We probably shouldn’t use the word “proven.” There are definitely statistically significant differences in quite a few areas.
By taking the difference between the means of two samples (men vs. women, in this case) and then dividing by the pooled standard deviation one gets effect size (d ). A d of 0.1 or less is considered nonexistant or trivial. 0.2 is considered small. 0.5 is moderate. A moderate score would correspond to, for example, a physical difference evident to the naked eye, such as height difference between 14-year old and 18-year old girls. A d of 0.8 or greater is considered large. If d=0.4, the pooled standard deviation is 40 percent of the difference between the means of the samples.
In mental rotation tasks (mentally rotating 3D objects and selecting which images “match”) men outperform women. (d=0.6 Voyer et al., 1995)
Males have been shown to outperform females in some aspects of mathematical performance. Scores on the Math component of the SAT have consistently favored males (d=0.5, Reisberg, 1998)
Females have been shown to outperform men in some verbal skills. Tests measuring verbal fluency (rapidly naming things that start with ‘k’, or types of fruit, for example), spelling, grammar, and verbal memory produced d values between 0.1 and 0.4 favoring women.
Using factor analysis, researchers looked at test scores from 187,000 German medical students’ applications. Reporting on three factors - reasoning, perceptual speed, and memory - they found reasoning favored men (d=0.56), memory favored women (d=0.5), and no difference in perceptual speed.
Some of the most marked differences are found in aspects of sexuality. Men are more accepting of casual sex (d=0.81). There are large differences in what men and women seek in sexual partners. Women are attracted to older partners, men to younger (d=0.9). Men are more concerned with physical attractiveness (d=0.6). Women are more concerned with a partners status or wealth (d=0.5). One of the greatest sex differences is found in interest in visual sexual stimuli. Men score higher than women (d=1.3).
There are also emotional differences, such as aggression - d=0.5, favoring men.
On that note, I have to go to hockey practice.