I'm trying to analyse a data set using an ANOVA but have significant heteroscedasticity - transforming the DV using a log-transformation seems to remove this issue, but I wanted to check if I should also be transforming my IVs for the output to be meaningful? Two IVs are binary, and one is continuous.

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Simply logging the DV shouldn't be too much of an issue. Although, it might be worth it to try to see what results you get from using a Kruskal-Wallis Rank Sum Test.

Refer to this comment for a decent explanation between the ANOVA and Kruskal-Wallis

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