This is a pretty sparse field, given the human tendency to look for and to magnify any gender differences and the similar tendency to ignore gender similarity as a similarity. When the two sexes are the same, the category "gender" drops out of the analysis altogether.
Usually. But I spotted two studies which are about gender similarity. I haven't vetted either one of them, but the point is to popularize some studies from the other side of the fence, so to speak, the types which tend not to get popularized much.
First, one study has analyzed whether sex differences are something that can be analyzed as taxonic:
But what of all those published studies, many of which claim to find differences between the sexes? In our research, published recently in The Journal of Personality and Social Psychology, we shed an empirical light on this question by using a method called taxometric analysis.The authors point out that some other characteristics indeed seemed to be taxonic in their study: physical size, athletic ability and sex-stereotyped hobbies like playing video games and scrapbooking.
This method asks whether data from two groups are likely to be taxonic — a classification that distinguishes one group from another in a nonarbitrary, fundamental manner, called a “taxon” — or whether they are more likely to be dimensional, with individuals’ scores dispersed along a single continuum.
The existence of a taxon implies a fundamental distinction, akin to the difference between species. As the clinical psychologist Paul Meehl famously put it, “There are gophers, there are chipmunks, but there are no gophmunks.”
A dimensional model, in contrast, indicates that men and women come from the same general pool, differing relatively, trait by trait, much as any two individuals from the same group might differ.
We applied such techniques to the data from 13 studies, conducted earlier by other researchers. In each, significant differences had been found. We then looked more closely at these differences to ask whether they were more likely to be of degree (a dimension) or kind (a taxon).
The studies looked at diverse attributes, including sexual attitudes and behavior, desired mate characteristics, interest in and ease of learning science, and intimacy, empathy, social support and caregiving in relationships.
Across analyses spanning 122 attributes from more than 13,000 individuals, one conclusion stood out: instead of dividing into two groups, men and women overlapped considerably on attributes like the frequency of science-related activities, interest in casual sex, or the allure of a potential mate’s virginity.
Even stereotypical traits, like assertiveness or valuing close friendships, fell along a continuum. In other words, we found little or no evidence of categorical distinctions based on sex.
Though I think the reasons for the sex-stereotyped hobbies themselves may not be taxonic but based on complex societal influences and individual interests and the dance between the two of them. For example, video games have been coded as male and they also mostly have topics which are traditionally male-linked. Likewise, scrapbooking has been coded as female and is largely about children. Yet it would be easy enough to think of topics for scrap books which would appeal to men or boys and it would also be easy to create video games that would appeal to women and men. In short, it's not that there is something inherently sex-linked about the acts of playing video games or scrapbooking.
In any case, this study seems to me to repeat something that might be obvious: Individuals differ in all sorts of ways and very few schema allow us to put all women into one class and all men into another class. But of course those who believe that men and women are inherently and eternally two different types of creatures altogether will never be persuaded by anything of this sort.
Another study of interest in this context has to do with whether fathers can tell when it is their child who is crying, rather than some other child. Past studies have suggested that mothers are better at this than fathers. This study finds no difference. Here is the abstract:
Previous investigations of parents’ abilities to recognize the cries of their own babies have identified substantial and significant sex differences, with mothers showing greater correct recognition rates than fathers. Such sex differences in parenting abilities are common in non-human mammals and usually attributed to differential evolutionary pressures on male and female parental investment. However, in humans the traditional concept of ‘maternal instinct’ has received little empirical support and is incongruous given our evolutionary past as cooperative breeders. Here we use a controlled experimental design to show that both fathers and mothers can reliably and equally recognize their own baby from their cries, and that the only crucial factor affecting this ability is the amount of time spent by the parent with their own baby. These results highlight the importance of exposure and learning in the development of this ability, which may rely on shared auditory and cognitive abilities rather than sex-specific innate predispositions.
The whole question of how human mothers differ from other animal mothers is fascinating. I haven't read enough in the field to say much, yet, but it seems that some applications to human child-rearing from the rest of the animal kingdom are based on theories which might not apply to primate mothers in the first place.
For example, the early theories of the importance of bonding seem to have come from species where bonding (almost an imprinting, along the Konrad Lorenz lines) is crucial for proper mothering. But those species are not primates, and primate studies suggest that cultural learning is an important part of learning how to mother in chimpanzees, for example.
As I mentioned above, I haven't looked at this study in detail. But what it seems to suggest is that those parents who spend time with their children get good at recognizing that child's cry, whether they are mothers or fathers. If earlier studies did not take into account the time spent with the child, their results could have followed from the fact that most infant care is done by mothers, not from some difference in parenting instincts between mothers and fathers.