a correlation that is not simply an artifact of your statistical analysis, but is actually "present in the data", so to speak.
How will you be able to distinguish between the two?
You also seem to be using the word "correlation" to mean "any kind of relationship or dependency" which is not what it normally means.
Redundancy helps. Use multiple analysis methods, show someone else your results, etc. If everything turns out the way it's supposed to, then that's strong evidence that the correlation is "real".
EDIT: It appears I've been ninja'd. Yes, I am not using the term "correlation" in the technical sense, but in the colloquial sense of "any dependency". Sorry if that's been making things unclear.
Another month, another rationality quotes thread. The rules are: