Oxford University, one of the most prestigious universities in the world, is concerned that its female students are doing far less well than its male students on math and computer science exams, and has adopted a novel remedy which critics have reportedly slammed “as ‘sexist’ as they believe it suggests that women are the weaker sex.”
Since it involves nothing more than extending the time for students to take such exams, and the extension applies equally to male and female students alike, it is hard to see how it could reasonably be characterized as “sexist,” says public interest law professor John Banzhaf, who nevertheless suggests that the change might do little to eliminate the disparity because of what may be called tail differences.
Many claim the females do as well in math as males, and there is considerable data to back up that claim. However, for least 40 years, boys have consistently earned significantly higher math scores on the SATs, and almost twice as many boys continue to land in the 700 to 800 SAT score range (800 is perfect).
This large gap between the genders has been documented for many math tests, including the AP calculus test, the mathematics SAT, and the quantitative portion of the Graduate Record Exam (GRE).
One explanation, says Banzhaf – the mathematician who invented the “Banzhaf Index” – and one reason why simple fixes such as more time to complete exams is not likely to eliminate these big differences, is that although both genders have about the same average (mean) grade, males do better at the very high end of the performance curve, just as they do worse than females at the lower end of the curve.
In mathematical terms, the mean math grades for both genders may be about the same, but the standard deviation for males is substantially higher, suggests Banzhaf.
To understand this, picture two graphs of math grades, one for females and one for males. They may both be centered at the same point because the mean or average is about the same, but the curve for males is substantially wider; i.e. it has a greater standard deviation.
As a result, when you get to the very highest levels of performance (e.g., the top 5%), there are far more males than female. By the same token, when one looks at the very poorest levels of performance (e.g., the bottom 5%), males also predominate over females.
For example, studies have shown that the ratio of males to females who score in the top 5% in high school math has remained constant at 2 to 1 for the past 20 years. The same appears to be true for the students who scored 800 on the math SAT in 2007.
While there are many reasons being offered to explain this very high but also very persistent gender difference, one could simply be the difference in the distribution of the math grades as represented by two different curves: the one for female grades being significantly narrower (having a smaller standard deviation) than the one for males. This refers to what mathematicians call the “tails.”
For example two researchers “found that the gender gap widens dramatically when examining the right tail of the performance for students who participate in the American Mathematics Competition.”
Although a federal judge once found that awards based upon SAT scores unlawfully discriminated against females because they didn’t perform as well in math as males, the underlying cause – that males have longer tails than females – may not be easily changed.