The meaning of zero

Dan Wetzel, writing for Yahoo! Sports, noted that no doping cases has been reported at the just-concluded Winter Olympics.  He said:

WINNERS: The athletes

Not one doping disqualification at the Games. Enough said.

If he has read Chapter 4 of Numbers Rule Your World, he will realize that zero does not mean zero. No doping disqualification is not the same as no dopers. Doping tests are not 100% accurate. Negative findings don't mean a whole lot. There is such a thing as false negatives.

Comments

[Tom]

Good observation. Some web searching reveals that there were about 2600 athletes participating in the games, and 30 were banned for failing drug tests the day before the opening ceremonies. During the games, about 2500 drug tests were administered. So no disqualifications during the games.

As I'm sure Chapter 4 discusses, I have to wonder what the the false negative rate is. Not knowing anything about the tests used, I have learned that urine tests used for most drug screening have a false negative rate of 60% to 70% (the few studies I found reported Sensitivities of 30% to 40%: P(- | Drugs) = 1 - P(+ | Drugs)). In other sectors (e.g. workplace drug screening), a negative screening result is accepted as indicative of no drug consumption, so no further testing is done. If we knew more about the testing and doping patterns for Olympic athletes, then given the test Sensitivity and number of athletes who tested positive we might be able to calculate how many athletes were doping but not caught. My guess is that there could be as many as 30 more athletes who were doping but not caught.

[Kaiser]

Tom: Your comments are right on. While the media loves to talk about false positives, they miss the real story of doping tests, which are the false negatives. Even if we count the 30 which did not officially happen during the games, the positive rate was less than 1%. Such a low positive rate means very few false positives, which, as I explain in Chapter 4, means quite a few false negatives.
I also discuss whether test labs are more afraid of the false positive error or the false negative.