I believe you read the | as "Therefore" (possibly going for ⊢ ?), as in "The probability that someone who scored highly on this test is also suicidal is .93" They want to know that the probability that someone who is suicidal scores highly on the test. The test could be good at identifying suicidal thoughts in only a small portion of the population, since they have demonstrated a good false-positive rate (i.e. 93% of subjects that it identifies as suicidal are); but not good at identifying which members of a population are suicidal - that is, if given to all of a population, only find some small percentage of people with suicidal thoughts.
Read the pipe as "given" (or "when"). P(A|B) = "probability of A given B".
You've got people who are actually suicidal. You've got people for whom the test comes back positive. There are two subtly yet crucially different metrics. The paper reports the answer to: if someone is positive, will the test come back positive? The flipside is very important for customers of the test: if the test comes back positive, does that mean I am suicidal?
P(+|suicidal) = the probability that the test comes back positive given the patient is actually suicidal = 0.93
P(suicidal|+) = the probability that the patient is suicidal, given that the test came back positive.
As a degenerate case, imagine Nat's Suicidal Tendency Detector.
10 PRINT "SUICIDAL"
It will correctly detect every single suicidal patient put in front of it. P(+|suicidal) = 1. IT'S A MIRACLE BREAKTHROUGH!
That test's critical failure is P(suicidal|+) ... it's identical to the rate in the population. As you could have guessed by reading the source code, taking the test doesn't give you any more information about the patient's suicidal tendencies.
Whew. Hope that was coherent! Google "conditional probability" if you want the math of how to work with these.
