more fun with sexual means

I, and about a zillion other people, responded to Gina Kolata's article in the NYT last week, in which medians and means were confused, in an article claiming that men had more sexual partners on average than women.

There is a follow-up article by Kolata in today's Times (Sunday).

There was blogospheric clamor for the full distribution of the number of sexual partners of men and women; the original report from the CDC, it turns out, doesn't have that, but groups people into four groups -- those who have had 0 or 1 sexual partners, 2 to 6, 7 to 14, and 15 or more. This strikes me as insufficient resolution. In particular, zero is much different than one, as any virgin could tell you. Two seems a lot different than six, as well; two sexual partners could be someone who had sex with their spouse and one other person, whereas six sexual partners in a lifetime, although not a lot, can't have such a simple story behind it.

In any case, I'll reproduce the table. (The numbers are percentages.)

Partners	0-1	2-6	7-14	15+
Men	16.6	33.8	20.7	28.9
Women	25.0	44.3	21.3	9.4

The claimed medians for the number of sexual partners for men and women are seven and four, respectively. But 50.4% of men have had six or less sexual partners, according to this data. My earlier claim that the data might support a two-peaked distribution for women seems unlikely, but can't be ruled out at this resolution. (But I've seen enough other distributions that would explain the difference in medians that I don't really believe my own theory any more.) You can't extract means from this data -- and in fact at this resolution, it's theoretically possible that all the men could have 0, 2, 7, or 15 sex partners, for a mean of 6.46, and all the women 1, 6, 14, or [large number] sex partners, for a mean of at least 7.3 (if [large number] is in fact 15), making the female mean actually higher than the male mean. It would be simple (though I won't do it) to tweak the numbers so that the two means came out exactly equal.

Kolata (who has a master's in math, according to Wikipedia), however, claims that the data is inconsistent, in that there's no way to make the means equal: "I got between 40 percent and 75 percent more male than female partners depending on how you guess the average on each interval." I wonder what she tried. Sure, I'm just showing that it's possible the means are equal, not that it's likely. But someone with mathematical training should know better.

The high-school prom theorem

The Myth, The Math, The Sex, in yesterday's New York Times. Gina Kolata talks about the fact that studies consistently report that on average, men have had more sexual partners than women. The article refers to, among other things, the study I wrote about in July. David Gale offers a proof of what he calls the "High School Prom" theorem -- which is that the total number of sexual partners of men and women should be the same, and therefore the population means should be the same. Apparently the sex researchers are aware of this, but cannot find a better way to collect the data.

Last time I wrote about this I claimed that the most likely thing was that women were either not having sex at all or having lots and lots of sex (the "madonna-whore complex"), and that that would create the observed difference in the medians. (The study reported medians, not means.) I acknowledged that self-reporting might create problems, but I phrased it in terms of people "forgetting" who they'd had sex with. In retrospect this is probably not the best way to phrase it; people lie about who they've had sex with.

I forgot to take that into account, because I wouldn't lie about such things. (Especially not in an anonymous survey!) But I tend to be more honest than other people, both because I have ethical objections to dishonesty and because I am not very good at keeping alternate versions of the world which correspond with my lies in my head. In short, I think it's wrong and I'm bad at it.

I suspect that mathematicians in general don't like lying, because it goes against everything that our profession stands for. (Also, there are persistent rumors that mathematicians are more likely than the average person to be autistic, and autistic people in general aren't good at lying because it requires having a "theory of other minds" -- that is, being able to understand what people are thinking, apart from what is actually true about the world.) But I imagine that being a mathematician is compatible with being good at lying, or at least with coming up with believable lies -- we do it all the time in proofs by contradiction. Collecting data on how likely people are to lie, though, is probably even harder than collecting data on people's sexual habits.

David Gale also says that "It is about time for mathematicians to set the record straight". To what extent is it the duty of mathematicians to point out when other people claim to be doing things which are mathematically impossible?

sex and the smart kids

A story that's recently been making the rounds has been this post mentioned in the Gene Expression blog in April about how "smart kids don't have sex". So far I've also seen it at slashdot, livejournal's "mathsex" community, and the Dilbert blog; it was also mentioned in Marginal Revolution back in April.

The Gene Expression post reproduces the plot which shows that "teens with IQs ranging from 75 to 90 had the lowest probability of virginity (the authors note this is also the same IQ range where propensity towards crime peaks)." "Teens" here means grades seven through twelve, so technically, at least in a lot of states, having sex is a crime for these people. And even if you ignore age of consent laws (as I think most teenagers are likely to do), there's still a strong message from parents and other authority figures that they shouldn't be having sex, and it's hard to find a place to do it. My suspicion is that both of these are tied in with some willingness to break rules. Why a willingness to break rules is correlated with a slightly below-average IQ, I don't know.

This post then goes on to consider college students, and to cite an article from the November 2001 issue of Counterpoint, a joint MIT-Wellesley publication, which has some charts purporting to show that likelihood of being a virgin is correlated with, um, scientificalness of one's major? (The choice of the word "scientificalness" is deliberate here, in that it's not a real word.) I'm inclined not to trust their results here because of sample size; they polled 287 Wellesley students and 236 MIT students, and break up the 287 students into 18 majors and the 236 MIT students into 15 majors. This means than, on average, they polled sixteen students in each major, and are then comparing those numbers.

The headline that grabbed me was the livejournal headline, "83% of undergraduate [...] students in math are virgins". 83%? Sounds like "five out of six" to me, or "ten out of twelve". Furthermore, 83% of Wellesley math majors were virgins; 29% of MIT math majors were virgins. Wellesley's a women's school; most MIT math majors are male. Similarly, they claim to be able to say which dormitories have more virgins than others; however they only mention eight of MIT's ten undergraduate dorms, and five of its several dozen Greek organizations. I can only assume that they got nobody from those places, which leads me to think that their samples from the dorms they did get a sample from weren't too big either.

And it's notoriously difficult to get information about people's sexual histories, even in an anonymous survey. One way I've heard of getting decent aggregate information is the following: instruct the subject to go into a closed room, and flip a coin. If it comes up heads, they are to answer the question (let's say it's "do you masturbate regularly?") truthfully. If it comes up tails, they are to flip the coin again, and answer the question "did the coin come up heads on the second toss"? From the results one can get a good estimate of the percentage of people who would have answered the first question "yes", but nobody feels incriminated.

I'm done criticizing the "study" in Counterpoint. (I remember criticizing it when I was an undergrad; I started at MIT in September of '01, and even after two months it was clear to me that something was fishy here.) But if "smart people" are having less sex, why? First, note that it's not "smart people" so much as "smart kids". There might be some correlation between "being smart" and "following rules", at least if you're using getting into a selective college as a proxy for intelligence. And as I said before, following the rules of society as a whole means not having sex outside a "committed relationship", whatever that is. But on the other hand, I think a lot of intelligence comes from knowing which rules to follow and which rules to break. MIT prides itself on creating the people who will lead the scientific and technological worlds in the future, and to get to that point people are going to have to break the rules, to ask the questions which haven't been asked, to do the things that the old farts have already said are impossible. What makes you think these kids aren't going to have sex?

Then again, "peer pressure" always seemed to me to be weak to nonexistent at MIT. So if college students are only having sex because they feel they "should" be having sex, then they're not going to.

As to whether mathematicians are more or less sexual than the general population, I can't really comment on this. I know I haven't had sex in a while, but other than that I can't really say; most of the people who I feel comfortable talking about sexual matters with are not mathematicians. There seems to be a tendency towards social awkwardness in the "smart kids" in high school, and less so in college, but I think after college it goes away; once people get out in the larger world they tend to find the people around whom they are comfortable. In the absence of the rule-breaking behavior I mentioned before, I would guess that the people having the most sex would be the ones right in the middle of the intelligence distribution, because people tend to have sex with people like them, and there are more people like the average people -- that's what being average means. (I am deliberately saying "average" instead of "mean", "median", or "mode", because intelligence is approximately normally distributed so these are all the same.) This is probably true for a lot of other things as well. The people having the most sex aren't the rich, beautiful people. The people having the most sex are probably of average financial status, average looks, average intelligence, ..., because finding a partner is easiest if you're Just Like Everyone Else.

madonna-whore complex

The median number of lifetime sexual partners for women is 3.7, for men 6.8, according to this study by the CDC which I read about at blogadilla blogadilla. The information was collected by computer, because, as is pointed out at blogadilla, "your average co-ed isn’t going to admit to some researcher that she had sex with 23 guys named Biff last Spring Break."

This seems a bit suspicious to me, because if you ask all the men in the world how many sexual partners they have had, and then you ask all the women the same question, the numbers should be approximately the same. So the mean number of sexual partners should be the same for men and for women. There are a few things that could make the means be different, even if both people involved agree they had sex:

• Not all sex acts involve one man and one woman. Anecdotal evidence suggests there are more gay men than lesbians. But anecdotal evidence also suggests that there are more straight-identified women who have had sex with other women than straight-identified men who have had sex with other men. So I'm not sure which way this effect should go.


• If one partner in a sex act (that already happened) is dead and the other isn't, that'll skew things. But women live longer than men and the woman is probably on average the younger partner in a sex act, so there are probably more couples where the man has died than the woman, lowering the average for men.

But let's ignore those; those don't seem like they'd cause much difference in the means. The factors that would really skew the means are:

• If two people engage in acts of physical intimacy, one of them might say that they've "had sex" but the other wouldn't. I'm not sure which gender is likely to do what here.


• Since this relies on self-reporting, we have to remember that people might forget who they've had sex with.

But the big thing here is that the article is talking about the median, not the mean. I suspect that the means are pretty similar, and that the distribution of the number of sexual partners is a lot more skewed for women than for men. In other words, I have provided mathematical evidence for the Madonna-whore complex. (That's Madonna the mother of Jesus, not Madonna the singer.)