方差分析稳健性的蒙特卡罗研究

A Monte Carlo Study of the Robustness of ANOVA

许多外语教学研究者在使用方差分析时往往过于相信它的稳健性,忽略其假设,致使统计结论的效度可能受到威胁。本文通过蒙特卡罗实验调查不同样本量中出现非正态性和方差不齐性时方差分析的稳健性。比较组偏态值相同或峰态值相同且较小时,方差分析稳健。偏态和峰态同时存在于比较组中,则方差分析的稳健性取决于偏态和峰态值的具体组合形式,有时也受到样本量的影响。在正态性时,若方差不齐性小,方差分析几乎总是稳健的。在非正态性和方差不齐性混合时,只有在少数情况下方差分析才稳健。文中提出了方差分析不稳健性的解决办法。

Many foreign language teaching researchers tend to believe in its robustness too much,ignoring its assumptions when conducting an ANOVA,as a result of which,the statistical conclusion validity may be threatened.This article conducts Monte Carlo experiments to investigate the robustness of ANOVAs under non-normality and variance heterogeneity across different sample sizes.ANOVAs are robust either when the comparison groups have the same skewness values or when they have the same small kurtosis values.In the presence of both skewness and kurtosis among the comparison groups,the robustness of ANOVAs,sometimes influenced by sample size,depends on particular combinations of the values of skewness and kurtosis.Given the small variance heterogeneity,ANOVA is almost always robust under normality.When non-normality and variance heterogeneity coexist,ANOVAs are robust only in some conditions.Solutions to the non-robustness of ANOVAs are also suggested.