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Comment by jawns | Hacker News Reader

I wrote "Correlated: Surprising Connections Between Seemingly Unrelated Things" (http://www.correlated.org), and one of the things I run into a lot when promoting the book is the "correlation doesn't imply causation" line.

Obviously, the statistics I present in the book and on the website are tongue-in-cheek, but I like to take issue with that line, because typically, people don't fully understand what it means. I use a variation of the line in the OP's post -- that "nothing other than correlation implies causation."

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I don't like that phrase. While I get what it's going toward, it makes it feel as though some kind of "special" correlation implies causation.

Really, correlation is just one part of a package of other things which all together imply causation.

http://www.amazon.com/Causality-Reasoning-Inference-Judea-Pe...

When something implies correlation it doesn't mean there actually is correlation. It just means it might be worth to look deeper into that direction, right? Therefore you need all these different attributes to show a causation exists, but a single one should be enough to imply causation.

note: I might actually really confusing my word definitions here, btw.

You can't exactly imply correlation (in simple models) you merely observe it. You can imply causation since it's a theoretical claim, not just an observation.

What I meant to say before is that correlation cannot imply causation in and of itself because it is merely an observation—you must also build a framework of causal assumptions within which your observed correlation could have only arisen if there was a causal relationship of interest. That final statement is the "implication" we're all talking about.

So, "correlation along with an acceptable and proper set of counterfactual assumptions is capable of imply causation sometimes". Just rolls off the tongue, really.

You're joking right? Uncorrelated things can easily be causal.

Could you please give an example? It may be that he is defining causal more narrowly and correlate more broadly than you are.

How about this? Playing soccer causes broken hips, but soccer playing is in fact anti-correlated with broken hip incidence. Why? Because most broken hips occur among extremely old people, who generally don't play soccer.

[I'm not sure whether this is actually statistically true, but you get the idea, and I'm sure there's a similar example which actually is true.]

Just because old people tend to break their hips more often than younger people wouldn't necessarily make soccer anti-correlated with hip injuries. In your example, if you compared two groups that are identical, the only difference being one plays soccer and the other doesn't, you'd find a correlation between soccer and broken hips.

Anything non linear or multivariate:

http://en.wikipedia.org/wiki/Correlation_and_dependence

Ie unemployment is not correlated with age since both young and old people tend to be unemployed...it is a non-linear relationship.

The right way to disprove "Nothing other than correlation implies causation." would be to find one causation whose existance we know from something other than causation.

But you won't find it. Think about any causation. Now ask yourself why we now that it exists. The answer will always be correlation.

Causal calculus, mutual information, random forest importance scores, various hypothesis tests and other methods can all imply causation as well or better (especially in the case of non-linear or multivariate association) then correlation. All these methods and more are widely used in literature.

Those methods still rely on correlation. To be clear: We are not only talking about linear correlation here, which is only one of several kinds of correlations.

No they don't. They work directly with underlying estimates of probability distributions, entropy or impurity decrease in machine learning models.

Another example: mendelian inheritance patterns in a pedigree study.

If you know of a good measure of non linear correlation please let me know. And publish a paper in science or nature like the MIC/MINE people did (a measure that has issues in practice).

To estimate probability distributions, you need data that is non-random. Non-random means there's a pattern. That's another word for correlation.

In using those methods you may never calculate correlation as a number, but when those methods find something you still rely on the fact that there is a correlation.

What correlation proves that the movements of the stock market are causal?

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