Better in every group, worse overall
A hospital compares two kidney-stone treatments. Treatment A has a higher success rate than Treatment B for small stones, and also a higher success rate for large stones. Yet when you pool all patients, Treatment B has the higher overall success rate.
How can a treatment win in every subgroup but lose overall, and which number should you trust?
Your answer
This one is open-ended. Work it through, then check your reasoning against the full solution.