To accommodate these random effects, and to highlight the areas of activity linked specifically to the process under investigation, statistics are used to look for the most significant difference above and beyond background brain activity. This involves a multi-stage process to prepare the data, and to subsequently analyse it using a statistical method known as the general linear model.
A study will usually scan a subject several times. To account for the motion of the head between scans, the images will usually be adjusted so each of the voxels in the images corresponds (approximately) to the same site in the brain. This is referred to as realignment or motion correction, see image realignment.
Functional neuroimaging studies usually involve several participants, who will have slightly differently shaped brains. All are likely to have the same gross anatomy, but there will be minor differences in overall brain size, individual variation in topography of the gyri and sulci of the cerebral cortex, and morphological differences in deep structures such as the corpus callosum. To aid comparisons, the 3D image of each brain is transformed so that superficial structures line up, a process known as spatial normalization. Such normalization typically involves not only translation and rotation, but also scaling and nonlinear warping of the brain surface to match a standard template. Standard brain maps such as the Talairach-Tournoux or templates from the Montréal Neurological Institute (MNI) are often used to allow researchers from across the world to compare their results.
Images are often smoothed (similar to the 'blur' effect used in some image-editing software) by which voxels are averaged with their neighbours, typically using a Gaussian filter or by wavelet transformation, to make the data less noisy.
Analyses may also be conducted to examine differences over a time series (i.e correlations between a task variable and brain activity in a certain area) using linear convolution models of how the measured signal is caused by underlying changes in neural activity.
Because many statistical tests are being conducted, adjustments have to be made to control for Type I errors (false positives) potentially caused by the comparison of levels of activity at a large number of voxels. In this case, a Type I error would result in falsely detecting background brain activity as activity related to the task. Adjustments are made, based on the number of resels in the image and the theory of continuous random fields in order to set a new criterion for statistical significance that adjusts for the problem of multiple comparisons.
Most simply, they can be presented as a table, displaying coordinates that show the most significant differences in activity between tasks. However, differences in brain activity are more often shown as patches of colour on an MRI brain 'slice', with the colours representing the location of voxels that have shown statistically significant differences between conditions. The gradient of color is mapped to statistical values, such as t-values or z-scores. This creates an intuitive and visually appealing means of delineating the relative statistical strength of a given area of activation. Recently, an alternative approach has been suggested, in which the statistical map is combined with the map of the original difference in brain activity (or, more generally speaking, with the original contrast) and colorcodes are attributed to the latter.
Differences in activity may also be represented as a 'glass brain', a representation of three outline views of the brain as if it were transparent. Only the patches of activation are visible as areas of shading. This is useful as a quick means of summarizing the total area of significant change in a given statistical comparison.