Adaptif Robust Scott-Knott Yöntemi

Year 2025, Volume: 15 Issue: 2, 67 - 78, 31.12.2025

Necati Alp Erilli

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

References

• Bhering, L. L., Cruz, C. D., de Vasconcelos, E. S., Ferreira, A., & de Resende Jr, M. F. R. (2008). Alternative methodology for Scott-Knott test. Crop Breeding and Applied Biotechnology, 8(1).
• Chlioui, I., Abnane, I., & Idri, A. (2020). Comparing statistical and machine learning imputation techniques in breast cancer classification. In Computational Science and Its Applications–ICCSA 2020: 20th International Conference, Cagliari, Italy, July 1–4, 2020, Proceedings, Part IV 20 (pp. 61-76). Springer International Publishing.
• Conrado, T. V., Ferreira, D. F., Scapim, C. A., & Maluf, W. R. (2017). Adjusting the Scott-Knott cluster analyses for unbalanced designs. Crop Breeding and Applied Biotechnology, 17, 1-9.
• Cordeiro, M. W. S., Júnior, V. R. R., Monção, F. P., Palma, M. N. N., Rigueira, J. P. S., da Cunha Siqueira Carvalho, C., ... & De Oliveira, L. I. S. (2023). Tropical grass silages with spineless cactus in diets of Holstein× Zebu heifers in the semiarid region of Brazil. Tropical Animal Health and Production, 55(2), 89.
• Demšar, J. (2006). Statistical comparisons of classifiers over multiple data sets. Journal of Machine Learning Research, 7, 1–30.
• Hubert, L. J., & Arabie, P. (1985). Comparing partitions. Journal of Classifications, 2(1), 193–218.
• Johnson, R. A., & Bhattacharyya, G. K. (2019). Statistics: principles and methods. John Wiley & Sons.
• Kampstra, P. (2008). Beanplot: A boxplot alternative for visual comparison of distributions. Journal of Statistical Software, Code Snippets, 28(1), 1–9. https://doi.org/10.18637/jss.v028.c01
• Konietschke, F., Bösiger, S., Brunner, E., & Hothorn, L. A. (2013). Are multiple contrast tests superior to the ANOVA? The International Journal of Biostatistics, 9(1), 63–73.
• Kutner, M. H., Nachtsheim, C. J., Neter, J., & Li, W. (2005). Applied linear statistical models. McGraw-hill.
• Mair, P., & Wilcox, R. (2020). Robust statistical methods in R using the WRS2 package. Behavior research methods, 52, 464-488.
• Montgomery, D. C. (2017). Design and analysis of experiments, John Wiley & Sons.
• Naves, E. R., Scossa, F., Araújo, W. L., Nunes-Nesi, A., Fernie, A. R., & Zsögön, A. (2021). Hotter chili peppers by hybridisation: heterosis and reciprocal effects. bioRxiv, 2021-09.
• Ottoni, A. L., Nepomuceno, E. G., De Oliveira, M. S., & De Oliveira, D. C. (2020). Tuning of reinforcement learning parameters applied to SOP using the Scott–Knott method. Soft Computing, 24(6), 4441-4453.
• Paixão, G. C., Schneider, R. M., Bongiovani, M. C., Amaral, A. G. D., & Boina, R. F. (2023). Removal of phosphorus and nitrogen from swine manure using a natural coagulant. Engenharia Sanitaria e Ambiental, 28, e20230032.
• Pereira, R. B. D., Peruchi, R. S., de Paiva, A. P., da Costa, S. C., & Ferreira, J. R. (2016). Combining Scott-Knott and GR&R methods to identify special causes of variation. Measurement, 82, 135-144.
• Rand, W. M. (1971). Objective criteria for the evaluation of clustering methods. Journal of the American Statistical Association, 66(3), 846–850.
• Resende, N. S., de Souza, V. R., Carvalho, E. E. N., de Jesus Junqueira, J. R., & Boas, E. V. D. B. V. (2022). Stability and antioxidant activity of bioactive compounds in Cerrado fruit juices during storage. Research, Society and Development, 11(8), e38211831043.
• Scott, A. J., & Knott, M. (1974). A cluster analysis method for grouping means in the analysis of variance. Biometrics, 507-512.
• Wang, S., He, Y., Shi, R., Jing, C., Liu, Y., & Tong, H. (2023). An empirical study on regression techniques for software defect number prediction. In 2023 30th Asia-Pacific Software Engineering Conference (APSEC), 637-638), IEEE.
• Westfall, P.H., & Young, S.S. (1993). Resampling-based multiple testing: Examples and methods for p-value adjustment. New York: Wiley.
• Wilcox, R.R. (2011). Modern statistics for the social and behavioral sciences: A practical introduction. CRC Press.
• Willavise, S.A., Carmer, S.G. & Walker, W.M. (1980) Evaluation of cluster analysis for comparing treatment means. Agronomy Journal 72: 317-320.