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Critical Thinking & COVID-19 VI: Testing

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Every year I go through a section in Moore and Parker’s classic Critical Thinking book on medical testing. Until now, it has been a fairly abstract thing for my students, but now medical testing is a critical part of responding rationally to the pandemic. One type of test is to determine whether a person is infected. Another is to determine whether a person had the infection. While these tests are a critical source of information it is important to be aware of the limitations of testing. Since I am not a medical expert, I will not comment on the accuracy of specific methods of testing. Instead, I will look at applying critical thinking to testing. An ideal medical test would always be accurate and never yield a false positive. Real medical tests have, for various reasons, less than 100% accuracy in the field and a good test will fall into the 90-99% range. This means that a test can falsely show that a person is or was infected or falsely show they are or were not infected. So how do you judge whether a person is infected or was infected based on a test result? Intuitively, the chance a person was infected (or not) would seem to be the same as the accuracy of the test. For example, if a COVID-19 test has an accuracy of 90%, then the seemingly rational inference would be that if you test negative, then there is a 90% chance you did not have COVID. Or, if you test positive. There is a 90% chance you had COVID. While this seems sensible, it is not accurate and involves a confusion about conditional probabilities.  I will keep the math to a minimum because math, as Barbie said, is hard. So, suppose that I test positive for having COVID and the test is 90% accurate. If I think there is a 90% chance, I had COVID, I am probably wrong and here is why. The mistake I would be making is failing to recognize that the probability that X given Y is distinct from the probability of Y given X. In the case of the test for COVID, testing positive is the effect of COVID and obviously. . .

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News source: A Philosopher's Blog

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