No, the SAT doesn’t just “measure income”

I started this post to refute some specific arguments, but I changed my mind midstream and decided to add a lot more material than I initially envisioned. This is best viewed as being akin to a FAQ (Frequently Refuted Objections – FRO?) relating to the standardized tests and their use in higher education.

SAT and income are not perfectly correlated

The SAT is certainly modestly correlated with parental income, but it is simply not true that the SAT is nothing more than a measure of family income.

I will briefly plot the 2011 SAT reading scores by income level to illustrate that the r**2 is considerably less than one.

There is significant overlap across the entire income distribution:

Box and whisker plot of simulated test scores
Simulated distribution by actual test taker counts

On the relationship between negative home owner equity and racial demographics

There are a large and growing number of popular media articles alleging racial discrimination in the mortgage market.   It is simply assumed that if lenders are less willing to extend credit to blacks or make loans in “black neighborhoods” as often or with similarly favorable terms as they do whites or “white neighborhoods” that this apt to be explained by explicit racism or (subconscious) bias.  These naive arguments persist despite tremendous evidence that there are observable and unobservable differences that have profound effects on credit risk.

I will briefly describe some of this evidence before making my own modest contribution using data from and the US census. You can click here if you are familiar with this literature already and wish to skip ahead to my analysis.

1- Blacks have much lower credit scores (e.g., FICO) 

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The difference in between the white and black means is about 1 standard deviation.

Racial differences in homicide rates are poorly explained by economics

There are large racial differences in the homicide rates in the United States.  The FBI and other government organizations are not always forthcoming with detailed data, but you can quite readily estimate it (approximately) with the victimization/mortality data from the CDC and other sources (most crimes being committed intra-racially)


The black homicide rate is about 10 times higher than the white rate. It has been this way for quite some time (i.e., even as the rates have changed the differences themselves have remained fairly stable).

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Similar patterns can be found elsewhere, but I find the homicide statistic useful and interesting for many different reasons, namely:

On a recent Brookings blog post hyping economic inequality as a predictor of well-being

I recently came across a Brookings Institution blog post regarding the relationship between economic inequality and various measures of well-being.

Setting aside the lack of statistical controls and probable confounds, the practical significance implied by their own plots was actually rather trifling.

Small update to prior post on school suspension rates, comparing racial/ethnic differences with national aggregates

In my last post I displayed a plot showing a striking correlation for single-motherhood rates and out-of-school suspension rates between racial/ethnic groups using national averages.


I am well aware that aggregating linearly correlated variables will tend to produce (much) stronger correlations than you’d see with more granular data (e.g., state, county, family, individual, etc).  On the other hand, I am familiar enough with these statistics to know that you will see substantially weaker correlations here with other common predictors.  Hispanics/latinos, for instance, tend to be worse off than than blacks by many economic measures, rarely appreciably better off, and yet their discipline problems are much less (even, interestingly, less than whites in California controlling for median family income).  Likewise, the distance between asians and non-hispanic whites tends to be modest on economic dimensions, but their suspension rates are roughly half the non-hispanic white average.

For the benefit of others, I decided to generate some plots of predictors aggregated at a national level for comparison’s sake (note: I reversed the x-axis to keep the graphic relationship the same where necessary).

On the relationship between school suspensions, race, single-motherhood, and more.

As a follow up to my prior post on single-motherhood and mobility and in response to various assertions of discrimination against blacks in the school system, I decided to take a data-driven look into the relationship between race and school suspension rates.

There is, of course, ample evidence that discipline rates vary dramatically between racial/ethnic groups.

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Blacks get suspended at vastly disproportionate rates whereas “asians” (census/OMB definition), on the other hand, are about half as likely as whites are to get suspended.  Contrary to conventional wisdom, though, this pattern tends to be pretty consistent nation wide and the south is not notably “worse” with respect to disparities here.

On Philip Cohen’s knee-jerk response to Chetty’s “causal mobility” data and its association with single-motherhood

Philip Cohen, a sociologist that blogs at Family Inequality, recently argued, in response to the proposition that single-motherhood is strongly associated with economic mobility, that the single-motherhood effect is “entirely in the % black effect”.

While I do not necessarily disagree with the notion that racial demographics are strong predictors (albeit probably for different reasons than he does) and I do not necessarily believe that the single-motherhood association is (mostly) causal, his strong language is clearly at odds with the data.  In fact, his statements are not even well supported by his own stats.

On the effects of wealth on the B-W gaps, a response to questions posed by a commenter

Max, a commenter, asked:

Could you do an analysis on racial differences in educational outcomes after controlling for parental education, parental occupation, household wealth, neighborhood wealth, neighborhood education, single parent status, native language etc.? I’ve seen you control for family income and parental education (and occasionally both), but I’ve never seen you control for more beyond that (perhaps I’ve missed something!). In Chapter 16 of Affirmative Action for the RichThe Future of Affirmative Action, Dalton Conley of New York University used the Panel Study of Income Dynamics to show that parental wealth (not income) and parental education are the best predictors of college completion, which means that they may also be good predictors of other educational outcomes. He also discussed the data showing that racial wealth gaps are much larger than racial income gaps, which implies that wealth could account for a larger portion of the achievement gap than income. Could you do a similar analysis for IQ? The reason I’m asking for all this is that Carnevale and Strohl control for all of these factors and are left with a very small race effect:

I have heard this bit about wealth before.  I am deeply skeptical that wealth can mediate much, if any, of the B-W gap.

Before I dig into this though, let’s take a very brief look at some of the studies Max cited (see here and here) :

County level homicide rates by race/ethnicity of victim

In my last post, I plotted the overall US county-level homicide rate (all groups combined) by racial/ethnic demographics.  Much of that correlation is being driven by high black-on-black homicide rates throughout the country.

If I plot the rate by the race/ethnicity of the victim this pattern becomes clear and the group-level correlation weaken somewhat (especially asians and whites), but it’s still there…