TITLE: When we say that test has 25% false negatives, do we mean P(~e|H)=0.25 or P(H|~e)=0.25?
QUESTION [1 upvotes]: P(H) means probability of hypothesis H, namely probability of picking a sick person out of the pool of people who took the test. P(~e) means probability of negative result of a test for sickness. In other words, it's probability that the test will say that randomly picked person is healthy.
Here P(~e|H) would mean probability of picking a person with negative test result from the pool of sick people. As for P(H|~e), it would mean probability of picking a sick person out of pool of people with negative test result.
It makes me wonder, what exactly do we mean when we talk about false negatives? Do we mean P(~e|H) or P(H|~e)? And why?

REPLY [2 votes]: $P(\lnot e|H)$ is the false negative probability - here, it is the probability that you test as not sick when you are actually sick. The test has incorrectly given the negative result.
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