(American Enterprise Institute) By Mark Perry —
In response to my recent CD post about the gender differences on the math SAT scores over the last half century “2016 SAT test results confirm pattern that’s persisted for 50 years — high school boys are better at math than girls,” AEI research assistants Wendy Morrison and Grace Finley responded today on the AEIdeas blog with the post “Actually, SAT results don’t confirm boys are better at math than girls.” Here’s a slice that summarizes their position:
Put simply…..the only reason boys scored higher than girls is because the boys who are the worst at math didn’t take the SAT — not because “boys are better at math than girls.” This is consistent with data Dr. Perry himself cites, that far more girls take the SAT each year than boys.
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Dr. Perry also cites girls’ “superior overall high school records” and over-representation in math classes as evidence that “female high school students are better prepared academically”, making the lower female average math score all the more surprising and suggestive of lower female ability. We argue that this finding – lower male high school GPAs but higher male SAT math averages – could also be consistent with our hypothetical, in which a larger proportion of boys underperform academically compared to girls, and those boys simply choose to not take the exam.
Here’s an edited version of an email that I sent this evening to Wendy and Grace:
I am familiar with the argument you present, it has been described here as a “sampling artifact” by University of Wisconsin Professor Janet Hyde and her co-authors:
In 2007 the SAT was taken by 798,030 females but only 690,500 males, a gap of more than 100,000 people. Assuming that SAT takers represent the top portion of the performance distribution, this surplus of females taking the SAT means that the female group dips farther down into the performance distribution than does the male group. It is therefore not surprising that females, on average, score somewhat lower than males. The gender gap is likely in large part a sampling artifact.
Although that is a seemingly plausible argument, I don’t think the math test data over a 50-year period support the “sampling artifact” explanation for the following reasons:
1. I just found some earlier SAT math test scores by gender and I now have annual test score data back to 1967, which represents 50 years of SAT test data. In the earlier years in the 1960s through the mid-1970s there were more males than females taking the SAT test (and for many years after that there was only a slight majority in favor of women taking the SAT test) and there was still a significant gender difference in favor of high school boys for the math test. That is, even in the earlier years when there wasn’t a “surplus of females taking the SAT” or a “sampling artifact” there was still a significant male advantage in math test scores.
2. Another problem with the “sampling artifact” explanation of boys consistently outperforming girls on the math SAT over the last 50 years, is that if it were true that an increasing number (“surplus”) of girls taking the SAT test over time was increasingly “dipping further down into the distribution of female talent,” that would suggest that female scores on the math SAT test should be falling over time. But the data show that average female test scores have been gradually rising over time, not falling. The “sampling artifact” explanation of higher male math test scores would also suggest that the gap between female and male test scores should be widening over time as more girls take the test, when in fact the gap has been relatively stable and has in fact narrowed slightly. So the “sampling artifact” explanation really isn’t consistent with the female math SAT test scores gradually improving over time and the stable (and slightly narrowing) gender gap in SAT math test scores.
3. The data for 2016 are not yet available, but the graph above shows the male-female ratios on the 2015 math test by test score intervals of 10 points. Even if the “sampling artifact” could explain why average female SAT math test scores are lower than average male test scores, that explanation still wouldn’t explain the data in the graph above showing that boys outperform girls for perfect, and near-perfect, math SAT test scores by a ratio of about 2:1. That is, even if an increasing number of female test-takers were lowering average female test scores by “dipping farther down into the distribution of female talent,” the “sampling artifact” explanation can NOT and does NOT explain the gender math differences favoring high school boys at high levels of mathematical aptitude clearly illustrated in the graph above.
Specifically, at the highest level of math performance on the SAT test last year for perfect scores of 800, there were 11,098 males and 5,570 females achieving those scores, meaning that nearly 2 males achieved perfect scores for every one female (male-female ratio of 1.99-to-1). Adjusted for the fact that more females (903,719) than men (794,802) took the SAT test in 2015, the percentage of males who earned perfect scores of 800 points was 1.4% compared to the percentage of females with perfect scores of 0.62%. That produces an adjusted male-female ratio of 2.26-to-1 (vs. the 1.99 unadjusted ratio) for high school students who had perfect 800-point scores. For scores of 750 points and above (98th and 99th percentiles), boys outnumbered girls by a ratio of 1.83-to-1 (36,927 to 20,210) and when adjusted for the differences in sample size, the male-female ratio was 2.08-to-1 (4.64% vs. 2.23%) for scores between 750 and 800.
Bottom Line: You could perhaps make the case that the SAT math test doesn’t accurately measure mathematical aptitude, but I’m not familiar with any strong advocates of that position. So assuming that the SAT math test does measure some important characteristics of mathematical abilities, I think we would have to conclude that “it is clearly the case that the best performers in mathematics are boys” (as Christopher comments), even if we can’t say that boys are better than girls on average because of the “sampling artifact” argument. But as I argue above, I find the “sampling artifact” explanation completely unconvincing and unsupported by the data over the last 50 years, and therefore conclude that “Actually, 50 years of test scores DO confirm convincingly that boys outperform girls on the SAT math test.”
Related: I highly recommend watching my original, classic “movie” below (“Boys vs. Girls on the 2010 SAT Test”) where I debunk the bogus “statistical artifact” myth of gender differences on the SAT math test.
