I would like to talk about antibody tests. There are too many people in my bubble who don't understand why a specificity of say 95% doesn't mean 95% of people get the correct result.

So, statistics rant:

In addition to

Specificity (aka one minus percentage of false positives)

and

Sensitivity (aka one minus false negatives)

There is actually one more number that determines how reliable a test is: How likely you are to have the thing you're testing for.

Let's say you test a person that you know nothing else about for Covid-19 antibodies and the test has a 95% specificity and a 99% sensitivity. If 30% of the population actually have covid antibodies the person has a 11% chance of a false positive.

If 10% of the population have covid antibodies, your chance of a false positive is 33%.

If 5% of the population have covid antibodies, your chance of a false positive is 51%.

If 2% of the population have covid antibodies, your chance of a false positive is 73%.

If 1% of the population have covid antibodies, your chance of a false positive is 85%.

Let's talk about a reasonable assumption for prevalence in the population. In Germany we have about 140k confirmed covid cases (confirmed by PCR tests while active). Germany has a population of 83M, so 0.15% of the population have definitely had Corona.

For this, 1.73M tests were conducted, so 8% came back positive. What is a reasonably assumption for actual number of infections? If the people who were tested had been drawn by random from the German population 8% of German people are infected. That's the upper bound.

Testing of course wasn't random. So the lower bound is 0.15% and the upper bound is 8%. I'd assume 1-1.5% is a reasonable assumption for the actual prevalence. This leaves you with many more false positive than correct positive results.

I'm not saying antibody testing is useless. Even with low specificity compared to prevalence it's a useful research tool for doing population statistics. It just shouldn't be relied upon for individual behavior modification.

I also assume tests will get better in due time. AFAIK currently they range from 0.9-0.95 in specificity.

BTW, If you want to Google the maths behind this your search term is Bayes Theorem.