>>11633306

>Accuracy in general just describes the proportion of true test results among all evaluated cases.

exactly. out of all tests, whether the test came back positive or negative, 95% of them were correct. The test can be true even if the result is negative.

Theres actually a wikipedia page for this exact problem, and below I will basically be rewording the examples they give on the wikipedia page

https://en.wikipedia.org/wiki/False_positive_paradox

Assume there are no false negatives, which we have to do because one "accuracy" figure is not enough to completely describe the problem, and in general, in the real world, tests for diseases aim for 0 false negatives. Then suppose that the infection rate is 80%. In a population of 100 people, we would expect 80 true positives, 15 true negatives, and 5 false positives. 80 + 15 true tests / 100 gives us the 95% accuracy figure. Then, 80 / 85 = 94% is the probability that you are infected if you test positive.

Now assume the infection rate is 2%. That means that out of 100 people with a 95% accurate test, 2 is a true positive, 93 are true negatives, and the last 5 are false positives. Now the probability that you are infected if you test positive is a mere 2/6 = 33%

If we assume false negatives is nonzero, then the chance that you are infected if you test positive goes down. E.g. in the second case, if we make 1 true positive into a false negative, that means that now we have 1 false negative, 1 true positive, 94 true negatives and 4 false positives. Now the chance that you are infected if you test positive is 1/4 = 25%.