Testing Covid Statistics

I was listening to a story on the radio about how a message from a government expert to the Prime Minister of Great Britain had been leaked. This was not the story, as it happens regularly, but I was alerted by what he was supposed to have said. He was informing the PM that the results of the covid testing should be regarded carefully. He claimed that even with quite accurate tests of over 90% reliance, the results are misleading and that, of the people given a positive test, probably only 25% actually have the disease. Furthermore, he said that this figure could be even lower in some regions, and could be as low as 3%.

This seems bizarre. It means if I take a test which is considered highly reliable, and I get a positive result, then if I live in certain areas, I still have 97% chance of not having the disease. 97% of the results could be false positives. Really?

And, why does the region of the country matter? It makes no sense! Or doesn’t it?

The adventurous should go and do the Maths. The key variables are, of course, the accuracy of the test, and most crucially the level of incidence of the disease in the population. This last one varies from region to region.

If you want some structure to your investigation, there is a prompt sheet here.

If you just want the answer, read on.

The key is the incidence of the disease. If a large enough proportion of the population do not have the disease, then the small percentage of the errors in this large group can be much greater than the large percentage of correct results in the the small population who have the disease. This means that as the disease wanes in a population, an accurate test will show up more and more false positive results.

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