Dengesiz deney düzenlerinde sağlam test istatistiklerinin karşılaştırılması

Year 2013, Volume: 6 Issue: 2, 79 - 85, 01.06.2013

Derya Karagöz

Abstract

Bu çalışmada, tek yönlü varyans analizinde varyansların homojenliği ve dağılımın normalliği varsayım bozulumları ele alınmıştır. Aykırı değer içeren normal olmayan Weibull dağılımı için farklı varyanslı gruplarda sağlam Brown-Forsythe (RBF) ve sağlam Geliştirilmiş Brown-Forsythe (RMBF) test istatistiği önerilmiştir. Weibull dağılımı için geliştirilen sağlam test istatistiklerinin davranışı benzetim çalışması yapılarak 1. tip hata olasılıkları bakımından, yüzdelik ve yüzdelik en küçük kareler dayalı sağlam tahmin yöntemine göre grup sayısı k=3, 9 için incelenmiştir. Dengesiz gruplarda, eşit olmayan ortalamalı ve homojen olmayan varyanslı deneme kombinasyonları ele alınmıştır. Önerilen sağlam test istatistiklerinin varsayım bozulumlarına karşı iyi bir performansa sahip olduğu gösterilmiştir.

Keywords

ANOVA, Weibull Dağılımı, Welch, Brown-Forsythe, Geliştirilmiş Brown-Forsythe. Yüzdelik, Yüzdelik En Küçük Kareler.

Comparing Robust Test Statistics in Unbalanced Designs

Abstract

Comparing Robust Test Statistics in Unbalanced Designs In this study, the violations of the assumptions, heteroscedasticity and non-normality are consedered in the one-way ANOVA. Robust Brown-Forsythe (RBF) and robust modified Brown-Forsythe (RMBF) test statistics are developed for the non-normal data assumed to be Weibull distribution with outliers. In the simulation study, using different experimental designs, type I error risks of the improved robust test statistic for the Weibull distribution are obtained with respect to 2 different robust methods which are quantile and least square quantile. Unbalanced sample sizes with homogeneous and heterogeneous variances are considered for k=3,9 groups. The simulations results show up that the proposed robust tests have a good performance.

Keywords

ANOVA, Weibull Distribution, Brown-Forsythe, Modified Brown-Forsythe, Quantile, Quantile Least Square.

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