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
Dear Charles,
I came across your website and these resources, and have a quick question about ART ANOVA. I’m wondering whether it’s appropriate to use on my data, which is very skewed and non-normally distributed (participants did really well, so the values cluster around 1).
I conducted a behavioral experiment with a mixed design (2 groups of participants, each of them completed 2 tasks, one simple and one complex one). The participants first saw a bunch of stimuli and then they were asked some questions after each task, and my dependent variable was accuracy. Additionally, I introduced another constraint to the stimuli they were shown (Group 1 saw type A stimuli in Task 1, and type B stimuli in Task 2; vice versa in Group 2, which saw type B stimuli in Task 1, and type A stimuli in Task 2. This was done to prevent learning from Task 1 to Task 2, and to see whether the type of stimuli also have an effect). So not everyone saw every condition.
I did a bunch of Wilcox tests (non-parametric alternatives to paired and unpaired t-tests) first, but there is no way I can test for the effect of type A and type B stimuli (Group 1 Task 1 and Group 2 Task 2 ::: Group 1 Task 2 and Group 2 Task 1), because then I collapse data across both groups, and violate the assumptions of the Wilcoxon tests. Would it be correct to run an ART ANOVA in this case? My reasoning is that it’s the only way to get the group:task effect, which is essentially the stimulus type (A/B) effect. Am I on the right path here?
I’d really appreciate your input, and thank you for your work! Your website has been of tremendous help!
Kindly,
Mimi
Hello Mimi,
I am very pleased to see that the Real Statistics website has been useful to you.
The scenario you describe seems quite complicated and so I don’t know whether ART ANOVA without some modification from the version that I have described would be appropriate.
Charles
Thanks very much Charles for your response, it real helped me to move on with the analysis. Thank you again for good clarification.
Joseph
Glad I could help, Joseph.
Charles
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.
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