# If a study indicates no correlation between two variables, does it also indicate a lack of casual relationship? [duplicate]

Of course, correlation does not equal causation. But I am having trouble understanding if there is no correlation between two variables, would this indicate a lack of casual relationship between them as well?

If possible, I would really like an example to help wrap my head around this.

• Your question has already been answered here stats.stackexchange.com/questions/357255/… and here stats.stackexchange.com/questions/26300/… Mar 17, 2019 at 1:51
• @Peter If $X\sim\text{Unif}(-1,1)$ and $Y=X^2$; then $\text{corr}(X,Y)=0$. Why couldn't that be causal? Mar 17, 2019 at 5:28
• @CarlosCinelli zero correlation is not the same as independence (which the first of your suggested duplicates asks about). However, the second one is relevant (via contraposition; if $A\implies B$ then $\lnot B \implies \lnot A$). Mar 17, 2019 at 5:31
• @Glen_b Oof. Rookie blunder! Thx. Mar 17, 2019 at 13:02