Yeah - there are also a lot more men than women in prison.
There has been a lot of research on this topic. You can not measure the testosterone in a group and make a prediction about who is going to commit a crime. If you measure testosterone on criminals, you can't make any prediction about what kind of crime they did.
There are weak associations such as risk taking (possible facilitated through increased dopamine transmitters), but there are much stronger links between criminals. To mention a few: Social economical status, social support structure, and childhood trauma is much better predictors than high testosterone.
Hormones are a terrible explanation for crime, even if they often have a weak association. Did you know that women are much more likely to have committed a crime during pms? The crime statistics support the link, but ask a researcher and they will list multiple reason why such correlation make for very weak association rather than strong evidence of a link between hormones and crime.
Well, if the group is mixed, with both men and women, then you can predict that 95% of the violent crimes will be committed by people with higher testosterone (i.e. men). Surely in that sense it's about testosterone, not genitalia?.
That's why it's very surprising to hear that the _level_ of testosterone among men has no predictive power.
Many research papers has been written on the topic of testosterone and violence, including meta studies. The general conclusions is... there is a weak link between testosterone and violence. No cause and effect, but there is a small amplification of existing behavior, a common finding among endogenous studies.
The full reason is complex, but a simplification is that testosterone increase preexisting behavior in relation to social status hierarchy. It makes individuals spend more energy in defending their place on the ladder (spending more time looking at faces to recognize threat, increased response to threatening faces, more suspicion against ambiguous faces). This in turn has a link towards violence, but only in cultures where status is given as an reward for violence.
But there is an additional complexity that should be mentioned. A lot of the effects of hormones such as testosterone only happen as a result of changing levels of hormones rather than absolute values. The absolute value has less of a predictive effect then changes over a short time frame.
I have a couple guesses:
1. This may be a period in which men experience the greatest status uncertainty and so may resort to violence in an attempt to solidify their place in a social hierarchy.
2. This is generally the age range during which many disorders that are more prevalent or severe in men (such as schizophrenia, bi-polar, etc.) begin to manifest.
1) I have not read any study however that looked at periods of social uncertainty, but it sounds plausible.
2) My guess would go towards the relation of frontal cortex maturation. Before fully maturation, other parts of the brain "step in" and handle some of the frontal cortex' role, but by around age 25 they stop doing that.
So, do you mean that such disorders originate from the frontal cortex, and that the reason they manifest by 25 or so is because it is at that point that the frontal cortex is no longer "supported" by other parts of the brain and it's flaws become apparent? Interesting if so.
You could alternatively look at the negative manifestations of variability, like increase crime and violence, and try to socially discourage it. Expose males to "crime is bad. bad men go to prison where they cannot have sex with women for many years. if you do crime you are bad." Observe whether crime rate of men relative to women decreases. If it does not, it is evidence that social encouragement is not responsible for the difference in crime.
You could also do a control where you discouraged men from achieving. "Nerds are gross" and see if that leads to a victory for feminism.
https://en.wikipedia.org/wiki/Judit_Polg%C3%A1r
The article has some quotations about Judits opinion:
"I always say that women should have the self-confidence that they are as good as male players, but only if they are willing to work and take it seriously as much as male players."
and after a tournsment in 1988 (12yo)
"These other girls are not serious about chess...I practice five or six hours a day, but they get distracted by cooking and work around the house."
Well, no, it hasn't, because whatever the one family does can't change society at large and the messages/treatment women receive from it. The quotes you provide are examples of that.
I first heard of this when researching chess. Men rank ~200 ELO points higher than women at chess, which is a fairly significant amount. Men also seem to do better at several other non-physical competitions like Go, video games, and Jeopardy. Plus, the history of math and science is dominated by men at the top.
It seems like men are not smarter on average, but they do peak higher (and valley lower).