[alasdair_]

> If there's a real correlation between A and B (i.e. the correlation isn't a coincidence), that must mean that either A causes B, B causes A, or a third factor causes both A and B.

How can you ever tell that the correlation isn't a coincidence? (see: pirates are correlated with global warming http://sparrowism.soc.srcf.net/home/pirates.html) that seems a bit hand-wavey.

"Oh, that's not a REAL correlation..." sounds a bit like "Oh, that's not a TRUE Scotsman..."

[Zarel]

Pirates being correlated with global warming isn't a coincidence; pirates decreasing and global warming are both (indirectly) caused by the Industrial Revolution.

It's true that you can never be completely sure that any correlation isn't a coincidence, just like you can't be sure that the sun will rise tomorrow. You can, however, be sure beyond a reasonable doubt with enough of a sample size and a strong enough correlation.

Out of curiosity, do you personally believe it's likely (say, >5% chance) that it's a coincidence that girls have better grades than boys?