If you get a blood test to diagnose a rare disease, and the test (which is very accurate) comes back positive, what's the chance you have the disease? Well if "rare" means only 1 in a thousand people have the disease, and "very accurate" means the test returns the correct result 99% of the time, the answer is ... just 9%. There's less than a 1 in 10 chance you actually have the disease (which is why doctor will likely have you tested a second time).
Now that result might seem surprising, but it makes sense if you apply Bayes Theorem. (A simple way to think of it is that in a population of 1000 people, 10 people will have a positive test result, plus the one who actually has the disease. One in eleven of the positive results, or 9%, actually detect a true disease.) The video below from Veritasium explains this Bayesian Trap quite elegantly:
That's all from us here at the blog this week. We'll be back with more on Monday. In the meantime, have a great weekend!