“The Cross Section Illusion”, 2014-06-07 (; similar):
If you are concerned with American obesity rates and turn to the cross sectional data to try and figure out what is going on, it is easy to reach a flawed conclusion. The correlation between education and obesity, for example, seems quite clear. The poorer and less educated an American is, the more likely he or she is to be obese. Looking at this data it seems reasonable to suggest that something about poverty is making people more obese—perhaps cruddy processed food is the only thing America’s poor and less educated can afford to buy, or maybe the poor live in urban areas where people do not exercise. These hypotheses are plausible… until you look at the time series. It then becomes apparent that the rich and educated are gaining weight at the same rate as the poor. Poverty cannot explain this.
It is very difficult to make meaningful claims about causation—or even correlation!—on the basis of cross section data alone. Often times seemingly perfect, statistically-significant correlations disappear when the same variables are viewed over a longer stretch of time. In other cases—as in this one—time series data reveals that the real story isn’t about variance between two groups at all, but about the rate at which each group is changing. It is all too easy to be fooled by the Cross Section Illusion.
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