  Random Field Theory has been used in the fMRI literature to address the
multiple comparisons problem. The method provides an analytical solution for
the computation of precise p-values when its assumptions are met. When its
assumptions are not met the thresholds generated by Random Field Theory can be
more conservative than Bonferroni corrections, which are arguably too stringent
for use in fMRI. As this has been well documented theoretically it is
surprising that a majority of current studies (~80%) would not meet the
assumptions of Random Field Theory and therefore would have reduced
sensitivity. Specifically most data is not smooth enough to meet the good
lattice assumption. Current studies smooth data on average by twice the voxel
size which is rarely sufficient to meet the good lattice assumption. The amount
of smoothing required for Random Field Theory to produce accurate p-values
increases with image resolution and decreases with degrees of freedom. There is
no rule of thumb that is valid for all study designs but for typical data (3mm
resolution, and greater than 20 subjects) residual smoothness with FWHM = 4
times voxel size should produce valid results. However, it should be stressed
that for higher spatial resolution and lower degrees of freedom the critical
smoothness required will increase sharply. This implies that researchers should
carefully choose appropriate smoothing kernels. This can be facilitated by the
simulations we provide that identify the critical smoothness at which the
application of RFT becomes appropriate. For some applications such as
presurgical mapping or, imaging of small structures, probing the
laminar/columnar structure of the cortex these smoothness requirements may be
too great to preserve spatial structure. As such, this study suggests
developments are needed in Random Field Theory to fully exploit the resolution
of modern neuroimaging.
