Simpson's paradox (iii)

here are some (near) realistic situations where it could be important to consider Simpson's 'paradox'

who is the better batter overall?

who was the better batter in each of the two years being considered?

research seems to show that overall there is a better survival rate without a drug than with the drug

however, splitting the cohorts into those who began treatment in poorer health and those who began treatment in good health, a different view emerges: