If I take a set of measurements and test correlation of variable $A$ vs variable $B$ and get a significant correlation, that makes sense to me. But what if further analysis reveals that of those factors, there is only a significant positive correlation within one group, and that group is over-represented. Is the global correlation still valid, or is it, upon more detailed inspection a sample-bias effect?
Here is some graphs to explain:
The global correlation
The group separated correlations