I believe I'm looking for a test to determine if there is a significant change in matched ranks between two conditions. In case that's not what I'm looking for here's an outline of my problem.
I am trying to analyze electroencephalogram (EEG) data. We have 64 different channels placed around the head which we record voltage data from, and we have 13 measurements of each condition (different subjects). We are trying show that two conditions have significantly different topographies. That is to say that there is a different pattern of +voltage and -voltage across the 64 channels. There are a couple of factors that complicate this a bit. First, each topography is mean 0. This is an artifact of the reference used. Second and more important, the topographies are heteroscedastic. Even when we try to normalize the standard deviation, we get some really wonky results testing for interactions between channel x condition using standard ANOVAs that make me think we have some oddness in our data set that is throwing our results off (maybe higher moments, not sure). Rank transformation is looking mighty attractive, but I've read enough to know looking for interactions with ANOVAs and rank transformed data isn't kosher.
So, I think I'm looking for a test that will test the change in rank within the 64-channel topography across conditions. Ideally this would be a repeated measures-type analysis, but not critical.
My completely naive idea is to rank each channel, then find the change in rank across a single subject by simple subtraction, then submit those rank-differences to a Kruskal-Wallis test to see if there is a consistent change in ranks across channels. Is such a test prone to the same errors as the interactions in a Rank Transformed ANOVAs? Is there a better, or more standard test for a change in rank?
Sorry for the rather long question and thanks to anyone who has read this far =)
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