Larry Summers Vindicated? Global Study Shows Greater Male Variability in Math, Reading Scores
The tables above show selected statistics from the paper Global Sex Differences in Test Score Variability (see summary here), published by two economists, one from the London School of Economics and the other from the Helsinki School of Economics. Analyzing standardized test scores in reading and mathematics from the OECD’s "Program for International Student Assessment" (PISA), a survey of 15-year olds in 41 industrialized countries, the authors found that:
Our analysis of international test score data shows a higher variance in boys' than girls' results on mathematics and reading tests in most OECD countries. Higher variability among boys is a salient feature of reading and mathematics test performance across the world. In almost all comparisons, the age 15 boy-girl variance difference in test scores is present. This difference in variance is higher in countries that have higher levels of test score performance.
Sex differences in means are easier to characterize: It is evident from the PISA data that boys do better in mathematics, and girls do better in reading. This has a compositional effect on the variance differences as well. The higher boy-girl variance ratio in mathematics comes about because of an increased prevalence of boys in the upper part of the distribution, but the higher variance in reading is due to a greater preponderance of boys in the bottom part of the test score distribution. Because literacy and numeracy skills have been shown to be important determinants of later success in life (for instance, in terms of earning higher wages or getting better jobs), these differing variances have important economic and social implications.
We therefore confirm that 15-year-old boys do show more variability than girls in educational performance, with specifics that differ according to whether mathematics or reading are being studied and tested. These results imply that gender differences in the variance of test scores are an international phenomenon and that they emerge in different institutional settings.
1. The results above show that for both the U.S. (Table 1) and the global group of 41 countries (Table 2), the mean math test scores for 15-year boys are significantly higher than the average score for girls, but the reverse is true for reading test scores: girls score significantly higher than boys on average in reading.
2. For both the U.S. and the 41 countries in the global group, the variability of boys' test scores for both reading and mathematics is significantly greater than the variability of girls' test scores (at the 1% level in all cases), suggesting that there are more boys in the upper and lower tails of the test score distributions.
3. Looking at the top 5% and the bottom 5% of test scores, we can see that boys are overrepresented in almost every case:
a. In the bottom 5% of reading scores, there are 245 boys for every 100 girls in the U.S. (220 boys for every 100 girls for the world group), and in the top 5% of reading scores there are 167 girls for every 100 boys (172 girls for the global group).
b. In the bottom 5% of math scores, there are 121 boys for every 100 girls in the U.S. (94 for the global group), and in the top 5% there are 172 boys for every 100 girls (170 girls for the world group).
In other words, the results indicate that boys' test scores are significantly more variable than girls' test scores, resulting in boys being significantly overrepresented in both the bottom 5% and the top 5% of students in the U.S., and these outcomes are a global phenomenon.
Bottom Line: Can Larry Summers get his job back as president of Harvard, for saying basically the same thing?
"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."?