The other night, I was chatting with my brother-in-law, who recently qualified as a doctor. He is a very conscientious and hard-working fellow who spends a lot of time reading up on the latest research and findings in medical journals (which, I have to say, are surprisingly far more palatable than economics journals).


One thing he was complaining about was the nature of statistics, and how hard it was to correctly interpret findings from medical tests and experiments, and referred to a recent article that looked at how many doctors got the correct answer to a statistical problem. Most of them failed.

In part, I think this reflects the fact that statistical theory is not really a core component of learning to become a doctor; it’s generally more important to know how the body works, etc. But I thought it would be interesting to ask a variant of the question here, and see what answers people came up with. Please use the comments box below to submit your views – if necessary, I’ll come back in a bit with the answer.

The question: A test for cancer is 90% accurate in both directions – 90% of the time, it returns a positive result among those people with cancer, and 90% of the time it correctly says that those people without cancer don’t have it. So, if your patient is tested for cancer, and the result is positive, what is the likelihood that the patient has cancer? (The incidence of cancer in the population as a whole is 1%).

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