If you have a positive COVID test, how likely is it that you actually have COVID?

[Disclaimer: this post provides the math behind how to answer this question without actually answering the question]

If you get a positive test for COVID-19, how likely are you to have the disease? Well, this depends on a number of factors including the baseline prevalence of COVID-19 in your area as well as the test accuracy (i.e., sensitivity and specificity). Oftentimes, highly accurate tests may not be a good predictor if you have the disease if the prevalence is very low (which unfortunately is not the case currently for COVID-19).

So a key question is, if I get a COVID-19 positive test result, how likely am I to have the disease. A video from 3 Blue 1 Brown helps explain the math behind this in an intuitive way, explaining Bayes Factor and differences in these calculations when probabilities compared to odds are used.

The video is a great refresher on Bayesian statistics and their relevance for medical testing.

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