The application of neuroimaging techniques has become increasingly prevalent as a method for characterising the neural substrate of cognitive and emotional processing. Functional magnetic resonance imaging (fMRI) using blood oxygenation level dependent (BOLD) contrast produces large spatial arrays of BOLD time series. The anatomical localisation of brain activations is derived from statistical procedures that assess each of these series individually and construct a spatial map of the results. Although sensitive statistical methods for handling this multiple-comparison problem have been proposed, their implementation has not kept pace with advances in imaging technology and computational power that allow such large volumes of data to be generated and processed. This report presents a practical implementation of the permutation test, a computationally intensive method that improves on more traditional, parametric estimates of significance in the context of multiple comparisons [Blair & Karniski 1994].
In general, statistical methods applied to regional brain activation aim to answer two fundamental questions. The first of these is the omnibus question: does the experimental manipulation have any significant effect as measured by the test statistic? The second question is the more relevant one for imaging research: given that the omnibus test is satisfied, what specific regions or coordinates give rise to the effect?
One of the most straightforward methods of addressing this question of localisation is to treat each voxel as an experiment in its own right, repeating a single parametric test in a voxel-by-voxel manner. Although this method controls Type I error within any particular voxel considered by itself, it fails to control Type I error over the image as a whole. For example, with a typical 
level of 0.05, one of every twenty voxels will be identified as activated. These spurious signals impair localisation of real brain activation by cluttering the image.
The convention in many fMRI studies has been to address the problem of false positives by using a stringent ,
often computed as a Bonferroni correction for the number of comparisons. While this strategy does reduce the number of false positives to an acceptable level, it also eliminates genuinely activated voxels whose signals happen to be weak.
The shortcoming of Bonferroni correction and like methods becomes more apparent when one considers the spatial structure of fMRI data. The strategy of independent testing with
adjustment assumes that the fMRI time series at each voxel are uncorrelated. This assumption is not met, for several reasons:
(1) fMRI techniques measure not neural activity per se, but BOLD contrast. Thus the observed signal represents some convolution of neural activity with local vascular structure, which may extend into neighbouring voxels.
(2) Activated brain regions may encompass multiple neighbouring voxels.
(3) Anatomical connections between distant regions may produce correlated activities in those regions.
(4) Physical limitations of MR methods give the output of the scanner an appreciable point spread function, blurring neighbouring voxels into each other.
In addition to the issue of spatial dependencies among observations, there is the assumption, implicit in most parametric tests, that the observations are drawn from a normal distribution. The neurophysiological and vascular processes that lead to BOLD constrast are not well understood, and departures from the normal distribution may exist. Such violations of the parametric assumption exert their greatest effect in the distribution's tails -- exactly the regions most important for significance testing.