Suppose that an article claims that there is a cause-effect relationship between a certain explanatory variable A and a response variable B.
If I were to test whether a confounding variable C exists in the study, what are the statements that I would have to prove in order to establish C as a confounding variable?
I know that I must show that the following statements are true:
Variable C must have an association with variable A.
At the same time, variable C must have an association with variable B.
Also, variable C must not be an intermediate in the cause-effect relationship (i.e. it cannot be A $\rightarrow$ C $\rightarrow$ B).
Are there any more statements I must prove in order to establish variable C as a confounding variable?
Can someone provide an example of a well-established confounding variable?
Also, just a side question, is it possible to have a confounding variable in an experiment? Or, do confounding variables only appear in observational studies?