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RichardHughes comments on Taking "correlation does not imply causation" back from the internet - Less Wrong
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A discussion I had in the reddit comments on that Slate post made me invent this fake argument:
A: People who drink water inevitably end up dead. Therefore drinking water causes death.
B: No, that is correlation, not causation.
C: No, it is not correlation. To calculate correlation you divide the covariance of the two variables by the variance of each of the variables. In this case there is no variance in either variable, so you're dividing by zero, so correlation is not even defined.
I think it's an improvement to go from saying "there is obviously something wrong with A's argument" to actually being able to point out the divide-by-zero in the equation.
Disagree. Our target audience - humans - rarely if ever thinks of 'correlation' in terms of its mathematical definition and I suspect would be put off by an attempt to do so.
This is entirely true - as a mere human, my interest plummeted at "covariance", and I'd still like to think I'm SOMEWHAT equipped to handle correlation/causation. Just not numerically. So, as a roughly average human, I say your suspicions are correct.
The point still applies. What do you mean by “correlation” --formally or informally-- when one (or both) of the variables is constant across the population?
The specific fake argument used is flawed because of that. When people make the correlation-causation error, how often are they doing it based off of a variable that's constant across the population? Do people ever really develop 'drinking water causes x' beliefs?
It's a valid point and very true, but I suspect that it isn't applicable to the issue at hand.