A new problem known in statistics as Simpson's paradox:
Imagine you get a prize for drawing a black bead from an urn (without looking) and you always get the choice of two urns to draw from.
In the first choice you have urn A with a single black bead (and no other bead) and urn B with 2 black beads and 1 white bead. You'd not hesitate long to see that urn A is the better choice for you.
In the second choice you have urn A' with 4 black beads and 6 white beads and urn B' with 1 black and 2 white beads. You take a little longer to find that 4/10 is larger than 1/3 but again you'd opt for urn A'.
Now the total contents of the A urns (without missing a bead) are put together in one urn A'' and the total contents of urns B are put together in urn B''. Which urn do you prefer now?

Wolfgang