eli5: how does the probability of something being wrong (e.g., a false negative on an at-home/rapid antigen test) change when you do the same test multiple times?

Question

if there is a 98% chance the results will be correct (making it ~1/50 times it will be incorrect), would taking the test twice make the chance of it being incorrect ~1/100? then after three times ~1/200? or would it not change at all and still be 1/50?

In: 0

Answer 1

As others have mentioned, this is not really how error works, especially in medical tests. Not every false result is the same, indeed in medical testing we prefer to have false positives instead of false negatives. Why? Well imagine being the person that didn’t have cancer but went through chemo, and compare that to the person that DOES have cancer but doesn’t get treatment; I’d take the unnecessary chemo every time. So, medical tests are designed to, as much as is physically possible, have no false negatives and only false positives. This is why step 1 is always to repeat the test, to help rule out a false positive. For more information about error in testing, check out the Veritasium video on [Bayes’ theorem](https://youtu.be/R13BD8qKeTg)