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

The SAT Zombie Apocalypse

It’s the most wonderful time of the year: Halloween in an election year! ‘Tis the season for a bevy of fright flicks designed to put your girlfriend in your arms and a bad taste in your mouth. Granted, high-art horror, like Antichrist, Pan’s Labyrinth, and The Passion of the Christ, usually do not enter this season’s strategic lineup, but it is good to know that today’s zombies have taken up running because, really, who wants to see a bunch of fat zombies?

This year is special because a multitude of new Americans might very well bring to fruition one-party democracy, much like 20th-century Mexico. Pundits are lauding the Hispanic-American population boom, as if it were an accomplishment akin to putting a flag on the moon or Iwo Jima. Meanwhile, a few bitter white men are expected to vote for the Republican presidential candidate because they have no pity for the new majority.

Halloween season also brings scary stories about falling SAT scores. At Breitbart.com, Ben Shapiro lamented that “2012’s high school seniors have the worst SAT reading scores since 1972; they scored 486 on reading, out of a possible 800.” The Washington Post reported that the scores “reached a four-decade low.” The good news and the bad news are that the elite media are reporting falsehoods, again. Shapiro can take a deep breath because his copy-and-paste error (his Pinker error?) dropped ten points from the actual reading score. However, being too lazy to investigate the scores prior to 1972, the earliest year shown in the annual SAT report, gives the false impression that verbal scores were ever worse than now. In fact, reading scores before Woodstock stood far above the present.

A single year is unlikely to provide a momentous pivot in any of the multiple-decade trends, many of which, it seems, only my readers are aware. It is worth mentioning that the male mathematics advantage slightly grew despite the fact that the upper score limit held down an increased proportion of men relative to women.

Here are some updated graphs:

SAT examinees mirror the demographic changes in America, but racial score gaps (not counting Asians) declare their constancy. With its gargantuan participation levels of highly engaged students, the SAT offers relatively noise-free output and immunity to the growing criticism of differential motivation confounding IQ tests that lack incentives. Still, Alexander Abad-Santos, at the Atlantic’s blog, promised that the “sweeping assumption that minority test-takers are naturally worse than their non-minority counterparts at the ‘reading’ section doesn’t tell the entire story.” He read this assumption into words that the Post apparently removed from their article that “the declining national reading averages may in part reflect the ever widening pool of students who take the SAT…. Nearly half were minorities….” Abad-Santos seems unmoved by the new numbers. Perhaps the data require a fresh style of presentation—something that fits the spirit of the season. I think back to how the Centers for Disease Control produced an animated graph that defined the obesity epidemic as we know it. America has diversified but not with uniformity. Maybe this calls for a map that illustrates the score changes like an infectious outbreak—or a zombie apocalypse!

Forget the numbers. This night of the testing dread is in full color. White (and light pink) represent superior scores. Red is mid-range. Yellow and the more yellow shades of orange mark the worst states (and Washington, DC, the gold star).

Now, compare those results with this map of the percentage of white and Asian SAT takers out of those who identified their race.

State SAT scores do reflect demographic change, but also test participation. Maine is among the whitest states, but its SAT scores fell when it greatly increased the proportion of students who take the test. Delaware did the same. I have expressed some doubts about the effects on scores of participation rates for various groups, but racial and gender groups cannot achieve total participation in a test, like states can. That phenomenon pushes students to take part regardless of their ability or desire to attend college. Midwestern states seem to fare best, but those states emphasize the ACT rather than the SAT. In a state like Illinois, which currently has 100% ACT participation and 5% SAT participation among high-school graduates, a student who takes both tests probably outperforms most of his or her classmates. That student may want to take the SAT to apply to a more prestigious university outside the region.

According to the Washington Post, “questions about whether the SAT is biased in favor of middle-class and wealthy students have led many colleges and universities to use other gauges or to accept an alternative exam, the ACT, which edged out the SAT in 2012 for the first time…” With regard to racial groups, ACT scores act just like those of the SAT.

The ACT even had the same surge of people who would not respond to the racial identity question, except ACT non-responders peaked in 2007 instead of 2003.

Over the years, African Americans, Hispanic Americans, and Native Americans have fallen further behind whites on the ACT.

The map of ACT scores does show a developing North-South divide somewhat like the demographic map. However, it mostly looks red because the District of Columbia used to be such an outlier. Likewise, certain New England states with low ACT participation served as outliers at the other end.

To better account for state test preferences, I created a composite SAT-ACT map. I designed a crude linear formula based on a conversion table to convert ACT scores to SAT equivalents. Then I weighted each of the two tests according to the relative participation for each state. In accordance with the conversion table, I did not consider writing scores.



Even though I kept the same color scheme as the other SAT maps, the white and pink disappeared because the map reduces the influence of overachievers who take both tests when their state has a clear preference. A worsening North-South divide clearly presents itself.

I consider this the best and most reliable map, but participation issues limit even it. I controlled for the relative participation between the tests, but not for the overall participation rates. The states that moved to total or near total participation on one of the tests were Colorado, Delaware, Illinois, Kentucky, Louisiana, Maine, Michigan, Mississippi, North Dakota, Tennessee, Utah, and Wyoming. Only Delaware and Maine have chosen to go with the SAT. By contrast, Arizona sticks out for its extremely low participation on both tests. Clearly, Arizona has an unfair score advantage, and Iowa and California also do not have especially high testing rates, either. I decided to program a map that punishes the scores of states in which the combined participation percentages of both tests is less than 100% by a factor proportional to its deficit below 100%. The punishment is somewhat arbitrary and probably quite excessive, but at least it shows that the American Southwest has inflated scores. I consider this neither to be a “score” map nor truly “controlled,” so I reset the color ranges.

For clarity, here is a map just of the addition of the participation percentages for both tests without regard to scores. States like Florida are seeing high rates of participation on both tests because they have not settled upon a single standard.

State participation changes confound state scores in multiple ways, but a movement towards full participation on the ACT could settle this issue. States increasingly seem to favor the ACT over the SAT, which I suspect is partly due to the false impression that ACT scores are less racist. Demographic changes correspond to falling test scores, and one can see it, at least in terms of a North-South divide, on these maps. America is bearing a zombie apocalypse, which is sweeping the nation and coming for our brains.










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

The Hispanic Asian Flynn Effect

Recently, activist and entrepreneur Ron Unz used results from a short English vocabulary test, called Wordsum, to argue that Mexican Americans have risen in intelligence, shrinking their intellectual disadvantage relative to white Americans by two-thirds. David Sanders (an alias) countered this claim, using one of my previous posts on racial group differences in SAT performance.

Here is how Unz responded:

Although several different arguments were made, the strongest and most detailed focused on an examination of the ethnic distribution of American SAT scores between 1980 and 2010 [sic], performed by another highly quantitive racialist blogger. The article pointed out that there was virtually no net change in the substantial Hispanic/white performance gap on the SAT during those four decades. Since the SAT is a far better proxy for IQ than my Wordsum values, and the number of participants across those years number in the millions, any possibility of a large rise in Hispanic IQ would seem completely disproven. My claims had focused on American-born Mexican-Americans rather than Hispanics in general, but since the former group represented a large and rapidly growing portion of the latter, my argument would seem to have suffered a very serious blow.

However, this is incorrect…. With some effort, I managed to obtain the ethnic distribution of SAT test-takers back to 1975 and then compared these results with the ethnic distribution of 18-year-olds during those years, found in the Census-CPS [Current Population Survey] data.

Just as I had suspected, the changes were dramatic. In 1975, 22% of whites took the SAT, and this had risen to 33% by 2011, a substantial rise of 50%. However, during these same decades, the percentage of Hispanic test-takers had grown from 6% to 32%, an enormous rise of over 400%. Thus, in 1975 white 18-year-olds were nearly four times more likely to take the SAT, but by 2011 the ratios were almost exactly the same…. Since the white/Hispanic gap remained unchanged during this tremendous broadening of the Hispanic testing pool rather than greatly widening, the only possible explanation would seem to be a huge rise in average Hispanic academic performance, just as was reflected in the Wordsum-IQ scores….

Thus, upon closer examination the SAT evidence cited for the alleged lack of Hispanic gains actually becomes very powerful evidence for strong Hispanic gains.

After going through reports from CPS, I have been unable to replicate these numbers precisely. Most of the reports that I found give combined totals of 18- and 19-year-olds, so I divided those in half, which I consider a fair estimation. I also cannot locate a report for 2011. Assuming CPS has released it somewhere, the notion that the participation gap dropped from nine percentage points to one in a single year defies credulity.

For white students, my results are similar to those of Unz. Their participation rose from 21% to 34%, an increase of 61%. If one looks at the full range, rather than just the bookend years, the rise is 19% to 34%, 79% higher. I found that Hispanics rose from 7% to 25%, which is a 257% increase. That is still a huge jump, even if it is not 433%. The rates of change of participation in the graph look similar, but Hispanic students start much lower.

However, discussion of the exact calculations is moot because both sets are based on a falsehood. Take a close look at the graph. Notice anything strange? In 1987, non-Mexican Hispanic students suddenly resolved to take the SAT in much greater numbers. Before one goes searching for a mind-blowing ‘80s Spanish public service announcement, I must reveal (again) that the College Board added a third category of Hispanic in 1987, in addition to Mexican and Puerto Rican, and this new category was “other Hispanic.” A group of people who had previously been something other than Hispanic consequently metamorphosed into Hispanic people with sombreros, I think. Other Hispanic students (or, as I prefer, “Hispanica Miscellanea”) rival Mexican-American students in number. The dramatic quality of the rise in Hispanic participation merely represents an artifact of definitional change. Calculations with a starting year of 1987 give a white student range of 23% to 34% (a 48% increase), an African-American student range of 12% to 29% (a 71% increase), and a Hispanic student range of 14% to 25% (a 79% increase).

Unz was making the point that SAT data support a secular rise in Hispanic cognitive ability, according to the fundamental law of participation level-actual ability direct correlation. This law allows us to assume that Hispanics are becoming smarter if they can take the test in greater numbers while only slightly worsening their score performance relative to white students. My only problem with the law is that the SAT dataset is riddled with countervailing examples, as I previously discussed.

One counterexample is particularly illustrative. In 1998, CPS discovered the existence of a group of people called the Asian Americans. This extraordinary new tribe possesses a pleasing aesthetic, but they can only eat with primitive sticks. After a detailed analysis of Asian SAT performance and participation, I can confidently state the broad conclusion that Asians are different.

As the above graph proves, Asian Americans so enthusiastically partake in the SAT that they achieve participation proportions greater than all of them. It seems that some proportion of Asian SAT takers are foreign students unrecognized by the US Census. I wonder if the Hispanic-American community also includes a group of census-undercounted individuals who nonetheless live here. Asian students are the one racial group whose SAT performance is taking off, and they have achieved this while increasing their test participation 105%, and I already dispelled attempts to use foreign-student involvement to explain away Asian score advancement. For emphasis, I shall present this graph of the Asian-Hispanic score gap in standard deviations, superimposed over the Asian-white score gap, with the colors of the latter set to grey.

In fairness, my essay raised the possibility to white aptitude decline relative to other groups and included in the reasoning a possible decline of white participation. If those who do not identify their race are largely white, as I hypothesized, then white students have decreased their participation from 43% in 2003 to 37% in 2010. However, that would also mean that white students had increased their participation since 1987 by 87%, at their peak, which is a greater increase than that of Hispanics, and the possible rise and fall left no footprint in the graph of the Hispanic-white gap.

Despite the racial disquiet that the SAT invokes, the test might actually be hiding the full extent of the racial gaps. First of all, the College Board altered its scoring algorithm in 1996 with the explicit purpose of narrowing racial gaps. Second, unlike the score range of many IQ tests, the SAT score range is, itself, sufficiently narrow so as to construct a secure floor for the bell curve’s far left and a ceiling that holds down the absolute best. I have perhaps overemphasized in the past the fact that African-American students have a larger gap with white students on the SAT mathematics subtest than on the writing and reading subtests. I cannot rule out that the subtest differences result purely from the massive number of African Americans who occupy the floor of the reading and writing subtests, as I previously graphed. Likewise, I can now reveal additional years of the white and Asian mathematics subtest bell curves that demonstrate substantial increases in perfection or near perfection of what was already outstanding Asian mathematics success.



Therein lies the crux of the issue. If all Unz wanted to prove was that the “Strong IQ Hypothesis” fails to account for the malleability of cognitive results, he could have cited the Asian advancement on the SAT. By bothering to analyze SAT results over time and by describing the progress of Asians, I have already implicitly acknowledged that some things do change and environment matters, at least under some circumstances. Usually, efforts to deny the existence of, minimize the importance of, or supply loose elasticity to IQ share the same impetus as the linguistic pursuit of calling “race” a “social construct.” The canards aspire to overrule by abstraction or technicality evidence for sociological generalizations labelled “stereotypes” or to beg the question regarding biological causality without dirtying one's hands with biological evidence. Recognizing an Asian academic model only reinforces a stereotype, to which even many Asians strain to take offense. That the SAT does not yet demonstrate an unmet potential in Hispanic Americans provides no paradox of proven unmet potential. To even engage the issue is to take for granted a stereotype. All good people are asleep and dreaming.