A test for coronavirus presents a rate of 2% false positives  (the test returns positive despite the person not being infected with coronavirus). The Office for National Statistics (ONS) has data on the number of coronavirus cases within private households, excluding hospitals and care homes. This measure is known as the community population and it is a better estimate of the levels of coronavirus among the people that you are most likely to come into contact with. The estimate given is between 0.02% and 0.12% of the community population with 0.06% being the average . We are going to use 0.1%, in other words, 1/1000 of the community population has coronavirus.
My question is: If people are tested at random, and a person tests positive, what is the probability of that person actually having the coronavirus?
Consider that out of 1000 people that are administered the test, one will expected to be infected with coronavirus. Out of the remaining 999 healthy people, the test will identify about 20 with coronavirus (it is 98% accurate). To get our final answer, we divide the number of infected (1) by the number of true and false positives (21). That is just under a 5% chance of having coronavirus despite having tested positive. Putting it another way, you have more than a 95% chance of not having coronavirus even if you test positive.
Inspiration: Fooled by Randomness: The Hidden Role of Chance in Life and in the Markets by Nassim Nicholas Taleb
I didn’t know the false positive rate for the test was that high. It does raise the question of how much value for money there is in contact tracing. If many of the individuals who supposedly have Covid-19 do not have it, how much of the money invested in contact tracing is actually being used effectively?
On a broader note, I think the pandemic has raised serious problems about the effectiveness of political systems in dealing with certain types of complex issues. It will be interesting to see if political systems adapt to deal with these types of issues in a better manner.
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