UKC

Very interesting article in the Guardian, does a good job of explaining Bayes’ theorem, and how this relates to Coronavirus testing, and in particular why tests may turn up false positives more often than you’d expect.

https://www.theguardian.com/world/2021/apr/18/obscure-maths-bayes-theorem-r...

"Obscure maths theorem"...?

Yes, slightly overselling the case there. Though if you stopped 100 people in the street, how many of them would have heard of it; so, perhaps, obscure to the general population, though not to statisticians.

Perhaps of relevance, also obscure to doctors. I suspect if you stopped 100 doctors in the street, most would not have heard of it. 
 

overall, i thought it did a decent job of explaining the effect of prevalence on the performance of diagnostic tests to people unfamiliar with the concept; and I’ve not seen this elsewhere in the media, so I’ll let them off with their exaggeration over how obscure Bayes’ theorem actually is...

To most people exponential growth appears to be an obscure concept. 

The credibility of the article wouldn't hinge on it describing a theorem as obscure, or not, I don't suppose.

It did. Your observation about doctors is a bit worrying...

I thought that was a very good article, one of the clearest explanations I've seen. It is a shame that with a title that contains "obscure maths theorem" a lot of people will not even look at it.

The thing is that probability and statistics are tough. I found them the toughest part of maths A level, and the average person has virtually no concept of how they work. The popularity of the national lottery is ample evidence of this. There are lots of people of average intelligence out there who think that the risk of side effects from a Covid vaccine is significant compared to the risk of not having a vaccine. 

One part is a bit misleading:-

"In fact, last week government data showed that the false positive rate for LFTs since 8 March was 18%. This rate will rise if prevalence falls – which might become problematic if, for instance, it means an entire class of children has to take time off school."

That implies that more people will start testing positive as the prevalence rate decreases, which isn't the case - the percentage of the positives identified which are false will increase, but the number of positive results won't increase (unless the number of tests increases). If the nation can cope with the number of classes off due to a positive test today then it can cope in the future. Simply re-testing those people will eliminate the vast majority of those false positives. False negatives are more of a problem because they will allow a carrier to continue spreading and keep the virus in circulation.

They should look at this page https://www.bbc.co.uk/news/world-56763490 where the risks are spelt out nicely.

I would hope that more than 20 years after the Sally Clarke case,  most doctors would be aware of Roy Meadows and the dangers of ignoring Bayesian statistical principles.

That's a good link, thanks.

Although from that it appears that while for 55 year olds getting jabbed is a no-brainer, it's not nearly as extreme for a 25 year old. For them, not getting vaccinated is approx double the risk of getting vaccinated. Since the risk is so small for 25 year olds anyway, from a purely selfish standpoint they have no real need to get vaccinated.

These articles always end up far too complicated as they have to tell a story and fill more than two lines. 
 

1/1000 false positives just means that you should always get at least one person testing positive in every thousand tests. Regardless of how many are actually positive. 

And that’s all that counts really. 

As soon as you start talking about probabilities you have to know how many positives and how many negatives you’re picking from. 
 

And it only works if it’s a truly random pick. 
 

The rate of false positives is always constant and so the number of false positives depends on the number of tests. 
 

Ultimately, the test is so the government can spot increases within the population, it’s not really so that people can be isolated. They don’t want kids then going for PCR tests because if you’re carrying out 40m LFTs a week you’d need to carry out tens of thousands of PCR tests just for the false positives.