SAT Scores and Family Income

Much has been written about the relationship between SAT scores and test-takers’ family income. Generally speaking, the wealthier a student’s family is, the higher the SAT score.

Let’s take a look at how income correlated with scores this year. About two-thirds of test-takers voluntarily report their family incomes when they sit down to take the SAT. Using this information, the College Board breaks down the average scores for 10 income groups, each in a $20,000 range.

First, here are the individual test sections:

Source: College Board

Source: College Board

Source: College Board

Here are all three test sections next to each other (zoomed in on the vertical axis, so you can see the variation among income groups a little more clearly):

SAT scores by income class" />

Source: College Board

A few observations:

• There’s a very strong positive correlation between income and test scores. (For the math geeks out there, the R 2 for each test average/income range chart is about 0.95.)
• On every test section, moving up an income category was associated with an average score boost of over 12 points.
• Moving from the second-highest income group and the highest income group seemed to show the biggest score boost. However, keep in mind the top income category is uncapped, so it includes a much broader spectrum of families by wealth.

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Who else can pay top dollar for SAT prep classes but the relatively wealthy? This study/data confirms an empirical “fact” for lack of a better word.

What the College Board should do is add a question to the student’s test after they complete the test (to avoid negative outcomes):

1. Did you take an SAT prep course?
2. What is your ethnic background only going back 2 generation – parents and grandparents. Were they immigrants or native born?
3. Check off parents’ professions
4. Single parent household or traditional family? Divorced/Separated?

Without this data, I highly doubt that their *supposed* goal of enhancing student achievement has not substantially played out. The data suggest that all they do is keep the same people in the same socio-economic class.

The R-square value is very misleading. The .95 is the R-square predicting the test score *means* from income category, so it is inflated by aggregation (i.e., all the variation of scores around each mean is omitted). The actual correlation between an individual’s score and family income is probably closer to the .2 range.

Nice graphs. Do we have an idea of what causes the increase in scores? Is it that the wealthier families live in better school districts, or is it that they can pay for SAT test prep?

It would be nice to see some indication of the spread within each income group. I suspect that the range would be greater for the less well-off students.

But what is the variability? It likely swamps these slight trends.

Family income may be strongly correlated with a child’s SAT score, but I definitely question causation. Instead, my guess is that, on average, higher income families have more intelligent parents, and they have smarter children because of genetics. (note that I said “on average”…obviously there are many exceptions).

Unless you are controlling for the parents’ education level and intelligence, what you have just presented is meaningless.

Also, it should be noted that your data depends on a 17 year olds self-reported family income. I have to believe that this is a questionable source at best.

Even at the top of these graphs, the mean scores are not very impressive to begin with.

The visual presentation is problematic: the vertical axis applies to data where the highest mean (579) is roughly 125 – 130% of the lowest (425). The horizontal axis applies to data where the end value for the ninth decile ($200,000) is 1,000% of the end value for the first decile ($20,000). A severalfold increase in income produces an increase in SAT scores that is a small fraction of the increase in income; doubling income produces a 10% or less increase in SAT scores (compare the SAT scores of the $60,000 and the $120,000 deciles for instance, and consider whether they have any meaningful effect on admissions). If the two axes were presented proportionally, the slope would be much, much less. That there is a correlation, no doubt. But it’s a very small effect. The depiction greatly exacerbates the perception of inequality.

Admissions offices take numerous factors into account in the admissions decision. I doubt these differences are meaningful in the admissions process. Colleges admit people, not means of deciles.

Your#2-4 should come out in the university app, so no big deal. But I’m w/ you on #1 – if there were only some way to outlaw test prep classes or normalize the scores. . . But the whole premise of this article, family income, comes out in the university app too so, although interesting, this article shouldn’t upset anyone too much.

Manturo, it does not confirm what you say it does, as others have stated, you are confusing correlation with causation.

Here is a different study looking at race, income, and education level in case you are interested:
//lagriffedulion.f2s.com/testing.htm

Since the “Knowledge is Power” concept (Thank you, Sir Francis Bacon) is a foundation of our modern culture, these findings can’t be surprising at all. For all the defects in the analysis exposed by my fellow commentators, there is no more obvious proxy for Knowledge other than SAT scores and no more obvious proxy for Power than money (and Income is more readily known and understood by 17 year olds than Net Worth).

While on a generalized basis, these charts may seem to be saying something, they say nothing about the character or ability of an individual on any level. These charts also ignore the effects that schooling resources (see local tax base) and domestic support (in light of job, health and marital circumstances at home) have, which contributes to a student’s confidence about what is expected of him and what he can achieve.

It underscores though, the marvelous achievements by people who have escaped their underpriviledged circumstances by education and demonstrates why, for better or worse, every student should take standardized tests seriously.

I second what Eliot Smith said above, and would file this snippet under “Bad Statistical Reporting”. My issues:

1) I suspect that the within-group variance is higher than the between-groups variance. But independently of my suspicions, this should have been reported, or at least the predictive power of income on individual test outcomes;

2) The first three charts correctly use a y-axis range starting at 0, while the 4th one doesn’t thus amplifying differences. Bad, Tufte says, bad!

3) Reporting test results vs incomes suggests a strong causal relationship among the two. But this relationship could be weak or even non-existent, after controlling for other variables.

There are many, *many* surprises when studying the predictors of economic performance.

Income has very little do do with it.

If you read the latest report on SAT scores and the increasing scores for Asians and the decreasing scores for African American and Latinos it has to do with culture. By culture I am the focus an leaning and hard work, what is called by Malcolm Gladwell et al. “deliberate practice”.

In Asian culture as well as in the children of the professional class, top 10 % of income, the very long tradition of meritocracy and hard work is ingrained from many generations back. You cannot succeed because you are lucky, you must work hard and diligently. This is also supervised and children are given all the help they need, mostly from time spent by parents tutoring their kids. (College SAT prep courses have in studies been shown to give near zero gains on SAT scores, so money is not the issue, time and effort is.)

Ability is not enough, you have to study hard. Asians do homework a factor of 2 as regards to whites and whites do homework on a factor of 3-5 times for African Americans and Latinos. If I am not mistaken an average inner city high school student does 2 hours of homework per week.

How can you get good SAT scores if you only do homework less than 2 hours per week?

More income distribution is not the answer since higher income for inner city parents have made very little impact, the tremendous amount of money spent on inner city schools have the last 50m years made very little impact.

so what is the cure? I don’t know but we have to do somehting different.

My suggestion si to take after the very good example of low income Asians, a large load of homework. I think that we also should require parents that are on social security benefits and welfare should be required to spend at least 10 hours of homework supervision with their kids. Maybe all inner city schools should be made over to charter schools that require students to stay in school nearly 10-12 hours.

To conclude income has very little to do with school achievement. School achievement, being able to reach your maximum capacity only comes from hard grueling work, very long hours. The less fortunate you are the harder you have to study, the more hours you have to spend. It seems that the US system is the opposite, the more unfortunate you are the demands on your time and effort is lowered.

“For the math geeks out there, the R2 for each test average/income range chart is about 0.95″

This is the second time in a couple weeks that I’ve seen a NY Times blog claiming the results of a statistical regression. In both instances, the regression was meaningless because the specification was invalid. I’d suggest leaving the calls to math geeks aside unless you want pedantic responses like this. Suffice it to say that your R-squared does not help prove that “there’s a very strong positive correlation between income and test scores” because (first of all) your specification does not actually measure income against test scores.

Yeah, and what a pathetic commentary on our society, that R2 is only for math geeks. Try multivariable calculus. . .

While there are certainly many exceptions, it is not a stretch to suggest that those who are the smartest and work the hardest will succeed the most financially. It is also not a stretch to suggest that intelligence and a work ethic are passsed from parents to their children. Hence, the results of the survey are to be expected.

Why outlaw test prep classes? Would you outlaw tutors that impact that all-important GPA? Do you expect students to excel in sports and other extra-curriculars without coaches or moderators? Stop looking at tests like the SAT as IQ tests; they are not meant to capture an intrinsic measure of a student. These tests can be prepared for just like any college exam. Students that prepare deserve any score gains they earn.

Mark T, you’re way off base. Check the original College Board study from which these figures are extracted and you will see that the SAT score ranges which encompass the middle 50 percent of all test-takers in each test are narrower than the score ranges bewteen the lowest and highest income deciles reported above. And individual colleges typically report a 100 point or smaller difference in individual test scores among the middle 50 percent of students in their freshman class. Students earning SAT scores like those at the higher income deciles will be offered admission to colleges that will simply not be forthcoming to students earning scores like those at the lower end.

I’m not defending the data presented in this brief. It obfuscates the real underlying relationships. Family income is correlated with, most likely causally, the educational attainment of these students’ parents, and with their parents innate abilities. Presenting a set of charts which show that SAT scores rise with parents’ income is sexy; presenting a set of charts which show that SAT scores rise with one’s parents educational attainment is far less controversial.

#5 Doug: Higher income familes have smarter children because of the caliber of dinner table conversation in higher income homes. Genetics, schmenetics.

Most minority students who work hard have as much opportunity as white kids. Even if their performance is lower, they are the beneficiary of preferential treatment in fhe form of affirmative action, quotas and other policies regarding “diversity.” Sadly, Asians are a minority group yet they are often discriminated against because of their high achievement.. If any one group has the right to gripe, it’s the poorer Asians who work hard but do not get preferential treatment like their African American and Hispanic peers.

We have got to stop looking for excuses and blaming money, schools, class, race, social status, income, etc. The sad fact is that non-performers come from homes that do not demand performance.

This is a free country. No one tells you to have kids or how many to have. If parents take full responsibility for turning off the TVs, computers, cell phones, PDAs and all the other distractions and demanded that their kids study, study, study, their children will succeed.

As the sons of an immigrant father, who worked days and nights, my brother and I grew up without material wealth. We enjoyed the basics of a loving home and the joy of a close, tight-knit family life. With our SAT scores, your chart would have my father a millionaire. Hogwash! ATTITUDE IS EVERYTHING! Bless Cooper Union and NYU for giving my brother and I full scholarships!

If you follow the link you will find that the standard deviation of the score is reported within each income bracket. The SD is roughly 100 points (there is some slight variation in the SD within groups). Thus, the highest income bracket represented has a mean score more than a standard deviation higher than the bottom income bracket represented. I do not mean to state that this is causative.

Some additional comments:

80 percent of test takers are in the top 40% of their high school class by GPA, the pool is self-selected as college-bound–the poor here are NOT the worst students in school. BUT, within that self-selected group high-school GPA correlates strongly with SAT score as does the years taken of core academic subjects.

The income brackets contain unequal numbers of students (these are not deciles).

Scores also have strong relationships with parental education levels and race.

Agree with many of the folks above.

Unfortunately “the R2 for each test average/income range chart is about 0.95″ is a largely meaningless analysis.

How about running a regression that measures individual test-taker incomes against individual test scores?

Further, Doug is absolutely right that relying on self-reported income data from 17 year olds is troubling.

These concerns aside, I’d be interested to know what the longer-term trend is, perhaps over a 20 or 30 year period.

My impression is that a larger percentage of high school students are taking the SAT than did in the 1970s and 1980s, especially towards the bottom of the income distribution, but I don’t know for sure.

I would also suspect that the correlation has become stronger during the past 10-20 years given the decline of the US manufacturing sector and the relatively high-wage factory jobs that disappeared along with it.

Eliot Smith has it exactly right here. Aggregation will swamp out within-group variance in test scores, and the R^2 value you provide is properly interpreted as “how closely the effect of income on average test scores is approximated by a linear model,” not as a “very strong positive correlation” between individual test scores and income. These are *very* different. In fact, it is possible to have an R^2 of near 1 for the former while having an R^2 for the latter that is arbitrarily close to 0.

At the risk of being too pedantic, let me offer an example that clarifies this distinction. Say that I randomly split all 300+ million Americans into 5 groups, and assign each group a different amount from $1 to $5. I then pay every individual in a group the corresponding dollar amount. Now say that I regress average yearly income in each group against the amount of money given to that group. I will find an R^2 that is extremely close to 1: there are simply so many people in my sample that the preexisting individual variance aggregates to nearly zero, and the tiny systematic change I induced by giving a few dollars dominates each average.

Of course, if I regressed individuals’ yearly income against the amount of money I paid them, I would get a completely different result. The R^2 would be virtually zero, because the amount of money I provide is a trivially small fraction of the variance in Americans’ income. Thus even a very impressive correlation in averages tells us nothing about correlation in the individual values.

I think you’ve recognized that there’s some issue here, because you italicize “average” where the R^2 of 0.95 is mentioned. But the preceding sentence about a “very strong positive correlation” between income and test scores is still not right, especially when it appears to call upon the R^2 as supporting evidence.

As others have already noted, this is either grossly misleading or statistically meaningless. Without taking IQ and other variables into account, this is just omitted variable bias.

As for the role of culture: Note that Asian kids from the *bottom* quartile of the income distribution tend to outperform black and Latino kids from the top third or fourth of the income distribution on the SAT Math. So that’s a good example of how weak the income effect is when you’re cutting across races/cultures.

Okay. I am not much of an economist but I think this research lacks very important question. What hides behind high family income? Is it, like some mentioned, SAT prep courses or is it genes? Most of the time high family income means that people are smarter which, again, most of the time means that their kids are smarter. Is not that what hides behind family income? Simple IQ?

While twin adoption studies show that genetics have a very powerful effect on IQ and income (which are themselves strongly correlated), I’m curious if commenters here have a view on those successful people who come from uneducated middle or lower-middle class families. Those people presumably wouldn’t have the high IQ gene or the high income gene (unless they are the same). But we all know such people who are brilliant who don’t have brilliant or high-income parents.

I know anecdotal evidence is not generally a reliable way to refute data, but there are too many people in this category for it to not call this result into question. Right?