Power and Type I Error for ANOVA Under Random Mixtures of Normal Distributions

Öz

This study investigates the performance of the classical one-way ANOVA F-test under random mixtures of normal distributions. Using extensive simulation studies, we assess Type I error rates and statistical power across various conditions, including different group sizes, sample sizes, mixture proportions, and within-group variance structures. Results show that when group distributions are balanced and variances are equal, ANOVA maintains nominal Type I error rates. However, with increased mixture imbalance and heterogeneous variances, Type I errors inflate and statistical power decreases, particularly in small samples or when more groups are involved. The findings underscore the sensitivity of ANOVA to violations of its assumptions and highlight the need for alternative methods in the presence of complex, non-normal data structures.

Anahtar Kelimeler

• ANOVA
• Type I error
• statistical power
• mixture distributions
• simulation study
• normality assumption.

Normal Dağılımların Rastgele Karışımları Altında ANOVA için Güç ve 1.Tip Hata

Öz

Bu çalışmada, klasik tek yönlü ANOVA F-testinin, normal dağılımların rastgele karışımlarından üretilen veriler üzerindeki performansı değerlendirilmiştir. Simülasyon çalışmalarıyla, grup sayısı, örneklem büyüklüğü, karışım ağırlıkları ve grup içi varyans farklılıkları gibi çeşitli senaryolarda Tip I hata oranları ve test gücü hesaplanmıştır. Sonuçlar, grup içi dağılımlar dengeli ve varyanslar eşit olduğunda ANOVA'nın nominal anlamlılık düzeyini koruduğunu; ancak karışım dengesizliği ve varyans heterojenliği arttıkça Tip I hata oranlarının yükseldiğini ve test gücünün azaldığını göstermiştir. Özellikle küçük örneklemler ve daha yüksek grup sayılarında bu etkiler daha belirgin hale gelmektedir. Elde edilen bulgular, ANOVA'nın varsayımlarındaki ihlaller karşısında ne kadar duyarlı olabileceğini ortaya koymakta ve bu gibi durumlarda alternatif yöntemlerin kullanılmasının önemine işaret etmektedir.

Anahtar Kelimeler

• ANOVA
• Tip I hata
• test gücü
• karışım dağılımları
• simülasyon çalışması
• normallik varsayımı.

Kaynakça

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