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A comment on Berkson's Paradox. Parent comment

Re:Berkson's Paradox by caddemon on Thursday March 25, 2021 @04:41AM (#26577739)
Interesting, I only ever heard of Simpson's paradox in the context of comparing overall averages versus subgroup averages.

I guess this paradox could then be thought of as a special case of Simpson's paradox? Since the out group will exclude people with both traits there should also be a negative correlation there, which disappears in the overall population. But in Berkson's case it seems they're implying the subgroup correlation is spurious whereas with Simpson's it could go either way.

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Re:Berkson's Paradox by kgwgk on Thursday March 25, 2021 @04:47AM (#26577777)
> Since the out group will exclude people with both traits there should also be a negative correlation there

Not necessarily. Imagine the traits are distributed uniformly and independently in [-1 1]. There is no correlation:

    ******
    ******
    ******
    ******
    ******
    ******
If you select people with at least one positive trait you will find negative correlation in the group + but the correlation will still be zero in the group -.

    ++++++
    ++++++
    ++++++
    ---+++
    ---+++
    ---+++
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Re:Berkson's Paradox by caddemon on Thursday March 25, 2021 @05:00AM (#26577856)
Makes sense, I was picturing more of a diagonal boundary but you're right the paradox doesn't specify the shape of the boundary. Thanks!
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