Consider four variables: X, Y, M, and Z. The causal statements are:
1. X affects M.
2. M affects Y.
3. Z affects both X and Y.
4. Y does not affect Z.
5. X does not affect Z.
Assume there are no other direct paths. Consider these claims:
1. Z is a confounder of X → Y.
2. M is a mediator of X → Y.
3. Z lies on a backdoor path from X to Y.
4. Conditioning on M blocks the total effect of X on Y.