I'm doing a study on visual selective attention (VSA) and how this is influenced by gender and video gaming. So my dependent variable is VSA (continuous) and my two independent variables are gender and video gaming (both categorical).

I want to see if these two variables affect VSA but also test for interaction effects between gender and video gaming. For this I should use a two-way between-groups ANOVA. The problem is that my data is not normally distributed.

I've read on this forum that ANOVA's are "robust" tests with a large sample (mine is 120) so I can do this test anyway, while other authors argue against it.

What should I do? Is there a non-parametric test I can do that still tests interaction as well. Or is there perhaps a totally different test I could do that will give the same result?

  • $\begingroup$ possible duplicate of What is the non-parametric equivalent of a two-way ANOVA that can include interactions? $\endgroup$ – gung - Reinstate Monica Oct 12 '14 at 20:33
  • $\begingroup$ An important question here is in what way are your distributions non-normal? 1st, note that only the residuals need be normal, not Y & certainly not IVs (see here: what-if-residuals-are-normally-distributed-but-y-is-not, if you need more info). But even if your residuals aren't quite normal, the Central Limit Theorem can cover for you if they aren't too far off & you have enough data. OTOH, if your response variable is non-normal in the sense that it's binary, you need Logistic regression. Etc. $\endgroup$ – gung - Reinstate Monica Oct 12 '14 at 20:35
  • $\begingroup$ ... and if it's counts, you need appropriate analysis for counts. Some idea of what your data and your residuals from an anova look like would help (is there heteroskedasticity and right skewness? Maybe a gamma GLM would help). Or you might consider a bootstrap procedure (one that deals explicitly with the possibility of interaction). $\endgroup$ – Glen_b -Reinstate Monica Oct 12 '14 at 21:15

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