Thursday, October 24, 2013

Black Suits, Gowns, & Skin: SAT Scores by Income, Education, & Race

People with highly educated or wealthy parents score higher on the SAT than those from poor, uneducated families. Obvious statistic is obvious, but how important are dollars and degrees compared to race? The College Board, the organization that oversees the SAT, holds tight to its information on the subject, but incomplete leaks have occurred for 1995, 1997, 2003, and 2008. 1995’s top income bracket only started at $70,000, so the wealthiest African-American students that year did not outscore even the poorest white students. As shocking as that fact is, it provides no controls for confounding variables and neglects the currently largest minority, Hispanic Americans. Therefore, I decided to approach the question using multiple linear regression of state data. ("M" in the graph below stands for the math subtest. "V" stands for the critical reading or verbal subtest.)

First, I shall review the important news from this year’s SAT and ACT score reports. I used the ACT-to-SAT conversion equation that I extracted from the conversion table to construct a summary graph of overall ACT-SAT scores for each race and gender. Asian scores continued to rise, despite the College Board’s South Korean crackdown, which was based upon suspicions of widespread cheating. Meanwhile, overall scores fell, and whites, Native Americans, and men declined this year more than any of the previous sixteen available years.

Native Americans now barely score higher than Hispanic Americans. Native-American ACT scores slipped especially fast, and their average score on the optional ACT writing exam now equals those of African Americans. Since many white people have Native-American ancestry, and Canadian and US Native Americans tend to have high amounts of European ancestry, Native-American score trends could reflect changing cultural attitudes about racial identification, but their absolute number of test participants has not changed greatly.

I previously commented on evidence for possible white decline. So far, the evidence is subtle. If future scores demonstrate long-term decline, it could signify the “dumbing down” of education or culture, dysgenics, minority-centered education reforms, or low rates of whites taking test preparation services.

Because Asian score increases have been steady and measured, I believe that these represent genuine progress, even with or perhaps due to the same root causes as the reported cheating scandals among Asians. However, I suspect that Asian progress will eventually level off because most racial score gaps have stayed remarkably constant, and I think nature influences testing potential, especially among those of adequate means.

SAT annual reports provide scores of students grouped by their parents’ income and education levels. These graphs of that data should not surprise anyone.

The fluctuation of income categories tells an interesting story about the past two decades. The number of people with six-figure incomes took off not that long ago.

Despite the fact that levels of (parents’) education have been trending upwards, coming from an educated family increasingly predicts obtaining a higher SAT score. This graph of educational advantage is a Cohen’s d graph with the vertical axis zoomed in. I defined those parents with a bachelor’s or graduate degree as “educated.” (This graph uses the older term for the critical reading subtest, verbal.)

Parents’ education and income show clear links to SAT scores, but so do many other variables. When I mapped state SAT scores, I discovered that Midwestern states achieved higher scores than other states because a small percentage of studious Midwesterners took the SAT, and most other college-bound students in those states only took the ACT. Simple linear regression of state SAT scores with only participation rate as the predictor variable explains 78 percent of variance (P = 10-273). Usually psychology research conducts this kind of analysis with a sample population, but I cannot access the College Board’s raw data, obviously. I am trying to reverse-engineer an SAT database with 16 years of state data. However, a single data point for an income category could represent tens of thousands of people or as few as three. Plus, the year could potentially influence scores due to inflation or even societal changes in cognitive abilities, the so-called Flynn effect. I can appropriately control for those variables, but controlling for race would require estimation because racial group proportions are not broken down every year within each income bracket and educational degree. Therefore, I turned income and education levels into continuous variables for multiple linear regression.

For linear regression, I turned income into a continuous variable by dividing the number of students whose parents earn six-figure incomes by the number whose parents earn less than $20,000 per year. I compared results for this income “gap” to an income “divide” based on the number whose parents earn more than $60,000 per year divided by those whose parents earn less. I created a variable for education based on the number whose parents achieved at least a bachelor’s degree divided by the number whose parents did not. The racial variable was the number of whites and Asians divided by the number of another race. Simple linear regression for state population size showed that it was a significant predictor of SAT scores (P=4.3 x 10-47) that explained 22 percent of variance. However, it became insignificant with all further analysis except when the other predictor variables were either participation, year, and income gap or participation, year, education, and income divide with or without race. Year did not produce a significant P value for simple linear regression (P = 0.5) but always did in multiple linear regression of income or education, lowering scores over time like a reverse-Flynn effect. Both income gap and income divide were significant predictor variables in multiple linear regression, but income divide slightly better predicted SAT scores, explaining 86 percent of variance with year and participation variables, compared to 85 percent for income gap with year, size, and participation variables. Multiple linear regression with participation rate, year, income divide, and education explained 90 percent of variance with all variables achieving statistical significance, but the addition of education caused the P value of the income divide to worsen from 10-83 to 10-3. When I added race as an additional variable, the income divide was no longer a significant predictor of SAT scores (P = 0.4). Most of the impact of income on SAT scores stems from its ability to predict parents’ education levels. Multiple linear regression with the remaining significant variables (state sample size, participation rate, year, education, and race) explained 92 percent of SAT variance.

Graphs of actual SAT scores for income brackets and education levels show the distinctiveness of children whose parents have graduate degrees. Trendlines are given with R-squared variances for the highest and lowest categories.

The graphs for income or education with race reach the provocative result that race affects scores more among the lower rungs of society. As the data only represents state racial proportions, the results leave room for debate. For instance, the furthest left data in the graphs below represent Washington, DC, which I actually treated as a state. Higher-income families there are probably more likely to be white or Asian-American than are lower-income families. Many racially diverse states like California have industries or attractions that pull in successful, educated whites. Nevertheless, one could use these results to defend upper-class affirmative-action beneficiaries or to call for a new class-based system to benefit the many poor, but intelligent whites and Asian Americans.

Also of note is the fact that these graphs look totally awesome.

Anonymous (1998). Why Family Income Differences Don't Explain the Racial Gap in SAT Scores The Journal of Blacks in Higher Education (20), 6-8 DOI: 10.2307/2999198

Anonymous (2008). Why Family Income Differences Don't Explain the Racial Gap in SAT Scores The Journal of Blacks in Higher Education (62), 10-12

Ezekiel Dixon-Roman, Howard Everson, & John McArdle (2013). Race, Poverty and SAT Scores: Modeling the Influences of Family Income on Black and White High School Students’ SAT Performance Teachers College Record, 115 (4), 1-33