5.7 Example: doping (revisited)

Recall the example of detecting doping athletes from Section 3.19.

The test returns positive for 95 out of every 100 doping athletes (0.95 sensitivity). The test returns negative for 95 out of every 100 non-doping athletes (0.95 specificity). It was speculated that 2 out of every 100 athletes are doping (0.02 base rate). We used these numbers to work out the probability of an athlete doping given that they tested positive as around 0.28.

A related question is this: How much more likely are we to see a positive test result when the athlete is doping compared to when the athlete is not doping? This question is important as it tells us how informative a positive test result is. This is the type of question that an LR is used to address.

First break down the question down into competing propositions and the available evidence.

Competing propositions:

• \(H_p\): the athlete is doping,
• \(H_d\): the athlete is not doping.

Evidence:

• \(E\): a positive test result.