A is correlated with B/ A has an impact on B I've been reading papers to collect materials for my bachelor thesis,
and I came across this question and wasn't sure if my understanding of the concept is correct.
Is "A is correlated with B" the same as " A has an impact on B"?
Further, if a study says "A is correlated with B" or " A has an impact on B"
Can it both be understood as the higher A becomes, the higher B becomes?
 A: *

*Counterexample: Acne causes kids to start middle school.


No...they simply happen to coincide because both occur around the time kids are 10-12 and therefore starting middle school.


*This is true for positive correlation only. In the case of negative correlation, the opposite is true: the higher A becomes, the lower B becomes. There's another aspect that differs from the way "correlation" is used in common speech. In formal statistics, correlation refers to a linear relationship, specifically the normalized covariance (divide covariance by the product of each variable's standard deviation).


$$cor(A,B) = \dfrac{cov(A,B)}{\sigma_A\sigma_B}$$
What this means is that if an increase in A from 4 to 5 results in an average increase of 3 units in B, then an increase in A from 5 to 6 also results in an average increase of 3 units in B.
A: On the first question, no. For instnace, it could be the other way around "B has an impact on A", both ways "positive feedback loop" or none (A and B are correlated because a third variable is causing them). As it was pòinted out in the comments, correlation and causation are not the same thing. Please note that many research studies will use the term "impact" very loosely. Be careful! Click here for further discussion
On the second question, if the correlation is positive, then yes. You should expect higher values of B as A increases. But correlation can also be negative.
