As I mentioned earlier, I’m teaching a first-year seminar this
semester called “Science or Nonsense?” On Monday and Wednesday
this week we discussed some math/stats/numeracy topics. We
talked about the Sally Clark murder trial, the prosecutor’s
fallacy, the use of DNA testing in law enforcement, Simpson’s
paradox, the danger of false positives, and the 2009 mammogram
screening recommendations. I made a GeoGebra applet to
illustrate the dangers of false positives. So I thought I’d
share that here. Here’s the statement of the problem. Suppose
Lenny Oiler visits his doctor for a routine checkup. The doctor
says that he must test all patients (regardless of whether they
have symptoms) for rare disease called analysisitis. (This
horrible illness can lead to severe pain in a patient’s
epsylawns and del-tahs. It should not to be confused with
analysis situs.) The doctor says that the test is 99% effective
when given to people who are ill (the probability the test will
come back positive) and it is 95% effective when