Medical testing

How worried should you be if a medical test comes back positive? No medical test is completely accurate, and so there is always the chance of what we call a false positive, where the test returns a positive result yet you don’t actually have the disease or condition. This week we caught up with Colin Aitken, Professor of Forensic Statistics at the University of Edinburgh, who explained to us that it’s much more likely than you might think that you’ll receive a false positive result.

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Consider a test for a disease that affects 1 in every 100 people. If you have the disease, it returns a positive result 99% of the time, while if you don’t have the disease it returns a negative result 95% of the time. The probability of a false positive result is just 1%, so you might think that the probability of you having the disease if you test positive is 99%. Actually, this isn’t the case – this is another example of what we call the prosecutor’s fallacy; the probability that you have the disease given that you tested positive is not the same as the probability that you’ll test positive given that you have the disease. The chance that you have the disease if you test positive is actually only 1 in 6, or around 17%. Colin will explain why in Week 4 of the course!

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