I’ve literally just finished a neuropsych essay on this very subject. Well, the subject was “Is there a relationship between the size of the brain and intelligence?” but I included evidence for sex differences.
The answer to the aforementioned question is a decided YES, found repeatedly in dozens of studies using various measures of brain size (often MRI) and intelligence (usually in IQ scores, but other methods have been used). The correlation between brain size and intelligence ranges between 0.35 and 0.69, and averages at about 0.44. A moderate correlation.
Here’s what I found on sex differences.
“Broca may have been one of the first people to confirm a sex difference in brain size in 1861. With a sample of a few hundred brains, he found that male brains were on average 181 grams heavier than female brains. Even when controlled for height and age, the average difference was still 113 grams. This difference has been found across the races, and according to researchers, body size differences only account for 30% of the sex difference in brain size (Rushton, 1997). Since men tend to have larger brains than women, and brain size and intelligence are related, one would expect males to have a higher average intelligence. However, despite these two facts, it has long been insisted that there are no sex differences in intelligence – an example of illogical thinking known as the “Ankney-Rushton anomaly”. Lynn (1999) has conducted a developmental study, taking into account the different rates of growth of boys and girls, and has found that at the age male growth overtakes female growth (at age 16), men develop a 4 point IQ advantage that lasts into adulthood. This finding is consistent with the brain size-intelligence theory, because of men’s larger brains in relation to women’s. Another developmental study found that there is a direct relationship between the narrowing and broadening of sex differences in intelligence and brain size over the ages of 7 to 18 ages. Because girls and boys have different growth rates, their respective brain sizes also have different growth rates, and the differences in their IQs at different developmental stages indicate that the IQ score is associated with brain size (Lynn et. al., 2000). Ankney (1992, 1995, in Rushton, 1997) hypothesised that these sex differences in brain size and intelligence were evolutionary in origin. Men’s role in human societies as a hunter made it necessary for them to develop more brain tissue, required for processing spatial information. However, Wickett et. al. (2000) unexpectedly found that the higher the spatial imaging loading of a test, the less it is correlated with brain volume. Lynn (1994, in Rushton, 1997) proposed that over time men’s brains enlarged to enhance their social dominance [nb. the primary area of evolutionary brain enlargement in primates is the neocortex, which is strongly associated with complex social behaviour], and thus make them more reproductively successful.”
For those of you who mentioned Stephen Jay Gould, he was academically bitch-slapped by the Rushton (1997) article I mentioned, Race, intelligence, and the brain: The errors and omissions of the “revised” edition of S.J. Gould’s The Mismeasure of Man (1996), found in Personality and Individual Differences, 23, 169-180. In particular he was crucified for ignoring all data which (conclusively) contradicted his theories, and omitting paragraphs that were in his first edition because they turned out to be so blatantly incorrect, instead of using the opportunity to correct them.
I should add that I am an intelligent female, I am not sexist, and I’m not saying this is any excuse for men to go around with inflated egos. But I also think that it’s silly to deprive ourselves of knowledge that isn’t PC. Anyway, there is some question about whether it is justifiable to compare men and women in the first place, and Rushton (1997) admits that his definition of intelligence as a sum of verbal comprehension, spatial, and reasoning abilities allow that 4 point difference in IQ he claimed; IIRC 2.3 of men’s 4 IQ point advantage is in spatial abilities. (For the record, it is well documented that men tend to have superior spatial abilities, as is evolutionarily expected.) I haven’t read anything that suggests that women have a wider range of IQ scores, but I certainly don’t think women on average are idiots, and I think that there are logical explanations for these results.