Confounding
A common cause can make $x$ and $y$ associated even when $x$ does not cause $y$.
If $z$ influences both $x$ and $y$, you will see correlation between $x$ and $y$ even with no causal arrow $x \rightarrow y$. Acting on $x$ then fails to change $y$ the way the correlation suggested.
Ice cream and drowning
Ice cream sales and drowning deaths rise together in summer. Temperature (season) confounds both. Banning ice cream will not save swimmers — you intervened on the wrong variable.
What to do
Randomize $x$ when you can, or adjust for measured confounders under explicit assumptions. Correlation tables alone cannot tell you which arrows exist.
Key takeaways
- Confounder = common cause.
- Spurious correlations mislead interventions.
- Need causal assumptions or randomization — not only correlations.