A repeated measures analysis (Bayesian or otherwise) with dependent measurements
Hi JASP experts,
This is a general question about assumptions that, I think, is applicable to both Bayesian and traditional repeated measures ANOVAs.
@Cherie and I have eye-movement data of participants searching through a set of books. I'll simplify the design a bit for the sake of the discussion, but we can provide the actual data if that's useful.
There are two book categories, A and B. For each trial we have quantified the gaze duration on each of the categories, giving two measures per trial. These measures are dependent, because if they look at A then they cannot look at B. In other words, high gaze durations for A are predictive (though not perfectly) of low gaze durations for B, and vice versa.
Then we have an experimental condition with two levels, X and Y. We're interested in whether this condition affects gaze duration, such that participants look more at A in condition X and more at B in condition Y.
An intuitive appealing way to analyze this is with a repeated measures, in which we treat book category as a factor, so we have a 2 (book category: A, B) × 2 (condition: X, Y) design with gaze duration as dependent measure. And then we'd be interested in the book category × condition interaction (not in the main effects of book category or condition).
Now here's where things get tricky.
- I'm pretty sure that it's ok to look at the main effect of condition on gaze duration, because X and Y are independent.
- I suspect that it's problematic to look at the main effect of book category on gaze duration, because A and B are not independent. But I'm not 100% sure about this.
- And what about the book category × condition interaction. Is that valid? And if not, how would we ideally analyze a dataset like this?
I find it hard to wrap my head around this issue, so I really hope that someone can shed some light on this for us!