I don't want to detail the conversation too much, or distract from the excellent points you have made... But how is this simpson's paradox? Simpson's paradox i

I don't want to detail the conversation too much, or distract from the excellent points you have made... But how is this simpson's paradox? Simpson's paradox is easier to understand geometrically. https://en.m.wikipedia.org/wiki/File:Simpson_paradox_vectors.svg https://en.m.wikipedia.org/wiki/File:Simpson_paradox_vectors... L1 and L2 in the diagram have smaller slopes than B1 and B2, and yet their sum is higher. It's not hard to characterize when this happens. So the canonic example is that a drug might be more effective against all sub-cases (e.g. mild, severe illness) and yet appear less effective overall. You, on the other hand, seem to be describing selection bias.