{"id":45,"date":"2009-07-07T11:54:06","date_gmt":"2009-07-07T08:54:06","guid":{"rendered":"http:\/\/www.muratakyildiz.com\/wordpress\/?p=45"},"modified":"2024-02-09T16:27:36","modified_gmt":"2024-02-09T13:27:36","slug":"kruskal-wallis-testi-ve-bir-spss-kruskal-wallis-nasap","status":"publish","type":"post","link":"https:\/\/www.istatistik.gen.tr\/?p=45","title":{"rendered":"Kruskal-Wallis testi ve bir SPSS \u00f6rne\u011fi (Kruskal Wallis Nas\u0131l Yap\u0131l\u0131r)"},"content":{"rendered":"

K say\u0131da grup i\u00e7in parametrik olmayan Kruskal-Wallis testi 3 ya da daha fazla grubun\/\u00f6rneklemin ayn\u0131 evrenden gelip gelmediklerinin belirlenmesi i\u00e7in kullan\u0131l\u0131r. Bu testin parametrik kar\u015f\u0131l\u0131\u011f\u0131 olan tek fakt\u00f6rl\u00fc varyans analizi (oneway anova) i\u00e7in gerekli olan varsay\u0131mlar (bkz: tek fakt\u00f6rl\u00fc varyans analizi) kar\u015f\u0131lanamad\u0131\u011f\u0131nda, Kruskal-Wallis testi kullan\u0131l\u0131r
\n<\/p>\n

Kruskal-Wallis testinin varsay\u0131mlar\u0131:
\na) \u0131ncelenen de\u011fi\u015fkenin alt\u0131nda s\u00fcrekli bir da\u011f\u0131l\u0131m yatmaktad\u0131r.
\nb) \u0131ncelenen de\u011fi\u015fken, en az\u0131ndan s\u0131ralama \u00f6l\u00e7e\u011fi d\u00fczeyinde \u00f6l\u00e7\u00fclm\u00fc\u015ft\u00fcr.<\/p>\n

E\u011fer s\u0131f\u0131r hipotezi do\u011fruysa gruplar aras\u0131nda s\u0131ralar\u0131n tesad\u00fcfi olarak da\u011f\u0131lm\u0131\u015f olmas\u0131 gerekir<\/p>\n

A\u015fa\u011f\u0131daki \u015fekilde bu durum, A, B ve C gruplar\u0131n\u0131n 1’den 9’a kadar olan s\u0131ralar\u0131 belirli bir kurala g\u00f6re de\u011fil (\u00f6rne\u011fin A grubundakiler hep d\u00fc\u015f\u00fck s\u0131ra numaralar\u0131n\u0131 almas\u0131, C grubundakilerin hep b\u00fcy\u00fck s\u0131ra numaralar\u0131n\u0131 almas\u0131 gibi) tamamen rastgele bir \u015fekilde ald\u0131\u011f\u0131n\u0131 g\u00f6stermektedir.<\/p>\n

\"\"<\/p>\n

\u00dc\u00e7 grubun s\u0131ra numaralar\u0131 topland\u0131\u011f\u0131nda, bu s\u0131ra toplamlar\u0131n\u0131n birbirine \u00e7ok yak\u0131n oldu\u011fu g\u00f6r\u00fcl\u00fcr.<\/p>\n

E\u011fer s\u0131f\u0131r hipotezi yanl\u0131\u015fsa, gruplar aras\u0131nda s\u0131ralar sistematik bir da\u011f\u0131l\u0131m g\u00f6sterir.<\/p>\n

\"\"<\/p>\n

Burada A grubu daha \u00e7ok d\u00fc\u015f\u00fck s\u0131ra numaralar\u0131n\u0131, C grubu ise b\u00fcy\u00fck s\u0131ra numaralar\u0131n\u0131 al\u0131yor g\u00f6r\u00fcnmektedir. B grubu ise bu ikisinin aras\u0131nda kalan s\u0131ra numaralar\u0131n\u0131 al\u0131yor g\u00f6r\u00fcnmektedir. Bu gruplar\u0131n s\u0131ra numaralar\u0131 topland\u0131\u011f\u0131nda, birbirlerinden g\u00f6receli olarak daha uzak s\u0131ra toplamlar\u0131na sahiptirler. Dolay\u0131s\u0131 ile b\u00f6yle bir ko\u015fulda gruplar aras\u0131nda fark beklemek daha do\u011fald\u0131r.<\/p>\n

Gruplar aras\u0131ndaki s\u0131ra ortalamalar\u0131n\u0131n birbirinden farkl\u0131 olup olmad\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in yap\u0131lacak Kruskal-Wallis testinde Kruskal-Wallis de\u011feri a\u015fa\u011f\u0131daki form\u00fclle hesaplan\u0131r:<\/p>\n

\"\"<\/p>\n

N= Gruplardaki Toplam Ki\u015fi\/G\u00f6zlem Say\u0131s\u0131<\/p>\n

\"\"= Grup S\u0131ra Ortalamas\u0131<\/p>\n

n= Her Bir Gruptaki Ki\u015fi Say\u0131s\u0131<\/p>\n

A\u015fa\u011f\u0131daki \u00f6rnekte \u00fc\u00e7 farkl\u0131 gruptan (akademisyen, politikac\u0131, din adam\u0131) al\u0131nm\u0131\u015f kontrol oda\u011f\u0131 puanlar\u0131 bulunmaktad\u0131r. Bu \u00fc\u00e7 grubun kontrol oda\u011f\u0131 puanlar\u0131n\u0131n birbirinden farkl\u0131 olup olmad\u0131\u011f\u0131 ara\u015ft\u0131r\u0131lmaktad\u0131r. Gruplarda \u00e7ok az say\u0131da ki\u015fi bulunmas\u0131ndan dolay\u0131 nonparametrik bir test olan Kruskal-Wallis testi kullan\u0131lm\u0131\u015ft\u0131r.<\/p>\n

\"\"<\/p>\n

Yukar\u0131daki Kruskal-Wallis e\u015fitli\u011fi bu \u00f6rne\u011fi uygulanacak olursa:<\/p>\n

\"\"<\/p>\n

KW= 8,81 olarak hesaplan\u0131r. Bu de\u011ferin tek ba\u015f\u0131na hi\u00e7 bir anlam\u0131 yoktur. Bu \u00f6zelliklere sahip (ki\u015fi say\u0131s\u0131, grup say\u0131s\u0131) \u00f6rneklemler i\u00e7in \u00f6nceden belirlenmi\u015f olan “fark varsa, KW de\u011feri en az \u015fu kadar olmal\u0131d\u0131r” bilgisini veren Kruskal-Wallis tablosuna bakmak gerekmektedir. Bu tablodan edinece\u011fimiz kritik de\u011fer ile az \u00f6nce hesaplad\u0131\u011f\u0131m\u0131z KW de\u011feri kar\u015f\u0131la\u015ft\u0131r\u0131l\u0131r. E\u011fer, “fark vard\u0131r” karar\u0131 verilmesi i\u00e7in gerekli olan en d\u00fc\u015f\u00fck KW de\u011ferini veren tablo de\u011ferinden daha b\u00fcy\u00fck bir KW de\u011feri hesapland\u0131ysa bu gruplar aras\u0131nda, denetim oda\u011f\u0131 bak\u0131m\u0131ndan fark oldu\u011funa karar verilir.<\/p>\n

Fakat Kruskal-Wallis testi, kar\u015f\u0131la\u015ft\u0131r\u0131lan gruplar i\u00e7indeki, herhangi iki grup aras\u0131ndaki farka duyarl\u0131d\u0131r. Bir ba\u015fka deyi\u015fle, hesaplanan Kruskal-Wallis de\u011ferini, tablo Kruskal-Wallis de\u011ferinden daha b\u00fcy\u00fck olmas\u0131 t\u00fcm gruplar\u0131n birbirinden farkl\u0131 oldu\u011fu anlam\u0131n\u0131 ta\u015f\u0131maz. Kruskal-Wallis gruplar\u0131 topluca de\u011ferlendirir, herhangi iki grup aras\u0131nda (ya da daha fazla grup aras\u0131nda) fark varsa, anlaml\u0131 farkl\u0131l\u0131k bildirir. Fakat hangi gruplar aras\u0131nda fark oldu\u011funu bildirmez. Bunu bulabilmek i\u00e7in, post-hoc testler denilen kar\u015f\u0131la\u015ft\u0131rmalara ihtiya\u00e7 duyulur.<\/p>\n

Post hoc test her bir grubu bir di\u011feriyle kar\u015f\u0131la\u015ft\u0131r\u0131r. Bu kar\u015f\u0131la\u015ft\u0131rma i\u00e7in, “iki grup aras\u0131nda fark vard\u0131r karar\u0131 verilebilmesi i\u00e7in s\u0131ra ortalamalar\u0131 aras\u0131nda en az ne kadar fark olmal\u0131d\u0131r” sorusuna yan\u0131t aran\u0131r. A\u015fa\u011f\u0131daki form\u00fcl, Kruskal-Wallis i\u00e7in bu soruyu yan\u0131tlamaktad\u0131r.<\/p>\n

\"\"<\/p>\n

N= Toplam ki\u015fi say\u0131s\u0131<\/p>\n

n= gruptaki ki\u015fi say\u0131s\u0131<\/p>\n

Yukar\u0131daki \u00f6rnek i\u00e7in hesaplanacak olursa:<\/p>\n

\"\"<\/p>\n

Kritik Fark = 7,38 bulunacakt\u0131r.<\/p>\n

Demek ki, yukar\u0131da kar\u015f\u0131la\u015ft\u0131r\u0131lan gruplar\u0131n s\u0131ra ortalamalar\u0131 aras\u0131nda 7,38 <\/strong>ya da daha fazla farkl\u0131l\u0131k varsa, bu iki grup aras\u0131nda “tesad\u00fcfen ger\u00e7ekle\u015fmi\u015f olmayla a\u00e7\u0131klanamayacak”, anlaml\u0131 bir farkl\u0131l\u0131k vard\u0131r karar\u0131 verilebilecektir. Buna g\u00f6re:<\/p>\n

Din Adam\u0131 \u2013 Politikac\u0131 = 2 < 7,38<\/p>\n

Politikac\u0131 \u2013 Akademisyen = 6,75 < 7,38<\/p>\n

Din Adam\u0131 \u2013 Akademisyen = 8,75 > 7,38 <\/strong><\/p>\n

Yukar\u0131da kar\u015f\u0131la\u015ft\u0131r\u0131lan \u00fc\u00e7 gruptan sadece Din Adam\u0131 ile Akademisyen gruplar\u0131 aras\u0131nda kontrol oda\u011f\u0131 bak\u0131m\u0131ndan anlaml\u0131 bir farkl\u0131l\u0131k bulunmaktad\u0131r. Din Adam\u0131 ve Politikac\u0131 ile Politikac\u0131 ve Akademisyen gruplar\u0131 denetim oda\u011f\u0131 bak\u0131m\u0131ndan birbirine denktir.<\/p>\n

\u015fimdi de SPSS kullanarak Kruskal-Wallis testinin nas\u0131l uygulanaca\u011f\u0131n\u0131 g\u00f6relim.<\/p>\n

Verilerimiz, en basit haliyle spss dosyam\u0131zda \u015fu \u015fekilde g\u00f6r\u00fcnmelidir.<\/p>\n

\"\"<\/p>\n

Analiz i\u00e7in \u00dcstteki Analyse men\u00fcs\u00fcne girerek Non-parametric tests b\u00f6l\u00fcm\u00fc a\u00e7\u0131lmal\u0131d\u0131r. A\u00e7\u0131lan men\u00fcden ise k independent samples (k say\u0131da ba\u011f\u0131ms\u0131z \u00f6rneklem) men\u00fcs\u00fcne girilmelidir. A\u015fa\u011f\u0131daki resimde bu yol g\u00f6sterilmi\u015ftir.<\/p>\n

\"\"<\/p>\n

Buraya t\u0131kland\u0131\u011f\u0131nda a\u015fa\u011f\u0131daki pencere a\u00e7\u0131l\u0131r:<\/p>\n

\"kruskal8\"<\/p>\n

Bu pencerede Grouping Variable yazan k\u0131sma gruplar\u0131 g\u00f6steren de\u011fi\u015fken Test Variable List k\u0131sm\u0131na ise gruplar aras\u0131nda hangi de\u011fi\u015fken bak\u0131m\u0131ndan fark aran\u0131yorsa o de\u011fi\u015fken at\u0131l\u0131r. A\u015fa\u011f\u0131daki resim bu s\u00fcreci g\u00f6stermektedir.<\/p>\n

\"\"<\/p>\n

Gruplama de\u011fi\u015fkeni at\u0131ld\u0131ktan sonra hemen alt\u0131ndaki Define Range se\u00e7ene\u011fi aktif olarak, grup(? ?) \u015feklinde bir durum ortaya \u00e7\u0131km\u0131\u015ft\u0131r. Burada Define Range d\u00fc\u011fmesine t\u0131klayarak, ka\u00e7 grup oldu\u011funun SPSS’e bildirilmesi gerekmektedir. A\u015fa\u011f\u0131daki resim bunu g\u00f6stermektedir:<\/p>\n

\"\"<\/p>\n

Burada Minumum k\u0131sm\u0131na 1, Maximum k\u0131sm\u0131na ise 3 yazarak 1 ile 3 kodu aras\u0131nda kalan gruplar da dahil olacak \u015fekilde analiz yapmak istedi\u011fimizi SPSS’e bildirmi\u015f olduk.<\/p>\n

B\u00f6ylece bu \u00f6rnekte, 1, 2 ve 3 kodu verilmi\u015f olan deney (1), kontrol (2) ve izleme (3) gruplar\u0131 aras\u0131ndaki fark\u0131n incelenmesi sa\u011flanm\u0131\u015f olacakt\u0131r. Continue t\u0131klanarak devam edilir. Kar\u015f\u0131m\u0131za \u015fu pencere \u00e7\u0131kar:<\/p>\n

\"\"<\/p>\n

Burada Options d\u00fc\u011fmesine t\u0131klanarak a\u00e7\u0131lan pencereden Descriptives se\u00e7ene\u011fi i\u015faretlenir<\/p>\n

\"\"<\/p>\n

Yine Continue t\u0131klanarak devam edilir. Son olarak kar\u015f\u0131m\u0131zda \u015fu ekran kam\u0131\u015ft\u0131r. Art\u0131k OK tu\u015fu t\u0131klanarak analiz yap\u0131labilecek duruma gelinmi\u015ftir.<\/p>\n

\"\"<\/p>\n

OK t\u0131kland\u0131\u011f\u0131nda analiz yap\u0131l\u0131r ve SPSS bize \u015fu \u00e7\u0131kt\u0131y\u0131 verir:<\/p>\n

\"\"<\/p>\n

Burada ilk iki tablo betimsel istatistikleri bildirmektedir. Gruplarda ka\u00e7ar ki\u015fi bulundu\u011fu, bu gruplar\u0131n s\u0131ra ortalamalar\u0131 gibi. Karar vermemizi sa\u011flayacak olan tablo Test Statistics tablosudur. Chi-Square olarak g\u00f6r\u00fcnen de\u011fer, daha \u00f6nce yukar\u0131da form\u00fclle hesaplam\u0131\u015f oldu\u011fumuz Kruskal-Wallis (KW) de\u011ferine denk gelmektedir (\u0131ki \u00f6rnekte de\u011ferlerin farkl\u0131 olmas\u0131, bu \u00f6rneklerin farkl\u0131 ara\u015ft\u0131rmalar olmas\u0131ndand\u0131r). SPSS, bizim i\u00e7in gerekli olan tablo kar\u015f\u0131la\u015ft\u0131rmas\u0131n\u0131 kendisi yapmakta ve bu kar\u015f\u0131la\u015ft\u0131rma sonucunda, “s\u0131ra ortalamalar\u0131 aras\u0131nda anlaml\u0131 fark yoktur” deme olas\u0131l\u0131\u011f\u0131n\u0131 Asym. Sig (Asymptotic Significance) ile bildirmektedir. E\u011fer bu de\u011fer, 0,05’e e\u015fit ya da daha k\u00fc\u00e7\u00fckse, kar\u015f\u0131la\u015ft\u0131r\u0131lan s\u0131ra ortalamalar\u0131ndan en az ikisi aras\u0131nda, istatistiksel a\u00e7\u0131dan \u00f6nemli (manidar) yani anlaml\u0131 bir farkl\u0131l\u0131k vard\u0131r karar\u0131 verilebilir. E\u011fer bu de\u011fer 0,05’ten daha b\u00fcy\u00fckse, bu gruplar\u0131n s\u0131ra ortalamalar\u0131n\u0131n hi\u00e7 birisi aras\u0131nda anlaml\u0131 farkl\u0131l\u0131k yoktur, bu gruplar birbirine denktir karar\u0131 verilebilir. Fakat unutulmamal\u0131d\u0131r ki bu karar %5 yani 0,05 d\u00fczeyinde al\u0131nm\u0131\u015f bir karard\u0131r. Yani, bu karar\u0131n %5 olas\u0131l\u0131kla yanl\u0131\u015f olmas\u0131 ihtimali bulunmaktad\u0131r.<\/p>\n

Soru ve \u00f6nerilerinizi a\u015fa\u011f\u0131daki yorum b\u00f6l\u00fcm\u00fcne yazabilirsiniz<\/p>\n","protected":false},"excerpt":{"rendered":"

K say\u0131da grup i\u00e7in parametrik olmayan Kruskal-Wallis testi 3 ya da daha fazla grubun\/\u00f6rneklemin ayn\u0131 evrenden gelip gelmediklerinin belirlenmesi i\u00e7in kullan\u0131l\u0131r. Bu testin parametrik kar\u015f\u0131l\u0131\u011f\u0131 olan tek fakt\u00f6rl\u00fc varyans analizi (oneway anova) i\u00e7in gerekli olan varsay\u0131mlar (bkz: tek fakt\u00f6rl\u00fc varyans analizi) kar\u015f\u0131lanamad\u0131\u011f\u0131nda, Kruskal-Wallis testi kullan\u0131l\u0131r<\/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-45","post","type-post","status-publish","format-standard","hentry"],"_links":{"self":[{"href":"https:\/\/www.istatistik.gen.tr\/index.php?rest_route=\/wp\/v2\/posts\/45","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=45"}],"version-history":[{"count":9,"href":"https:\/\/www.istatistik.gen.tr\/index.php?rest_route=\/wp\/v2\/posts\/45\/revisions"}],"predecessor-version":[{"id":919,"href":"https:\/\/www.istatistik.gen.tr\/index.php?rest_route=\/wp\/v2\/posts\/45\/revisions\/919"}],"wp:attachment":[{"href":"https:\/\/www.istatistik.gen.tr\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=45"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.istatistik.gen.tr\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=45"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.istatistik.gen.tr\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=45"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}