If you took an antibody test that was 90 percent accurate, and it determined that you had coronavirus antibodies, how confident should you be that you actually have those antibodies?

Most people say about 90 percent, with the average answer being above 50 percent. This makes sense. After all, 90 percent accuracy is pretty high.

But the predictive value of an antibody test with 90 percent accuracy is 32 percent if the base rate of infection in the population is 5 percent. Put another way, there is an almost 70 percent probability in that case that the test will falsely indicate a person has antibodies.

The reason for this is a simple matter of statistics. The lower prevalence there is of a trait in a studied population — here, coronavirus infection — the more likely that a test will return a false positive.