Doesn't that depend on how common positive responses were? If only 1% of people said they had a given fetish, you don't have a sample size of 19k, you essentially have a sample size of 190 people to estimate their political-compass center. That's far less certain.
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If only 190 out of 19k people are political-compass-center, and only 190 out of 19k people are into feet or whatever, but 180 of those are overlapped (pol. compass-center & into feet), then that's an overwhelmingly strong correlation, despite the sparsity of positive responses.
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Sure, that would be an incredibly strong correlation. But is that what we have here? Sounds more like if there were 190 people into feet, they were split 55-45-45-45 across the four quadrants. That'd be a weak correlation, and you can't go "but 19K sample size"; it's 190 people.
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We can check how much evidence the data provides for the hypothesis that the "true" correlation is as observed, vs the hypothesis that the "true" correlation is 0 and the observed correlation is noise. Aella's data supports the former hypothesis ~10B times more than the latter.
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In other words: yes, sometimes the data is shaped such that it looks a little correlated, but we shouldn't read much into it b/c even the hypothesis saying the data is (normally distributed and) uncorrelated predicts a little observed correlation. Aella's data isn't like that.
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(And tbc, some of her likelihood ratios on the points near the center are small, like 5-to-1ish. And I agree that shouting "sample size!" alone doesn't do much. But some of the LRs she's reporting are *insane*, and I don't think they should be dismissed.)
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I don't have access to the source data, but I don't understand how that's possible. She has O(200) people for something like necrophilia. The null hypothesis is that 50% of them are to the left of her median responder, and 50% are to the right.
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(I know that's not precisely the same as the question she was asking, which instead checked which quadrant relative to (0,0) but it's extremely similar and easier to reason about).
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It's possible to get an extremely robust conclusion from a sample size of those 200. That would require >70% of them to be on one side. But she said they were weak correlations. 55% of them being right of median isn't enough to reject the null, much less at p<.0000000001
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If you had 10k people in each bucket, then yeah, 52% of a bucket being right-of-median would be extremely unlikely to occur by chance. But the test is only as good as your smallest bucket, and for the super rare ones, that's O(hundreds) at most.
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Necrophile data (men):
no interest: 14445
slight interest: 573
moderate interest: 213
extreme interest: 281
im tryin to get the divisions by quadrant the data loading just takes forever
authleft
no interest: 4195
slight interest: 61
moderate interest: 29
extreme interest: 43
authright:
no interest: 618
slight interest: 31
moderate interest: 15
extreme interest: 19
libleft:
5811
225
81
95
libright:
2588
91
33
44
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disclaimer: i wasnt super neat with the data cause sample was huge; also ignored centrist responses
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