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 ffspring.
Parents' IQs may indeed play a role here, but I suspect that money really is a key variable. Wealthier families can afford to send their children to better schools and more expensive SAT preparation courses. Wealthier parents are also more likely to have attended college, and thus more likely to encourage their kids to get into a good schools. Poorer kids tend to receive less academic encouragement, and thus may devote less time to schoolwork.
The point is that there are many possible explanations for this trend; Mankiw probably picked the one that's most ideologically appealing to him. But he's essentially falling into the same trap that he's cautioning others to avoid.
Update: I think what Mankiw should have said is: "There are many alternative explanations for this data. Correlation doesn't imply causation. I suspect that biology may be one key variable that people on the left are less willing to acknowledge. The appropriate way to measure this data is to statistically control for certain genetic factors like IQ, rather than assume that biology is unimportant."