Monday, January 28, 2008

Causation vs Correlation

A lot has been written on the topic of causation vs correlation, usually in refuting "studies" that are published based on an agenda.

I had reason to think seriously about this topic, as a result of something the American Farmer wrote.

There is a relationship between data that is not strong enough to be causation, and stronger than mere correlation. I'll call it foundation.

Note: I think this is prevalent in education, maybe not so much in data analysis. It seems almost self-evident in education, as one of the examples I'll give shows, but I've never seen this idea used in analyzing data, so in that realm, this is a new idea to me. If someone has presented this thought before, I'd like to know, so I don't claim to have dreamed up something new, even if I arrived at this conclusion independently.

Example of causation vs correlation vs foundation, using math:

Arithmetic is a learned skillset. Algebra is also a learned skillset. For the sake of brevity, we'll call Arithmetic (a) and Algebra (b).

(b) is never found without (a). Some would say that, therefore, (a) causes (b). However, since (a) can be found without (b), this is proof that (a) causes (b). BUT, for a true causality relationship to exist, (a) must ALWAYS cause (b), and that is obviously not true. Plenty of people can add, subtract, multiply, and divide, but can't solve a quadratic equation. So, (a) doesn't CAUSE (b).

BUT... since (b) is never found without (a), ie, anyone who can solve a quadratic equation can also add, subtract, multiply, and divide, we can accurately say that (a) is a FOUNDATION for (b). (b) cannot exist without (a), but (a) can exist without (b).

When one can exist without the other, but the inverse is not true, we can call that not causation, or correlation, but foundation.

Comments welcome.

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