Dear FSL experts,

As a beginner, I have some general theoretical questions about fMRI analyses. Very thankful to anyone who could help me out!

1) It seems that in behavioural analyses, the importance of effects is quantified&compared based on the "effect size" statistic, whereas in MRI this is based on "how significant" they are, i.e. on how small the p-value (or, equivalently, how large the t-value) is. Would it not make sense for activation maps to be colour-indexed by e.g. cohen's d instead, rather than taking a higher t-value to mean "stronger activation" when it really means "more reliable activation"?

2) Some studies find a long list of regions for contrast A>B, but none when the conditions are reversed in the contrast (B>A). Does that really mean that in the entire brain there isn't any region where the BOLD signal is significantly higher for B than for A? This would seem to imply a violation of some sort of conservation law: assuming a more-or-less constant amount of cerebral bloodflow is available during both conditions, then surely if there are regions where this bloodflow is distributed differently between conditions, then this should come out of both contrasts, not just one.
This question is, I guess, equivalent to "why isn't the result of a B>A contrast simply the opposite of A>B?"

3) Is the relation between the concepts of "activation" and "deactivation" similar to the relation between a "A>B" contrast and a "B>A" contrast? in other words, if "deactivations" are found in a "A>B" contrast, are they equivalent to "activations" in a "B>A" contrast?

4) In order to obtain the activation statistical map in a functional analysis, when would each of these methods be applied (either instead of, or in addition to the other two methods)?
    A. correlation between the time series of the HRF-convoluted BOLD and that of the behavioural stimulus that was used
    B. 1-sample t-test between the BOLD and a resting baseline
    C. 2-sample t-test, i.e. contrast, between condition A and condition B
Is it the case that each method is only suited to one particular type of question, or is there in fact overlap between them?

5) One could say that fMRI experiments can prove A correlates with B (A~B), where A is the event (e.g. stimulus) and B is the evoked BOLD signal. However, in general, for two events A and B, if A~B and if temporal precedence and lack of 3rd variable can be proved, i.e. if it can be shown that A consistently happens before B and there is no obvious C factor that is a cause for both A and B, then this allows one to infer "A=>B" from "A~B". Those two extra conditions are often met in fMRI, so why it that it's wrong to interpret fMRI results causally?

Thanks!
Francesco