## The Gender Gap in Math Is Not Universal

“Maryam Mirzakhani is the first woman to ever win the Fields Medal, known as the Nobel Prize of mathematics, in recognition of her contributions to the understanding of the symmetry of curved surfaces,” according to Bjorn Carey, a writer for the *Stanford Report*.

Mirzakhani was born, raised, and educated at the undergraduate level in Iran. I might have been shocked by this detail, based on the bad press the Middle East gets on women’s rights, if I hadn’t just finished analyzing global student math test scores over the summer.

As part of useR! 2014, the Organisation for Economic Co-operation and Development (OECD) provided data for an analysis competition from the Programme for International Student Assessment (PISA) 2012 on test scores that examine the skills of 15-year-old school students around the world.

The data contain scores on math, science, and reading, along with loads of other information about the students’ backgrounds and schooling. Between 3,000 and 33,000 students were tested for each of more than 60 countries, yielding data on 485,490 teenagers.

Along with two of our graduate students at Iowa State University, Luke Fostveldt and Alex Shum, and a colleague from Schneider Electric in Cedar Rapids, Ian Lyttle, I analyzed the relationship between test scores and gender. The submissions to the competition can be viewed here.

What I learned from making a few pictures of the data surprised me.

Figure 1 looks at the math gender gap. Math scores were averaged separately for girls and boys for each country. The difference between boys and girls was calculated and a simple t-test was conducted to determine the significance of the magnitude of the difference. The dotplot shows the different means in order of country, with the biggest gender gap to the smallest.

What surprised me was there are five countries in which the gender gap is reversed. It was even more shocking to notice the country names: Jordan, Qatar, Thailand, Malaysia, and United Arab Emirates. There also are many countries in which there is no significant difference in the average math test scores. Overall, the biggest differences are about 30 points, which is quite small relative to the overall scale. Scores are reported on a 0–1,000 scale, averaging approximately 450.

The same analysis was conducted for the reading scores, with equally surprising results.

Figure 2 shows the dotplot of the difference between the averages for each country. The differences range from 12–80 points in favor of girls. Girls score better than boys do, on average, in every country.

Averages paint patterns with a broad brush. A big message in this data is that the biggest source of variation is from individual to individual.

Figure 3 shows top scores and lowest scores for each country for girls and boys. Although, on average, girls do better than boys do on math in the United Arab Emirates, the top score is obtained by a boy, and it is approximately 200 points higher than the top girl’s score. For the USA, this is flipped: The top score is achieved by a girl, and it is almost 80 points higher than the top boy’s score. In about a dozen countries, the top score is achieved by a girl.

On the other hand, if we look at the lowest scores for each country, we see that many can be attributed to boys. For the top scores, the United States is a little lower than halfway down the chart, indicating the best math talent in the country performs worse than half the countries in the study. However, in terms of low scores, the United States is in the top 10, which says it does not have a wagging tail.

We hear so much about the gap in favor of boys in the United States, and also my home country, Australia, in the news. There is clearly substantial angst about it, and it is clearly real in these countries and many others. However, the PISA data would suggest it is not insurmountable. There are many countries where there is no math gap, and a handful of countries where it is reversed.

What is alarming is the reading gap, where universally boys perform worse, on average, than girls. We don’t hear anything about this, but it has to be a problem for the boys of today. Reading is a critical component of communication.

#### About the Author

Dianne Cookis a professor of statistics at Iowa State University and an ASA Fellow. Her primary research interest is on visualizing data using interactive graphics. She earned her PhD from Rutgers University in 1993, while working closely with researchers at Bellcore, on grand tour and projection pursuit methods, implemented in the software XGobi. At ISU, she teaches data mining, multivariate analysis, data technologies, and introductory statistics, and she works with graduate students in the Human Computer Interaction program and bioinformatics and computational biology programs.

**Visiphilia**covers the practice, developments, and innovations in statistical graphics; the interplay between statistics, computer science, and information visualization; and the effective use of visualization in statistical practice.