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

Depends on the real cause of false negative

Is it a problem where X% of the time the solution/tester is just bad and won’t come up positive? If so then multiple tests may be more accurate

Is it a problem where you’re on the edge of its detection window? If so then multiple tests may be more accurate

Or is it a problem where you’re below the level it can detect at all?

If your test is 100% sensitive to results 1,000 or higher, 50% sensitive to 800 or higher, and 0% sensitive to 400 and lower then if you’re at 300 taking multiple tests won’t do the trick, but if the ultra fancy gold standard test is sensitive down to 5 then during the clinical testing of the test kit it would have been reported as a person who had the sickness but didn’t test positive on the tester.

It all depends on the cause of the false negative and its impossible to know if it really is a false negative without going through the ultra sensitive test which accurately answers the question anyway