Evan Harrington, Ph.D. wrote
I'd like to solicit advice on conducting a factorial ANOVA (between subjects) using ranked data.
A student devised the design and I'm looking for advice to give her on how to appropriately analyze the data. Instead of using interval scales she used a ranking system where each subject had to choose from 8 options, and each option had to be ranked relative to each other, resulting in a set of ranks that are yoked (to some extent; some options are forced toward the end of the spectrum of ranks).
The ranking system lends itself well to the Friedman test (provided you ignore the independent variables and analyze the data as a whole). I assume the student had the Friedman test in mind when creating the scoring system. However, I am looking for a way to capitalize on the 2x2 factorial design. I've done a fair amount of digging and I've come up with some interesting work by Conover & Iman (1981), Larry Toothaker, and by Puri & Sen (1985) -- the consensus seems to be that you can analyze ranked data (if the ranking is done as you would for the Kruskal-Wallis, for instance) provided that you analyze the ANOVA main effects without interaction (or vice versa) but if you attempt to analyze the whole model there is a strong chance of anomalous results.
I have some ideas about testing contrasts on the data, or keeping it based on Kruskal-Wallis, but I wanted to check and see if anyone had thoughts on how to adjust the ANOVA to deal with ranked data of this type.
Thanks
Evan Harrington, Ph.D.
Department of Forensic Psychology
The Chicago School of Professional Psychology
325 N. Wells Street
Chicago, IL 60654
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