Paper Reading #20 : The Aligned Rank Transform

References
The Aligned Rank Transform for Nonparametric Factorial Analyses Using Only Anova Procedures by Jacob O. Wobbrock, Leah Findlater, Darren Gergle, and James J. Higgins.  Published in the CHI '11 Proceedings of the 2011 annual conference on Human factors in computing systems.


Author Bios

• Jacob O. Wobbrock is currently an Associate Professor in the Information School and an Adjunct Associate Professor in the Department of Computer Science & Engineering at the University of Washington. 
• Leah Findlater is a postdoctoral researcher in The Information School, working with Dr. Jacob Wobbrock. She holds a PhD from the University of British Colombia.
• Darren Gergle  is an Associate Professor at Northwestern University and has a PhD from Carnegie Mellon University.
• James J. Higgins is currently a Professor at Kansas State University and holds a PhD from the University of Missouri-Columbia.

Summary
Hypothesis
    The Aligned Rank Transform is a useful and easily accessible tool for pre-processing nonparametric data so that it can be seen and manipulated on a level beyond current nonparametrics tests.

Methods
     The ART procedure consists of 5 steps: 

1. Computing residuals: for each raw response Y, compute residual = Y - cell mean
2. Computing estimated effects for all main and interaction effects: these are calculated such that Ai is the mean response Yi for rows where factor A is at level i. AiBj is the mean response Yij for rows where factor A is at level i and factor B is at level j. And so on.
3. computing the aligned response Y', assigning average ranks Y'' where Y' = residual + estimated effect.
4. performing a full-factorial ANOVA on Y''.

Results
     The paper re-examined three different studies using their ART procedures to demonstrate its usefulness.  The first case showed how ART can uncover interaction effects that may not be seen with Friedman tests.  The second case showed how the ART can free analysts from the distributional assumptions of ANOVA.  The last case demonstrated the nonparametric testing of repeated measures data.  
Contents
     The authors presented their Aligned Rank Transform tool, which useful for the nonparametric analysis of factorial experiments and makes use of the familiar F-test.  They discuss the exact process in detail, then go on to show three examples of where it could prove useful and effective with real data.


Discussion
I am not particularly qualified to comment much on the usefulness or ingenuity of this project, but it seems to me like the authors did a fine job of creating a tool or technique to handle data that was previously more cumbersome and less obvious.  I cannot find any faults with the paper, and I think that they did a good job of selecting several different test cases to highlight particular areas of usefulness with the ART.