Is the ANOVA F-Test Robust to Variance Heterogeneity When Sample Sizes are Equal?: An Investigation via a Coefficient of Variation
Is the ANOVA F-Test Robust to Variance Heterogeneity When Sample Sizes are Equal?: An Investigation via a Coefficient of Variation
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当样本量相等时，方差分析 F 检验对方差异质性是否具有鲁棒性？：通过变异系数进行的调查
DOI：
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发表时间：
1977
期刊：
影响因子：
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通讯作者：
H. Keselman
中科院分区：
文献类型：
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作者：
Joanne C. Rogan;H. Keselman
许多研究已经检查了方差异质性对方差分析（ANOVA）F检验的I型错误的经验概率的影响，并且普遍的结论是，当样本量相等时，ANOVA对方差异质性具有稳健性。然而，Box（1954）报告了当不等方差与相等样本量配对时，5%标称水平的I类错误率为0.12。本文探讨了这一发现，检查不同程度和模式的方差异质性不同的样本量和治疗组的数量。数据表明，1型错误率随方差异质性程度的变化而变化，因此，不应假设方差分析F检验在样本量相等时始终对方差异质性具有稳健性。
Numerous investigations have examined the effects of variance heterogeneity on the empirical probability of a Type I error for the analysis of variance (ANOVA) F-test and the prevailing conclusion has been that when sample sizes are equal, the ANOVA is robust to variance heterogeneity. However, Box (1954) reported a Type I error rate of .12, for a 5% nominal level, when unequal variances were paired with equal sample sizes. The present paper explored this finding, examining varying degrees and patterns of variance heterogeneity for varying sample sizes and number of treatment groups. The data indicate that the rate of Type 1 error varies as a function of the degree of variance heterogeneity and, consequently, it should not be assumed that the ANOVA F-test is always robust to variance heterogeneity when sample sizes are equal.