SATs, Standard Variation, and Pseudo-Meritocracy

Wherein we are a traitor to our SAT percentile.

We recently stumbled across this article about the relationship between family income and SAT scores. The College Board conceded that there’s a very strong income effect:

sat-scores-income-sections

Here’s the tricky thing though: look at the vertical axis. The average score for reading, even among the wealthiest students, is only 565 out of 800 (math and reading scores are similar so for purposes of this post, I’ll focus on reading scores). 565 is not bad, and certainly beats the hell out of the 435 average for the poorest students. But it’s not exactly elite college territory either. What we really would like to know is how many students do really well–head-turning well, to the point where admissions officers will notice (and, of course, that the U.S News and World Report rankings take into account SAT scores has nothing to do whatsoever with admissions policy). Maybe even throw some real financial aid your way. So, let’s ask how many students in each income group get a 700 or higher (again, we’re looking just at reading). Only about 3.5 percent of students score 700 or higher, so this seems like a reasonable ‘holy smokes lookit that!’ threshold.

Here’s where the standard deviation comes in. If we look at the original College Board report (pdf), we can find not only the average scores for each income group, but also the standard deviation:

SATscores

So, some readers will ask, “What the hell is a standard deviation?” To keep things very simple, it allows us to understand how scores are dispersed around an average. In other words, we can estimate the shape of the ‘bell curve.’ This allows to estimate how many students score within certain ranges, assuming the scores are normally distributed (are actually bell curve shaped). Because the SAT scores are normalized, we can do this!

When we estimate how many students score 700 or higher, here’s what we find:

smartvspopSAT

The first thing to note is that even among the wealthiest students, only a small fraction score higher than 700. But the other thing to notice is that wealthy students are dramatically over-represented: those in families with incomes greater than $200,000 are overrepresented nearly three and a half-fold, while the poorest students are underrepresented five fold. There seems to be an inflection point at the $80,000 income mark–in a nation where the median income for households with children hovers around $60,000.

Of course, even among the poorest, there are students who score high. Some of them will manage to attend elite schools and do well. Maybe even give stirring commencement speeches on occasion. But let’s not fool ourselves: this is a heavily biased system that has the trappings of merit. Enough lower-income students do well and enough upper-income students do poorly such that your parents’ income isn’t iron-clad destiny.

That’s why this system really should be called a pseudo-meritocracy. It’s not so absolutely biased such that it’s a de facto caste system, but there are real advantages to being wealthy.

Same as it was, I suppose.

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3 Responses to SATs, Standard Variation, and Pseudo-Meritocracy

  1. Eric Zuesse says:

    Please contact me at the.eric.zuesse@gmail.com to discuss these figures.

  2. I think Hoxby and Turner discuss this stuff, or maybe Hoxby and another coauthor in an earlier paper. The point of Hoxby and Turner being that even among the outlier poor kids, they’re still not going to the elite schools because they don’t know they can (and can in many cases for less than going the state school route), and they’ve got credit constraints just for the application (even though they can get a pass to apply from their guidance counselor office, many don’t know they can or they just don’t for stigma or inconvenience reasons).

  3. pyoachim says:

    nitpick–would you please use decent labels for your columns?!?! “smart':pop” is not informative!

    But my real question, how does the College Board get family income data? I don’t think I had any clue what my family income was when I took the SAT. In fact, OVER HALF the test takers gave no response. Could this just be test score and reported income are both correlating with self-esteem or something?

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