Comparing Groups

One of the most obvious and important classes of questions that are addressed with human functional brain imaging is the search for differences between groups. For example, can fMRI be used to detect the early onset of Alzheimer's disease? Does a remedial training program in reading cause changes in brain activity preferentially for one diagnostic classification of dyslexia versus another? Does a given drug treatment lead to greater area of functional brain activity? All these questions have as an essential component the attempt to make quantitative distinctions between different groups of subjects.

Functional MRI (and functional brain imaging more broadly) can be used to address at least two types of questions. One question might be thought of as the attempt to represent "typical" brain function and associated networks of activity. In that context, collecting increasingly more data about a single brain doing a single task might be useful because the error bars associated with any particular aspect of the brain activity might be expected to decrease with increased measurement. In statistics, this is called a fixed effects model. On the other hand, to determine whether there are differences in brain function and networks of activity between two putatively different groups of subjects, it is important to sample many of members of each group, even if the individual measurement of any one member of the group is noisy. In particular, knowing with extreme precision that two members of one group differ from two members of another group is only useful if the within-group variation (i.e., between brains) is as small as the within-brain variation (i.e., between multiple measurements of the same brain). If not, then the exceptional precision of the measurement ofthe small number ofsubjects is not useful. In statistics, this is the random effects model.

The practical implication of the fixed versus random effects model of variance for functional neuroimaging is that it is better to have measurements on many brains if the goal is to claim group differences. On the other hand, it may be better to have many measurements on a few brains if the goal is to delineate functional systems as precisely as possible.

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