A doctor has performed clinical trials to determine the relative efficacies of two drugs, with the following results:
Which drug is better?
Here are two conflicting responses:
- Drug I was given to 2020 people, of whom 219 were cured. The success rate was 219/2020, which is much smaller than the corresponding figure, 1010/2200, for drug II.
Therefore drug II is better than drug I.
- Amongst women the success rates of drugs are 200/2000 and 10/200, and amongst men 19/20 and 1000/2000.
Drug I wins in both cases.
G.Grimmett, D.Stirzaker, Probability and Random Processes, 2001.