Dear Francesco,
While still writing Donald has already answered, but anyway:
> are negative t-values for contrast B>A the same as positive t-values for contrast A>B?
Yes, values in T and contrast images just differ with regard to sign then.
> why are some studies doing both?
t contrasts in SPM correspond to one-sided t tests, thus you have to set up two separate contrasts to look at A - B > 0 and A - B < 0.
> "deactivated" – a term whose intuitive interpretation there seems to be disagreement on
To avoid confusions you should talk about "deactivation" only with regard to implicit baseline (e.g. results from a simple contrast [-1 0]) or an explicitely modeled rest period (assuming A B Rest it would be [-1 0 1]. This is the "deactivation" whose origin is not properly understood still, but note that it also affects interpretation of "activations", which are by no means as straightforward as we often think (see e.g. Xu, in press, Neurosci Biobehav Rev, http://dx.doi.org/10.1016/j.neubiorev.2015.08.018 for a recent review). Also note that the meaning of "implict baseline" and "Rest" and correspondingly, deactivation, will differ depending on paradigm / design structure. In rapid event-related designs BOLD response might never return to "baseline", so you might miss some expected activations, e.g. in motor cortex or attention networks, in case subjects e.g. press buttons / "pay attention to the same extent" all the time. And well, there's never really "rest" anway.
In contrast, assume two task conditions with sig. positive activation relative to rest, but larger values in condition A. B would be associated with lower activation relative to A, but it would still be positive, so "deactivation" would be misleading.
When reporting results you should always explicitely state whether there are no deactivations/decreases or whether you don't look at the corresponding directions. In general I would always look at both directions & report results, as otherwise, more complex contrasts can't be interpreted correctly. (Group 1 Cond A - Group 1 Cond B) > (Group 2 Cond A - Group 2 Cond B) might result in a sig. cluster, but this could also be due to negative estimates for Group 2 Cond B and zero otherwise. In that case it would be incorrect to state "Increases in activation during A relative to B were larger in Group 1 than in Group 2".
Best
Helmut
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