I'm a rookie with statistics, and I'm struggling to understand this:
- it is well known that a confounding factor can cause a spurious association, leading to rejecting a true null hypothesis (i.e. due to the confounding factor Z, I could conclude that there is a causal relationship between X and Y, while one is not there)
- the question is: can the opposite also be true? I.e. can a confounding factor lead to failing to reject a false null hypothesis? (i.e. somehow 'masking' a possibly existent causal association.) If yes, what would be a convincing example?
Best Answer
Yes
Rephrasing the opposite of a confounder: It is definitely possible that an unobserved variable yields the impression that there is no relationship, when there is one.
Confounding usually refers to a situation where an unobserved variable yields the illusion that there exists a relationship between two variables where there is none:
This is a special case of omitted-variable bias, which more generally refers to any situation wherein an unobserved variable biases the observed relationship:
It's easy to imagine a scenario where this would have a canceling effect on the estimate instead:
(I wrote $\rho=0$ for the illustration, but the unobserved relationship does not have to be linear.)
You could call this phenomenon omitted-variable bias, cancellation, or masking. Confounding usually refers to the kind of causal relationship shown in the first figure.