More on the Gender Gap for NAEP Test Scores

The chart above is based on NAEP test scores (data here) for U.S. 12th grade high school students in economics, mathematics, science, reading and writing. The data show that:
1. Male high school students scored higher than female students on the economics, mathematics and science exams, and those differences in test scores were all statistically significant (1% level or higher).
2. Female students scored higher than male students on the reading and writing exams, and those differences were statistically significant (1% level or higher).
3. For all five exams, the standard deviation for male test scores was higher than the standard deviation for female students, confirming previous studies that have found that regardless of the differences in mean intelligence or test scores between males and females, the variability of male intelligence (and/or test scores) is usually greater than the variability of female intelligence (or test scores).
4. At the 90th percentile of performance, the gap between male and female test scores increases for the economics, mathematics and sciences exams, compared to the gap for all students on those exams. As Dr. T says in a comment on this CD post, "exceptional boys do much better than exceptional girls," and this is a direct consequence of the fact that male test scores have a higher variance (and standard deviation) than female test scores. In other words, even if the mean scores were the same for males and females on these exams, the top 10% of male students would have higher test scores on average than the top 10% of female students.
5. Female students scored 13 points on average higher than males for the reading exam, and 18 points higher for the writing exam, and both differences were statistically significant (1% level or higher).
6. At the 90th percentile, the female-male gap narrows by 2 points for the reading exam (from 13 to 11 points) and by 3 points for the writing exam (from 18 points to 15 points). This could be explained by the greater male variance in test scores for the reading exam (standard deviation of 39 for males vs. 37 for females) and for the writing exam (standard deviation of 35 for males versus 33 for females). Male students are worse on average than females for the reading and writing, but are overrepresented in the upper tails of the distribution (3-4 standard deviations above the mean) compared to females, and this allows males at the 90th percentile to come closer to matching female test scores compared to males at the mean.
Bottom Line: Male high school students outperform female high school students for economics, math and science; and female high school students outperform males students in reading and writing. Additionally, the variability of male test performance (and probably intelligence) is greater than the variability of female test performance, and this applies to ALL of the five subjects. In other words, there will probably always be more male than female geniuses (3-4 standard deviations above the mean) and more male than female idiots (3-4 standard deviations below the mean). Thanks to Dr. T, whose comments inspired this post.
Originally posted at Carpe Diem.