“Megan”:http://fromthearchives.blogspot.com/2007/08/sampling-bias.html of _From the archives_ won’t be surprised that “this _NYT_ article”:http://www.nytimes.com/2007/08/12/weekinreview/12kolata.html?_r=1&oref=slogin, claiming that:
One survey, recently reported by the federal government, concluded that men had a median of seven female sex partners. Women had a median of four male sex partners. Another study, by British researchers, stated that men had 12.7 heterosexual partners in their lifetimes and women had 6.5. But there is just one problem, mathematicians say. It is logically impossible for heterosexual men to have more partners on average than heterosexual women. Those survey results cannot be correct.
is already “getting”:http://ezraklein.typepad.com/blog/2007/08/i-caught-a-fish.html “play”:http://www.chrishayes.org/blog/2007/aug/13/im-back/ in the blogosphere. The only thing is that it _isn’t_ logically impossible, at least as the author presents it. Ask “Andrew Gelman”:http://www.stat.columbia.edu/~cook/movabletype/archives/2007/08/medians.html
Jeff’s response: MEDIANS??!! Indeed, there’s no reason the two distributions should have the same median. I gotta say, it’s disappointing that the reporter talked to mathematicians rather than statisticians. (Next time, I’d recommend asking David Dunson for a quote on this sort of thing.) I’m also surprised that they considered that respondents might be lying but not that they might be using different definitions of sex partner. Finally, it’s amusing that the Brits report more sex partners than Americans, contrary to stereotypes.
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Doormat 08.13.07 at 3:55 pm
Well, to be fair, the data for the UK is (implicitly) reported as an “average”, not a “median”, and it’s reasonable to assume, unless you have information to the contrary, that “average” = “mean”. Furthermore, it’s impossible to have a median of 12.7 sexual partners. To defend my fellow mathematicians, I think we all know what “median” means.
Henry 08.13.07 at 4:02 pm
I suspect that that’s just Andrew Gelman getting in a dig with his elbows, rather than a serious claim of basic incompetence. But the point, as I see it, is that the author of the article probably doesn’t know what the difference between a mean and a median is (I imagine that the UK research does report differences in averages, but you wouldn’t know it from the NYT article).
bi 08.13.07 at 4:29 pm
Doormat: I know a guy who has exactly 12.7 heterosexual partners. You see, one of his girlfriends was 70% heterosexual and 30% homosexual.
Dan Karreman 08.13.07 at 4:34 pm
different definitions of sex + sex tourism + bragging factor = problem solved
lemuel pitkin 08.13.07 at 4:48 pm
Yes, the point is valid if you are using mean rather than median. False reporting (including different definitions of sex) are almost certainly the biggest explanation. Prostitution can’t be, since prostitutes are part of the universe. Sex tourism could genuinely result in different means, but come on, how big a factor is that?
Richard Lewontin has a wonderful essay on the inability of surveys to capture the reality of sexual behavior, which has a good discussion of this issue.
It also mentions that on the big NORC sex survey that set the standard for these things in the 1990s,
conchis 08.13.07 at 5:52 pm
One of CDC people is quoted as saying: “I would say that men have more partners on average…”
wtf?
Miracle Max 08.13.07 at 6:12 pm
The file “Boxing Helena” could explain the .7th partner.
she don't want me around no more... 08.13.07 at 6:18 pm
+ bragging factor
Wait, are you saying the 12.7 figure is the product of exaggeration?? Poor chaps…
J Thomas 08.13.07 at 6:20 pm
Prostitutes and other women who have a lot of sex may be part of the sample, but will they report accurately?
Once I was flirting with a beautiful woman, and this topic came up, and she said she lost track around 70. I think I succeeded at not looking too startled or disapproving, and complimented her on her memory. I’d never before met a woman who claimed to have gotten past 30 without loosing track.
I can imagine there might be many more women with high numbers, since a man would have to persuade many women while a woman need only be easy to persuade. And if those women give underestimates then it could all work out.
jonathan 08.13.07 at 6:22 pm
Finally, it’s amusing that the Brits report more sex partners than Americans, contrary to stereotypes.
What stereotype is that? The bumbling-Brit Hugh Grant/Monty Python stereotype? The football hooligan stereotype? The Austin Powers shagadelic stereotype? The all-Europeans-are-decadent-lazy-hedonists-that’ll-sleep-with-anything-as-long-as-it’s-still-warm stereotype (a comparatively recent one, but gaining ground daily)?
Help me out, here. I’m gonna have to explain this to my Brit wife when I get home.
will 08.13.07 at 6:24 pm
“I would say that men have more partners on average…â€
Sounds plausible because the language is sloppy. Of course the mathematical averages must identical, because Npartners_women = avg_women*Nwomen, Npartners_men = avg_men*Nmen. By definition, Npartners_women = Npartners_men, and Nwomen ~= Nmen.
Nevertheless, the typical or so-called “average” woman probably has fewer partners than the typical or “average” man, which would be captured by the medians.
Robin 08.13.07 at 6:40 pm
There was a study a while ago suggesting that women lie and underreport: http://www.newscientist.com/article.ns?id=dn3936
“Scientists previously explained this anomaly by suggesting men were exaggerating their tally, while women were understating their total. But now Terri Fisher at Ohio State University and Michele Alexander at the University of Maine suggest that men are in fact more truthful in such surveys.
Women change their answers depending on whether or not they believe they will be caught out not telling the truth, the researchers found. The number of sexual partners a woman reported nearly doubled when women thought they were hooked up to a lie detector machine.”
david 08.13.07 at 7:05 pm
I read about this phenomenon somewhere a few years ago, and apparently men and women use different methods for determining how many people they’ve slept with. Men, when given one of these studies, are more likely to give a ballpark estimate, while women are more likely to count up specific partners. I guess this could have some effect on the Brits’ averages, but probably not on the Americans’ medians, since I can’t imagine counting vs. estimating making much of a difference if you’ve only had sex with 4-7 people.
Also, the difference between the Brits and the Americans could be due to using medians vs. means. For example, I’d guess that a fair number of American men claim to have had sex with more than 14 women, while I doubt that anyone was claiming to have had sex with fewer than zero women. So the Brits might still be prudes after all.
One more thing: I haven’t read these surveys, but the people conducting them would have to be incompetent not to give a relatively clear definition of “sex partner.” So my guess is that respondents are just lying–either the men are exaggerating, or women understating, or both.
david 08.13.07 at 7:06 pm
Oh, well I guess that post by robin settles it then.
yoyo 08.13.07 at 7:11 pm
“oh that time with Chet? That didn’t ‘count'”
Matt Kuzma 08.13.07 at 7:17 pm
The statement “But there is just one problem, mathematicians say. It is logically impossible for heterosexual men to have more partners on average than heterosexual women.” pretty clearly indicated that he’s getting confused between median, mean, and average.
I’m going to remember this story for when my children complain about having to learn something outside their favored discipline. Even if you’re going to be a reporter, you still need to pay attention in algebra class.
jacob 08.13.07 at 8:11 pm
the author of the article probably doesn’t know what the difference between a mean and a median is
I’m fairly certain that Gina Kolata, who has been a science reporter at the Times for at least the last 25 years knows the difference between a median and a mean. The article may or may not be any good, but there’s no reason to assume this level of ignorance on the part of someone who has reported on science news her entire career.
On the merits, I would generally agree with post 4 about the inaccuracies reporting and the different definitions of sex. That said, my intuition–that men would define sex more narrowly and phallocentricly , to mean only “vaginal penetration leading to male climax” and that women would have a broader definition–would lead to the opposite results, in which men would report fewer sex partners than women.
neil 08.13.07 at 8:19 pm
Npartners_women = Npartners_men is much too simplistic. People die.
bi 08.13.07 at 8:51 pm
jacob:
Well, given that her idea of “science news” involves omitting entire interviews and ignoring caveats of study results, surely she knows what she’s doing. Is she ignorant, or is she just being catty? Surely the truth lies somewhere in the middle.
jacob 08.13.07 at 9:22 pm
Bi:
Neither of the two things you linked to suggest in the slightest any ignorance or the sort of innumeracy that Henry suggested. One of them criticized her (or rather, her editors, since it’s hardly as if reporters get to decide what does on the front page) for sensationalism. The other accused her of being too pro-technology and pro-corporate, but also acknowledges “One, she is an absolutely brilliant reporter. She has a good grasp of science and she is fast. From the point of view of watching a working journalist, she is just amazing.” Downie also singles out for praise her work on mathematics. (Frankly the “charge” that she interviews people and then doesn’t use the interviews in her reporting is absurd, since all reporters do this all the time, and should.)
Saying that a science reporter doesn’t understand the difference between a median and a mean is a serious charge of professional malpractice. Surely we can dispute the quality of Times science reporting–even Kolata’s work in particular–without throwing around unsubstantiated, ad hominem charges. That’s all I’m asking for.
mollymooly 08.13.07 at 9:25 pm
If we’re being picky, then please specify *arithmetic* mean.
2 more fudge factors for ye: (1) Perhaps women only count a threesome once (2) Alcohol/drug-initiated liaisons: perhaps women are less able to remember such encounters; perhaps men are more likely to fill in any memory blanks with some wish-fulfilling ex post facto consummation.
Matt Weiner 08.13.07 at 10:15 pm
Those aren’t fudge factors so much as sources of errors in the results. Which is Gale’s original point.
Jordan 08.13.07 at 11:12 pm
I covered this in Slate today. The numbers from the UK (which is from a 2001 Lancet study called “Sexual Behaviour in Britain: Partnerships, Practices, and HIV Risk Behaviours” if you want to look it up) are indeed means. And I think it is highly, highly unlikely that Gina Kolata doesn’t know the difference between a mean and a median. Rather, I expect she made a conscious choice to gloss over the distinction in this article, and I think that was the wrong choice.
Matt Weiner 08.14.07 at 12:25 am
And if I read Jordan’s second page correctly, the Brits don’t report higher numbers of partners than Americans; the numbers quoted are the British mean and the American median, but the British median is the same as the American median.
Keith M Ellis 08.14.07 at 1:14 am
This is silly. There’s a bunch of reasons to believe that both the mean and median would diverge in this way before you even consider intentional false self-reporting.
First, I simply don’t believe that the researchers will adequately represent prostitutes in their sample. And the demographic of prostitutes (streetwalkers, quid pro quo drug addicts) which are most likely to be undersampled are also those who are most likely to have an extreme outlying number of sex partners. Very, very few men will have the number of sex partners that a run of the mill street prostitute has.
Second, someone in the linked thread mentioned that the question asked was “since you’ve been 18 years old”, which would skew the average if the sex excluded across that boundary line isn’t equally distributed between the sexes. And there’s every reason to believe that it’s not. Age differences in sex tend to find the men older and the women younger.
Third, there is the large problem concerning the definition of sex. Before we even consider that men have the social incentive to be more inclusive and women less inclusive for these reporting purposes, there’s the simple matter of sexual violence. Given the high rates of sexual violence against women and the high rates of women who’ve suffered it, especially as compared to men, then it’s easy to see that a number of men will be inclined to view as sex an act that the female partner saw as non-consensual and probably will not report in the count of sex partners.
Third, in the comments of the linked thread there is a quote of a standard used for determining “sex” that is intended to include more than intercourse. That’s all well and good, but the wording then bases the definition upon a specifically enjoyment and sexual arousal. This is problematic, as the commenter argues, because women are more likely to engage in non-aroused sex than are men.
Finally, when we move into the realm of intentional inaccuracies of self-reporting, the implicit assumption among those who argue the explanation hinges upon this is that the distribution of inaccurate self-reporting is even. And it needn’t be, and more to the point, almost certainly isn’t.
The distribution of sexual partners for each sex is very likely not in either case evenly distributed. If there are outlying women with large numbers of sex partners, thus explaining a divergent median, then it’s also reasonable that it’s those very women who are most likely to undereport, thus falsely skewing the average without requiring the majority of women to be underreporting. Furthermore, there’s probably a contingent of outlying men with zero sex partners who are also highly motivated to falsely self-report.
Taken together, all these factors lead me to expect that most respondents will be honest and yet we’ll see these results where even the average is divergent and the median even more so. And that is to say, the results are mostly correct.
Walt 08.14.07 at 2:03 am
I once knew a woman who claimed to only slept with two men. It turned out that preconditions to count in her total was that she had to have slept with them at least twice, and planned ahead on sleeping with them both times (as opposed to “spur of the moment”). The real total turned out to be 13.
Keith M. Ellis, I refute completely by anecdote, which we all know is the only foolproof method by which to reach the truth.
bad Jim 08.14.07 at 3:30 am
Over at Salon, Tracy Clark-Flory contacted Gale about the mean/median issue. He replied:
Justin 08.14.07 at 4:01 am
An especially cute part of the article was Dr. Gale’s assertion that a prostitute effect would have to be negligible. It really does show an endearing faith in the male psyche to find it so hard to believe that many men could’ve gone to three prostitutes in their lives.
jen was here 08.14.07 at 4:56 am
It is impossible for guys and girls to have a different percentage….
Unless they are prostitutes like the guy stated above and she didnt report correctly. But somewhere someone is lying about how many people they slept with…..
bi 08.14.07 at 5:05 am
jacob:
You know, “ad hominem” doesn’t mean what you think it means. “Michael Moore is fat” is an ad hominem. “Gina Kolata blatantly ignores caveats of study results” is not.
If it’s acceptable to bring up her “25 years” of science reporting as some sort of point, why’s it verboten to point out exactly what she’s been doing these 25 years? If the latter’s an ad hominem, then surely the former will be a transfer fallacy (or maybe an honour-by-association fallacy).
I’m leaning more towards Jordan’s hypothesis, anyway.
3pointshooter 08.14.07 at 6:18 am
At a recent reunion from my law school class I got to speaking with a woman I had literally not exchanged 1 word with while in school, even though it was a relatively small class and she was pretty attractive. Within 5 minutes she asked me to come home with her.
We ended up sharing a cab with another friend of mine, and they got to talking about their respective “number”. My male friend was quite sure his number was bigger, and was chuckling about it. I was pretty sure he was higher, since he’s lived a number of years in SE Asia, and he has scores with and without prostitutes. When finally called on to give his score, he says, “including prostitutes – 550”. She just smirked, and says “3200”, and then pointed at me, and says “you’ll be 3201”.
Given how quickly she propositioned me, I have little doubt in the accuracy of her number. I also have a pretty good sense that she’s one of the women responsible for tipping the mean number to even…
bad Jim 08.14.07 at 8:08 am
A bit of nonsense for the general merriment: a quote from I don’t remember where:
“You often see bright men with dumb women, but you hardly ever see a smart woman with a dumb man.”
This suggests that smart women are in short supply, which strikes me as not that unlikely. The oversupply of smart men is the part I find incredible.
chris armstrong 08.14.07 at 9:51 am
31: ‘“You often see bright men with dumb women, but you hardly ever see a smart woman with a dumb man.†This suggests that smart women are in short supply, which strikes me as not that unlikely.’
Er, no it doesn’t. But finding a man making such a basic error in the very act of criticising womens’ intelligence is fun, so thank you anyway.
John Quiggin 08.14.07 at 10:01 am
Gina Kolata got an award from Steve Milloy’s (Astroturf/Big Tobacco/Exxon) TASSC outfit back in 1995, which says it all for me. Here’s Sourcewatch.
Tim Worstall 08.14.07 at 10:46 am
“Even if you’re going to be a reporter, you still need to pay attention in algebra class.”
Why? This is statistics, isn’t it?
jacob 08.14.07 at 12:56 pm
Bi:
What I was dismissing as ad hominem was the claim that Kolata doesn’t know the difference between a median and a mean, which is tantamount to saying that she is absurdly unqualified for the job she’s done for the past 25 years. The objections you raised are I think perfectly legitimate–just not germane to the question of her numeracy.
kharris 08.14.07 at 6:50 pm
Will says that the typical woman probably has fewer partners than the typical man, but I think Will is not imagining the small-of-stature, shy, non-athletic male. A similar female could find a partner (my number is 555-…) if she were not picky. A low-end male is often a pathetic creature, when it comes to mating opportunity. This is true among, bovines, equines, baboons, hunter-gatherers and college boys.
As to the disparity between US and UK males’ success rates, there is a simple explanation. In many parts of the US, population density is very low. Women are scarce. If there is one woman within a day’s drive who is a willing partner, you’re lucky, boys. So especially for males in the vast grasslands and the western mountains, even one partner is something of an accomplishment. You don’t know what it’s like…
J. Ellenberg 08.14.07 at 8:33 pm
I’m sorry, I just have to repeat again that there was no difference between the British and American numbers. The reported medians were 7 for men, 4 for women in both cases. The apparent difference is a result of the Times reporting the median for the US study and the mean for the UK study.
J Thomas 08.15.07 at 3:09 am
What I did was to get a copy of the CDC report and used the data in its tables. It groups people into four groups and gives the percentage of men and women in each group:
0-1 partner: Men, 16.6. Women, 25.0.
2-6 partners: Men, 33.8. Women, 44.3.
7-14 partners: Men, 20.7. Women, 21.3.
15 or more partners: Men, 28.9. Women, 9.4.
From these figures you can estimate the total partners claimed by each sex. I got between 40 percent and 75 percent more male than female partners depending on how you guess the average on each interval.
There you have it. GIGO.
Dilemma resolved.
Katherine 08.15.07 at 10:04 am
The point of the article, and the analysis of the figures as quoted in comments #27 and #40 above, was the continuing erroneous survey results on male and female sexual behaviour. And, in a wider point I think, the numerous times in which these erroneous figures have been used to justify cod-scientific conclusions about male/female gender roles and sad excuses for evolutionary biological “reasoning” about the differences.
The point of the article was not to bitch on about means, medians or statistical analysis (or not) by scientific reporters. It’s a bit sad that this has been lost.
Katherine 08.15.07 at 10:39 am
And I’d also like to call bullshit on this statement in comment #9: since a man would have to persuade many women while a woman need only be easy to persuade
This is exactly the kind of bullshit that flawed survey results are used to justify.
kharris 08.15.07 at 12:14 pm
j. ellenberg,
If we pay strict attention to your point, we miss all the fun of thinking up reasons that Brits and Yanks might have very different sexual lies. When statistics stand in the way of having a good time, I say stuff stats.
Speaking of a good time, once again, my mumber is 555-….
bi 08.15.07 at 2:55 pm
“justify cod-scientific conclusions about male/female gender roles and sad excuses for evolutionary biological ‘reasoning’ about the differences”
Exactly which scientific paper, in which scientific publication, uses these survey results to “reason” about biological differences?
Or maybe it doesn’t whether this entire premise is true, and what’s important is that it serves at the pleasure of “a wider point”?
will 08.15.07 at 3:16 pm
“Will says that the typical woman probably has fewer partners than the typical man, but I think Will is not imagining the small-of-stature, shy, non-athletic male.”
Aww, man. It’s as if kharris looked up my Facebook profile.
Katherine 08.15.07 at 3:47 pm
Bi, either I’m being stupid, or your sentence doesn’t scan. Nevertheless, I meant these kinds of figures, the like of which is fairly frequently bandied about, rather than this particular set of figures. Sorry if that was not clear.
Matt Weiner 08.15.07 at 7:55 pm
Brits and Yanks might have very different sexual lies
Looks like their sexual lies are pretty similar.
J Thomas 08.16.07 at 3:03 am
And I’d also like to call bullshit on this statement in comment #9: since a man would have to persuade many women while a woman need only be easy to persuade
OK, you’ve called. Want to raise?
What is your objection?
brooksfoe 08.16.07 at 9:27 am
To my knowledge, no one has yet pointed to the obvious distortions in these figures caused by men who rape women while they are unconscious, which might explain some of the disparity.
bi 08.17.07 at 8:01 am
s/doesn’t whether/doesn’t matter whether/
“I meant these kinds of figures, the like of which is fairly frequently bandied about, rather than this particular set of figures”
… Oh, _duh_. As always, truth needs no facts.
battlepanda 08.18.07 at 2:39 am
The article was a missed opportunity. Kolata got bogged down in getting a mathematician to laboriously prove a trivial point. Look how lightly the New Scientist took care of the issues that made up the meat of Kolata’s article:
“In surveys since the 1960s, men typically report having more sexual partners and than do women – a statistically impossible feat.”
She also got caught out for the sloppiness of conflating the mean with the median, which shows not that she is stupid but that she might have thought her readers are.
But no matter. As Katherine said above, we’re missing the larger point:
“And I’d also like to call bullshit on this statement in comment #9: since a man would have to persuade many women while a woman need only be easy to persuade
This is exactly the kind of bullshit that flawed survey results are used to justify.”
Nice. I see a lot of weaving and dodging and just plain shitting on occam’s razor in this thread because this article upends people’s cozy expectations. Let’s unpack that statement (#9) a little. “A man would have to persuade many woman” — It’s normal for men to want to have many partners — and “a woman need only be easy to persuade” — a woman who have many partners is an abnormal slut.
As the New Scientist article I mentioned, researchers at Ohio university found that:
“Women change their answers depending on whether or not they believe they will be caught out not telling the truth, the researchers found. The number of sexual partners a woman reported nearly doubled when women thought they were hooked up to a lie detector machine.”
Somehow I find this a more plausable source of the gap than all those women getting raped in their sleep without remembering it.
bi 08.19.07 at 5:33 am
“I see a lot of weaving and dodging and just plain shitting on occam’s razor in this thread because this article upends people’s cozy expectations.”
Where “Occam’s Razor” entails taking one comment #9 and calling it “a lot of weaving and dodging”. And that comment isn’t even from a scientist writing in a scientific publication.
But I don’t see anything suggesting that the survey was made specifically to allow people to conclude silly things about gender roles. Nothing at all. If people want to conclude weird things from the survey results, is it the survey’s fault? Or maybe Occam’s Razor demands that we see an ulterior agenda behind the survey itself even if none’s apparent.
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