Testing errors go the opposite of what you’re thinking.

Stephanie Caccomo, a spokesperson for the FDA, says the positive predictive value, or likelihood a positive test result correctly reflects that a patient has  COVID-19, depends on how widespread the disease is—and that situation is changing quickly. “Based on what is known about the pathophysiology of COVID-19, the data provided and our previous experience with respiratory pathogen tests, the false-positive rate for authorized tests is likely to be very low, and the true-positive rate is likely to be high,” Caccomo says. “However, performance characteristics are specific to each test.” And there is a risk of a false-negative result if the sample is not taken correctly, says Vincent Racaniello, a professor of microbiology and immunology at Columbia University. This possibility could explain why people recovering from the disease sometimes test negative initially and then positive later, he says.

Scientific American

Here’s How Coronavirus Tests Work—and Who Offers Them

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https://www.scientificamerican.com/article/heres-how-coronavirus-tests-work-and-who-offers-them/