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The unclear mathematical theory that controls the reliability of Covid testing

This is often critical to know when considering “lateral flow tests” (LFTs). The rapid Covid tests that the government has made accessible to everybody in England, free, up to twice a week.

The thought is that in time they may well be used to provide individuals authorization to go into crowded social spaces such as bars, theatres, etc., and be more certain that they don't have, and so will not spread, the disease. They’ve been utilized in secondary schools a few times now.

The government says – accurately – that the “false positive rate”, the chance of a test returning a positive result in an individual who does not have the infection, is less than one in 1,000. And that’s where we came in: you might think that means, in case you’ve had a positive result, that there’s a less than one in 1,000 chance that it’s wrong.

It’s not. And that’s because of a fascinating little mathematical anomaly known as Bayes’s theorem, named after the Rev Thomas Bayes, an 18th-century clergyman and maths geek. Imagine you experience a test for an uncommon illness. The test is incredibly precise: if you have the infection, it'll accurately say so 99% of the time; if you don’t have the disease, it'll accurately say so 99% of the time.

So if you get a positive result, in this case, your chance of really having the disease is 99 in 9,999 or fair beneath 1%. In case you took this test completely at face value, at that point, you’d be frightening a lot of individuals, and sending them for intrusive, possibly unsafe medical methods, on the back of a misdiagnosis.

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