Some mathematicians have finally pointed out the really, really obvious problem behind a popular theory of sex differences: Men are purported to have more sex partners than women … but the math doesn’t add up. Folks loving the idea that men and women are intrinsically, inherently, biologically, different have long loved to cite things like the fact that men have more sex partners than women, which shows up in virtually any survey. It’s not logically possible, but people still cite the numbers as if they mean something. (“You keep using that word. I do not think it means what you think it means.”) Gee, I wonder if people studying and proclaiming numerous sex differences could be infected by any other forms of biased thinking?
update: broadsheet had the best headline: Chaste women + promiscuous men = impossible and some good commentary too in the article and one or two helpful points in the comments. Unfortunately, most of the commenters are stuck on arguing about the differences between median and mean (average), quibbling about the math professor’s take, and failing to understand that (a) the NYT article just did a sloppy representation of what the math professor said; and (b) at least some part of what the math professor is really getting at is the popular understanding and use of such studies (including frequent media stories). (Many of the commenters have fallen into the trap of never going back to the source to try to figure out what they’re talking about, so they’re arguing about misquotes and misunderstandings of third-generation reports about data. No wonder there’s confusion about median and mean.)
The NYT article of course didn’t help clarify anything about median or mean (that is after all part of the problem that leads to the necessity of the math professor speaking up) but they did, to their credit, get the lede implication right: The thing this really casts doubt on is the big, all-encompassing theories of human nature that argue that men are inclined to X, and women inclined to Y, because of their y and x genes respectively. So, the numbers in the surveys could be right or wrong, but the conclusions about “women’s nature” and “men’s nature” are not well-supported by relying on the median. It would have been cool if they had talked about the implications of mean and median for social sciences behavior: Are averages or medians more susceptible to social pressures, for instance? Seems plausible that those numbers would have different artifacts but I don’t know, and the NYT didn’t help.
Anyway, as the professor suggested, the numbers have to be off somewhere, because while, yes, mean and median are different, you’ve still gotta make those numbers reconcile somehow. In other words, if median and mean are different, then there have to be differences in mean among subgroups that generate the median. In other words, if most women are more chaste than most men, then some women have to be having a lot more sex than either most women or men.
The most recent survey (NCHS 2007 survey of sex & drug behavior of US adults) that precipitated this discussion showed that 29% of US men report having 15 or more female partners, and 9% of women report having 15 or more male partners. It’s a little difficult to imagine that the 9% of women have so many more partners than the 29% of men, on average, that they make up for the 91% of women who had fewer … My guess is that there is greater variability among female sex habits, that there is some real, intentional fudging in the self-reported data, and that there is some methodological and definitional problems in how men and women define sex (I’m thinking of rape: I know that some people forced to have sex nonconsensually would not “count” that person as a sex partner, whereas it seems plausible that the rapist might well count their victim as a sex partner, especially if the rapist didn’t so self-define).
The greater variability point, if true, is itself interesting: Since “greater variability” shows up so frequently in sociobiological arguments about there being more male geniuses and idiots, you’d think the “greater variability” argument would be of interest to them in the realm of sexual behavior, too.
update: slate covered it too, with the mean/median point. while focusing on the trees, slate managed to notice the forest in a single paragraph toward the end.