One of the questions I commonly receive about MRI research on pedophilia is: How do we know what causes what? Comparing the brain scans of pedophiles with non-pedophiles gives us a correlation, and correlation does not necessarily mean causation.
It is true that correlation does not equal causation, but that does not mean we are powerless about it either. To understand how to attack this kind of problem, we need to recall a few important (but pretty rarely discussed) principles of science:
First, no scientific statement will ever be 100% proven. There is no such thing as a perfect study. That is, anyone will always be free to reject any result, claiming the lack of perfection of whatever study(ies).
Next is parsimony: Because we cannot prove anything, the best science can do is explicate each of the possibilities and to pick the best answer available. In science, the best means the most parsimonious; that is, the simplest explanation for the data.
Finally, we need to remember that there exist only three possible interpretations of a correlation:
third variable, W, causes both X and Y.
Although it is true that we cannot conclude that X causes Y directly from a correlation, we can come to that conclusion indirectly, using a process of elimination to show that the other two possibilities are inferior (less parsimonious) explanations for the correlation. This is best shown by concrete example:
For folks who do not already know about them, my team and I have found that pedophiles differ from teleiophiles (i.e., "adult-ophiles") in terms of their IQ and memory test scores, physical height, handedness, history of school grade failures, history of head injuries before (but not after) age 13, and on MRIs (in large regions of white matter).
In conducting our work, we purposefully focussed on variables that had a very specific property: We chose characteristics that happened or were set before the sexual offenses occurred. Although we can calculate only a correlation between handedness (for example) and having committed sexual offenses, we know that handedness is present even before birth. (Fetuses have a preference for which thumb they suck in utero, for example.) So, even though we have only a correlation, we know that sex offenses cannot cause handedness. Thus, of the three causal possibilities, we can already rule one out. It was this logic that led us to study height (cannot be changed by commiting an offense), experiencing childhood head injuries (can't go back in time), etc.
So, we now have two possibilities: X causes Y, or some still unknown variable causes both X and Y. The still-unknown variable explanation is still in the cards, but it is a much less parsimonious explanation. That is, although it is certainly remains possible that some third variable causes both the brain differences and pedophilia, there is no known behavior capable causing the white matter differences that we detected. So, for the "third-variable" explanation to be true, we would have to posit the existance (on the basis of no evidence) of factors unlike any ever reported before. So, despite that that is possible, it is not the most parsimonious explanation.
So, that's where we are today. We do not have proof of causality, and we never will. (It isn't as if we will ever be able to randomly assign subjects to groups.) Rather, X causes Y is the best explanation we have.
And that's the best a scientist can hope for.