Larry Summers Redux and "Fulfilling the Potential of Women in Science Through Social Engineering"

From John Tierney's column in yesterday's NY Times "Daring to Discuss Women in Science":

"[Former Harvard President Larry Summers] acknowledged that there were many talented female scientists and discussed ways to eliminate the social barriers they faced. Yet even if all these social factors were eliminated, he hypothesized, the science faculty composition at an elite school like Harvard might still be skewed by a biological factor: the greater variability observed among men in intelligence test scores and various traits. Men and women might, on average, have equal mathematical ability, but there could still be disproportionately more men with very low or very high scores.

These extremes often don’t matter much because relatively few people are involved, leaving the bulk of men and women clustered around the middle. But a tenured physicist at a leading university, Dr. Summers suggested, might well need skills and traits found in only one person in 10,000: the top 0.01 percent of the population, a tiny group that would presumably include more men because it’s at the extreme right tail of the distribution curve."

MP: What Summers actually said was: "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."

Actually, there is persistent statistical evidence both that: a) boys outperform girls on the SAT math test (there is a difference in means), and b) there is significant "right tail disparity" on the SAT math test, i.e. boys are overrepresented for math scores on the high end (there is a difference in variability).  

The top graph above (data here) shows the persistent male-female SAT math test gap over time.  The 35-point gap in math test scores in 2009 (average score of 534 for boys and 499 for girls) is basically unchanged from the 36-point test score gaps in 1973 (525 vs. 489) and 1974 (524 vs. 488).  In other words, the male-female SAT math score gap has persisted for decades for a large sample size of more than 30 million American high school students who have taken the SAT since 1972. 

The bottom graph shows the "right tail disparity" for the 2009 math SAT test (data here).   For example, for perfect scores on the math SAT of 800, males (6,928) outnumbered females (3,124) by a ratio of 2.22 to 1. That is, 69% of test-takers who got perfect math scores were males vs. 31% of perfect scores by females. Or we could also say that there were 222 high school boys who got perfect SAT math scores for every 100 high school girls.

The graph further shows that boys outperformed girls at all 23 math test scores between 580-800 (10 point intervals, with male-female ratios above 1.0), and then for math test scores between 200 points and 570, girls outnumbered boys (male-female ratio below 1.0). Adjusting for the fact that 107,000 more girls (n=818,760) than boys (n=711,368) took the SAT in 2009 makes this evidence even stronger, since 0.974% of boys scored 800 on the SAT math test (6,928 out of 711,368) vs. 0.386% of girls (3,124 out of 818,760), for a ratio of 2.52 to 1 in favor of boys for perfect math test scores of 800, even greater than the 2:22 to 1 ratio for unadjusted scores.

Bottom Line: Based on math SAT scores, boys score significantly higher on average compared to girls by 30+ points, this gender gap in favor of boys is persistent over four decades, boys are significantly overrepresented for math test scores on the high end, and boys outnumber girls by a ratio of more than 2:1 for perfect 800 scores. 

Tierney also discusses new pending, federal legislation called “Fulfilling the potential of women in academic science and engineering,” which  if passed would empower the White House science adviser to oversee regular “workshops to enhance gender equity, and increase awareness of gender bias.”  Given the huge gender differences in the math SAT (both in mean and variance), isn't it possible that men are overrepresented in science and engineering because they have greater aptitude in those areas? If that's the case, no amount of federal legislation, short of mandated quotas, will result in the perfect gender parity outcomes that the gender activists seem determined to achieve.

Maybe the legislation should more accurately be called "Fulfilling the potential of women in academic science and through social engineering?