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.

Topics

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

4 thoughts on “Aligned Rank Transform (ART) ANOVA”

  1. Thanks very much Charles for your response, it real helped me to move on with the analysis. Thank you again for good clarification.

    Joseph

    Reply

  2. I have the fish data collected for say a year in an area called Bagamoyo, the data have both sexes (Male and female), on such data I estimated the relative condition factor (Kn) for individuals, again I managed to categorize the data collection period into two seasons (SEM and NEM). Therefore I wanted to to check if the interaction between fish sex and season had significant effect on the condition factor of fish in Bagamoyo. Can I use this statistical test ( Aligned Rank Transform (ART) ANOVA) to test this? Given that data were tested and seemed to be not normally distributed even after transformation, moreover, these data showed that homogeneity of variances were normally distributed.

    Reply

    • Hello Joseph,
      1. As long as the individuals in the twos seasons are different, then 2 factor ANOVA or ART if the assumptions are not met seem appropriate.
      2. I assume that you meant that the homogeneity of variances assumption is not met (since there is no normality of variances assumption).
      Charles

      Reply

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