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Tuesday, September 30, 2003

Dubious use of statistics 


God I hate those anti-drug/anti-smoking commercials. A line from one that appears frequently: "One in three roadside drivers tested for drugs tested positive for marijuana." This is supposed to mean that marijuana is "more dangerous than you think", since it's the only other line in the commercial. It might or might not be, but the first statement doesn't have anything to do with the dangers of marijuana, even though the commercial tries to make the link.

So what does it mean that "one in three roadside drivers tested for drugs tested positive for marijuana"? It means that when a cop pulls someone over, the cop might give the driver a roadside drug test if the cop has reason to believe that the driver is under the influence of drugs at the time. For those drivers who are tested, a third tested positive for marijuana. More important is what this does not mean. It does not mean that a third of the people pulled over are on marijuana. It does not mean that a third of those in traffic accidents are on marijuana. And lastly, it does not mean that marijuana is the cause of a third of all traffic accidents.

In fact, the statement does not say anything at all about a causal relationship, or even a correlation, between smoking marijuana while driving and being involved in a traffic accident. If their intended message is that being under the influence of marijuana increases one's risk of getting into a traffic accident, then it is untrue and dishonest. If their intended message is that being under the influence of marijuana increases one's risk of being pulled over, then it is still untrue and dishonest. The statement does not say anything about one's odds of being pulled over if one were under the influence of marijuana, compared to those who are not. If their intended message is that marijuana is just as dangerous as other drugs, then it is still untrue and dishonest. Presumably, two-thirds of those tested either tested positive for other drugs, or did not test positive. That one-third number is useless in assessing the dangers of marijuana in causing a driver to be pulled over unless we also have statistics on the rate of use of marijuana as a proportion of all illegal drugs. If more than a third of incidents of drug use are with marijuana, then it is in fact less dangerous than other drugs, at least in terms of the dangers of being pulled over by a cop.

By following the statement "one in three roadside drivers tested for drugs tested positive for marijuana" with "it's more dangerous than you think", the commercial is trying to imply a causal relationship that does not exist. Their best hope might be that the audience it's aiming to convince are too doped up on drugs to realize the fallacy of the link. The rest of us become a little more skeptical of the drug war.
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