How to lie With Statistics

First a very simple but important point about statistics. Statistics cannot be used to establish causation, they can only show correlations. As an example, the governor of a certain state is concerned about the test scores of high school students in the state. One of his aides brings up an interesting statistic: there is a very strong link between student test scores and the taxes paid by the parents of the student. The parents of high scoring students pay more taxes. The aide’s suggestion for increasing student test scores is unusual; sharply increase tax rates. Surely student test scores will follow! The fallacy, of course, is that even though there is a correlation between test scores and parents taxes, there is likely no causal connection. A better explanation is that there is some hidden variable that explains the correlation. In this case the obvious choice is the income of the parents. This determines the taxes paid. And since the quality of high school that a student attends is to a large extent determined by the parent’s income, we see a causal link from parent’s income to both taxes and test scores.