The second row was less obvious - maybe if it fits on the page, add a single line of explanation showing how the principle in the first example applies to the actual numbers?

How about this - just a simple tweak:

Great visual representation. I know you posted links, but can you tell me what figures exactly did you use to get the 93.5% specitivity?

Here is a screenshot of my Excel calculator, with explanatory notes:

It duplicates the BMJ calculator but allows percentages. The 'helper' at the side allows for total cases and tests. From this and the three inputs in the coloured boxes, it determines what the specificity needs to be to match.

Of course, the BMJ PCR calculator is right not to allow percentages - because these tests are unsuitable for such low figures. This is the main argument against these PissyArgh tests.

I like the idea but worry it might be reasonably questioned thus. As the actual prevalence gets higher the ratio of false positives drops dramatically. Say 10% of those tested actually have the lurgy and there is a 1% error rate then the false positives drop to 9%. 11 cases of which 10 are correct. And anecdotally at least to my knowledge members of the public can only get tested if they have symptoms. I just don't know how much of the testing being done is random. It's probable that declining lab standards mean the accuracy of tests has fallen but do we have evidence. I think we need to be as scrupulously honest as possible (unlike SAGE). It's possible that there is an actual second ripple going on.

I like the idea but worry it might be reasonably questioned thus. As the actual prevalence gets higher the ratio of false positives drops dramatically. Say 10% of those tested actually have the lurgy and there is a 1% error rate then the false positives drop to 9%. 11 cases of which 10 are correct. And anecdotally at least to my knowledge members of the public can only get tested if they have symptoms. I just don't know how much of the testing being done is random. It's probable that declining lab standards mean the accuracy of tests has fallen but do we have evidence. I think we need to be as scrupulously honest as possible (unlike SAGE). It's possible that there is an actual second ripple going on.

If the true prevalence is high, this test does become more accurate. That is the way it is. And the more testing there is, the more the tests will be representative of the general public. There have been a total of nearly 30 million tests so far.

A 1% error rate could be achievable. It was demonstrably the case in July/August. But the actual error rate is not known directly and estimates are not published. However, ONS make a fresh estimate every week of the actual level of infection in the general public. I have asked a couple of times how they do this but I have never received a reply. Given an actual prevalence and the measured prevalence, we can arrive at a current specificity of 95.3%, or an error of 4.7%. This is all we have to go on at the moment.

And anecdotally at least to my knowledge members of the public can only get tested if they have symptoms.

That's the theory, but in practice a lot of people without symptoms must be getting tested.

I know of about a dozen people who have had tests, only two of whom had symptoms. The rest needed to test negative in order to get back to work/school, either after returning from abroad or because they were in contact with someone with symptoms who had a test.

But even in the Spring, when testing was limited to ill people in hospital, only 25% of symptomatic people were testing positive for covid. The symptoms are non-specific so the even the majority of people with "covid" symptoms do not have covid.