"False positives are a problem. Many pinned their hopes on antibody tests, which purportedly show whether someone has been infected by the coronavirus. One such test claims to correctly identify people with those antibodies 93.8 percent of the time. By contrast, it identifies phantom antibodies in 4.4 percent of people who don’t have them. That false-positive rate sounds acceptably low. It’s not.
Let’s assume 5 percent of the U.S. has been infected so far. Among 1,000 people, the test would correctly identify antibodies in 47 of the 50 people who had them. But it would also wrongly spot antibodies in 42 of the 950 people without them. The number of true positives and false positives would be almost equal. In this scenario, if you were told you had coronavirus antibodies, your odds of actually having them would be little better than a coin toss."