In a previous post on the slightly elevated average intelligence of military personnel relative to the civilian population, Dr. Bruce Charlton suggested separately breaking out the GSS data for men and women. Converting Wordsum results with the assumption that the mean score for whites, by gender, is equivalent to an IQ of 100 with a 15 point standard deviation, the average IQ for men and women who are currently working for or have previously worked for either the military or the Department of Defense:
Men -- 103.5
Women -- 93.3
The respondent pool of 40 men and 39 women is small, but the difference in averages is two-thirds of one standard deviation. It's not trivial, although it is at odds with the military's official statistics, so it's necessary not to see these results as at all definitive.
Thinking the gap might be the result of differences in background, I checked the educational attainment of each gender. The average for the military men is 13.21 years and for military women 13.28, so we're not comparing male officers with enlisted women.
I can't muster much in the way of useful speculation as to why the gap exists. If I had to venture a guess, it'd be that girls who want to become soldiers or police officers tend to have testosterone and athleticism levels further above the female average than aspiring male soldiers and police officers do relative to other males, as the number of girls who want to go into these professions is much smaller than the number of boys who do. Consequently, these characteristics better predict a martial career for women than they do for men, who are selected for by other means, of which above average intelligence is one (as military personnel are, on average, more intelligent than non-military personnel are).
When I was in ROTC, all five of my fellow female cadets probably had IQs under 110 and testosterone levels that put them at the 110th percentile among women. The only especially sharp woman I came across during my time with the military was a JAG who had been awarded officership because she had a JD and taught courses for the program (she was also married to a full colonel). She never went through ROTC or OCS, and only went through basic a couple of summers after she started teaching.
Whatever the reason, this suggests that restricting direct combat roles exclusively to men is a good idea, since greater intelligence reduces the likelihood of military personnel suffering injuries.