Blog Post

AEIdeas

There has been a long-standing, and often very emotional debate about whether there are any gender differences in mathematical ability. If you have any doubts about how emotional and irrational the debate can get, just ask economist Larry Summers, who was forced to resign as president of Harvard (in part) for daring to suggest that there is statistical data showing that the variability of male math intelligence is different (greater) than the variability of female math ability. Specifically, Summers made this completely innocuous statement in 2005 that amazingly led to his ouster as president of Harvard:

It does appear that on many, many different human attributes – height, weight, propensity for criminality, overall IQ, mathematical ability, scientific ability – there is relatively clear evidence that whatever the difference in means-which can be debated – there is a difference in the standard deviation, and variability of a male and a female population. And that is true with respect to attributes that are and are not plausibly, culturally determined. If one supposes, as I think is reasonable, that if one is talking about physicists at a top twenty-five research university, one is not talking about people who are two standard deviations above the mean. And perhaps it’s not even talking about somebody who is three standard deviations above the mean. But it’s talking about people who are three and a half, four standard deviations above the mean who are in the one-in-5,000, one-in-10,000 class.

Note that Summers wasn’t saying that men necessarily have greater mathematical ability than women, only that the variability (or standard deviation, the most common statistical measure of variability) of male math ability is greater than the variability of female math ability. Implication? More male than female math geniuses, but also more males than females with math aptitude far below average who are “math idiots” or who have severe learning disabilities.

On the other side of the debate is Janet Hyde, professor of psychology at the University of Wisconsin, who has made statements like this that summarize her position:

There just aren’t gender differences anymore in math performance. So parents and teachers need to revise their thoughts about this. Stereotypes are very, very resistant to change, but as a scientist I have to challenge them with data.

Well, I’m going to have to challenge Professor Hyde and her followers with some data from a recently-released OECD study “The ABC of Gender Equality in Education: Aptitude, Behaviour, Confidence.” The study contains test results from students worldwide in 65 OECD (and partner) countries who participated in the Programme for International Student Assessment (PISA) 2012. According to the OECD, “Around 510,000 students between the ages of 15 years 3 months and 16 years 2 months participated in PISA 2012 as a whole representing about 28 million 15-year-olds globally.”

So it’s a pretty comprehensive study of the cognitive abilities of 15-year-olds, and allows us to determine empirically whether or not there are gender differences in mathematical abilities of high school students around the world. The students also took tests in reading and science, but I’ll focus here on the math test results, although I’ll just note that girls significantly out-performed boys on the reading test by 39 points on average and slightly out-performed boys on the science test by 3 points on average.

Some of the PISA 2012 math test results are summarized in the chart above, based on the raw data are available here (see Table 1.3a). Here are some of the key findings on the differences in mathematical ability by gender from the PISA 2012:

1. The mean score for boys on the math test for students in all 65 countries (477.5 points) was 8 points higher than the mean score for girls (469.5 points), see the middle bar in the chart. By individual country, boys scored higher on the math test than girls in 52 countries (statistically significant differences in 38 of those countries), with the largest differences in favor of boys in Colombia (25.5 points), Luxembourg (25.1 points), Chile (25 points) and Costa Rica (23.6 points). Girls scored higher than boys in 13 countries, with statistically significant differences in 5 countries (Qatar, Iceland, Jordan, Malaysia and Thailand).

2. The average standard deviation for male scores (92.2 points) in the 65 countries was higher than the standard deviation for female scores (86.1 points) by more than 6 points. By individual country, the standard deviation of male math test scores was higher than the female standard deviation in all of the 65 countries except Liechtenstein, and the difference in variability was statistically significant in 45 countries. These empirical findings from the PISA 2012 confirm Summers’ statement above that there is substantial evidence that the variability of male math ability (among many other factors) is greater than the variability of female math ability.

3. What’s especially interesting is that as you consider math test scores at the higher percentiles, the gender gap in favor of men widens considerably. For example, boys scoring at the 95th percentile (for boys separately) had an average test score (630.7 points) for the 65 countries that was 18.4 points higher than the average female score at the 95th percentile for girls (612.4 points). By individual country, boys scored higher than girls on the math test at the 95th percentile in 63 out of 65 countries, and the male advantage was statistically significant in 43 countries. The countries with the largest male advantages at the 95th percentile were Israel (42.6 points), Colombia (41.5 points), Costa Rica (34.7), Korea (34.6) and Italy (33.2).

At the 90th percentile, boys scored 16.5 points higher than girls (598.4 vs. 581.9), and at the 75th percentile there was a 12.7 point difference in favor of boys.

4. On the lower end of math scores, girls outperformed boys at the 5th percentile (329.9 vs. 328 points) by about 2 points and at the 10th percentile by 0.8 points (359.8 vs. 359.0 points).

Bottom Line: The PISA 2012 international math test results reveal significant gender differences in favor of boys on standardized tests of mathematical ability, similar to the gender differences in favor of boys on the math SAT test as I reported on CD last October. For more than 40 years, American high school boys have outperformed girls by more than 30 points on the math SAT test in every year between 1972 and 2014, which translates to a percentile difference of 10 points or more (55th percentile for boys vs. the 45th percentile for girls in 2014). For perfect tests scores of 800 points on the math SAT test, boys outnumbered girls by more than 2-to-1 in 2014, providing more evidence that boys have greater abilities than girls on average at very high levels of math performance. Stated differently, boys outnumber girls on the extreme high-end of the distribution of mathematics ability, which is a direct result of the fact that the variability of male math abilities is greater than female variability. The PISA 2012 math test results also show that 15-year-old boys outperform girls on average globally, and the male advantage in math test scores increases at higher percentiles like the 75th, 90th and 95th percentiles. Compared to the 8-point male advantage on average for the 65 countries, the average male advantage on the PISA 2012 math at the 95th percentile increases to 18.4 points (and is above 30 points in ten countries).

Given the significant gender differences in favor of boys on the math SAT test and now on the PISA 2012 math test, Professor Janet Hyde and others may have to revise their stereotypes that “there just aren’t gender differences anymore in math performance.” As an economist, I have to challenge them with data, which clearly do show significant gender differences in favor of boys for average math performance and for the greater variability of male math performance.