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Orion Anderson's avatar

"This is where my concept of ‘correlations’ breaks down. I think this effect we’re seeing is real and meaningful ... . But the correlations here are negligible. "

It's a base rates issue. If A is rare and B is common, then A can't be strongly correlated with B even if A strictly implies B; most cases of B will have nothing to do with A.

For instance, imagine an adventurer's guild. Each member is either a fighter or a wizard, and either a human or an elf. Half the humans are fighters, and half the humans are wizards. All the elves are wizards. So conditional on being an elf, the likelihood of being a wizard is doubled. Intuitively that's a strong relationship. But what's the correlation between species and job? It depends on the ratio of elves to humans.

With 10 humans and 10 elves you get 10 elf wizards, 5 human wizards, and 5 human fighters. The job/species correlations is R = 0.58.

With 90 humans and 10 elves you get 10 elf wizards, 45 human wizards, and 45 human fighters. Now the job/species correlation is only R=0.3. With 990 humans and 10 elves, the correlation drops to R=0.1.

Basically, even though knowing someone is an elf tells you a lot about their job, if elves are very rare then knowing who the elves are doesn't help you much if you're trying to predict everyone's jobs.

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Isaac King's avatar

Predictably, many people in the comments are interpreting "X is correlated with Y" as "X causes Y", not realizing that it could equally well be Y causing X, or some third thing causing both.

May be worth editing the title to "Are people with rape fetishes more likely to report being sexual assault survivors?" to try to ward off those people jumping to conclusions.

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