{"id":800592,"date":"2019-02-04T21:38:22","date_gmt":"2019-02-05T04:38:22","guid":{"rendered":"https:\/\/www.questionpro.com\/blog\/spearmans-rank-coefficient-of-correlation\/"},"modified":"2019-02-04T21:38:22","modified_gmt":"2019-02-04T21:38:22","slug":"spearmans-rank-coefficient-of-correlation","status":"publish","type":"post","link":"https:\/\/www.questionpro.com\/blog\/tr\/spearmans-rank-coefficient-of-correlation\/","title":{"rendered":"Spearman korelasyon katsay\u0131s\u0131: Form\u00fcl + Hesaplama"},"content":{"rendered":"
Spearman’\u0131n s\u0131ra korelasyon katsay\u0131s\u0131 veya Spearman korelasyon katsay\u0131s\u0131, s\u0131ra korelasyonunun parametrik olmayan bir \u00f6l\u00e7\u00fcs\u00fcd\u00fcr (iki de\u011fi\u015fken aras\u0131ndaki s\u0131ralaman\u0131n istatistiksel ba\u011f\u0131ml\u0131l\u0131\u011f\u0131). <\/span><\/p>\n Charles Spearman’\u0131n ad\u0131yla an\u0131lan bu terim genellikle Yunanca ‘\u03c1’ <\/strong>(rho) harfiyle g\u00f6sterilir ve \u00f6ncelikle veri analizi<\/a> i\u00e7in kullan\u0131l\u0131r. <\/span><\/p>\n \u0130ki s\u0131ral\u0131 de\u011fi\u015fken aras\u0131ndaki ili\u015fkinin g\u00fcc\u00fcn\u00fc ve y\u00f6n\u00fcn\u00fc \u00f6l\u00e7er. Ancak Spearman korelasyon katsay\u0131s\u0131ndan bahsetmeden \u00f6nce Pearson korelasyonunu anlamak \u00f6nemlidir. Pearson korelasyonu, e\u015fle\u015ftirilmi\u015f veriler aras\u0131ndaki do\u011frusal ili\u015fkinin g\u00fcc\u00fcn\u00fcn istatistiksel bir \u00f6l\u00e7\u00fcs\u00fcd\u00fcr. <\/span><\/p>\n S\u0131ralama de\u011fi\u015fkeninin hesaplanmas\u0131 ve anlaml\u0131l\u0131k testi i\u00e7in a\u015fa\u011f\u0131daki veri varsay\u0131m\u0131n\u0131n do\u011fru olmas\u0131 gerekmektedir: <\/span><\/p>\n Verileriniz yukar\u0131daki varsay\u0131mlar\u0131 kar\u015f\u0131lam\u0131yorsa, Spearman Katsay\u0131s\u0131na ihtiyac\u0131n\u0131z olacakt\u0131r. Spearman korelasyon katsay\u0131s\u0131n\u0131 anlamak i\u00e7in monotonik fonksiyonun ne oldu\u011funu bilmek gerekir. Monoton bir fonksiyon, ba\u011f\u0131ms\u0131z de\u011fi\u015fken artt\u0131k\u00e7a ya hi\u00e7 azalmayan ya da hi\u00e7 artmayan bir fonksiyondur. Monotonik bir fonksiyon a\u015fa\u011f\u0131daki resim kullan\u0131larak a\u00e7\u0131klanabilir:<\/span><\/p>\n G\u00f6rsel, monotonik fonksiyonla ilgili \u00fc\u00e7 kavram\u0131 a\u00e7\u0131klamaktad\u0131r:<\/span><\/p>\n Monotonik ili\u015fki, Pearson katsay\u0131s\u0131nda kullan\u0131lan do\u011frusal ili\u015fkiye k\u0131yasla daha az k\u0131s\u0131tlay\u0131c\u0131d\u0131r. Monotonluk Spearman korelasyon katsay\u0131s\u0131 i\u00e7in nihai gereklilik olmasa da, de\u011fi\u015fkenler aras\u0131ndaki ili\u015fkinin monoton olmad\u0131\u011f\u0131 zaten biliniyorsa, monotonik bir ili\u015fkinin g\u00fcc\u00fcn\u00fc ve y\u00f6n\u00fcn\u00fc ger\u00e7ekten belirlemeden Spearman korelasyonunu takip etmek anlaml\u0131 olmayacakt\u0131r.<\/span><\/p>\n Daha fazla bilgi edinin: \u00d6rneklerle \u00c7im Analizi<\/a><\/p>\n n=<\/em> iki de\u011fi\u015fkene ait veri noktas\u0131 say\u0131s\u0131 <\/span><\/p>\n di=<\/em>“ith” eleman\u0131n\u0131n r\u00fctbelerindeki fark<\/span><\/p>\n Spearman Katsay\u0131s\u0131, \u2374, +1 ile -1 aras\u0131nda bir de\u011fer alabilir, <\/span><\/p>\n \u2374 de\u011feri 0’a ne kadar yak\u0131nsa, iki r\u00fctbe aras\u0131ndaki ili\u015fki o kadar zay\u0131ft\u0131r. <\/span><\/p>\n Spearman’\u0131n S\u0131ralama Korelasyon Katsay\u0131s\u0131 ile devam etmeden \u00f6nce verileri s\u0131ralayabilmeliyiz. Bir de\u011fi\u015fken artt\u0131\u011f\u0131nda di\u011fer de\u011fi\u015fkenin monoton bir ili\u015fki izleyip izlemedi\u011fini g\u00f6zlemlemek \u00f6nemlidir. <\/span><\/p>\n Her seviyede, iki de\u011fi\u015fkenin de\u011ferlerini kar\u015f\u0131la\u015ft\u0131rman\u0131z gerekecektir. Hesaplamalar \u015fu \u015fekilde yap\u0131l\u0131r: <\/span><\/p>\n 9 \u00f6\u011frencinin Tarih ve Co\u011frafya derslerinden ald\u0131klar\u0131 puanlar a\u015fa\u011f\u0131daki tabloda belirtilmi\u015ftir.<\/span><\/p>\n Ad\u0131m 1-<\/strong> Elde edilen verilerin bir tablosunu olu\u015fturun. <\/span><\/p>\n Ad\u0131m 2-<\/strong> \u0130ki veri setini s\u0131ralayarak ba\u015flay\u0131n. Veri s\u0131ralamas\u0131, s\u00fctundaki en b\u00fcy\u00fck say\u0131ya “1”, ikinci en b\u00fcy\u00fck say\u0131ya “2” ve benzeri bir s\u0131ralama atanarak elde edilebilir. En k\u00fc\u00e7\u00fck de\u011fer genellikle en d\u00fc\u015f\u00fck s\u0131ralamay\u0131 alacakt\u0131r. Bu i\u015flem her iki \u00f6l\u00e7\u00fcm seti i\u00e7in de yap\u0131lmal\u0131d\u0131r. <\/span><\/p>\n Ad\u0131m 3-<\/strong> Veri setinize \u00fc\u00e7\u00fcnc\u00fc bir d s\u00fctunu ekleyin, d burada s\u0131ralamalar aras\u0131ndaki fark\u0131 ifade eder. \u00d6rne\u011fin, ilk \u00f6\u011frencinin fizik s\u0131ralamas\u0131 3 ve matematik s\u0131ralamas\u0131 5 ise, s\u0131ralamadaki fark 3’t\u00fcr. D\u00f6rd\u00fcnc\u00fc s\u00fctunda d<\/em> de\u011ferlerinin karesini al\u0131n. <\/span><\/p>\n Ad\u0131m 4-<\/strong> T\u00fcm d<\/em> kare de\u011ferlerinizi toplay\u0131n, yani 12<\/strong> (\u2211d kare)<\/span><\/p>\n Ad\u0131m 5-<\/strong> Bu de\u011ferleri form\u00fcle ekleyin <\/span><\/p>\n =1-(6*12)\/<\/span>(9(81-1))<\/span><\/p>\n =1-72\/720<\/span><\/p>\n =1-01<\/span><\/p>\n =0.9<\/span><\/p>\n Bu veriler i\u00e7in Spearman’\u0131n S\u0131ralama Korelasyonu 0,9’dur ve yukar\u0131da belirtildi\u011fi gibi \u2374<\/strong> de\u011feri +1’e yak\u0131nsa m\u00fckemmel bir s\u0131ralama ili\u015fkisine sahiptirler.<\/span><\/p>\n Daha fazla bilgi edinin: Konjoint Analizi – Tan\u0131m, T\u00fcrler, \u00d6rnek, Algoritma ve Model<\/a><\/p>\n Bu b\u00f6l\u00fcmde, anketiniz i\u00e7in Spearman’\u0131n S\u0131ra Korelasyon Katsay\u0131s\u0131n\u0131 nas\u0131l \u00e7al\u0131\u015ft\u0131rabilece\u011finizi \u00f6\u011freneceksiniz. <\/span><\/p>\n Ad\u0131m 1:<\/strong> Anketlerim \u2192 Anket Se\u00e7\u2192Analitik b\u00f6l\u00fcm\u00fcne gidin <\/span><\/p>\n Ad\u0131m 2:<\/strong> Analiz alt\u0131nda Korelasyonel Analiz \u00fczerine t\u0131klay\u0131n <\/span><\/p>\n Daha fazla bilgi edinin: GAP Analizi – Tan\u0131m, Y\u00f6ntem ve \u00d6rnekli \u015eablon <\/a> <\/p>\n\n
<\/em><\/p>\n
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Spearman korelasyon katsay\u0131s\u0131: Form\u00fcl ve \u00d6rnekle Hesaplama<\/strong><\/h3>\n
\u0130\u015fte,<\/p>\n
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\n Tarih <\/span><\/td>\n R\u00fctbe<\/span><\/td>\n Co\u011frafya<\/span><\/td>\n R\u00fctbe<\/span><\/td>\n d<\/span><\/td>\n d kare <\/span><\/td>\n<\/tr>\n \n 35<\/span><\/td>\n 3<\/span><\/td>\n 30<\/span><\/td>\n 5<\/span><\/td>\n 2<\/span><\/td>\n 4<\/span><\/td>\n<\/tr>\n \n 23<\/span><\/td>\n 5<\/span><\/td>\n 33<\/span><\/td>\n 3<\/span><\/td>\n 2<\/span><\/td>\n 4<\/span><\/td>\n<\/tr>\n \n 47<\/span><\/td>\n 1<\/span><\/td>\n 45<\/span><\/td>\n 2<\/span><\/td>\n 1<\/span><\/td>\n 1<\/span><\/td>\n<\/tr>\n \n 17<\/span><\/td>\n 6<\/span><\/td>\n 23<\/span><\/td>\n 6<\/span><\/td>\n 0<\/span><\/td>\n 0<\/span><\/td>\n<\/tr>\n \n 10<\/span><\/td>\n 7<\/span><\/td>\n 8<\/span><\/td>\n 8<\/span><\/td>\n 1<\/span><\/td>\n 1<\/span><\/td>\n<\/tr>\n \n 43<\/span><\/td>\n 2<\/span><\/td>\n 49<\/span><\/td>\n 1<\/span><\/td>\n 1<\/span><\/td>\n 1<\/span><\/td>\n<\/tr>\n \n 9<\/span><\/td>\n 8<\/span><\/td>\n 12<\/span><\/td>\n 7<\/span><\/td>\n 1<\/span><\/td>\n 1<\/span><\/td>\n<\/tr>\n \n 6<\/span><\/td>\n 9<\/span><\/td>\n 4<\/span><\/td>\n 9<\/span><\/td>\n 0<\/span><\/td>\n 0<\/span><\/td>\n<\/tr>\n \n 28<\/span><\/td>\n 4<\/span><\/td>\n 31<\/span><\/td>\n 4<\/span><\/td>\n 0<\/span><\/td>\n 0<\/span><\/td>\n<\/tr>\n \n <\/td>\n <\/td>\n <\/td>\n <\/td>\n <\/td>\n 12<\/strong><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n <\/p>\n
QuestionPro ile korelasyon katsay\u0131s\u0131 nas\u0131l yap\u0131l\u0131r<\/strong><\/h3>\n
\nAd\u0131m 3:<\/strong> Ayr\u0131nt\u0131l\u0131 bir rapor almak i\u00e7in Spearman Katsay\u0131s\u0131 Olu\u015ftur d\u00fc\u011fmesine t\u0131klay\u0131n<\/span><\/p>\n
\nYukar\u0131daki \u00f6rnekte, iki de\u011fi\u015fken olan \u0130\u015f deneyimi ve Ayl\u0131k gelir aras\u0131ndaki ili\u015fkiyi bulmak i\u00e7in Spearman korelasyon katsay\u0131s\u0131 kullan\u0131lm\u0131\u015ft\u0131r. Genel bir kan\u0131ya g\u00f6re, ayl\u0131k gelir i\u015f tecr\u00fcbesi ile birlikte artmal\u0131d\u0131r, bu da iki de\u011fi\u015fken aras\u0131nda pozitif bir ili\u015fki olmas\u0131 gerekti\u011fi anlam\u0131na gelir ki bu da 0.97 olan rs de\u011feri ile kan\u0131tlanm\u0131\u015ft\u0131r<\/span><\/p>\n