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Just realized I neglected to respond to the following from Matthew:

> I think I may have misunderstood, but are you saying something like
> "it's true that thresholded maps are worse for localization, but
> then again, you've got to look across studies"?  If so, then surely
> we should use the better map, whether we are looking across studies
> or not?

I was agreeing that thresholded maps are nearly useless for
localization, but I don't feel on the whole they're any better or
worse than unthresholded maps.  Both can be misleading, and neither
should be presented without some specific reason.  But if you have a
single study and no a priori hypotheses about localization, it's going
to be hard to do more than generate a few hypotheses.

I was more trying to argue, just in response to your earlier question,
that the possibility of looking at multiple studies makes it clear
that thresholded maps do in fact contain localizing information.  The
fact that you can't draw reliable localizing conclusions from a single
study's thresholded map does not mean it doesn't contain localizing
information.  My own view is that thesholded maps are probably more
useful than unthresholded, because the thresholding effectively
restricts the hypotheses you'll implicitly consider as you peruse the
literature (although for this purpose I think more liberal thresholds
would be appropriate).  Drawing lines around the supra-threshold areas
on an unthresholded map addresses this problem, as would various forms
of less rigid reporting.

Just to be a little more concrete, if I see a dozen low-powered
studies with similar task contrasts, the thresholded maps make it easy
for me to make generalizations such as "motor planning almost always
activates the SMA, but never visual cortex."  Unthresholded maps,
which contain more information, support an unmanageably large number
of such comparisons.  To the extent people can whittle this down
informally by restricting their interest to local maxima or voxels
that are especially hot (e.g., "there's always a peak in the IPL"), I
think it remains true that thresholded maps support localization
better, it's just that the readers are choosing the threshold rather
than the author of the study.  On the whole, I prefer to let the
authors pre-filter the data for reliability, as long as they tell us
how they did so.  But I realize this is far from optimal, especially
if you want to support meta-analysis.

dan