FAQs on the exercise Conditional Probability Continued
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In the strep throat exercise I don’t understand how we come to the percent probabilities of event 2. Can anyone who understands this explain it to me. I understand event 1 - 20% of people have ST. I’m assuming event 2 is a dependent event because event 1 determines whether a person does or does not have ST. But otherwise I just can’t make it work. Would really appreciate some help. Thanks!
I recognize that this is an old topic and question but thought I would put this out here in case anyone else has a similar question.
In clinical testing, such as COVID tests, HIV, blood sample tests, etc. There is something call the sensitivity and specificity of tests. These tests are dependent tests because how well they work really depends on if the patient has the disease.
Sensitivity measures a given test’s ability to actually flag patients with the disease as positive. A highly sensitive test means that there are few false negative results, and thus fewer cases of disease are missed.
Specificity measures a given test’s ability to accurately screen out healthy patients as having negative results. A highly specific test means that there are a few false negative results.
The two measures often goes hand in hand and a good test has high sensitivity and high specificity. For example, a test that always test positive would be in theory perfectly sensitive, because it will catch all patients with a disease. But this test would also be zero when it comes to specificity, as it would have no ability to screen out negative patients.
In the given exercise, the event B is essentially talking about these measures. The strep throat test is 85% sensitive, because if someone has the disease it’s able to flag them 85% of the time. It performs better with its specificity, because it is able to identify true negative patients 98% of the time. The probability is dependent because it depends on whether the individual has the disease and performs differently based on that, hence why you see different values in branch 2.