Wendy Morrison and Grace Finley in AEI question whether this is true. We know there are significantly more boys among the top scorers, but is this true on average? Their first suggestion about why it may not be, high scoring boys dragging up the mean, is pretty inane. 1 percent of the population can’t drive up a mean by very much unless it was very non-normal. But their idea that low scoring boys might simply not take the test is plausible.
The ratio of boys to girls around that age is about 1.05. The ratio of boys to girls who took the SAT is a much lower, at .87. Thus, if girls participated in the test at the same rate as boys, you’d expect ~17 percent of the females who took it to not take it. Assume that these girls are all at the bottom of the score distribution and assume the distribution is normal. Thus, removing the bottom 17 percent of the scorers would result in the average moving from the 50th percentile to the 58.5th percentile. As InverseNormal(.585) = .215 SD’s, the female score would improve by .215 SD’s * (116 points/sd) = 25 points. As the female average score is 494, this would give them a new average of
419 519, still trailing the male average by 5 points. Of course, if you did reduce female participation by 17 percent, with the females comparing to the female average in the same way that the missing males compare to the male average, you wouldn’t shave off the entire bottom 17 percent, you’d take a varied sample mostly from the bottom 50 percent, so the improvement would be much less than 25 points. Thus, it is clear that boys do better than girls on the SAT and this can’t be explained by boys selectively not taking the test.
I looked at the data for eleventh graders on California’s 2015 state standardized test and found that girls score higher.(Too see this, go here and select “Review Results by Group/Subgroup.”) In California, you can’t drop out until you’re 18 years old, so the effect on eleventh graders should be small, and the gender ratio is much closer to it’s true value, at 1.033 males per female. In any case, it would advantage the boys, as a larger number of dumb boys would drop out. My hypothesis to explain this is that boys are more likely to slack off on a test where the result doesn’t effect them.
My comment on the post was deleted by AEI. I know that two people from the website clicked-through to my site, so I doubt it was immediately removed by a spam-bot because it contained a link. It was probably removed by someone at AEI, not necessarily the authors. Meanwhile, the following comment was not deleted:
Wendy Morrison and Grace Finley proving that girls and women just aren’t that good at math.
While I understand the urge to post these kinds of comments, and have on occasion indulged in it myself, keep in mind that they’d much rather get those kinds of comments than reasoned critique. I’ve noticed a similar effect on the Jewish Daily Forward website, with the most radical 1488er comments getting tolerated while more reasonable ones got memory-holed.
My comment at AEI is back up. Mark Perry emailed me to say it was not removed by anyone at AEI, it might have been removed automatically by the spam filter.