Turkiye Klinikleri Journal of Biostatistics

.: ORIGINAL RESEARCH
İki Sonuçlu Nitel Veriler İçin Farklılık/Uzaklık Katsayılarının Değerlendirilmesi: Bir Benzetim Çalışması
Evaluation of Dissimilarity/Distance Coefficients of Binary Data: A Simulation Study
İsmet DOĞANa, Nurhan DOĞANa
aAfyonkarahisar Sağlık Bilimleri Üniversitesi Tıp Fakültesi, Biyoistatistik ve Tıbbi Bilişim ABD, Afyonkarahisar, Türkiye
Turkiye Klinikleri J Biostat. 2022;14(2):63-9
doi: 10.5336/biostatic.2022-88302
Article Language: TR
Full Text
ÖZET
 Amaç: Bu çalışmanın amacı, 2 sonuçlu veriler ile ilgili türetilmiş veri setleri kullanarak farklı değerleri için belirlenen 23 farklı uzaklık katsayısını tanıtmak, özelliklerini ortaya koyarak değerlendirmektir. Gereç ve Yöntemler: Bu çalışmada, 2 sonuçlu veriler için ileri sürülen uzaklık katsayıları ele alınmıştır. Çalışmada Phyton-random kütüphanesi 10≤n≤1000 kullanılarak aralığında yer alan 35 farklı n değeri için veri türetilmiştir. Verilerin türetilmesinde önce a,b,c ve d ile gösterilen gözelerden hangisine değer atanacağı sonra da ilgili gözeye atanacak değer belirlenmiştir. n=10 için 286, n=15 için 815 ve n≥20 için biner farklı veri seti çalışmada kullanılmıştır. Bulgular: İki sonuçlu veriler için tüm farklılık/uzaklık katsayılarının değer aralığının 0 (benzerlik yok) ile 1 (tam benzerlik) olması beklenmesine rağmen tüm katsayılar için bu aralık geçerli değildir. Dikkate alınan 23 farklı katsayı içerisinden 12 tanesi bu aralıkta değer almaktadır. Hiyerarşik kümeleme analizine göre farklılık/uzaklık katsayılarının çoğu birbirine benzemektedir. Sonuç: Genel olarak hemen tüm katsayılara ait değerler, örnekler daha benzer hâle geldikçe sabit bir minimumdan sabit bir maksimuma doğru artmaktadır. Ancak Sokal-Michener, Hamming ve varyans katsayıları, tüm değerleri için farklılık/uzaklık ile doğrusal olarak sorunsuz bir şekilde artmaktadır. Değer aralığının 0-1 olması ve farklılık/uzaklık artışı ile paralellik göstermesinden dolayı Sokal-Michener tarafından önerilen katsayı tüm katsayılar içerisinde öne çıkmaktadır. Cosine, Hamming, Euclid I ve Euclid II katsayıları n sayısından etkilenmekte diğer katsayılar etkilenmemektedir. Dolayısıyla farklılık/uzaklık katsayılarının önemli bir kısmının örnek büyüklüğünden bağımsız oldukları belirlenmiştir.

Anahtar Kelimeler: Farklılık/uzaklık katsayısı; hiyerarşik kümeleme; iki sonuçlu veri
ABSTRACT
 Objective: The aim of this study is to introduce 23 different binary dissimilarity/distance coefficients determined for different n,a,b,c and d values by using derived data sets and to evaluate them by revealing their properties. Material and Methods: In this study, the dissimilarity/distance coefficients put forward for binary data are considered. In the study, data were derived for 35 different values in the range of 10≤n≤1000 using the Phyton-random library. In the derivation of the data, firstly, which cell shown with will be assigned value, then the value to be assigned to the relevant cell was determined. 286 for n=10 , 815 for n=15 and 1000 different data sets for n≥20 were used in the study. Results: Although the value range of all dissimilarity/distance coefficients for binary data is expected to be 0 to 1, this range is not valid for all coefficients. Out of 23 different coefficients, 12 take values in this range. According to the hierarchical clustering analysis, most of the dissimilarity/distance coefficients are similar. Conclusion: In general, the values of almost all coefficients increase from a fixed minimum to a fixed maximum as the samples become more dissimilar. However, the Sokal-Michener, Hamming and variance coefficients increase linearly with dissimilarity/distance smoothly for all values. The coefficient suggested by Sokal-Michener stands out among all the coefficients because the value range is 0-1 and is parallel to the dissimilarity/distance increase. Cosine, Hamming, Euclid I and Euclid II coefficients are affected by the number of n and other coefficients are not. Therefore, it has been determined that a significant part of the dissimilarity/distance coefficients are independent of the sample size.

Keywords: Dissimilarity/distance coefficient; hierarchical clustering; binary data
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