[caddemon]

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.

[kgwgk]

> 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 -.

    ++++++
    ++++++
    ++++++
    ---+++
    ---+++
    ---+++

[caddemon]

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!