Hi Philipp,

I find it easiest to think about a t- or F-contrast in terms of the 
null hypothesis that it specifies.

> I have a basic questions on the interpretation of two different F contrasts
> in a model  with 8 regressors (no.1-4: of no interest; no.5-8: "of interest"):

I'll refer to these as [A B C D E F G H] below

> Contrast A:
> 0 0 0 0 1 1 1 1 

This specifies the null hypothesis E+F+G+H = 0, tested against the 
alternative hypothesis that this sum is non-zero (for an F-contrast; 
or >0 for a t-contrast).

> Contrast B:
> 0 0 0 0 1
> 0 0 0 0 0 1
> 0 0 0 0 0 0 1
> 0 0 0 0 0 0 0 1

This has the null hypothesis E = F = G = H = 0, i.e. you can interpret 
each row as a separate contrast, here each specifying that one 
regressor (with a 1 in its column) is 0. If any of E-H were 
significant for a particular region then this null would be rejected 
(i.e. that region would be declared significant)

> The questions on the regressors is/should be: are there brain areas
> significantly associated with any of the regressors?

To ask if any of them are interesting, your null hypothesis would be 
that none of them are. Hence your contrast B answers this question.

> In earlier postings explanations can be found stating that the hypothesis
> in Contrast A is much more restrictive than in B.

I'd say B has a more restricted null hypothesis or reduced model -- 
all E-H are zero; whereas A could include both this case and for 
example the case that E and F are large and positive but cancelled out 
by equally large negative G and H, along with many other situations. 
Though see below for whether some data might be significant for A and 
not B.

> b. If one of the regressors does not carry any weight, how much of a
> "dilution" effect is present in the two contrasts?

If, say, E explains very little variance, then both E+F+G+H=0 and 
E=F=G=H=0 would be dictated by the F,G,H, which is probably what you'd 
want. You'd only need to worry about E messing things up if you were 
looking for *all* E-H to be significant, rather than any of them. I'm 
not aware of a contrast that would test that; I think you'd have to 
test each regressor with a separate contrast and then look at the 
conjunction null of these. Anyway, that's not the question you said 
you were interested in.

> c. What is the meaning of a region appearing in B but not A? (I think it
> indicates that rather a single regressors brings in the effect, but I am
> not sure)

Hard to pin down, since various combinations of regressors could 
reject B's null but not A's. For example, the above mentioned case of 
positive/negative ones cancelling out. I think it would also be 
possible to find regions that were significant for A but not B, if for 
example all of E-H were positive but small, possibly B would conclude 
that none is significantly different from 0, while A would conclude 
that their sum was.

I hope this helps. Some of the finer points are rather difficult, and 
I may well have got them wrong, but I'm fairly confident in the 
simpler point that B is the right contrast for your question.

Best,
Ged.