It’s sort of a generalized approximation (like most layperson reports of data), but there appears to be some research behind it, though if that research is representative of the whole picture is beyond my ability to comment.
Though a number of studies have shown that most victims of intimate partner violence (IPV) are women, it’s not unanimous; John Archer(i) published a meta-analysis in 2000 showing women committed slightly higher rates of physical aggression than men in heterosexual relationships, but that women tended to be injured more frequently in intimate partner aggression, where he gives a number of 62% (implying that men make up 38% of injured partners, which isn’t far off from the initial claim in your question, though I wouldn’t overstate the significance of this one study producing a similar number on face value alone).
With the time I gave myself to blow off work and look for data, I had a hard time finding much even on simple incidence and prevalence rates. Much more common in my results were studies done with [female victims of intimate partner violence] as a subject population that look at specific dimensions within [domestic violence committed against women] (a lot of stuff about IPV’s influence on pregnancy which holy shit that’s a bleak thing to learn about).
Also in the mixed bag my (admittedly limited) research produced, there were a few studies commenting on IPV’s role in fear of crime, a large umbrella where men comprise most of the victims, but that don’t address your question(ii), or that, among intimate partner murder victims, most of them, about 77%, are female(iii).
(i) Archer, J. (2000). Sex Differences in Aggression Between Heterosexual Partners: A Meta-Analytic Review. Psychological Bulletin, 126(5), 651.
(ii) Broll, R. (2014). ‘Criminals Are Inside of Our Homes’: Intimate Partner Violence and Fear of Crime1. Canadian Journal Of Criminology & Criminal Justice, 56(1), 1-22. doi:10.3138/cjccj.2011.E24
(iii) Smith, S. G., Fowler, K. A., & Niolon, P. H. (2014). Intimate Partner Homicide and Corollary Victims in 16 States: National Violent Death Reporting System, 2003-2009. American Journal Of Public Health, 104(3), 461-466. doi:10.2105/AJPH.2013.301582
For a less empirical angle, among scholars and other clinicians I’ve spoken to, most of them have commented to me that the traditional conceptions of “the battered wife” and the data representing it are incomplete, and that recent findings seem “a lot more mutual,” that many couples assault each other equally/reciprocally in a way that older studies haven’t reflected. Take that for all the unsourced value it has.
Additionally, there’s a question of language (that influences perception and report rates). How is “domestic abuse” delineated from “intimate partner violence” from “having a fight” and, more importantly, does everyone share definitions?
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