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Simpson's paradox

Q: If drug B has a higher success rate (%age of cures) than drug A when given to women, and also when given to men, does it have a higher success rate when given to people in general?
[2 Apr 1997]

A: Not necessarily, eg

 WomenMen
 SuccessFailure SuccessFailure
A853145
B3111

Then for women B (75%) is better than A (73%) and for men B (50%) is again better than A (44%), but for people in general A (71%) is better than B (67%).

Q: ??? What's the smallest possible "paradoxical" situation (ie smallest total number of people)?
[2 Apr 1997]

A: If we insist that every entry is non-0 then

  WomenMen
SuccessFailure SuccessFailure
A3415
B1114

is pretty good (20 people). If we don't then

  WomenMen
SuccessFailure SuccessFailure
A2101
B1013

is even better (9 people). Is either minimal?

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