Aligned Rank Transform (ART) ANOVA

Aligned Rank Transform (ART) ANOVA is a non-parametric approach to factorial ANOVA that enables you to analyze the interaction as well as the main effects. As usual, ranked data is used, but first, the data for each effect (main or interaction) must be aligned before ranks are calculated.

This approach is useful when the data is not normally distributed. It can be used when the homogeneity of variances assumption is violated, although there is a risk of an inflated alpha value (alpha is up to about .07 when set to .05 for the interaction effect and up to .09 for the main effects.

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References

Wobbrock, J. O., Findlater, L., Gergle, D., Higgins, J. J. (2011) The Aligned Rank Transform for Nonparametric Factorial Analyses Using Only ANOVA Procedures. Conference: Proceedings of the International Conference on Human Factors in Computing Systems, CHI 2011, Vancouver, BC, Canada
https://faculty.washington.edu/wobbrock/pubs/chi-11.06.pdf

Leys, C. and Schumann, S. (2010) A nonparametric method to analyze interactions: The adjusted rank transform test
http://cescup.ulb.be/wp-content/uploads/2015/04/Leys_and_Schumann_nonparametric_interactions.pdf

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