Hi Darren,
> the z maps are an indication of whether or not the coefficient for a given
> functional model is greater than zero.
Yes indeed -- z-maps show whether a linear contrast of parameter estimates
(ie the betas in the GLM) is greater than zero. If the contrast vector
contains just a single 1, then this test whethers the individual
coefficient is greater than zero.
> Can the b values be converted to correlation coefficients or %variance
> accounted for (R^2)?
I'm sure they can because I've seen an equation for converting t-values
into Pearson moment correlation (r-values) although I don't remember it
off-hand. Perhaps someone more statistically savvy could help out with
this?
But because the two are equivalent, they provide exactly the same
information. In both cases, one is testing the fit between the model and
the observed data -- either as a t- or r-value. In fact, the early
Bandetinni et al (1993) paper proposed doing the analyses as a correlation
and some groups still report their results in that fashion. BTW, the
reason that Z-values are typically reported rather than t- or r-values is
that Z-values don't require degrees of freedom. A Z of 3.1 is always the
same whereas a t-value of 3.1 or r-value of 0.5 might be significant with
sufficiently high degrees of freedom.
> That is, I wonder how to weigh up the spatial extent vs the
> degree of fit. Surely it is possible to have a very focal, isolated
> activation with a very high degree of fit. Maybe this is implicit in the z
> scores already, although a correlation coefficient might be more readily
> understood.
This is an important issue. Cluster tests are based solely on spatial
extent and ignore the height of the voxels within the cluster. Voxel
stats (which is the z-value per voxel) are based solely on the degree of
fit at that voxel and ignore spatial neighborhoods. Jean-Bapiste Poline
and colleagues had a paper in NeuroIMage in 1997 (I think) where they
proposed a framework for combining these two types of information. I
thought it was pretty reasonable but I've never seen anyone use it and
none of the main software packages implement the idea.
To illustrate the point you make, imaging that your doing an auditory
experiment and you expect activation -- among other places -- in the
medial geniculate nucleus of the thalamus. This is a small region where
you expect high activation (high z-values). The neighboring
thalamic nuclei, however, are not responsive to auditory stimuli so you
wouldn't expect much in the way of spatial extent. In this case, a
cluster statistic is almost certainly the wrong approach because you
simply won't find a big enough cluster given the volume of active tissue
-- even though there is good reason to believe the activation. This is
preceisely the type of problem Poline et al. tried to deal with. Note,
though, that reporting the correlation value here would be the same as
reporting the t-value (or Z-value). In both cases you're doing the right
thing in this particular case -- reporting a voxel-level statistic.
Hope this was some help.
Cheers,
Joe
|