Scott Barry Kaufman in Scientific American:
A large number of well done studies have painted a rather consistent picture of sex differences in personality that are strikingly consistent across cultures (see here, here, and here). It turns out that the most pervasive sex differences are seen at the “narrow” level of personality traits, not the “broad” level (see here for a great example of this basic pattern).
At the broad level, we have traits such as extraversion, neuroticism, and agreeableness. But when you look at the specific facets of each of these broad factors, you realize that there are some traits that males score higher on (on average), and some traits that females score higher on (on average), so the differences cancel each other out. This canceling out gives the appearance that sex differences in personality don’t exist when in reality they very much do exist.
For instance, males and females on average don’t differ much on extraversion. However, at the narrow level, you can see that males on average are more assertive (an aspect of extraversion) whereas females on average are more sociable and friendly (another aspect of extraversion). So what does the overall picture look like for males and females on average when going deeper than the broad level of personality?