Musings on SAT Scores

The Scholastic Aptitude Test (SAT) is a test taken by many high school students in the USA for the purpose of college admissions. The SAT is one of two tests used for this purpose. The other is the ACT (not an acronym). Traditionally, the SAT was divided into two sections—verbal and math—which were scored separately. Possible scores range from 200 up to 800 for each section. In a given year, scores are comparable to one another, but the test scores across years may not be, as they may be scored and calibrated differently. In 2005, a writing section was added, but this discussion will only pertain to the math and verbal portions. Both the SAT and ACT are generally accepted by colleges, and states vary widely in the proportion of students that take one test vs the other. The east and west coast states tend to favor the SAT, while the midwest states favor the ACT. Scores on the SAT correlate highly with IQ (and are therefore very relevant to college admission), but are also depend strongly on education and English literacy (Deary, 2001).

Here is a heat map showing the preference for the SAT across the lower 48 states:

Heat map showing the percent of students taking the SAT across the lower 48 states. Image prepared using Tableau.

Across the 50 states and Washington, DC, the mean rate at which students take the SAT is 37% (median is 33%). This distribution is strongly bimodal, with one mode at 50-60% (including Washington, Oregon and Florida) and the other mode at 4-10% (including South Dakota, Mississippi and Iowa).

Unsurprisingly, math and verbal SAT scores correlate strongly and positively (r = 0.90, p < 0.001). Ohio is a notable outlier with average verbal scores (534), but the lowest math score in the data set (439). Across states, the mean math score is 532 (median is 525), and the mean verbal score is 533 (median is 527). However, the distribution of verbal scores are also quite strongly bimodal, with one mode at approximately 500, and the other mode at approximately 560.

Both math and verbal SAT scores correlate strongly and negatively with the percent of high school students taking the test (r = -0.77 and r = -0.89, respectively. P < 0.001). This relationship is particularly clear when comparing the SAT rate to the math scores. The data points are clustered into two groups--high rate, low scores, and low rate, high scores:

Scatterplot showing average state SAT math scores, and the percent of students taking the SAT. Image prepared using Matplotlib in Python 2.7.

A plausible explanation for this pattern is that it is common in many east coast high schools for students to be encouraged to take the SAT even if they do not intend to apply to college. Thus, students take the SAT at a rate of 82% in Connecticut, and the rest of the New England states are not far behind. Conversely, it may only the best students in ACT-dominant states who take the SAT. This is particularly plausible, as some scholars believe the SAT to be a more rigorous test (e.g. Kanazawa, 2008), and students wishing to get into the most prestigious schools may choose to take the SAT to better showcase their abilities.

References:

Deary, I.J. 2001. Intelligence: A Very Short Introduction. Oxford University Press, New York.

Kanazawa, S. 2008. IQ and the health of states. Biodemography and Social Biology, 54(2): 200-213.