28 May 2010
David Brooks has a column in today's New York Times about our difficulties assessing risk, in light of the oil leak in the Gulf of Mexico. One tendency he highlights is our excessive faith in devices aimed at minimizing risk. Although his general point is probably correct, I think he makes a statistical error in the example he uses to illustrate this tendency. Brooks seems to confuse numbers with rates.
He writes: "More pedestrians die in crosswalks than when jay-walking. That's because they have a false sense of security in crosswalks and are less likely to look both ways." I think that more pedestrians die in crosswalks than when jaywalking because more pedestrians cross the street in crosswalks than anywhere else. If the rate of dying is higher for pedestrians in crosswalks than when jaywalking, we might attribute the difference to our overconfidence in safety devices. However, the rate of dying need not be higher in crosswalks than elsewhere for more pedestrians to die in crosswalks. As long as many more people cross in crosswalks, it is likely that more will die in crosswalks. Brooks' point about risk assessment would have been stronger if he had considered not only the numerator (the number of deaths) but also the denominator (the number of people at risk of death) of the rate of pedestrian deaths that he's interested in.