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The large number of false positives is not due to a prior probability, but due to the number of people tested and the inaccuracy of the test.
by jsprogrammer 10y ago
The large number of false positives is not due to a prior probability, but due to the number of people tested and the inaccuracy of the test.
- JshWright 10y agoThat's not true at all. If the actual incidence is low, then the false positive rate will be higher (not the overall positive rate, the _false_ positive rate).
- jsprogrammer 10y agoHow is it not true? Prior probability has nothing to do with the false positive rate. False positive rate is a function of the inaccuracy of the test.
- JshWright 10y agoDr Carroll's Healthcare Triage series has been linked elsewhere in the thread, but there are a couple videos that are relevant to this discussion (namely, how Bayes' theorem applies to medical testing, and why the prevalence in the population matters (or, more accurately, the probability that the patient has the disease/drug in the first place, which is heavily influenced by the prevalence)) https://www.youtube.com/watch?v=UF1T7KzRnrs https://www.youtube.com/watch?v=UF1T7KzRnrs https://www.youtube.com/watch?v=Ql2jEJ-6e-Y https://www.youtube.com/watch?v=Ql2jEJ-6e-Y
- jsprogrammer 10y agoI am familiar with Bayes' theorem. It just doesn't apply in this situation. False positives are a function of the testing method, not a prior probability. If you wanted to know how likely your positive result is to be true, you would use the theorem.
- deleted 10y ago[deleted]
- traek 10y agoThe probability of a false positive result = probability of not doing meth * probability of getting a positive test result while not doing meth. P(+ ∩ M') = P(M') * P(+|M'). That pretty clearly depends on the prior probability, P(M).
- jsprogrammer 10y agoYou are calculating the probability for a randomly selected individual of the test to have been given a false positive result. That is different from the test's false positive rate, which is just P(+|M') [Where I assume M' represents that the subject had not used meth.] It doesn't matter what the prior probability is of a random person having used meth (or whatever you are testing for); it only matters how likely it is that someone who has not used meth will be given a positive result.
- M_Mouse 10y agoSay you have a test that determines, with some non-perfect level of accuracy, if a person is or has been president of the USA. If that test is performed only on women, the false positive rate will be 100% regardless of accuracy. All positive results would be false positives. If the test is preformed on any man leaving or entering the oval office, then the false positive rate will likely be significantly less then 100%, as there will be a president tested multiple times in that group, and when we test positive on him, it's not a false positive. If we test the population at large, most positive results are going to be false positives, simply because we're unlikely to actually have a former president get tested. But in theory the false positive rate could be slightly less then 100% if we got lucky. As the probability of an actual occurrence in the test group drops to zero, the rate of false positives approaches 100%, regardless of the accuracy of the testing method.
- jsprogrammer 10y agoI think we are talking about slightly different meanings of false positive rate. I think you might be talking about the rate relative to all positive trials. I think I am talking about the rate relative to all trials that don't meet the conditions of the test. So, you survey 100 women and your test tells me that 10 of them have been president, I say that your test has an observed false positive rate of 10%.