I have a question concerning the analysis of experimental data.
Imagine the following situation (which I simplify to make the point clearer):
I ask my participants to give a numerical answer to 3 questions, say, A, B, and C. So in total there are 3 data points per participant.
Now, I can compute several "expected" answers to question C according to competing theories. To simplify, imagine I consider theories X and Y, which yields two distinctive predictions for C: C-X and C-Y.
These "expected" answers are computed by combining the actual answers to questions A and B. For instance, let's say that theory X predicts that C equals A+B, while theory Y states that C should amount to the average of A and B (this is just an example, not the real case of my dataset).
Thus, note that my two "expected" predictions for C are based on a theory, but also on the actual answers given to A and B. This means that I have different predictions for each participant (since I also have different answers to A and B for each participant). And it also means that the predictions are not independent from the actual data of A and B (not the ones I want to model, i.e., answers to C).
Finally, note also that the theoretical predictions may correlate between them, since they are relatively similar computations on the same values (A and B).
My goal: As you may suppose by now, I would like to check whether the actual answers to C support theory X, or theory Y, or both, or none. A relative, rather than absolute, measure of support (e.g., "the evidence is 3 times more likely under theory X than uncer Y") would also be fine, but this sounds more like model selection and I'm not sure that this is what I want.
Would you help me decide the type of data analysis that suits better this situation? I can easily come up with simple solutions (e.g., a correlation model), but maybe they have drawbacks or there are more informative and sofistified alternatives... Any suggestion is welcome and I'm willing to learn!
EDIT: To further clarify, A, B, and C can be assumed continuous.