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Since equal variances are necessary for any ANOVA that contains between-subject factors – regardless of whether it also contains within-subject factors – all such cases need correction (or alternative, e.g. robust tests). Based on my understanding of papers on the HC3 correction for unequal variances (e.g. this and this), it would seem to me that in case of an equal variances assumption violation I can quite simply use this correction in any design, regardless of whether it contains any within-subject factors. So e.g. I can add white.adjust = "hc3" to any design in the aov() function in R, and unequal variances would be taken care of.

However, the ezANOVA documentation states the following:

white.adjust Only affects behaviour if the design contains only between-Ss predictor variables.

Is this true? I cannot find any source that would either confirm or disprove this. If it is true, is there an easily implementable alternative correction for mixed-designs (or do I have to use robust methods)?

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