Statistics for Cyclists
December 28, 2010
Here is a simple statistics problem that could cause a cyclist a lot of grief. Lets say that we know that 1 out of 1000 cyclists are doping with Chemical X (for you cartoon fans out there…this is a Power Puff Girls reference). Now, lets assume that we have a test to detect Chemical X that is 95% accurate. This means that it will produce 5% false positives (meaning that a tested cyclist that has not taken the drug will get a positive test result 5% of the time on average).
So now the question is….if we randomly test our sample of cyclists and one has a positive test results what is the probability that he actually took the drug?? Most will answer that there is a 95% chance that he is a cheater….because the test is 95% accurate…this seems reasonable but is completely wrong!
The correct answer is that we must take the ratio of know cheaters to the true and false positive test results. ie .. there will be 1 true cheater for every 51 positive test results. Therefore the true probability is 1/51……about 2% that he is a cheater give one positive test.
This is a scary thought for a young cyclist that is constantly being tested for Chemical X because even the insinuation that he is a doper can end his career. A positive test will destroy his character….but there is only a 2% chance that he is the real cheater!!!
