To make his point that socioeconomic status is a major driver of educational outcomes, Dan Pink made the following chart. SAT scores are on the vertical axis, and family incomes on the horizontal axis.

Sidestepping questions of what this correlation actually means, is there any plausible scenario that would result in a different relationship?

If we assume, as many are using the chart to assert, that parental income “buys” higher SAT scores, then we will see SAT scores rising with income. The same result would be expected if those at the bottom of the socioeconomic scale receive poor educations.

However, if we assumed the world was a perfect meritocracy and everyone had the same opportunities, we only need mild assumptions about correlations between parent and child talent and personality to get the same result. Those correlations could be through genetic or cultural transmission. If children resemble their parents in any way, and income and SAT scores reflect those underlying dispositions, we will see a positive relationship.

The only way we would see no relationship between parental income and SAT scores would be if there was zero correlation between parent and child traits, and we lived in a perfect meritocracy. I don’t believe that anyone can substantiate either of those claims. The question is one of degree.

So, in some senses, the chart does not tell us anything, and I am surprised that anyone might have expected any other result.