Turkiye Klinikleri Journal of Biostatistics

.: ORIGINAL RESEARCH
Etkileşimleri Test Etmek İçin Hizalanmış Sıra Sayıları Dönüşüm Yöntemleri
Aligned Rank Transform Methods for Testing Interactions
İsmet DOĞANa, Nurhan DOĞANa
aAfyonkarahisar Sağlık Bilimleri Üniversitesi Tıp Fakültesi, Biyoistatistik ve Tıbbi Bilişim ABD, Afyonkarahisar, TÜRKİYE
Turkiye Klinikleri J Biostat. 2021;13(1):120-30
doi: 10.5336/biostatic.2020-79049
Article Language: TR
Full Text
ÖZET
 Amaç: Bu makalenin amacı, normallik varsayımının sağ-lanmadığı faktöriyel deneme desenlerinde etkileşim teriminin önemlilik testi için uygulaması kolay ve etkili olan hizalanmış sıra sayıları dönüşümü işlemini tanıtmaktır. Gereç ve Yöntemler: Bir-çok istatistiksel testin geçerliliği, gözlemlerin normal dağıldığı var-sayımına bağlıdır. Ancak incelenen birçok karmaşık özellik, normal olmayan dağılımlara sahiptir. Dağılımın normal olmadığı durum-larda kullanılan çeşitli yaklaşımlar mevcuttur. Normallik veya varyansların homojenliğini ihlal eden verilerin söz konusu olduğu durumlarda, başlangıçta sıra sayısı dönüşümleri alternatif olarak önerilmiştir. Sıra sayıları dönüşüm işleminin dikkate alındığı çalış-malarda önce orijinal gözlemler sıra sayılarına dönüştürülmekte, ardından da sıra sayıları üzerinde parametrik bir istatistik hesap-lanmaktadır. Bulgular: Hem en küçük kareler tekniğine hem de sıra dönüşüm işlemine alternatif bir yöntem, hizalanmış sıra sayıları dönüşüm işlemidir. Hizalanmış sıralama dönüşümü, hem normallik gibi varsayım ihlallerinin etkisini en aza indirmekte hem de sırala-ma dönüşümü için bir sorun olan etkileşim terimlerinin önemlilik testine olanak sağlamaktadır. Hizalanmış sıra sayıları işlemine da-yalı testler sağlam ve güçlü testlerdir. Bu işlem, varsayım ihlalleri-ne ve aykırı değerlere karşı duyarlı değildir. Sonuç: Hizalanmış sıra sayıları dönüşüm işlemlerinin klasik varyans analizi işlemlerine karşı bilinen en iyi alternatifler olduğu ve normallik varsayımlarının şüpheli olduğu durumlarda kullanılması gerektiği sonucuna varıl-mıştır.

Anahtar Kelimeler: İstatistiksel analiz; nonparametrik etkileşim testleri; hizalanmış sıra sayısı testi; faktöriyel analiz
ABSTRACT
 Objective: The purpose of this article is to introduce aligned rank transform which is easy and effective to apply for the significance test of interaction term in factorial experimental design where normality assumption is not provided. Material and Meth-ods: The validity of many statistical tests depends on the assump-tion that observations are normally distributed. But, many complex traits studied have non-normal distributions. Several approaches exist to respond to non-normality. Rank transformations were ini-tially proposed as an alternative when dealing with data that violat-ed normality or homogeneity of variances. In studies where the rank transformation is taken into consideration, the original obser-vations are first converted into ranks, and then a parametric statis-tics is calculated on the ranks. Results: An alternative method to both the least squares technique and the rank transform process is the aligned rank transform procedure. The aligned rank transform minimizes the effect of violations of assumptions such as normality, but does not suffer some of the same problems of the rank trans-form, such as introducing interactions when they are not present or removing interactions when they are present. The aligned rank transform is a robust and powerful technique. This method is not sensitive to outliers and violations of assumptions on error distribu-tion. Conclusion: It concluded that the aligned rank transform pro-cedures appear to be the best known alternatives to the classical analysis of variance procedures, and should be used in situations where the assumptions of normality is suspect.

Keywords: Statistical analysis; nonparametric interaction tests; aligned rank test; factorial analysis
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