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Journals / Ziraat Mühendisliği / 2026 / Sayı: 372

Which Test is More Reliable for The Testing Statistical Significance of Canonical Correlation Coefficients?

Kanonik Korelasyon Katsayılarının İstatistiksel Önemliliğini Test Etmek için Hangi Test Daha Güvenilirdir?

Yasin Altay(ESKİŞEHİR OSMANGAZİ ÜNİVERSİTESİ, ZİRAAT FAKÜLTESİ, ZOOTEKNİ BÖLÜMÜ, BİYOMETRİ VE GENETİK ANABİLİM DALI)0000-0003-4049-8301
Soner Yiğit(ÇANAKKALE ONSEKİZ MART ÜNİVERSİTESİ, ZİRAAT FAKÜLTESİ, ZOOTEKNİ BÖLÜMÜ, BİYOMETRİ VE GENETİK ANABİLİM DALI)0000-0002-2899-2246
Pages
92–100
Publication Date
2021-08-01
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

On the other hand, the H test and P test generally obtained actual type I error rates which were outside Bradley limits.

📌 3 Key Takeaways

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Objective & Hypothesis:In this study, Wilks’ Λ (W), Hotelling-Lawley Trace (H) and Pillai’s Trace (P) tests which are used in testing of statistically significance for canonical correlation coefficients were compared in terms of actual type I error rate.
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Key Findings & Data:As a result of 10000 simulation experiments conducted, when samples were taken from multivariate distributions which are normal and deviate slightly or moderately from normality, the W test was conservative in terms of protecting actual type I error rate in all cases.
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Conclusion & Impact:On the other hand, the H test and P test generally obtained actual type I error rates which were outside Bradley limits.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Wilks’ Λ · Hotelling-Lawley Trace · Pillai’s Trace

Abstract

In this study, Wilks’ Λ (W), Hotelling-Lawley Trace (H) and Pillai’s Trace (P) tests which are used in testing of statistically significance for canonical correlation coefficients were compared in terms of actual type I error rate. As a result of 10000 simulation experiments conducted, when samples were taken from multivariate distributions which are normal and deviate slightly or moderately from normality, the W test was conservative in terms of protecting actual type I error rate in all cases. However, when there is excessively deviate from normality, actual type I error rates for the W test exceeded the upper limit of Bradley’s criterion (4.50-5.50%) almost in all cases. On the other hand, the H test and P test generally obtained actual type I error rates which were outside Bradley limits.

Özet

Bu çalışmada, kanonik korelasyon katsayılarının istatistiksel olarak önemlilik testinde kullanılan Wilks' Λ (W), Hotelling-Lawley Trace (H) ve Pillai's Trace (P) testleri gerçek tip I hata oranı açısından karşılaştırılmıştır. Yapılan 10000 simülasyon deneyi sonucunda, normal olan ve normallikten hafif veya orta derecede sapan çok değişkenli dağılımlardan örnekler alındığında, W testi gerçek tip I hata oranını tüm durumlarda koruma açısından muhafazakar olmuştur. Ancak normallikten aşırı derecede sapma olduğunda, W testi için gerçek tip I hata oranları hemen hemen tüm durumlarda Bradley kriterinin üst sınırını (%4,50-5,50) aşmıştır. H testi ve P testi ise genel olarak Bradley sınırlarının dışında kalan gerçek tip I hata oranları elde etmiştir.

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Cite This Article

Altay, Y., Yiğit, S. (2021). Which Test is More Reliable for The Testing Statistical Significance of Canonical Correlation Coefficients?. Ziraat Mühendisliği, Sayı: 372, 92–100. https://doi.org/10.33724/zm.948879

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