Let's do some maths...

... or for my US readers, some math.
This post is triggered by today's news that an at-home H.I.V. test has won F.D.A approval for sale in the USA. The article referred to gives these figures:

• The home test is accurate 99.98% of the time for people who do not have the virus.


• The test is accurate 92% of the time in detecting people who do.


• About 20% of the 1.2 million infected Americans do not know they have the disease.

The population of the USA is currently 311,591,917 (a figure with spurious accuracy) and we end up with the conclusion that there are just over 310 million people in the US who are not infected.

This is where it starts to get interesting. If everybody in the US took this test, except the people who already knew they were infected, then in round figures:

• 238,000 people would correctly be diagnosed as infected with H.I.V.


• 20,000 people would incorrectly be given the all clear.


• Around 310 million people would correctly be given the all clear, but


• 62,000 people or thereabouts (0.02% of the 310,600,000 who are in fact uninfected) would get a positive result.

So, comparing the first and the last figures, if there were a mass screening programme then 20% of the people with a positive result would not in fact be infected.

The other statistic today is that the people at CERN are sure to a 5σ level that they have found the Higgs Boson According to Professor Brian Cox, it roughly means that you're 99.9999% sure. And it seems that Peter Higgs is there in person. He says "I never expected this to happen in my lifetime and shall be asking my family to put some champagne in the fridge."

But in contrast to the H.I.V. test, the people at CERN have stopped short of claiming official discovery of the Higgs boson.