PPT Slide
What is the correlation between coffee consumption (X) and typing speed (Y) with tension level (Z) held constant statistically? In other words, for people of a fixed level of Z, what is the correlation between X and Y ? If the correlation between X and Y disappears when Z is held constant, then Z appears to be the reason for the X-Y correlation (third variable causation). If there continues to be a significant correlation between X and Y with Z held constant, then Z cannot be the reason for the correlation between X and Y (i.e., third variable causation by Z is ruled out).
Disadvantage of this method: you can test only a limited subset of possible third variables.