Merit’s Liquidity

Over the past year, multiple major media outlets and a powerful university president or two have been agitating about the correlation between parents’ income and SAT scores. Over that same time period, editors of various psychology journals were rejecting my regression study to determine the true influence of parents’ income on SAT scores while controlling for other possible factors because the study did not “make clear what the gap or problem is in the literature and exactly how the present study fills that gap.” If I cannot convince a journal that a lack of an examination on the influence of socioeconomic status in the entire 87-year history of America’s most important academic test is a gap in the literature, then what hope remains for my other project on the interplay of body-mass index and perspiration on navel lint accumulation?

Part of the problem resulted from my need to rely heavily on years of state averages, rather than the scores of individual students, but I am convinced that anyone who manages to gain access to individual data will merely corroborate my work at much greater expense. One editor conceded, “I agree that there is something we can learn from these data,” despite rejecting my work anyway. Ultimately, the new open-access journal, Open Differential Psychology published the study.

Last week, the College Board released the latest year’s SAT results. The organization cleverly released its “benchmarks” report the day before their usual, more detailed report. Reporters were too lazy to report on the subject two days in a row, let alone do any analysis. Blasé headlines declared scores “flat,” as they would for any two-consecutive-year analysis. I found the numbers fascinating. They dovetail with my study and other previous writings and flesh out some trends the media missed.

In my study I addressed the overlooked fact that correlations between parents’ education and (individual) SAT score and between parents’ income and SAT score have not been constant over time.

Family educational advantage seems to evince virtually undeviating growth as a predictor of SAT scores, but financial advantage seems to grow as the economy worsens. Rather than postulate that times of economic difficulty almost immediately make wealthy people smarter, one should focus on the exclusivity of the income category.

2014 brought new record advantages to students whose parents have bachelor’s or graduate degrees on the critical-reading and mathematics subtests. This fact can inform discussion about the notion of an “education bubble.” The expansion of college access has raised concerns over indebtedness, falling standards, and underemployment, but, while these concerns are likely to grow, education appears increasingly to benefit the following generation as if to demonstrate that the ability of higher education to sift and inculcate basic skills remains intact, or at least it did one generation ago.

The difference between the yearly trends for the SAT-score benefit of education to a family compared to the benefit of coming from a home with a higher income startled me, especially given the sharp drop in income advantage coinciding with the 2008 economic downturn. So, I graphed income’s SAT advantage with US gross domestic product (GDP) growth rate. The graphs almost perfectly coincide when the income divide compares families above $100,000 to those below that.

My regression study included a control for year, but an even more detailed study of the influence of family income could benefit by controlling for the state of the economy, as I suggested in my concluding remarks.

Perhaps additional or alternative variables could be identified. For instance, year was significant in some regression iterations but had small β values. Perhaps year is a proxy variable for other factors like the state of the economy.

The graph provides convincing evidence that there is some kind of causal relationship between the economy and SAT scores despite the relatively low influence of parents’ income on scores in the regression analysis. Student stress or mood seems more plausible as a mechanism than radical yearly changes in educational quality, but my point about exclusivity concerned whether economic slowdown weeded out low test performers from higher economic strata due to the heritable component of cognitive ability shared between the parents and the student. However, for that to be the mechanism, one would expect GDP to look more like a leading indicator of test performance or for the slope of the growth rate to tend to be the negative of the slope of test scores over time. This graph actually seems to indicate that poor economies weed out high test performers from higher economic strata. In The Bell Curve, Richard Herrnstein and Charles Murray claimed that the twenty-first century would continue “the emergence of a cognitive elite.”

The isolation of the brightest from the rest of society is already extreme; the forces driving it are growing stronger rather than weaker.

Of course, the economy of the 1990’s, when they wrote that, usually appeared to be growing stronger rather than weaker.

I can imagine two mechanisms for economic contraction weeding out smart families from the upper class: circumstances cause the power elite to lose interest in the power of ideas, and some upstarts’ ideas were not that good from the start. I suspect both are at work. The first mechanism supports a leftist or Marxist vision of ensconced aristocracy holding the privileges of power and leisure. If recessions interspersed with periods of anemic growth are “the new normal,” then The Bell Curve was partly wrong, and economic populism should be of interest to the so-called cognitive elite. On the other hand, when bad ideas create bad economies, perhaps the cognitive elite receive their just desserts. Some people who are obsessed with IQ research engage in some paradoxically simplistic thinking. As anyone who has surveyed the differential psychology literature about liberals versus conservatives or even the results for the SAT Student Descriptive Questionnaire can attest, the best indicator of dimness is indifference. Wrong ideas also sometimes require intelligent formulation. Spectacularly wrong ideas receive their negative appraisal in retrospect because they were compelling enough to do damage. Moreover, misbegotten hype might serve as a more commonly available vehicle of upward mobility for smart upstarts than truly transformative ideas.

Wisdom and top-down analytic ability sadly receive fewer lauds than the clichés “street smarts” and “common sense.” To illustrate the distinctiveness of wisdom from intelligence so as to support the notion that smart people might promote unwise ideas, I would like to analogize with my personal experience working with engineers and doctors. Many of the engineers whom I have known work hard on mundane projects but like to engage in fascinating discussions about politics, metaphysics, and, of course, the possibility of alien life forms. They contrast with neurologists and neurosurgeons whom I have met who regularly work with cases of alexia without agraphia and amygdalectomy but remain willfully indifferent to any profound questions these phenomena raise about the soul or free will. If emphasis on analytic ability (as opposed to memory) is analogous to “wisdom,” then the engineers are the aristocrats in this analogy, although engineers often zealously advocate for their upstart ideas. I think most people assume that doctors are smarter than engineers because becoming a doctor is harder and better reimbursed, but I would say engineers are deeper conversationalists, which manifests a certain type of wisdom to me.


Merit’s Mobility
Though the 90’s are long gone, Bill Clinton might still point out that this is not “midnight in America.” The American economy usually does expand, and smart people disproportionately tend to be the proverbial movers and shakers. Hints of this appear as evidence for their geographical mobility based on yearly maps of SAT and ACT data. Racial demographics also relate to test scores and have their own trends of time and place.

Last year, I graphed all data from state SAT reports for SAT scores of different family income brackets according to the proportion of each state’s population that belongs to the two highest scoring racial groups, whites and Asians. As the updated version above shows, students from the wealthiest category have the lowest association between state racial demographics and SAT score. One reader considered this “evidence against a genetic explanation.” Of course, homes earning less than $80,000 per year are not all dealing with “typical environmental problems of poverty.” Part of my study’s regression analysis looked at the effects on SAT scores that were common to both income and race. These effects existed when the income cutoff was $100,000 but not $20,000. Without completely dismissing the environmental hypothesis, I pointed out alternative factors that could be at work. An alternative explanation for the graph could be that higher income families with good test performance are more likely to live in racially diverse states compared to other income levels, since the racial proportions pertain to the states, not the income brackets, themselves. It turns out that SAT data does offer some support for my previous contention that “racially diverse states like California have industries or attractions that pull in successful, educated whites.”

Before revealing the map that demonstrates this, I shall review the latest SAT and ACT data by race. Composite ACT-SAT scores by race are very similar to the year before.

Native-American scores remain just slightly above those of Hispanic Americans after a significant drop in Native-American ACT scores from 2010 to 2013.

Overall, Asian scores have continued their amazing progress. The Asian SAT mathematics subtest advantage over whites rose to 64 points.

Asians are not closer to surpassing whites on the critical-reading subtest only because white scores rose by the same amount this year.

In contrast to all other groups, Asian SAT writing subtest scores rose in seven of the past nine years.

However, Asian progress on the ACT did appear to stop. Their scores on the reading and math subtests even slightly dropped. The average score drop for Pacific Islanders, for whom scores are available only in recent ACT data, was quite severe this year: almost a full composite ACT point. Fortunately for Pacific Islanders, this probably only resulted from a massive, 19-percent increase in ACT participation. Hawaiian students, who were 83 percent Asian-American, according to SAT numbers, bumped up their ACT participation from 40 percent to 90 percent, while their SAT participation rate barely budged at 63 percent. Asian students have been the one racial group who heavily favor taking the SAT rather than the ACT. This is likely due in large measure to foreign students. As the following graph shows, ACT participation surpassed that of the SAT, driven mostly by white students.

It would be tempting to surmise that foreign students are causing the continued progress of Asians on the SAT, but, as I previously discussed, the scores of foreign students (represented on the following graph as colored lines of a negative advantage for American students) still closely resemble Asian SAT scores (represented as gray lines for a negative white advantage), while the number of foreign students could not overwhelm the number of Asian students.

Indeed, Asian progress has been so impressive that it calls into question some assumptions of experts in differential psychology and adherents to the philosophy behind so-called “human biodiversity.” Rather than reveal a unitary Asian-white general intelligence gap, Asians have always had a large mathematics advantage. Rather than maintain a constant mathematics gap as Asians improve their English skills, Asian mathematics, reading, and writing skills improved in tandem. Rather than have SAT scores that coincide with research on the secular IQ gains, known as the Flynn effect, Asian SAT gains have been large at the same time as their IQ gains have been small, and white SAT gains have been small, as large IQ gains in Western societies have continued unabated. Frey and Detterman famously called the SAT an IQ test in 2004, but they offered no explanation for why their IQ-estimation equation essentially eliminated the reading subtest. Murray recently defended The Bell Curve by pointing out how little the black-white test score gap has changed. So, what is the precise meaning of that, given that the Asian-white gap has changed so greatly?

What should be clear from the preceding review of new data is that participation rates greatly matter. Hawaii’s ACT scores fell this year by almost two points on a scale from 11 to 36, following its participation increase. In order to appropriately map composite ACT-SAT scores, I must follow my previously described methodology for adjusting scores according to state SAT and ACT participation rates.

For comparison, here is the map of the percentage of white and Asian SAT-taking students over the years:

Student diversity increased especially among coastal states. I previously claimed, “Demographic changes correspond to falling test scores, and one can see it, at least in terms of a North-South divide, on these maps.” The most recent years of this participation-controlled composite SAT-ACT score map make me want to amend that assessment.

One can more easily notice the change by just looking at the oldest and newest maps without animation.

The earliest year does suggest a North-South divide, but the coastal states of California, Georgia, South Carolina, and North Carolina improved, while some Mountain states declined. The trend could be a fluke, and a few states buck the trend, but it fits with my previous explanation of diverse states attracting relatively well scoring students from wealthy families. The upper class wishes to live near beaches and in high-status states with impressive cultural and educational institutions. Many of the cognitive elite actually might like some kinds of racial diversity. Southern states like Louisiana have not improved, or, in the case of Mississippi, scores improved but were already extremely low. Perhaps the cognitive elite would be attracted to this Southern coast but find Southern culture too alienating, and maybe such a feeling of alienation from otherwise attractive settings makes liberal condescension slightly more understandable.

In an era that made “big data” a catchphrase, the colossal data pool that describes the colossal sample who took these tests inspires elite news outlets to make bar graphs of simple correlations and reports of flat scores. I call that flat reporting.










nooffensebut (2014). Parents’ Income is a Poor Predictor of SAT Score Open Differential Psychology, 1-19

Parents’ Income Poorly Predicts SAT Score

Abstract
Parents’ annual income lacks statistical significance as a predictor of state SAT scores when additional variables are well controlled. Spearman rank correlation coefficients reveal parents’ income to be a weaker predictor of average SAT scores for each income bracket within each state than parents’ education level as a predictor of average SAT scores for each education level within each state. Multiple linear regression of state SAT scores with covariates for sample size, state participation, year, and each possible combination of ordinal variables for parents’ income, parents’ education, and race shows income to lack statistical significance in 49% of the iterations with greater frequency of insignificance among iterations with higher explained variance. Cohen’s d comparisons of the yearly individual SAT advantage of having educated parents show a fairly consistently increasing positive relationship over time, whereas similar analysis of the yearly individual SAT advantage of having high-income parents shows variability somewhat coinciding with the business cycle.

Read the whole study at Open Differential Psychology.

See below for important excerpts and extra super-awesome graphs.

“Sackett et al (2009) recounted a series of accusations that the SAT merely measures family wealth. The College Board’s announcement of 2016 SAT reforms has stirred anew claims that 'the only persistent statistical result from the SAT is the correlation between high income and high test scores' (Botstein, 2014). Thus, income as an important predictor of SAT scores somewhat fits a view critical of the SAT, which is that financial resources and class privilege unduly enable higher SAT achievement. If the education component of socioeconomic status dominates over the income component, then the relationship between socioeconomic status and scores might instead more accurately reflect a family’s values towards education and a hereditary influence shared between test performance and educability.”

“This study seeks to thoroughly parse the effects of multiple covariates, including family income, parents’ highest education level, and potential confounding variables specific to state or multiple-year comparisons. To do this, full advantage will be taken from all sixteen years of state data.”

Income p-values without race as a covariate (p-values are shown on an inverse logarithmic scale)

Income p-values with race as a covariate (p-values are shown on an inverse logarithmic scale)

“The racial variable was the most consistently significant variable of these three ordinal variables for composite scores and subtests, which speaks to its independence from socioeconomic status. Race also explained much of the SAT advantage that appeared to be attributable to parents’ income prior to the addition of the racial variable in iterations with low income thresholds simultaneous with the education cutoff being graduate degree.”

Critical-reading and mathematics standardized coefficients compared to adjusted R² values, organized by education first, race within each educational category, and income within each racial category

“Parents’ income has a significant association with SAT scores, but parents’ education is consistently stronger, and regression with effective controls for race, education, and other factors, usually suppresses the income variable to insignificance. The income variable achieved significance when the education threshold was high school diploma most likely because so few parents were dropouts that education was no longer effectively controlled, and parents’ income became a proxy variable for parents’ education…. Part of this dominance could result from heritability in test performance corresponding to parents’ educational attainment, given the high heritability estimates from twins studies for high-stakes standardized exams in the UK and the Netherlands (Bartels et al, 2002; Shakeshaft et al, 2013).”

“Figure 1 seems to contradict Dixon- Román et al in finding that the racial variable had its greatest influence at the highest education level and at high income levels.”

“Asian Americans have historically high average mathematics subtest scores but lower verbal/critical-reading average scores than the white majority…. Despite their likely small average verbal disadvantage and small population in many states, this study’s consistent regression results for Asian race match verifiable individual SAT-score phenomena. A study with fewer observations, a much smaller represented sample, or fewer or poorly chosen covariates might not have achieved that level of definition, but, fundamentally, states do not take the SAT; people do.”

Cohen’s d SAT advantage of having parents’ annual income above $60,000

“Family educational advantage seems to evince virtually undeviating growth as a predictor of SAT scores, but financial advantage seems to grow as the economy worsens. Rather than postulate that times of economic difficulty almost immediately make wealthy people smarter, one should focus on the exclusivity of the income category…. The declining relative income advantage on the mathematics subtest compared to the critical-reading subtest also could be related to structural changes to the economy since the decline of the high-technology boom of the 1990’s, which also fits this interpretation of persistence within families.”

For those readers who do not have a heart condition, I recommend the spirited and colorful statistics debate in the open peer-review forum. One may also find there data supplements of state data that required many months of typing out the data from 816 state reports into a database, which makes a fun toy.










nooffensebut (2014). Parents’ Income is a Poor Predictor of SAT Score Open Differential Psychology, 1-19

Ariel Investments. (2010). The Ariel Investments 2010 black investor survey: Saving and investing among higher income African-American and white Americans. Retrieved April 1, 2014 from http://www.arielinvestments.com/landmark-surveys/

Balf, T. (2014). The story behind the SAT overhaul. New York Times. Retrieved March 25, 2014 from http://www.nytimes.com/2014/03/09/magazine/the-story-behind-the-sat-overhaul.html.

Bartels M, Rietveld MJ, Van Baal GC, & Boomsma DI (2002). Heritability of educational achievement in 12-year-olds and the overlap with cognitive ability. Twin research : the official journal of the International Society for Twin Studies, 5 (6), 544-53 PMID: 12573186

Botstein, L. (2014). College president: SAT is part hoax, part fraud. Time. Retrieved March 25, 2014 from http://time.com/15199/college-president-sat-is-part-hoax-and-part-fraud/.

Buchmann, C., Condron, D., & Roscigno, V. (2010). Shadow Education, American Style: Test Preparation, the SAT and College Enrollment Social Forces, 89 (2), 435-461 DOI: 10.1353/sof.2010.0105

Dixon-Román, E.J., Everson, H.T., & McArdle, J.J. (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

Duckworth AL, Quinn PD, Lynam DR, Loeber R, & Stouthamer-Loeber M (2011). Role of test motivation in intelligence testing. Proceedings of the National Academy of Sciences of the United States of America, 108 (19), 7716-20 PMID: 21518867

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Everson, H.T., and Millsap, R.E. (2004). Beyond individual differences: Exploring school effects on SAT scores. (RR-2004-3). New York: College Board.

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Marioni RE, Davies G, Hayward C, Liewald D, Kerr SM, Campbell A, Luciano M, Smith BH, Padmanabhan S, Hocking LJ, Hastie ND, Wright AF, Porteous DJ, Visscher PM, & Deary IJ (2014). Molecular genetic contributions to socioeconomic status and intelligence. Intelligence, 44 (100), 26-32 PMID: 24944428

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Prescott, B.T., and Bransberger, P. (2012). Knocking at the College Door: Projections of High School Graduates (eighth edition). Boulder, CO: Western Interstate Commission for Higher Education.

Sackett PR, Kuncel NR, Arneson JJ, Cooper SR, & Waters SD (2009). Does socioeconomic status explain the relationship between admissions tests and post-secondary academic performance? Psychological bulletin, 135 (1), 1-22 PMID: 19210051

Sackett PR, Kuncel NR, Beatty AS, Rigdon JL, Shen W, & Kiger TB (2012). The role of socioeconomic status in SAT-grade relationships and in college admissions decisions. Psychological science, 23 (9), 1000-7 PMID: 22858524

Schmitt N, Keeney J, Oswald FL, Pleskac TJ, Billington AQ, Sinha R, & Zorzie M (2009). Prediction of 4-year college student performance using cognitive and noncognitive predictors and the impact on demographic status of admitted students. The Journal of applied psychology, 94 (6), 1479-97 PMID: 19916657

Shakeshaft NG, Trzaskowski M, McMillan A, Rimfeld K, Krapohl E, Haworth CM, Dale PS, & Plomin R (2013). Strong genetic influence on a UK nationwide test of educational achievement at the end of compulsory education at age 16. PloS one, 8 (12) PMID: 24349000

Trzaskowski M, Harlaar N, Arden R, Krapohl E, Rimfeld K, McMillan A, Dale PS, & Plomin R (2014). Genetic influence on family socioeconomic status and children's intelligence. Intelligence, 42 (100), 83-88 PMID: 24489417

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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

The SAT-ACT Score Map

(Note: Following this post, I shall focus on finishing the MAOA bibliography probably until it is up-to-date and until I can better quantify its data.)

In my last post on college-entrance exams, I left incomplete the task of properly controlling for test participation a state map of combined SAT and ACT scores. I had already explored group average SAT gaps by race and gender and SAT score distributions. Finally, I am posting above what I consider the definitive state map, which is properly controlled for test type and state participation levels.

The map demonstrates my contention that American demographic changes contribute to a North-South educational divide. Detailed mapping of potential academic decline can help inform discussion of policies like “immigration reform,” help extrapolate future global competitiveness of the American workforce, and delineate regional economic fault lines. In the explanation that follows, I compare the effects of state participation in the SAT and ACT and race with regression analysis. Then, I shall review an important study on the relative importance of these scores and what might augment or replace them.

Testing associations publish a standardized table to convert between ACT and SAT scores. The primary table converts between the composite ACT score and the combined SAT mathematics and critical-reading (formerly verbal) score. (I divided the scores in half for purposes of comparison with SAT subtest scores.) A separate table converts between the newer SAT writing score and the score for the optional ACT writing exam. However, I shall neglect the writing scores data at this time, but the previous post maps raw SAT writing scores.

My last attempt at ACT-to-SAT score conversion amounted to a crude estimate that only accounted for the highest and lowest ACT scores with a line drawn between for all others. The tests follow different scales with several possible SAT scores coinciding with almost all ACT scores. Therefore, I created a new formula based on linear regression of the plot of average SAT scores for each ACT increment. Since state ACT averages tend to hover around 21, this graph illuminates how my previous formula unfairly underestimated states that emphasize the ACT over the SAT.


As states increasingly have required the ACT for all high-school graduates, their average scores have declined. Plotting below each state’s yearly ACT and SAT score since 1998 by participation level confirms the association. All associations achieve statistical significance (P=9.54 x 10^-27 for the ACT, P=3.75 x 10^-33 for the weighted SAT-ACT scores) with the SAT, alone, achieving the greatest significance of any tested relationship in this entire effort (P=5.4 x 10^-245) and the largest coefficient of determination (0.769). Midwestern states that strongly emphasize the ACT achieved impressive average SAT scores and seem to have an outsized impact on this finding. The combined SAT-ACT participation rates are out of a possible 200%, which would require all high-school graduates to take the SAT and the ACT.


The comparison of score maps to demographic trends, which I presented with a map of the percentage of SAT examinees who are white or Asian, fits the familiar national racial group mean gaps. Simple linear regression better quantifies the effect of race, and multiple linear regression can tease apart the effect of state participation levels. Asians have the highest scores, but I lumped whites with Asians because Asians are a relatively small group. I would expect other racial gaps to be too confounding to separate Asians from the rest. The distinction I drew might seem arbitrary, but many institutions separate data on Asians and whites from that of “underrepresented minorities.” The graphs of scores by racial proportion appear to show that these are linear associations, all of which are significant (P=3.51 x 10^-53 for the SAT, P=1.33 x 10^-41 for the ACT, and P=1.48 x 10^-40 for the tests combined). Multiple regression shows that all associations remain significant. For the combined SAT-ACT score, participation had a P-value of 3.35 x 10^-22, and race had a P-value of 1.29 x 10^-29. The multiple regression model set score equal to 986 – 0.782 x participation (as a whole number) + 97.5 x the percentage white or Asian.


The residuals from subtracting this model from the raw data fit a Gaussian distribution, as expected. So, I recalculated the SAT-ACT composite scores by adding the residuals back to the model under the assumption of 100% (out of a possible 200%) participation.


While the score map might not appear identical to the map of demographic trends, one can make out a North-South gradient, and state efforts to adopt test requirements seem well-controlled. Further analysis could use ANCOVA for income categories or compare racial gaps within states. Composite writing scores could prove useful, despite the shorter timeframe for the SAT and the optional nature of the ACT written exam. In fact, the states of Texas, Nevada, and Florida might not seem to perform so badly in this map, given their diversity, but their raw SAT writing scores were especially low. Then again, immigration weighing down English writing skills could resolve with acculturation.

Now, I wish to review a 2009 study on the relative relevance of SAT and ACT scores. Schmitt et al compared the predictive value of those scores to high-school grades and twelve “noncognitive predictors”: knowledge, curiosity, adaptability, perseverance, ethics (“not cheating”), career orientation, healthy behaviors, interpersonal skills, “leadership,” community volunteer activities, “artistic and cultural appreciation,” and “appreciation for diversity” (“e.g. by culture, ethnicity, religion, or gender”). As the US Supreme Court revisits the issue of Affirmative Action in college admissions, universities might apply such predictors to lessen the influence of standardized tests. None of the “noncognitive predictors” could predict college grades even half as well as either high-school grades or the SAT/ACT scores, which had correlations of 0.531 and 0.539, respectively. Knowledge came closest, but I think knowledge is cognitive. Career orientation actually was alone in its statistically significant negative association with college grade-point average. The authors offered as their only explanatory hypothesis the poor performance of African Americans “for whom career mobility and a career orientation was a major reason for college attendance.” Indeed, career orientation was the strongest advantage for African Americans, who barely scored higher than whites on “appreciation for diversity.” Their only other advantage was perseverance. High-school grades underestimated African-American college grades, but not as much as SAT/ACT scores overestimated. Adding the “noncognitive” criteria to potential admissions selection would lower college grades, in general, but raise African-American and Hispanic-American admissions at the 15% most exclusive universities, at the expense of white and especially Asian-American applicants. However, African-American college graduation rates would fall eight percentage points at such institutions. SAT/ACT scores were significantly associated with higher college classroom absenteeism and lower “organizational citizenship behavior,” with which “appreciation for diversity” had a significant positive association. In other words, the more intelligent students were less inclined to go to all lectures, promote “the university to outsiders,” defend “it against criticism,” and participate “in student government or other clubs” to make the university “a better place.” The authors did not conclude that those are relatively unintelligent behaviors.










Schmitt N, Keeney J, Oswald FL, Pleskac TJ, Billington AQ, Sinha R, & Zorzie M (2009). Prediction of 4-year college student performance using cognitive and noncognitive predictors and the impact on demographic status of admitted students. The Journal of applied psychology, 94 (6), 1479-97 PMID: 19916657