But as has become clear this is a very complicated subject
Indeed it is. Most folks don't understand how the mathematics of population screening actually works. Even when the chances of a test giving a false positive result are extremely small, most folks who are tested and receive a positive result won't actually have the disease.
So, let me present JR's Covid testing guide for dummies:
If you are symptomless, have a random Covid test, and the test gives a positive result, then:
1) It's more likely than not that you
don't have Covid (so don't overworry),
but
2) It's absolutely vital that you self isolate for the prescribed period. Assuming an infection rate of 100 per 100,000 people (about right for where I live at the time of writing), your chances of having Covid after a positive result have just gone up from about 1 in a thousand to about 1 in 3.
In statistical terms, testing updates the prior probability of your having the disease, so its predictive value for a specific result depends both on the accuracy of the test, and the prior probability of the person being tested (essentially the prevalence of Covid in the sample of the population you are testing).
All this only applies to testing if you are asymptomatic. If you have another reason to suspect you may have Covid before taking the test (like having one or more symptoms), then the likelihood of your having Covid if you get a positive result increases dramatically.
I wonder how much the politicians actually understand?
However, the scientists who are advising them will know all this. I feel sorry for the scientists who have to explain the theory to the political leaders; it will likely be a nightmare to get the politicians to understand what is obvious to them.