- 期刊
Modern One-Way ANOVA F Methods: Trimmed Means, One Step M-estimators and Bootstrap Methods
摘要
單一變異數分析有二個主要的假設：常態性假設和變異數同質性假設，然而實際資料卻時常違反了這兩個基本假設。基於如此，本研究提出一些新的統計分析方法可以解決非常態性與變異數異質性所造成的問題，其方法有：削截平均數、單階M 估計值與bootstrap methods。這些強韌的統計方法的最大特徵在於：他們不需受制於常態性或變異數同質性假設，同時運用這些方法所得到的結果通常會有較小的第一類錯誤或較高的考驗力。本研究擬運用削截平均數、單階M估計值、bootstrap methods (a bootstrap-t method and a percentile method)方法於模擬資料。模擬資料依以下條件取樣：(1)由g-and-h distribution取出六種不同的分佈，(2)組別有4, 6，(3)不同樣本數的組合，(4)不同變異程度的組合。結果發現：變異數分析(ANOVA)在大多數的模擬資料都產生過大的第一類錯誤，在此提及的強韌的統計方法可降低非常態性與變異數異質性所造成的威脅問題。
並列摘要
One-way ANOVA F test is based on two main assumptions: normality and equal variances. In reality, however, violations of these two assumptions are common. This study emphasized on proposing modern alternatives for one-way ANOVA F test: trimmed means, one step M-estimators and bootstrap methods. These robust methods are insensitive to a slight departure from normality, which can obviate problems associated with means. 20% Trimmed means, one step M-estimators and bootstrap methods (a bootstrap-t method and a percentile method) with these two measures were used to compare groups based on comparing measures of location. Simulation studies were investigated according to four variables manipulated here: (a) six distribution shapes from the g-and-h distribution; (b) number of groups (4 and 6), (c) sample size, and (d) degree of variance heterogeneity. The outcomes were compared in terms of Type I error rates under these simulation cases. The results provided evidences for discarding the conventional ANOVA F tests. Also, the advantages of these robust methods under certain situations were apparently found. Finally, a few suggestions were made in the hope of improving upon current practice.