- Is correlation sufficient to establish that X causes Y? ---- No!
- Is correlation necessary to establish that X causes Y? ----- Yes!
If correlation is not a sufficient condition for causation, then what is?
Demonstrating causation is proving the existence of a cause (X) and effect (Y) relationship (causality); demonstrating the causative link, its mechanisms, and its direction.
Does correlation imply causation?
- Is a perfect correlation between X and Y ever sufficient to
demonstrate causation? What if the coefficient of determination is a
100% (a measure of the best fit of correlated data)?
- Does a perfect correlation even count as evidence (not proof)
towards establishing causation?
How can one demonstrate a cause and effect relationship between X and Y? X causes Y means that X is the cause (event), and Y is the effect (event)? How can one determine which of X and Y is the cause and which the effect?
How can one determine the direction of causation? How can one determine whether 'X is the cause and Y the effect' or whether 'Y is the cause and X the effect'.
"Correlation does not imply causation" means there is no way to legitimately deduce (i.e., derive) a cause and effect relationship between two variables X and Y solely on the basis of an observed correlation between them, no matter the strength of the correlation. Correlation alone cannot be sufficient to establish a cause and effect relationship (i.e., to demonstrate causation); more is required to determine which of X and Y is the cause and which the effect (i.e., the direction of causation).
Correlation is a necessary condition for causality, not a sufficient condition!
Correlation is not sufficient to demonstrate causality, no matter how strong the correlation between X and Y, because just because X and Y co-occur does not excluded the possibility that both X and Y are caused by a third variable Z.
Moreover, from the mere fact that X and Y co-occur one cannot deduce (deductively derive) the direction of causation from X to Y or in reverse; that is, correlation can never be sufficient to determine which one of the variables X and Y is the actual cause and which the effect!
The following causal relations exist between two events (X, Y), some such that exactly one of X and Y is the cause, and the other the effect called direct and reverse causation. Furthermore, there is a relation between X and Y such that neither X nor Y is the cause (in the case where both X and Y are the effects of a common cause Z), and the option in which both X is the cause of Y and (simultaneously) Y is the cause of X, where both X and Y are individually both the cause of the other and the effect of the other.
- H0: The Null Hypothesis: There is no connection between X and Y,
called: coincidental correlation.
- H1: Direct Causation: "X causes Y"; let this direction of causation
be henceforth 'forward'.
- H2: Reverse Causation: "Y causes X"; the reverse of 'forward' (i.e.
the "converse"). H3: "X and Y are both caused by a third variable Z".
- H4: Bidirectional Causation: "X causes Y" and "Y causes X". When X
and Y cause one another, simultaneously, at the same time, in the
same sense, it is referred to as bidirectional causation. Otherwise,
if 'X causes Y' and then 'Y causes X' and so forth, then this type of
causation is called cyclic causation
The following approaches to analyzing causality exist in contemporary philosophy:
- Empirical Regularity: constant conjunctions of events.
- Probabilistic: changes in conditional probability.
- Counterfactual: counterfactual conditions (conditionals with a
- Mechanistic: mechanisms underlying causal relations
- Manipulationist: invariance under intervention.
Example: Counterfactual analysis of causality:
According to the counterfactual view of causality, X causes Y iff without X, Y cannot be. It can be stated that X causes Y iff the two events (X,Y) are spatiotemporally conjoined, and X precedes Y. Causality seems to require not just a correlation, but a counterfactual dependence; that is, a conditional (if-then) statement with a false if-clause.
Causality can be predicted, not established, by a regression analysis, a method of analysis in which the potential causative variable is rendered into a regressor, an explanatory variable, apart and disparate from regressors representing variables other than the potential causative factor.