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

Year 2021, Issue: 372, 92 - 100, 01.08.2021

Yasin Altay Soner Yiğit

https://doi.org/10.33724/zm.948879

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.

Keywords

Wilks’ Λ, Hotelling-Lawley Trace, Pillai’s Trace, type I error rate, Monte Carlo simulation

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

Abstract

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.

Keywords

Wilks’ Λ, Hotelling-Lawley Trace, Pillai’s Trace, I. tip hata oranı, Monte Carlo simülasyonu

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