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Correlation & Causation

December 26, 2012 Leave a comment Go to comments

Correlation does not necessary imply Causation. There could be multiple reason for a ‘correlation’:

– Causality: X causes Y

– Reverse Causality: Y causes X

– Simultaneity: X causes Y, Y causes X;

– Endogeneity: W causes Y, and X is correlated with W.

– Spuriousness: No causation, just a fluke.

 

Determining causation( from wiki)

David Hume argued that causality is based on experience, and experience similarly based on the assumption that the future models the past, which in turn can only be based on experience – leading tocircular logic. In conclusion, he asserted that causality is not based on actual reasoning: only correlation can actually be perceived.[14]

In order for a correlation to be established as causal, the cause and the effect must be connected through an impact mechanism in accordance with known laws of nature.

Intuitively, causation seems to require not just a correlation, but a counterfactual dependence. Suppose that a student performed poorly on a test and guesses that the cause was his not studying. To prove this, one thinks of the counterfactual – the same student writing the same test under the same circumstances but having studied the night before. If one could rewind history, and change only one small thing (making the student study for the exam), then causation could be observed (by comparing version 1 to version 2). Because one cannot rewind history and replay events after making small controlled changes, causation can only be inferred, never exactly known. This is referred to as the Fundamental Problem of Causal Inference – it is impossible to directly observe causal effects.[15]

A major goal of scientific experiments and statistical methods is to approximate as best as possible the counterfactual state of the world.[16] For example, one could run an experiment on identical twins who were known to consistently get the same grades on their tests. One twin is sent to study for six hours while the other is sent to the amusement park. If their test scores suddenly diverged by a large degree, this would be strong evidence that studying (or going to the amusement park) had a causal effect on test scores. In this case, correlation between studying and test scores would almost certainly imply causation.

Well-designed experimental studies replace equality of individuals as in the previous example by equality of groups. This is achieved by randomization of the subjects to two or more groups. Although not a perfect system, the likeliness of being equal in all aspects rises with the number of subjects placed randomly in the treatment/placebo groups. From the significance of the difference of the effect of the treatment vs. the placebo, one can conclude the likeliness of the treatment having a causal effect on the disease. This likeliness can be quantified in statistical terms by the P-value[dubious – discuss].

When experimental studies are impossible and only pre-existing data are available, as is usually the case for example in economics, regression analysis can be used. Factors other than the potential causative variable of interest are controlled for by including them as regressors in addition to the regressor representing the variable of interest. False inferences of causation due to reverse causation (or wrong estimates of the magnitude of causation due the presence of bidirectional causation) can be avoided by using explanators (regressors) that are necessarily exogenous, such as physical explanators like rainfall amount (as a determinant of, say, futures prices), lagged variables whose values were determined before the dependent variable’s value was determined, instrumental variables for the explanators (chosen based on their known exogeneity), etc. See Causality#Statistics and Economics. Spurious correlation due to mutual influence from a third, common, causative variable, is harder to avoid: the model must be specified such that there is a theoretical reason to believe that no such underlying causative variable has been omitted from the model; in particular, underlying time trends of both the dependent variable and the independent (potentially causative) variable must be controlled for by including time as another independent variable.

 

 

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Categories: Data Mining, e-commece
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  1. February 16, 2013 at 9:30 PM

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