# Damned lies and Statistics

Mark Twain thought that “there are three kinds of lies: lies, damned lies, and statistics.” The point is that a statistic can be true, but totally misleading. For example, an article today shows how you can demonstrate that smoking is correlated with good health. Short version: More young people smoke than older people, and younger people tend to be healthy. A tobacco company executive can point to this data and claim that smoking in fact is good for health. The fact that a third omitted variable (youth), that was responsible for both was omitted is called an Endogeneity problem. One of my favorite examples of this is the fact that more people get their car stolen while eating ice cream, both correlated with an omitted variable (summertime). More generally, this is part of  Simpson’s Paradox, in which a “a trend that appears in different groups of data disappears when these groups are combined, and the reverse trend appears for the aggregate data.” For example, a University can admit a higher percentage of female applicants than male applicants into an engineering department, and a higher percentage of female applicants than male applicants into the English department, and still end up admitting a larger percentage of male applicants overall, if the English department is more selective in general and a larger number of women apply for that field. So maybe this is why we hate political spin so much: anything can sound good if you get to pick the standard of measurement: “we came in second, they came in second-to-last!” [in a race between two cars].