I've noticed that in SPM's function for converting uncorrected
p-values to FDR p-values (spm_P_FDR), there is a distinction drawn
between "corrected" and "adjusted" p-values, with reference made to:
Yekutieli & Benjamini (1999) (eqn 3)
http://dx.doi.org/10.1016/S0378-3758(99)00041-5
It is the *adjusted* p-values which spm_P_FDR actually returns, and so
I think these are the ones users report in their tables of voxel-wise
pFDR.

For the record, these terms were introduced in that reference and I've haven't seen the distinction widely adopted; most authors just write 'corrected FDR P-values'. But, for the purposes of clarity, I'll use the Yekutieli & Benjamini (YB) terms in quotes for this email.

Best way to distinguish 'corrected' from 'adjusted' FDR P-values is to look at the FDR inequality from Benjamini-Hochberg original paper:

p(i) <= alpha i / v

where p(i) are the ordered P-values p(1)<=p(2)<=...<=p(v), alpha is the desired rate at which to control FDR, and v is the number of voxels.

If you just change the inequality to an equality and solve for alpha, you get the YB definition of 'corrected' P-values

Pc(i) = p(i) v / i

The problem is that there is no guarantee that these 'corrected' P-values are monotonic; it may well be that

p(1) = 0.00001 Pc(1) = 0.06

but

p(10) = 0.00005 Pc(10) = 0.03

Hence, if you just used these 'corrected' P-value you'd reject the 10th smallest P-value as FDR-0.05 significant, but not the very smallest P-value!

So 'adjusted' P-values are just 'corrected' P-values with montonicity enforced, i.e.

Pa(i) = min(Pc(i),Pc(i+1),Pc(i+2),...,Pc(v))

So my question is, are the "adjusted p-values" returned by SPM
preferable to the corrected ones / FSL's q-rate? Or should they be
differently interpreted? Incidentally, SPM's "Qs -> P" step can be
very slow for large images...

The generic definition corrected P-value for multiple false positive measure BLAH is: Smallest alpha BLAH false positive rate for which a test is significant. This is what is meant by 'FDR corrected' and 'FWE corrected' P-values in SPM.

It is YB's 'adjusted' P-values that satistify this definition of corrected FDR P-values and hence the ones I'd recomend for use.