After a rocky rollout, higher-quality coronavirus antibody tests have emerged that, among other uses, are beginning to give a clearer picture of the pathogen’s spread.

But for people who are simply curious about whether they’ve unknowingly been infected, some doctors and public-health authorities are still hesitant to recommend antibody tests. The reliability of these tests for any one person, they say, comes down to a matter of probability: As with most other medical tests, that depends not only on a test’s quality but also…

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