The base rate fallacy
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As testing for Covid-19 immunity becomes widely available, it's important to understand the "Base Rate Fallacy" that leads people who test positive to reach false conclusions about the true probability that they are actually immune. Let's assume that 10% of the population is immune. Epidemiologists refer to this as the population's "base rate" of immunity. If the base rate is 10%, there's a 10% chance that a randomly-selected individual is immune. Now test that individual for immunity with a test known from clinical trials to result in 5% false positives. this means that 5% of the time, individuals testing immune actually are not. Let's also assume that the test doesn't result in any false negatives, meaning that everyone who is immune will test immune. When we use this test on our randomly selected individual and she tests positive (immune), what is now the probability that she really is immune? The answer is that a positive test changes