesaplamada setler aras\u0131 korelasyon analizini kullanabilir.<\/p>\n\n\n\n\n\n\n\n\n
\n

\u00d6\u011frenci No<\/em><\/strong><\/p>\n<\/td>\n

\n

Set1(\u00d6\u011frenme Yetene\u011fi)<\/em><\/strong><\/p>\n<\/td>\n

\n

Set2 (okuldaki ba\u015far\u0131)<\/em><\/strong><\/p>\n<\/td>\n<\/tr>\n

\n

1<\/em><\/p>\n<\/td>\n

\n

Muhakeme<\/p>\n<\/td>\n

\n

Anlama<\/p>\n<\/td>\n

\n

Analitik<\/p>\n<\/td>\n

\n

T\u00fcrk\u00e7e<\/p>\n<\/td>\n

\n

Mat<\/p>\n<\/td>\n

\n

Fen Bil.<\/p>\n<\/td>\n

\n

Sos. Bil.<\/p>\n<\/td>\n<\/tr>\n

\n

2<\/em><\/p>\n<\/td>\n

\n

25<\/p>\n<\/td>\n

\n

68<\/p>\n<\/td>\n

\n

98<\/p>\n<\/td>\n

\n

45<\/p>\n<\/td>\n

\n

52<\/p>\n<\/td>\n

\n

58<\/p>\n<\/td>\n

\n

90<\/p>\n<\/td>\n<\/tr>\n

\n

\u2026<\/em><\/p>\n<\/td>\n

\n

68<\/p>\n<\/td>\n

\n

75<\/p>\n<\/td>\n

\n

85<\/p>\n<\/td>\n

\n

78<\/p>\n<\/td>\n

\n

87<\/p>\n<\/td>\n

\n

95<\/p>\n<\/td>\n

\n

78<\/p>\n<\/td>\n<\/tr>\n

\n

\u2026<\/em><\/p>\n<\/td>\n

\n

45<\/p>\n<\/td>\n

\n

55<\/p>\n<\/td>\n

\n

30<\/p>\n<\/td>\n

\n

47<\/p>\n<\/td>\n

\n

60<\/p>\n<\/td>\n

\n

45<\/p>\n<\/td>\n

\n

93<\/p>\n<\/td>\n<\/tr>\n

\n

N<\/em><\/p>\n<\/td>\n

\n

50<\/p>\n<\/td>\n

\n

52<\/p>\n<\/td>\n

\n

47<\/p>\n<\/td>\n

\n

45<\/p>\n<\/td>\n

\n

74<\/p>\n<\/td>\n

\n

85<\/p>\n<\/td>\n

\n

74<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

SPSS program\u0131nda analiz i\u00e7in script yaz\u0131lmal\u0131 ya da MATLAB, M\u0131N\u0131TAB, SAS ya da STAT\u0131ST\u0131CA programlar\u0131ndan faydalan\u0131labilinir.<\/span><\/p>\n

Setleraras\u0131 Korelasyon Analizi i\u00e7in,<\/p>\n

    \n
  • De\u011fi\u015fken setlerinde yer alan de\u011fi\u015fkenlerin e\u015fit say\u0131da olmas\u0131 zorunlulu\u011fu yoktur.<\/li>\n
  • Stevens\u2019a g\u00f6re setleraras\u0131 korelasyonun g\u00fcvenilir ve tahminlerin tutarl\u0131 olmas\u0131 i\u00e7in birim say\u0131s\u0131 (n), setlerdeki toplam de\u011fi\u015fken say\u0131s\u0131n\u0131n en az 20 kat\u0131 olmas\u0131 \u00f6nerilmektedir.<\/li>\n
  • Veri setinde ayk\u0131r\u0131 de\u011ferlerin bulunmamas\u0131na <\/em>dikkat edilmelidir.<\/li>\n
  • Veri setinde gere\u011finden fazla problemle ilgili olmayan de\u011fi\u015fkenlerin olmamas\u0131 gerekir.<\/li>\n
  • Analiz edilecek de\u011fi\u015fkenler aras\u0131nda tam korelasyon bulunmamal\u0131d\u0131r.<\/em><\/li>\n<\/ul>\n

    Uyum Analizi:<\/span><\/strong> <\/strong>\u00c7apraz tablo bi\u00e7iminde g\u00f6sterilen de\u011fi\u015fkenler aras\u0131ndaki uyumlulu\u011fu ya da bir de\u011fi\u015fkenin kendi kategorileri aras\u0131ndaki uyumlulu\u011funda kullan\u0131lan kategorik veri analizi<\/span><\/em> y\u00f6ntemidir. Ayr\u0131ca bu istatistik, kategorik veri indirgeme y\u00f6ntemi olarak da kullan\u0131labilir. <\/p>\n

    Y\u00f6ntem, \u00e7apraz tablo ya da i\u00e7 i\u00e7e \u00e7apraz tablo bi\u00e7iminde g\u00f6sterilen de\u011fi\u015fkenlerin alt s\u0131n\u0131flar\u0131ndaki yo\u011funla\u015fmalar\u0131n\u0131 \u201c\u00f6klid uzakl\u0131\u011f\u0131\u201d ya da \u201cpearson ki kare\u201d uzakl\u0131\u011f\u0131 cinsinden hesaplayarak a\u011f\u0131rl\u0131kl\u0131 ana bile\u015fenlere g\u00f6re analiz eder.<\/p>\n

    Basit (r*c)<\/span> ve \u00c7oklu (r*c*m) Uyum analizi<\/span> olarak iki farkl\u0131 bi\u00e7imde uygulan\u0131r.<\/p>\n

    \u00d6rnek: Cinsiyet ve ya\u015f\u0131n g\u00fcnl\u00fck ya\u015fam aktivitesi \u00fczerindeki etkisi ara\u015ft\u0131r\u0131l\u0131yor olsun.<\/p>\n

    Cinsiyet: Kad\u0131n \/ Erkek (2 grup)<\/p>\n

    Ya\u015f:<20 (1) ;20-39 (2) ; >40 (3)<\/p>\n

    Aktivite: \u00c7okaktif (1) ; aktif (2); uyu\u015fuk (3)<\/p>\n\n\n\n\n\n\n\n\n\n
    \n

    Cinsiyet<\/p>\n<\/td>\n

    		\n

    Ya\u015f<\/p>\n<\/td>\n

    		\n

    Aktivite<\/p>\n<\/td>\n

    		\n

    Frekans<\/p>\n<\/td>\n<\/tr>\n

    \n

    E<\/p>\n<\/td>\n

    		\n

    1<\/p>\n<\/td>\n

    		\n

    1<\/p>\n<\/td>\n

    		\n

    2<\/p>\n<\/td>\n<\/tr>\n

    \n

    E<\/p>\n<\/td>\n

    		\n

    2<\/p>\n<\/td>\n

    		\n

    2<\/p>\n<\/td>\n

    		\n

    3<\/p>\n<\/td>\n<\/tr>\n

    \n

    E<\/p>\n<\/td>\n

    		\n

    3<\/p>\n<\/td>\n

    		\n

    3<\/p>\n<\/td>\n

    		\n

    5<\/p>\n<\/td>\n<\/tr>\n

    \n

    K<\/p>\n<\/td>\n

    		\n

    1<\/p>\n<\/td>\n

    		\n

    1<\/p>\n<\/td>\n

    		\n

    3<\/p>\n<\/td>\n<\/tr>\n

    \n

    K<\/p>\n<\/td>\n

    		\n

    2<\/p>\n<\/td>\n

    		\n

    2<\/p>\n<\/td>\n

    		\n

    4<\/p>\n<\/td>\n<\/tr>\n

    \n

    K<\/p>\n<\/td>\n

    		\n

    3<\/p>\n<\/td>\n

    		\n

    3<\/p>\n<\/td>\n

    		\n

    3<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

    SPSS 11.0 program\u0131nda analiz i\u00e7in: Spss<Analiz<Data Reduction<Correspondence Anaysis (P=2) \/ Optimal Scaling (p>2)<\/span><\/p>\n

    Hotelling T2<\/sup> Testi:<\/span><\/strong> <\/strong>\u0131ki ve daha \u00e7ok de\u011fi\u015fkenli (p\u22652) tek \u00f6rnek (g=1) ve iki \u00f6rnek (g=2) hipotezlerinin test edilir.<\/p>\n

    \u00d6rnek: Bir ilk\u00f6\u011fretim okulunda 8-A (NA<\/sub>=30) ve 8-B (NB<\/sub>=33) \u015fubelerinde okuyan \u00f6\u011frencilerin, T\u00fcrk\u00e7e, Matematik, Fen Bilgisi, M\u00fczik, Edebiyat ders ba\u015far\u0131lar\u0131 bak\u0131m\u0131ndan bu iki \u015fubedeki \u00f6\u011frenciler farkl\u0131l\u0131k g\u00f6stermekte midir?<\/p>\n\n\n\n\n\n\n\n\n
    \n

    \u00d6\u011frenci No<\/em><\/strong><\/p>\n<\/td>\n

    		\n

    T\u00fcrk\u00e7e <\/em><\/strong><\/p>\n<\/td>\n

    		\n

    Mat.<\/em><\/strong><\/p>\n<\/td>\n

    		\n

    Fen Bil.<\/em><\/strong><\/p>\n<\/td>\n

    		\n

    Edebiyat<\/em><\/strong><\/p>\n<\/td>\n

    		\n

    M\u00fczik<\/em><\/strong><\/p>\n<\/td>\n

    		\n

    \u015fube No<\/em><\/strong><\/p>\n<\/td>\n<\/tr>\n

    \n

    1<\/em><\/p>\n<\/td>\n

    		\n

    78<\/p>\n<\/td>\n

    		\n

    54<\/p>\n<\/td>\n

    		\n

    68<\/p>\n<\/td>\n

    		\n

    52<\/p>\n<\/td>\n

    		\n

    85<\/p>\n<\/td>\n

    		\n

    A<\/p>\n<\/td>\n<\/tr>\n

    \n

    2<\/em><\/p>\n<\/td>\n

    		\n

    25<\/p>\n<\/td>\n

    		\n

    68<\/p>\n<\/td>\n

    		\n

    98<\/p>\n<\/td>\n

    		\n

    58<\/p>\n<\/td>\n

    		\n

    100<\/p>\n<\/td>\n

    		\n

    A<\/p>\n<\/td>\n<\/tr>\n

    \n

    \u2026<\/em><\/p>\n<\/td>\n

    		\n

    68<\/p>\n<\/td>\n

    		\n

    75<\/p>\n<\/td>\n

    		\n

    85<\/p>\n<\/td>\n

    		\n

    95<\/p>\n<\/td>\n

    		\n

    78<\/p>\n<\/td>\n

    		\n

    A<\/p>\n<\/td>\n<\/tr>\n

    \n

    \u2026<\/em><\/p>\n<\/td>\n

    		\n

    45<\/p>\n<\/td>\n

    		\n

    55<\/p>\n<\/td>\n

    		\n

    30<\/p>\n<\/td>\n

    		\n

    45<\/p>\n<\/td>\n

    		\n

    60<\/p>\n<\/td>\n

    		\n

    B<\/p>\n<\/td>\n<\/tr>\n

    \n

    NA<\/sub>=30+NB<\/sub>=33 = 73<\/em><\/p>\n<\/td>\n

    		\n

    50<\/p>\n<\/td>\n

    		\n

    52<\/p>\n<\/td>\n

    		\n

    47<\/p>\n<\/td>\n

    		\n

    85<\/p>\n<\/td>\n

    		\n

    74<\/p>\n<\/td>\n

    		\n

    B<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

    SPSS 11.0 program\u0131nda analiz i\u00e7in: Spss<Analiz<General Linear Model(GML)<Multivariate<\/span><\/p>\n

    \u00c7ok De\u011fi\u015fkenli Varyans Analizi (MANOVA):<\/span><\/strong> Grup say\u0131s\u0131 (g\u22652) ikiden fazla oldu\u011funda Hotelling T2<\/sup> testinin alternatifidir.<\/p>\n

    \u00d6rnek2: 8-A(NA<\/sub>=30), 8-B(NB<\/sub>=33) ve 8-C (NC<\/sub>=27) \u015fubelerinde okuyan \u00f6\u011frencilerin T\u00fcrk\u00e7e, Matematik, Fen ve Edebiyat ders ba\u015far\u0131lar\u0131 \u015fubelere g\u00f6re farkl\u0131l\u0131k g\u00f6stermekte midir?<\/p>\n\n\n\n\n\n\n\n\n\n\n\n
    \n

    \u00d6\u011frenci No<\/em><\/strong><\/p>\n<\/td>\n

    		\n

    T\u00fcrk\u00e7e <\/em><\/strong><\/p>\n<\/td>\n

    		\n

    Mat.<\/em><\/strong><\/p>\n<\/td>\n

    		\n

    Fen Bil.<\/em><\/strong><\/p>\n<\/td>\n

    		\n

    Edebiyat<\/em><\/strong><\/p>\n<\/td>\n

    		\n

    \u015fube No<\/em><\/strong><\/p>\n<\/td>\n<\/tr>\n

    \n

    1<\/em><\/p>\n<\/td>\n

    		\n

    78<\/p>\n<\/td>\n

    		\n

    54<\/p>\n<\/td>\n

    		\n

    68<\/p>\n<\/td>\n

    		\n

    52<\/p>\n<\/td>\n

    		\n

    A<\/p>\n<\/td>\n<\/tr>\n

    \n

    2<\/em><\/p>\n<\/td>\n

    		\n

    25<\/p>\n<\/td>\n

    		\n

    68<\/p>\n<\/td>\n

    		\n

    98<\/p>\n<\/td>\n

    		\n

    58<\/p>\n<\/td>\n

    		\n

    A<\/p>\n<\/td>\n<\/tr>\n

    \n

    2<\/em><\/p>\n<\/td>\n

    		\n

    68<\/p>\n<\/td>\n

    		\n

    75<\/p>\n<\/td>\n

    		\n

    85<\/p>\n<\/td>\n

    		\n

    95<\/p>\n<\/td>\n

    		\n

    A<\/p>\n<\/td>\n<\/tr>\n

    \n

    4<\/em><\/p>\n<\/td>\n

    		\n

    45<\/p>\n<\/td>\n

    		\n

    55<\/p>\n<\/td>\n

    		\n

    30<\/p>\n<\/td>\n

    		\n

    45<\/p>\n<\/td>\n

    		\n

    B<\/p>\n<\/td>\n<\/tr>\n

    \n

    \u2026<\/em><\/p>\n<\/td>\n

    		\n

     <\/p>\n<\/td>\n

    		\n

     <\/p>\n<\/td>\n

    		\n

     <\/p>\n<\/td>\n

    		\n

     <\/p>\n<\/td>\n

    		\n

    B<\/p>\n<\/td>\n<\/tr>\n

    \n

    \u2026<\/em><\/p>\n<\/td>\n

    		\n

     <\/p>\n<\/td>\n

    		\n

     <\/p>\n<\/td>\n

    		\n

     <\/p>\n<\/td>\n

    		\n

     <\/p>\n<\/td>\n

    		\n

    C<\/p>\n<\/td>\n<\/tr>\n

    \n

    99<\/em><\/p>\n<\/td>\n

    		\n

    50<\/p>\n<\/td>\n

    		\n

    52<\/p>\n<\/td>\n

    		\n

    47<\/p>\n<\/td>\n

    		\n

    85<\/p>\n<\/td>\n

    		\n

    C<\/p>\n<\/td>\n<\/tr>\n

    \n

    100<\/em><\/p>\n<\/td>\n

    		\n

    50<\/p>\n<\/td>\n

    		\n

    52<\/p>\n<\/td>\n

    		\n

    47<\/p>\n<\/td>\n

    		\n

    85<\/p>\n<\/td>\n

    		\n

    C<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

    SPSS 11.0 program\u0131nda analiz i\u00e7in: Spss<Analiz<General Linear Model(GML)<Multivariate<\/span><\/p>\n

    \u00c7ok De\u011fi\u015fkenli Kovaryans Analizi (MANCOVA):<\/span><\/strong> Grup say\u0131s\u0131 (g\u22652) ikiden fazla normal da\u011f\u0131l\u0131m g\u00f6steren k\u22652 pop\u00fclasyona dair kurulan hipotezler ortak de\u011fi\u015fkenlere g\u00f6re test edilir.<\/p>\n

    K\u00fcmeleme Analizi:<\/span><\/strong> <\/strong>X veri matrisinde yer alan ve do\u011fal gruplamalar\u0131 kesin olarak bilinmeyen birimleri, de\u011fi\u015fkenleri ya da birim ve de\u011fi\u015fkenleri birbiri ile benzer olan alt k\u00fcmelere (grup, s\u0131n\u0131f) ay\u0131rmaya yard\u0131mc\u0131 olan y\u00f6ntemler toplulu\u011fudur (Tatl\u0131dil,1992). Yani k\u00fcmeleme analizi, yap\u0131lar\u0131 hakk\u0131nda kesin bilgilerin bulunmad\u0131\u011f\u0131 bir veri y\u0131\u011f\u0131n\u0131 i\u00e7indeki birimleri<\/u>, de\u011fi\u015fkenleri<\/u> ya da birim ve de\u011fi\u015fkenleri<\/u> birbiri ile benzer olan alt k\u00fcmelere (grup, s\u0131n\u0131f) ay\u0131rma y\u00f6ntemdir. K\u00fcmeleme analizi (1) a\u015famal\u0131 ve a\u015famal\u0131 olmayan (k\u00fcme say\u0131s\u0131 belli) olmak \u00fczere 2 \u015fekilde yap\u0131lmaktad\u0131r.<\/p>\n

    N=8 ve p=3 Ya\u015f, Boy ve A\u011f\u0131rl\u0131k de\u011fi\u015fkenlerinden elde edilmi\u015f \u00f6l\u00e7\u00fcmlere g\u00f6re 8 bireyi 3 k\u00fcmeye (a\u015famal\u0131 olmayan k\u00fcmeleme y\u00f6ntemi ile) ya da de\u011fi\u015fkenler dikkate al\u0131narak do\u011fal k\u00fcmelere (a\u015famal\u0131 k\u00fcmeleme y\u00f6ntemi ile) ay\u0131rmak m\u00fcmk\u00fcnd\u00fcr.<\/p>\n

    \u00d6rnek: N say\u0131da \u00f6\u011frenciden olu\u015fan bir grup olsun. Bu \u00f6\u011frencilerin de Matematik, T\u00fcrk\u00e7e, Sos. Bil. ve Fen Bil. Ders ba\u015far\u0131 puanlar\u0131 \u00f6l\u00e7\u00fclm\u00fc\u015f olsun. Buna g\u00f6re \u00f6\u011frencileri k\u00fcmeleme analizi y\u00f6ntemiyle derslerdeki performanslar\u0131 bak\u0131m\u0131ndan farkl\u0131 \u015fubeler olu\u015fturmada kullanabiliriz.<\/p>\n\n\n\n\n\n\n\n\n
    \n

    \u00d6\u011frenci No<\/em><\/strong><\/p>\n<\/td>\n

    		\n

    T\u00fcrk\u00e7e <\/em><\/strong><\/p>\n<\/td>\n

    		\n

    Mat.<\/em><\/strong><\/p>\n<\/td>\n

    		\n

    Fen Bil.<\/em><\/strong><\/p>\n<\/td>\n

    		\n

    Edebiyat<\/em><\/strong><\/p>\n<\/td>\n

    		\n

    M\u00fczik<\/em><\/strong><\/p>\n<\/td>\n<\/tr>\n

    \n

    1<\/em><\/p>\n<\/td>\n

    		\n

    78<\/p>\n<\/td>\n

    		\n

    54<\/p>\n<\/td>\n

    		\n

    68<\/p>\n<\/td>\n

    		\n

    52<\/p>\n<\/td>\n

    		\n

    85<\/p>\n<\/td>\n<\/tr>\n

    \n

    2<\/em><\/p>\n<\/td>\n

    		\n

    25<\/p>\n<\/td>\n

    		\n

    68<\/p>\n<\/td>\n

    		\n

    98<\/p>\n<\/td>\n

    		\n

    58<\/p>\n<\/td>\n

    		\n

    100<\/p>\n<\/td>\n<\/tr>\n

    \n

    \u2026<\/em><\/p>\n<\/td>\n

    		\n

    68<\/p>\n<\/td>\n

    		\n

    75<\/p>\n<\/td>\n

    		\n

    85<\/p>\n<\/td>\n

    		\n

    95<\/p>\n<\/td>\n

    		\n

    78<\/p>\n<\/td>\n<\/tr>\n

    \n

    \u2026<\/em><\/p>\n<\/td>\n

    		\n

    45<\/p>\n<\/td>\n

    		\n

    55<\/p>\n<\/td>\n

    		\n

    30<\/p>\n<\/td>\n

    		\n

    45<\/p>\n<\/td>\n

    		\n

    60<\/p>\n<\/td>\n<\/tr>\n

    \n

    N<\/em><\/p>\n<\/td>\n

    		\n

    50<\/p>\n<\/td>\n

    		\n

    52<\/p>\n<\/td>\n

    		\n

    47<\/p>\n<\/td>\n

    		\n

    85<\/p>\n<\/td>\n

    		\n

    74<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

    SPSS 11.0 program\u0131nda analiz i\u00e7in: Spss<Analiz<Classify<K-means cluster(a\u015famal\u0131 olmayan-k\u00fcme say\u0131s\u0131 belli) \/ Hierarchical Cluster (a\u015famal\u0131-k\u00fcme say\u0131s\u0131 belli de\u011fil)<\/span><\/p>\n

    K\u00fcmeleme analizi ile kendi aralar\u0131nda heterojen ve kendi i\u00e7inde birbiri ile homojen k\u00fcmler olu\u015fturulur.<\/p>\n

    Ay\u0131rma Analizi:<\/span><\/strong> <\/strong>X veri setindeki de\u011fi\u015fkenlerin iki ve daha fazla ger\u00e7ek gruplara ayr\u0131lmas\u0131n\u0131 sa\u011flayan, birimlerin p tane \u00f6zelli\u011fini ele alarak bu birimlerin do\u011fal ortamdaki ger\u00e7ek gruplar\u0131na, s\u0131n\u0131flar\u0131na en uygun d\u00fczeyde atanmalar\u0131n\u0131 sa\u011flayacak fonksiyonlar t\u00fcreten bir y\u00f6ntemdir (\u00d6zdamar,2002). Ay\u0131rma analizinin,<\/p>\n

    1- <\/span>Gruplar\u0131 birbirinden ay\u0131rmay\u0131 sa\u011flayan fonksiyonlar\u0131 bulmak <\/p>\n

    2- <\/span>Hesaplanan fonksiyonlar arac\u0131l\u0131\u011f\u0131yla yeni g\u00f6zlenen bir birimi s\u0131n\u0131flama hatas\u0131 minimum olacak bi\u00e7imde g tane gruptan herhangi birine atamak amac\u0131d\u0131r.<\/p>\n

    \u00d6rnek: 8-A, 8-B ve 8-C \u015fubelerinde \u00f6\u011frencilerin T\u00fcrk\u00e7e, Matematik ve Fen bilgisi ders ba\u015far\u0131lar\u0131na g\u00f6re \u015fubelere do\u011fru yerle\u015ftirilip yerle\u015ftirilmedi\u011fini (s\u0131n\u0131flaman\u0131n do\u011fru yap\u0131lma olas\u0131l\u0131\u011f\u0131n\u0131) ya da sonradan T\u00fcrk\u00e7e, Matematik ve Fen bilgisi test ba\u015far\u0131 puanlar\u0131 s\u0131ras\u0131yla 55, 65, 42 olan bir \u00f6\u011frenciyi istatistiksel olarak hangi \u015fubeye dahil edilece\u011fi konusunda karar verirken ay\u0131rma analizinden yararlanmak m\u00fcmk\u00fcnd\u00fcr.<\/p>\n\n\n\n\n\n\n\n\n
    \n

    \u00d6\u011frenci No<\/em><\/strong><\/p>\n<\/td>\n

    		\n

    T\u00fcrk\u00e7e <\/em><\/strong><\/p>\n<\/td>\n

    		\n

    Mat.<\/em><\/strong><\/p>\n<\/td>\n

    		\n

    Fen Bil.<\/em><\/strong><\/p>\n<\/td>\n

    		\n

    Edebiyat<\/em><\/strong><\/p>\n<\/td>\n

    		\n

    M\u00fczik<\/em><\/strong><\/p>\n<\/td>\n

    		\n

    \u015fube No<\/em><\/strong><\/p>\n<\/td>\n<\/tr>\n

    \n

    1<\/em><\/p>\n<\/td>\n

    		\n

    78<\/p>\n<\/td>\n

    		\n

    54<\/p>\n<\/td>\n

    		\n

    68<\/p>\n<\/td>\n

    		\n

    52<\/p>\n<\/td>\n

    		\n

    85<\/p>\n<\/td>\n

    		\n

    A<\/p>\n<\/td>\n<\/tr>\n

    \n

    2<\/em><\/p>\n<\/td>\n

    		\n

    25<\/p>\n<\/td>\n

    		\n

    68<\/p>\n<\/td>\n

    		\n

    98<\/p>\n<\/td>\n

    		\n

    58<\/p>\n<\/td>\n

    		\n

    100<\/p>\n<\/td>\n

    		\n

    A<\/p>\n<\/td>\n<\/tr>\n

    \n

    \u2026<\/em><\/p>\n<\/td>\n

    		\n

    68<\/p>\n<\/td>\n

    		\n

    75<\/p>\n<\/td>\n

    		\n

    85<\/p>\n<\/td>\n

    		\n

    95<\/p>\n<\/td>\n

    		\n

    78<\/p>\n<\/td>\n

    		\n

    A<\/p>\n<\/td>\n<\/tr>\n

    \n

    \u2026<\/em><\/p>\n<\/td>\n

    		\n

    45<\/p>\n<\/td>\n

    		\n

    55<\/p>\n<\/td>\n

    		\n

    30<\/p>\n<\/td>\n

    		\n

    45<\/p>\n<\/td>\n

    		\n

    60<\/p>\n<\/td>\n

    		\n

    B<\/p>\n<\/td>\n<\/tr>\n

    \n

    NA<\/sub>=30+NB<\/sub>=33 = 73<\/em><\/p>\n<\/td>\n

    		\n

    50<\/p>\n<\/td>\n

    		\n

    52<\/p>\n<\/td>\n

    		\n

    47<\/p>\n<\/td>\n

    		\n

    85<\/p>\n<\/td>\n

    		\n

    74<\/p>\n<\/td>\n

    		\n

    B<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

    SPSS 11.0 program\u0131nda analiz i\u00e7in: Spss<Analiz<Classify<Discrimination<\/span><\/p>\n

    Anabile\u015fenler Analizi:<\/span><\/strong> <\/strong>Birbirleri ile ili\u015fkili p>2 de\u011fi\u015fken i\u00e7eren veri matrislerinden, birbirleri ile ba\u011f\u0131ms\u0131z ve daha az say\u0131da yeni veri yap\u0131lar\u0131 elde etmek amac\u0131yla yararlan\u0131lan bir y\u00f6ntemdir. Bu y\u00f6ntemden aralar\u0131nda y\u00fcksek d\u00fczeyde korelasyon bulunan verilerden daha az say\u0131da ve aralar\u0131nda korelasyon bulunmayan yeni de\u011fi\u015fkenler t\u00fcretmek ve veri indirgemesi yapmak amac\u0131yla yararlan\u0131l\u0131r. <\/p>\n

    Ka\u00e7 anabile\u015fen olmal\u0131d\u0131r? Sorusu i\u00e7inse yayg\u0131n y\u00f6nelimler \u015f\u00f6yedir<\/u>:<\/p>\n

    *Birden b\u00fcy\u00fck \u00f6zde\u011fer say\u0131s\u0131 kadar anabile\u015fen se\u00e7ilebilir.<\/p>\n

    *Genel varyans\u0131n en az %67\u2019sini a\u00e7\u0131klayan say\u0131da anabile\u015fen se\u00e7ilebilir<\/p>\n

    *Grafik e\u011fimi ile anabile\u015fen se\u00e7imi yap\u0131labilir.<\/p>\n

    Fakt\u00f6r Analizi:<\/span><\/strong> <\/strong>Bu y\u00f6ntemin amac\u0131 <\/strong>p\u22652 \u00e7ok de\u011fi\u015fkenli veri yap\u0131lar\u0131n\u0131 aralar\u0131nda y\u00fcksek korelasyon bulunan de\u011fi\u015fkenleri bir araya getirerek yeni ve anlaml\u0131 fakt\u00f6r yap\u0131lar\u0131 olu\u015fturmakt\u0131r.<\/p>\n

    \u00d6rnek 3: 25 soruluk likert tipi bir \u00f6l\u00e7ek ka\u00e7 fakt\u00f6r ile temsil edilebilir? (A\u00e7\u0131klay\u0131c\u0131 Fakt\u00f6r Analizi)<\/p>\n\n\n\n\n\n\n\n\n
    \n

    \u00d6\u011frenci No<\/em><\/strong><\/p>\n<\/td>\n

    		\n

    Soru1 <\/em><\/strong><\/p>\n<\/td>\n

    		\n

    Soru2<\/em><\/strong><\/p>\n<\/td>\n

    		\n

    Soru3<\/em><\/strong><\/p>\n<\/td>\n

    		\n

    Soru4<\/em><\/strong><\/p>\n<\/td>\n

    		\n

    \u2026<\/em><\/strong><\/p>\n<\/td>\n

    		\n

    Soru25<\/em><\/strong><\/p>\n<\/td>\n<\/tr>\n

    \n

    1<\/em><\/p>\n<\/td>\n

    		\n

    5<\/p>\n<\/td>\n

    		\n

    3<\/p>\n<\/td>\n

    		\n

    5<\/p>\n<\/td>\n

    		\n

    2<\/p>\n<\/td>\n

    		\n

    3<\/p>\n<\/td>\n

    		\n

    1<\/p>\n<\/td>\n<\/tr>\n

    \n

    2<\/em><\/p>\n<\/td>\n

    		\n

    4<\/p>\n<\/td>\n

    		\n

    2<\/p>\n<\/td>\n

    		\n

    4<\/p>\n<\/td>\n

    		\n

    4<\/p>\n<\/td>\n

    		\n

    4<\/p>\n<\/td>\n

    		\n

    4<\/p>\n<\/td>\n<\/tr>\n

    \n

    \u2026<\/em><\/p>\n<\/td>\n

    		\n

    4<\/p>\n<\/td>\n

    		\n

    5<\/p>\n<\/td>\n

    		\n

    3<\/p>\n<\/td>\n

    		\n

    3<\/p>\n<\/td>\n

    		\n

    4<\/p>\n<\/td>\n

    		\n

    4<\/p>\n<\/td>\n<\/tr>\n

    \n

    \u2026<\/em><\/p>\n<\/td>\n

    		\n

    2<\/p>\n<\/td>\n

    		\n

    2<\/p>\n<\/td>\n

    		\n

    4<\/p>\n<\/td>\n

    		\n

    1<\/p>\n<\/td>\n

    		\n

    2<\/p>\n<\/td>\n

    		\n

    3<\/p>\n<\/td>\n<\/tr>\n

    \n

    N<\/em><\/p>\n<\/td>\n

    		\n

    3<\/p>\n<\/td>\n

    		\n

    3<\/p>\n<\/td>\n

    		\n

    3<\/p>\n<\/td>\n

    		\n

    3<\/p>\n<\/td>\n

    		\n

    3<\/p>\n<\/td>\n

    		\n

    5<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

    SPSS 11.0 program\u0131nda analiz i\u00e7in: Spss<Analiz<Data Reduction<Faktor\u2026<\/span><\/p>\n

    E\u011fer \u00f6rnekteki sorumuzu 25 soruluk likert tipi bir \u00f6l\u00e7ek 2 fakt\u00f6r ile temsil edilebilmekte midir? \u015feklinde \u00e7\u00f6z\u00fcmlenmek istenirse veri bu sefer Do\u011frulay\u0131c\u0131 Fakt\u00f6r Analizi ile analizi y\u00fcr\u00fctmek gereklidir.<\/p>\n

    \u00c7ok Boyutlu \u00d6l\u00e7ekleme Analizi:<\/span><\/strong> <\/strong> Bu y\u00f6ntem Fakt\u00f6r Analizinin alternatifidir. G\u00f6zlenen birimler, nesneler aras\u0131ndaki benzerlikleri ya da farkl\u0131l\u0131klar\u0131 a\u00e7\u0131klamada ara\u015ft\u0131rmac\u0131ya yard\u0131mc\u0131 olan ve boyutlar\u0131n alt\u0131nda yatan anlaml\u0131 yap\u0131lar\u0131 ortaya \u00e7\u0131karmaya y\u00f6nelik bir y\u00f6ntemdir. Fakt\u00f6r analizinde de\u011fi\u015fkenler ve aralar\u0131ndaki korelasyonlardan yararlan\u0131lmakta iken \u00c7B\u00d6A da birimler aras\u0131ndaki benzerlik ya da farkl\u0131l\u0131klardan yararlan\u0131larak daha az boyutta nesnelerin grafiksel olarak a\u00e7\u0131klan\u0131r. K\u0131saca bu analizde, birimlerin p tane \u00f6zelli\u011finden yararlanarak belirlenen birimler aras\u0131ndaki benzerlikleri olabildi\u011fince az say\u0131da boyut ile (d>2) a\u00e7\u0131klamak m\u00fcmk\u00fcnd\u00fcr.<\/p>\n

    \u00d6rne\u011fin Fen bilgisi, matematik, T\u00fcrk\u00e7e, Sosyal bilgiler test puanlar\u0131 de\u011fi\u015fkenler olmak \u00fczere 100 \u00f6\u011frencinin benzer alt gruplara ayr\u0131lmas\u0131nda \u00c7B\u00d6A nden faydal\u0131nabilir. Bu tip bir \u00f6rnekte birimler(case) analiz edilmi\u015ftir.<\/p>\n\n\n\n\n\n\n\n\n
    \n

    \u00d6\u011frenci No<\/em><\/strong><\/p>\n<\/td>\n

    		\n

    T\u00fcrk\u00e7e <\/em><\/strong><\/p>\n<\/td>\n

    		\n

    Mat.<\/em><\/strong><\/p>\n<\/td>\n

    		\n

    Fen Bil.<\/em><\/strong><\/p>\n<\/td>\n

    		\n

    Edebiyat<\/em><\/strong><\/p>\n<\/td>\n

    		\n

    M\u00fczik<\/em><\/strong><\/p>\n<\/td>\n<\/tr>\n

    \n

    1<\/em><\/p>\n<\/td>\n

    		\n

    78<\/p>\n<\/td>\n

    		\n

    54<\/p>\n<\/td>\n

    		\n

    68<\/p>\n<\/td>\n

    		\n

    52<\/p>\n<\/td>\n

    		\n

    85<\/p>\n<\/td>\n<\/tr>\n

    \n

    2<\/em><\/p>\n<\/td>\n

    		\n

    25<\/p>\n<\/td>\n

    		\n

    68<\/p>\n<\/td>\n

    		\n

    98<\/p>\n<\/td>\n

    		\n

    58<\/p>\n<\/td>\n

    		\n

    100<\/p>\n<\/td>\n<\/tr>\n

    \n

    \u2026<\/em><\/p>\n<\/td>\n

    		\n

    68<\/p>\n<\/td>\n

    		\n

    75<\/p>\n<\/td>\n

    		\n

    85<\/p>\n<\/td>\n

    		\n

    95<\/p>\n<\/td>\n

    		\n

    78<\/p>\n<\/td>\n<\/tr>\n

    \n

    \u2026<\/em><\/p>\n<\/td>\n

    		\n

    45<\/p>\n<\/td>\n

    		\n

    55<\/p>\n<\/td>\n

    		\n

    30<\/p>\n<\/td>\n

    		\n

    45<\/p>\n<\/td>\n

    		\n

    60<\/p>\n<\/td>\n<\/tr>\n

    \n

    100<\/em><\/p>\n<\/td>\n

    		\n

    50<\/p>\n<\/td>\n

    		\n

    52<\/p>\n<\/td>\n

    		\n

    47<\/p>\n<\/td>\n

    		\n

    85<\/p>\n<\/td>\n

    		\n

    74<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

    SPSS 11.0 program\u0131nda analiz i\u00e7in: Spss<Analiz<Scale<Multidimensional Scaling<\/span><\/p>\n

    Ayn\u0131 \u00f6rnek i\u00e7in e\u011fer test ba\u015far\u0131lar\u0131na (de\u011fi\u015fkenlere) g\u00f6re bir s\u0131n\u0131f olu\u015fturulacak ve her bir testi ayr\u0131 ayr\u0131 de\u011ferlendirip karar vermek yerine \u00c7B\u00d6A\u2019den yararlanarak hangi testi ya da testleri \u00f6l\u00e7\u00fct alarak \u00f6\u011frenci se\u00e7imi yapaca\u011f\u0131m\u0131z hakk\u0131nda karar vermemiz kolayla\u015facakt\u0131r.<\/p>\n

    Not: \u00c7B\u00d6A bir veri indirgeme y\u00f6ntemi olarak kullan\u0131ld\u0131\u011f\u0131nda veriler \u00f6zellikle nicel ise alternatif y\u00f6ntem Fakt\u00f6r Analizidir. Benzer olgular\u0131n olu\u015fturdu\u011fu gruplar\u0131 belirlemek i\u00e7in kullan\u0131lacak ise alternatif y\u00f6ntem a\u015famal\u0131 ya da a\u015famal\u0131 olmayan k\u00fcmeleme analizidir.<\/em><\/p>\n

    \u00d6ZDAMAR, Kaz\u0131m., Paket Programlar ile \u0131statistiksel Veri Analizi<\/strong>, Kaan Kitapevi, Eski\u015fehir, 1999<\/span><\/p>\n

    TATLID\u0131L,H\u00fcseyin., Uygulamal\u0131 \u00c7ok De\u011fi\u015fkenli \u0131statistiksel Analiz, <\/strong>Cem Web Ofset Ltd.\u015fti., Ankara, 1996<\/span><\/p>\n

     <\/p>\n<\/p><\/div>\n","protected":false},"excerpt":{"rendered":"

    T\u00fclin Acar’\u0131n \u00c7ok De\u011fi\u015fkenli \u0131statistiklerin Kullan\u0131m\u0131 konusundaki yaz\u0131s\u0131n\u0131 yaz\u0131n\u0131n devam\u0131nda bulabilirsiniz.<\/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-97","post","type-post","status-publish","format-standard","hentry"],"_links":{"self":[{"href":"https:\/\/www.istatistik.gen.tr\/index.php?rest_route=\/wp\/v2\/posts\/97","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=97"}],"version-history":[{"count":0,"href":"https:\/\/www.istatistik.gen.tr\/index.php?rest_route=\/wp\/v2\/posts\/97\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.istatistik.gen.tr\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=97"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.istatistik.gen.tr\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=97"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.istatistik.gen.tr\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=97"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}