Adaptif Robust Scott-Knott Yöntemi

Abstract

Çoklu karşılaştırma testleri, birden fazla grubun karşılaştırılması gereken analizlerde sıklıkla kullanılmaktadır. Bu testlerde klasik yaklaşımlar, normal dağılım ve varyans homojenliği varsayımlarına büyük ölçüde bağımlıdır. Bu çalışmada, Scott-Knott yöntemine dayalı ancak klasik varsayımlara daha az duyarlı yeni bir yöntem olan Adaptif Robust Scott-Knott (ARSK) önerilmektedir. ARSK yöntemi, merkezi eğilim ölçütü olarak trimean kullanmakta, bölme kararlarını bootstrap güven aralıklarıyla desteklemekte ve permütasyon testleriyle anlamlılık değerlendirmesi yapmaktadır. Ayrıca optimal küme sayısı gap istatistiğiyle otomatik olarak belirlenmektedir. ARSK ve klasik Scott-Knott yöntemleri beş simülasyon ve beş gerçek veri setinde karşılaştırılmış, sonuçlar Adjusted Rand Index (ARI) ile değerlendirilmiştir. Bulgular, özellikle çarpık, heterojen ve aykırı değerlere sahip veri yapılarında ARSK’nın biraz daha güvenilir ve açıklayıcı kümeler sunduğunu ortaya koymaktadır.

Keywords

• Scott-Knott yöntemi
• Çoklu karşılaştırma
• ARSK
• Trimean

Adaptive Robust Scott-Knott Method

Abstract

Multiple comparison tests are frequently used in analyses where multiple groups need to be compared. In these tests, classical approaches are heavily dependent on the assumptions of normal distribution and variance homogeneity. In this study, a new method called Adaptive Robust Scott-Knott (ARSK) is proposed, which is based on the Scott-Knott method but is less sensitive to classical assumptions. The ARSK method uses the trimmed mean as a measure of central tendency, supports partitioning decisions with bootstrap confidence intervals, and performs significance testing using permutation tests. Additionally, the optimal number of clusters is automatically determined using the gap statistic. ARSK and the classical Scott-Knott methods were compared on five simulation and five real data sets, and the results were evaluated using the Adjusted Rand Index (ARI). The findings reveal that ARSK provides slightly more reliable and explanatory clusters, particularly in data structures with skewed, heterogeneous, and outlier values.

Keywords

• Scott-Knott method
• Multiple Comparison
• ARSK
• Trimean

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