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Kindly comments on Taking "correlation does not imply causation" back from the internet - Less Wrong Discussion
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Comments (70)
Only to score points at the expense of the audience's vocabulary would one say "there is no variance in either variable" as opposed to saying "there are no people who avoid drinking water, nor people who don't end up dead, to compare to".
Let's not encourage this.
This is perfectly good common-sense reasoning but doesn't make the point that the correlation is undefined. I would've thought the audience for this, ie people involved in a correlation versus causation debate, would benefit from seeing that explicitly, if they don't already. Maybe we are judging the audience differently. If we assume that everyone knows dividing by zero is bad, but don't use any other technical term (including variance), maybe we can get the point across.
This is perfectly good common-sense reasoning that explains why the correlation is undefined. If your audience has any notion whatsoever of what correlation means, they will understand this. If not, trying to phrase the same argument in terms of math will not help; it will just make it impossible for your audience to engage with your argument.
If the audience is mathematically sophisticated, then writing out the formula for Pearson's correlation coefficient is just going to distract them from the real issue, which is that the saying should refer to statistical dependence, rather than correlation. In other words, C's argument only addresses the literal meaning of B's words, not the substance behind them.
I acknowledge that using the wrong terminology to the wrong audience will make their eyes glaze over and be counter-productive.
I disagree about that. Until I actually took a course in statistics, I wouldn't have been sure whether the correlation was undefined or just misleading in that case. Again, I agree that not everyone needs this level of precision.
An important issue, but a completely different one. If B said "that is statistical dependence, not causation", wouldn't they be equally wrong in exactly the same way?
B would be wrong in the exact same way. So the true reason that B is wrong needs to apply in both cases. On the other hand, appealing to the correlation formula only defeats the correlation version of the argument.
Ah, I see what you mean. You're right.