Friday, August 28, 2009

The Least Surprising Correlation of All Time

The NY Times Economix blog offers us the above graph, showing that kids from higher income families get higher average SAT scores.

Of course! But so what? This fact tells us nothing about the causal impact of income on test scores. (Economix does not advance a causal interpretation, but nor does it warn readers against it.)

This graph is a good example of omitted variable bias, a statistical issue discussed in Chapter 2 of my favorite textbook. The key omitted variable here is parents' IQ. Smart parents make more money and pass those good genes on to their offspring.

Suppose we were to graph average SAT scores by the number of bathrooms a student has in his or her family home. That curve would also likely slope upward. (After all, people with more money buy larger homes with more bathrooms.) But it would be a mistake to conclude that installing an extra toilet raises yours kids' SAT scores.

It would be interesting to see the above graph reproduced for adopted children only. I bet that the curve would be a lot flatter.