If tyour study is not exploratory in nature from the beginning, you should select ROIs according to your hypotheses and run the statistics. Of course, if your data quality is excellent, then you just run a whole-brain analysis and see what is left after FWE-correction. If this is consistent with your hypothesis - great. In addition, you have the chance to add some new findings, not expected from the very beginning.

The whole question of how to select ROIs is not terribly straightforward. I'm generally a big fan of ROI-based approaches, as I think they can be much more powerful than whole-brain analyses, but there are essentially two schools of though that are best exemplified by this pair of papers by Karl Friston et al. (http://www.ncbi.nlm.nih.gov/pubmed/16635579) and Saxe/Brett/Kanwisher (http://www.sciencedirect.com/science/article/pii/S1053811905025796)

Essentially the Kanwisherian (!) position is that the optimal way of defining fROIs is by a completely independent (i.e. separate set of data) localiser task. Friston's argument is that fROIs can be defined by using an orthogonal contrast from within the same task/experiment. Both methods have advantages and drawbacks, and both are pretty much acceptable these days.

The clear advantage of the Fristonian view is that you don't need an extra localiser task. It's also very useful in being able to decompose complex designs and view statistical interactions in a simple way. For instance, say you're interested in face processing, and have a balanced 2x2 factorial design with male vs. female faces as one factor, and happy vs. sad expressions as the other factor. You could, using appropriate contrasts, view the interaction of the two factors as a statistical map, however viewing interaction effects as SPMs is not generally that informative, as you can never be sure exactly which lower-level effect(s) is/are producing the activated voxels.

A better approach with that kind of design would be to define a simple t contrast of All faces > baseline. This would likely give you a nice fat blob in the fusiform face area. You could then use that ROI to pull out amplitude data related to each of your four conditions for each subject, average the data, and plot it in a simple histogram; it should be instantly clear what's going on in the data. Alternatively depending on your research question, it might also be preferable to use one of the main-effects of the factors (e.g. All male vs. female faces) to define the ROIs - this would likely give your more specific ROIs. These contrasts are still orthogonal to the lower-levels of your design and therefore independent; in fact, I had a long conversation with Tom Nichols about this, and he said that they're what statisticians call 'conditionally independent' but it boils down to the same thing.

An important aspect of this approach is that the statistical inference is done on the amplitude data pulled out of the ROI - not on the brain images. In a sense then, it doesn't matter how you define your ROIs - they can be defined at any (reasonable) corrected or uncorrected statistical threshold, and by any (reasonable) method. To (eventually - sorry) return to your original question then, I think selecting ROIs in 'unpredicted' locations is fine - and in fact it might even be somewhat scientifically irresponsible to ignore results from these locations. Clearly though, if you end up with 100 ROIs your results are going to be very onerous to interpret, and you'd have to do some kind of (Bonferroni-type) correction on your inference stats; this would be an argument for thresholding your ROI definitions at a 'standard' level e.g. p

Thank you for your input and for suggesting these papers. The question of how you select your ROI and define them is quite important. Although, the two approaches you mentioned have to do with fROI, correct? I am not sure you could apply the same logic to MRI, DTI datasets, right?

Ah - apologies if I misunderstood your question, and you were talking about anatomical ROIs. In that case, then of course you need to have strong a priori hypotheses about the areas you're going to select.

But, I still see no problem with also defining ROIs functionally in the same dataset - if (as you mentioned in your original question) you have identified some areas which are active that were unexpected/un-hypothesised. In that case, you'd still need to follow the recommendations in my original answer - define them using either a) an independent localiser, or b) a contrast that's orthogonal to your 'real' contrast-of-interest.

You might also find a combined approach to be the best, in terms of signal-to-noise. Anatomical definitions tend to be quite broad - e.g. it's rare that a given task activates the entirety of the cingulate cortex, for instance. A better approach might be to take your anatomical regions, and calculate the overlap between them and the functional activation clusters you get in each subject. This means that you still have a strong a priori constraint (the anatomy) but this is refined by only including voxels that are active within that area, for that subject. This should avoid you averaging in loads of noise (from inactive voxels) in your anatomical ROIs.

One other caution is to be careful of circularity. If you do a brain-wide search to find some significant voxels then average them, you can not compare them back to the original measure that you used to find them in the whole-brain analysis. This is the "voo-doo" correlation effect discussed by Vol et al. This is just justification for using either independent data for ROI selection or an orthogonal task.

Circularity is a problem we have to watch out for. Another good paper discussing this is: "Circular analysis in systems neuroscience: the dangers of double dipping." http://www.nature.com/neuro/journal/v12/n5/full/nn.2303.html

Thank you for the reference