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Mark Perry recently wrote a blog post about the average performance of high school girls and boys on the math section of the SAT, accompanied by a colorful tweet with the caption, “SAT results confirm pattern that’s persisted for 45 years — boys are better at math than girls.”
Dr. Perry’s conclusion — “high school boys are better at math than girls” – may not reflect the nuances that drive, at least in part, the summary statistics he cites.
As we illustrate below, something as simple as an average SAT score can obscure important underlying facts. To demonstrate this, imagine a hypothetical world in which girls are better at math than boys.
In this hypothetical world, four boys and four girls take the SAT, and the girls earn scores of 500, 500, 451, and 525, while the boys earn a 410, a 436, a 450, and an 800. Just as in the 2016 real world data, the female average is a 494, lower than the male average of 524. In this scenario, even though boys do better on average than girls, of the top five performers on the SAT, four are girls, and of the bottom three performers (there are eight people in this world, remember) all three are boys. It would be easy to argue that girls are “better” than boys at math in this world, even though on average boys score better than girls. (The old story about Bill Gates walking into a bar and causing the average income to jump into the millions comes to mind.)
Clearly averages can be deceptive as we’ve just shown, but this is not the only important caveat to Dr. Perry’s story. Dr. Perry’s tweeted conclusion implicitly assumes that boys and girls who take the SAT are basically the same – “representative,” the statisticians would say – of the general population of all boys and girls.
We have eight high schoolers in our hypothetical world. Now, let’s add four additional boys and four additional girls. Imagine that the four additional girls take the SAT and each scores a 494. Now imagine that the four additional boys don’t take the SAT because they do not plan on pursuing a college education. The male average remains a 524, and the female average remains a 494.
Put simply, in this scenario, 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.”
However, if in our hypothetical world it was possible to force each boy and girl to take the exam, we would likely see the male average drop, as the decision to not take the exam is almost certainly related to one’s expected outcome. For example, if when forced to take the exam, the four boys received scores of 350, 350, 450, and 450. This would bring the male average down to 462, well below the female average.
Put simply, in this scenario, 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.
Our hypothetical world is also consistent with the other data Dr. Perry presents. Dr. Perry writes that, “For the 117,067 students with SAT math scores in the highest 700-800 point range, high school boys represented 61.5% of those students (71,999) and the 45,068 girls in that group were 38.5% of the total.” In short, there are a larger number of very high performing boys than girls. This finding is consistent with our hypothetical, in which a few high performing boys are pulling up the male average.
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.
We certainly do not mean to suggest that our hypothetical distributions are exactly representative of the true distributions of math ability for boys and girls, or that the distributions of math ability for boys and girls are identical. However, because an alternate conclusion can be drawn from the statistics that Dr. Perry cites, a more thorough analysis is required.
Finally, we should also note that while performance is certainly related to innate ability, ability may not be the only factor that affects performance, and an examination of the evidence of the effects of gender narratives and culture on academic performance may be warranted.
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