Are transformations appropriate for my dataset?

Hi all, I have a question about transforming data before running a 4-way ANOVA:

I want to run a four-way ANOVA on my data set (factors: BWWW).
However, due to the nature of one of the between-factors, a ceiling effect is reached in most of these data subsets, but not all. This means that the negative skew in my data subsets (12 in total) ranges from -0.5 to -1.99.

My original plan was to apply a transformation to the datasets before analysis however I'm slightly concerned that to apply an effective transformation for the heavily skewed subsets, this transforms my less skewed subsets into a positive skew, which makes me tentative to do this.

I feel like I have two options here and wondered whether you could advise on which would be more appropriate:

1. Apply transformations and run 4-way ANOVA & follow up with post-hocs (cons: some datasets have been 'over-transformed' which could affect the validity of the significant interactions?)
2. Don't apply transformations, run the 4-way ANOVA and follow up any significant interactions with a non-parametric Sign and Friedman's tests (acting as a post-hoc) (con: 4-way ANOVA does not stand up by itself due to negative skews, and the interactions themselves aren't fully supported with the analysis in this method).

I'd be really interested to know your thoughts, especially on whether transforming the dataset is appropriate!
Hi Karabiner,

Thank you for replying! Sample size was 40 (2 groups: 20 in each group), and my dependent variables were accuracy and reaction times (analysed separately).

Best Wishes,



TS Contributor
So the rule of thumb seems to apply, that with n > 30 the ANOVA produces
valid results even if the distributions in the cells are nonnormal. I do not know
what a transformation would mean for the measured construct, though.
It would not remove the ceiling effect.

With kind regards

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Well-Known Member
You can always try it with and without the transformation. If the p values are about the same, then probably it doesn't really matter much.