Men and women are different. A seemingly obvious fact to most of humanity but a long-time subject of controversy within psychology. New large-scale results using better empirical methods are resolving the debate, however, in favor of the person in the street. The basic story is that at the broadest level (OCEAN) differences are relatively small but that is because there are large offsetting differences between men and women at lower levels of aggregation.
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Moreover, the differences in the subcategories are all correlated so while one might argue that even among the subcategories the differences are small on any single category when you put them all together the differences in male and female personalities are large and systematic.
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In other words, you can predict whether a person is male of female from their personality traits almost as well as by looking at their face.
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I have also pointed out that gender equality magnifies differences in gender choices and behavior which is probably one reason why fewer women enter STEM fields in societies with greater equality. Consistent with this, personality differences between the sexes are large in all cultures but “for all of these personality effects the sex differences tend to be larger– not smaller– in more individualistic, gender-egalitarian countries.”
Addendum: See John Nye and co-authors on testosterone and finger length for some biological correlations.
Sex Differences in Personality are Large and Important, by Alex Tabarrok