If surgical procedure A has a higher success rate than surgical procedure B in every hospital where they are used and yet procedure B has a higher overall success rate, then we suspect that

Statement I: this is nonsense and it can’t possibly be true. Statement II: this is an example of Simpson’s paradox. Statement III: it must be easier to achieve success at some hospitals than at others, whatever procedure is used. Statement IV: procedure B must be used predominantly in hospitals where it is easier to achieve success, while procedure A must be used predominantly where it is harder to achieve success. Statments II, III, and IV are true.