I’m looking at the effect defeat and entrapment inducing conditions have on subjective ratings of defeat and entrapment at three different time points (among other things).

However the subjective ratings are not normally distributed. I’ve done several transformations and the squareroot transformation seems to work best. However there are still some aspects of the data that have not normalized. This non-normality manifests itself in negative skewness in High entrapment high defeat conditions at the time point I expected there to be the highest defeat and entrapment ratings. Consequently I think it could be argued that this skew is due to the experimental manipulation.

Would it be acceptable to run ANOVAs on this data despite the lack of normality, given the manipulations? Or would non-parametric tests be more appropriate? If so is there a non parametric equivalent of a 4×3 mixed ANOVA?

**Answer**

It’s the residuals that should be normally distributed, not the marginal distribution of your response variable.

I would try using transformations, do the ANOVA, and check the residuals. If they look noticeably non-normal regardless of what transformation you use, I would switch to a non-parametric test such as the Friedman test.

**Attribution***Source : Link , Question Author : Community , Answer Author : Rob Hyndman*