[evan_au (OP)]

I heard someone say that a prototype coronavirus test gave the wrong answer 75% of the time.

Suppose I have a coronavirus test giving a binary answer: "Yes you have COVID-19", or "No, you don't have COVID-19".

If I present 100 samples, with 50% of samples containing virus, and 50% not having virus, then flipping a coin would get it right 50% of the time...

[chris]

This was the finding announced by UK Health Minister Matt Hancock at his Friday press conference. I believe what they are saying is that the sensitivity of the test for detecting a positive is profoundly weak and only picked up about 1 in every 4 cases that it should have done.

[Bored chemist]

If you have a test that always says "positive", and you test a population where only 25% are positive, then the test gets it wrong 75% of the time.

[alancalverd]

If a test is simple and quick enough, you can tolerate quite a high error rate. It depends on what you already know and what you are looking for.

Suppose someone reports having had Covid symptoms and recovered, and we have a 15-minute pinprick sample test for antibodies. If he scores 2 out of 3  positive, I would presume he now had immunity and was fit for work with potentially infective people. That's a pretty handy test.

[Petrochemicals]

I heard someone say that a prototype coronavirus test gave the wrong answer 75% of the time.

Suppose I have a coronavirus test giving a binary answer: "Yes you have COVID-19", or "No, you don't have COVID-19".

If I present 100 samples, with 50% of samples containing virus, and 50% not having virus, then flipping a coin would get it right 50% of the time...

By testing a  group of people and finding that they all have corona, mathmatically, if there where 100 people and only 25 had it, 75 percent are incorrect. You would have to wonder at the people testing, a 100 percent strike rate is questionable.

[chris]

If a test is simple and quick enough, you can tolerate quite a high error rate. It depends on what you already know and what you are looking for.

Suppose someone reports having had Covid symptoms and recovered, and we have a 15-minute pinprick sample test for antibodies. If he scores 2 out of 3  positive, I would presume he now had immunity and was fit for work with potentially infective people. That's a pretty handy test.

With certain assays that have a low margin for error, such as hepatitis B or HIV, we use a series of assays that look for separate targets in different ways, the rationale being that a single test might get a result wrong from time to time, but the likelihood of a series of tests all falling down at the same time is very low.

[Edwina Lee]

covid-19 usually infect the lining of the throat first, so testing a proper throat swap would detect the virus pending on the sensitivity of the test.
What if a whiff of viruses went straight into the lungs through deep breathing?  Then the virus is difficult to detect early on, and these are usually diagnosed through a CT scan (3D sectional photos of the lungs).
The precence of the virus in blood is a clear indicator of infection, but the blood does not get infected early on.
The virus may also be present in the faeces.
Even asymtomatic patients can transmit the virus.
So basically, no single simple test can reliably detect an infection early on to ascertain who is not infected.

Therefore, social distancing needs to be maintained to avoid infection.

[Edwina Lee]

A system analysis habit is to define what the question is accurately.
I think the question should be about 75% reliability. If one is asking the test to tell whether someone is covid-19 infected at one point in time, then the test returns a +ve answer for 75% of the time for infected cases, and no +ve for uninfected cases, then it is 75% reliable.  This made me realise just how complicated the question is.   

[Edwina Lee]

Here is my more complete understanding about covid-19 testing:-
The virus can be found in different places in the body without showing up in tests.
Usually, the virus infects the upper tract such as throat lining, nose lining etc.  This is usually mild infection and most patients recover without ever knowing they had been infected.  A swap test would show positive.  A blood test would show negative. A chest x-ray would show negative.  If a swap test shows +ve, and the virus has been conquered by the patient's immunity, this  coud be interpreted as false +ve. However, if patient swallows into the trachea, the lungs then get infected. Older people often  swallow wrongly into the trachea leading naturally to higher serious infections.
If a patient was infected directly by deep breathing, the lungs can get infected without upper tract infection showing up. This is the most asymptomless and most infectious scenario.
So, testing needs to be done very rigorously and repeatedly at intervals to get accurate results, as China eventually learnt to do.

[Colin2B]

Here is my more complete understanding about covid-19 testing:-
..............

Very interesting. Do you have any references for this?