ANOVA is fairly robust in terms of the error rate when sample sizes are equal. However, when sample sizes are unequal, ANOVA is not robust to violations of homogeneity of variance.
Does this mean when we have large-equal sample sizes we can skip the homogeneity test?
No. Violation of homogeneity means that errors at different points along the regression line (or different conditions in ANOVA) have different effects. Bigger samples don’t change that. You need To figure out if there is an underlying distributional issue creating the heterogeneity which may require the use of generalized linear models.
No. Violation of homogeneity means that errors at different points along the regression line (or different conditions in ANOVA) have different effects. Bigger samples don’t change that. You need To figure out if there is an underlying distributional issue creating the heterogeneity which may require the use of generalized linear models.
The following may be useful. Also see his books for useful alternatives. Article ANOVA: A Paradigm for Low Power and Misleading Measures of E...
The early literature on ANOVA suggested it was robust, but was rather limited in the degree of violations of assumptions being explored. Generally modest departures from normality and homogeneity of variance will not have much impact in large samples. However, it is fairly easy to show that extreme values and (especially) heavy tails (i.e., leptokurtosis) can dramatically impact ANOVA even in large samples.
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