I think Berkson’s paradox is explained by Why the tails come apart, with the added comment that it seems that the explanation applies not just to the tails of the distribution but in fact to any selected band (although the effect is most extreme in the tails). Simpson’s paradox is a paradox about ratio’s and different sample sizes, showing that if you average fractions you get different results than if you add enumerators and denominators, whereas Berkson’s paradox is selection bias (from the wikipedia page: conditioning on [A or B] anti-correlates A and B).
Also, can anyone explain the difference between Berkson’s paradox and Simpson’s paradox?
EDIT: The explanation here is helpful: http://theconversation.com/paradoxes-of-probability-and-other-statistical-strangeness-74440.
I think Berkson’s paradox is explained by Why the tails come apart, with the added comment that it seems that the explanation applies not just to the tails of the distribution but in fact to any selected band (although the effect is most extreme in the tails). Simpson’s paradox is a paradox about ratio’s and different sample sizes, showing that if you average fractions you get different results than if you add enumerators and denominators, whereas Berkson’s paradox is selection bias (from the wikipedia page: conditioning on [A or B] anti-correlates A and B).