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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

Q: What's the smallest possible "paradoxical" situation (i.e. smallest total number of people)? There are two versions of the problem depending on whether we allow entries to be 0.
2 Apr 1997

Q: Here's another striking version. A greengrocer sells apples at a fixed price per fruit, and oranges similarly. Each day an apple costs more than an orange. I buy fruit on several days. On average, did my apples cost me more per fruit than my oranges?
20 Mar 2011

Q: Call the above situation a 2-level paradox, because we're measuring the drugs' effectiveness at two levels: the gender level and the overall population level. Is it possible to have a 3-level paradox? For example, is it possible that drug A has a higher success rate on people, but drug B has a higher success rate on women and on men, but drug A has a higher success rate on each of young women, old women, young men and old men?
Haidar Al-Dhalimy, 2 Apr 2021

Spoiler


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