More on Statistical InjusticeA reader responds to my post below about false positives: “That's why you test each positive at least one more time - the odds for a double-false positive are extreme. … Of course universal testing generates false positives. The idea that one test alone is sufficient for punishment is ludicrous.”
Absolutely correct, though I’m often amazed at how often ludicrous laws get passed by legislatures and school boards. (I’m thinking specifically of the southern state that passed a law setting the value of pi at 3.14.) I wouldn’t be at all surprised to hear that school districts with across-the-board drug testing suspended athletes immediately upon their getting a positive test result. Does anyone out there know the standard practice?
Also, testing a second time shrinks the problem substantially, but does not eliminate it. By my calculations (and using Brad DeLong’s hypothetical numbers again), someone who gets two positive test results in a row still has an 8% chance of not having the disease. That’s about one person in every twelve. Also, my calculations are based on the assumption that the two tests’ results are independent events, which may not be the case – it might be that the false positive is triggered by the presence of a particular protein in your blood, for instance. (I’m not a doctor or a biologist, so I don’t want to make too strong a claim here, but it seems reasonable to think that false negatives and false positives are caused by something, and that something may be related to your physiology.) Fortunately, there may exist alternative tests for the same condition, as my reader observes elsewhere in his email, and such alternatives may be both more accurate and more likely to constitute an independent event.