
Causation without Correlation is Possible - IncidentalEcon
http://theincidentaleconomist.com/causation-without-correlation-is-possible/
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protez
No statistical method can prove causality. Also, there's no scientific method
to confirm any one of causal relationships, either. Causality exists only in
human mind. There's no methodic way to discern semipermanent coincidence (or
identical equivalence) from causality.

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zck
>Causation without correlation. ...Suppose the value of y is known to be
caused by x. The true relationship between x and y is mediated by another
factor, call it A, that takes values of +1 or -1 with equal probability. The
true process relating x to y is y = Ax.

>It is a simple matter to show that the correlation between x and y is zero.
Perhaps the most intuitive way is to imagine many samples (observations) of x,
y pairs. Over the sub-sample for which the pairs have the same sign (i.e. for
which A happened to be +1) y=x and the correlation is 1. Over the sub-sample
for which the pairs have the opposite signs (i.e. for which A happened to be
-1) y=-x and the correlation is -1. Since A is +1 and -1 with equal
probability, the contributions to the total correlation from the two sub-
samples cancel, giving a total correlation of zero.

It seems to me that this doesn't quite make sense. Sure, the correlation of
the average of the numbers is 0, but notice that |x - y| <= |2x|, or that |y|
= |x|. That seems like a rather large correlation to me, even though half the
time, x and y are positively correlated, and the other half, they're
negatively correlated.

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mwexler
A paragraph or so down, he says "That is, there are functions of x and
functions of y that are correlated." So, for your example, could we consider
Abs value as a function?

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tokenadult
The submitted article links out to a more scholarly article

[http://www.springerlink.com/content/l787673gxg8425g6/fulltex...](http://www.springerlink.com/content/l787673gxg8425g6/fulltext.pdf)

with diagrams about issues to consider in observational studies.

I always like to recommend Peter Norvig's article on interpreting research
studies

<http://norvig.com/experiment-design.html>

and in the medical context can also recommend Harriet Hall's lecture notes

<http://www.skepticstoolbox.org/hall/>

as examples of popular writings on research study interpretation that give
vivid examples and bring up important issues.

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PJNasty
It would be wonderful if the first line were true. "It is well known that
correlation does not prove causation."

Causality itself is hypothetical, an artifact of perception.

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IncidentalEcon
That's the subject of the next post on this topic, forthcoming.

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carbocation
Long story short: causation without correlation is possible if you are unable
to adjust for confounding.

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IncidentalEcon
The post suggests more, though doesn't illustrate it all (because I couldn't
think of a simple way to do so). The key is that x and y can be statistically
related yet still have zero correlation (because that is just one specific
measure of relatedness). Interpretations of causation are not data driven.
They come from theory.

The role of confounded factors came up in the examples because that is just an
easy way to illustrate the points.

