Matthew Yglesias has some very interesting graphs from a Peter Orszag speech, but I see them a little differently than he does. Take, for example, this one:

Yglesias takes this to mean that “family income has a big influence here.” Well, of course: Higher-income families can better afford to send their kids to college, and tend to emphasize more the values and skills kids need to get there. What’s surprising to me is that the relationship between income and enrollment isn’t stronger.

For example, take the very worst-off kids visible here — those with family incomes in the lowest fourth and scores in the lowest third. If you could raise their incomes to the top fourth, you’d only increase their chances of making it into college by 12 percentage points. By contrast, if you could bring their scores into the top third — not as dramatic a shift, in terms of how many people they’d be passing as their rank rose — you’d increase their chances 53 percentage points. That sounds pretty meritocratic to me.

Yglesias specifically points out the rather dramatic difference among students with test scores in the middle third: High-income students have a 59 percent chance of going, as opposed to low-income students at 33 percent. Even low-income students with top-third scores have a 68 percent chance, just 9 percentage points higher than high-income students in the tier below.

I’m skeptical of reading the graph this way, though, because “middle third” isn’t a particularly useful category. Nationally, about two-thirds of those who complete high school go on to college, meaning that (as we see in this graph) most of the top third will go and most of the bottom third won’t, but when it comes to the middle third, it really matters where in that third you are. Those close to the top of the middle third will have very good odds of going; those close to the bottom won’t. If higher-income middle-third students are more likely to be in the upper part, and if lower-income students tend to be in the lower part — which is almost certainly the case, though it’s impossible to tell to what degree — this will skew the results. I’d really like to see the numbers with the middle third broken in two.