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How do I statistically analyze a fluctuating relationship?

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How do I statistically analyze a fluctuating relationship?

Postby farrel » Wed Jan 09, 2013 8:05 pm

Hi guys, I've entered some uncharted territory and I'm not sure how to proceed. I need to statistically quantify how two variables fluctuate together over time.

In my study, I had ten sequential blocks of trials on a psychological task (block 1=first, block 10=last). For each block of trials my DVs are 1) average reaction times (RTs) to a target stimulus, and 2) average brain wave (BW) amplitude to the same target stimulus.

When I plot the data in a line graph over time (i.e., by block), these two DVs appear to be roughly anti correlated with one another - the lines for RT and BW look like two sawtooth waves that are perfectly out of phase.
(for example, in block 1 RT is high/BW is low, in block 2 RT is low/BW is high, in block 3 RT is high, BW is low, etc.).

Visually this relationship is pretty stunning, but I need a good way to represent the relationship statistically to show that the variables are indeed anti-correlated. I doubt a simple linear correlation will work here, so my question is, what test should I use to assess the strength of this relationship? Any help would be appreciated!
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