# Men and Women Cannot Can Have Different Average Numbers of Sexual Partners

I hadn't really ever thought about it, but surveys consistently report that heterosexual men have a larger number of sexual partners on average than heterosexual women. However, that really isn't logically possible, is it? I mean, last time I checked it took two to tango. Mathematician David Gale demonstrates why these results cannot be right in the NYTimes:

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.

It is about time for mathematicians to set the record straight, said David Gale, an emeritus professor of mathematics at the University of California, Berkeley.

"Surveys and studies to the contrary notwithstanding, the conclusion that men have substantially more sex partners than women is not and cannot be true for purely logical reasons," Dr. Gale said.

He even provided a proof, writing in an e-mail message:

"By way of dramatization, we change the context slightly and will prove what will be called the High School Prom Theorem. We suppose that on the day after the prom, each girl is asked to give the number of boys she danced with. These numbers are then added up giving a number G. The same information is then obtained from the boys, giving a number B.

Theorem: G=B

Proof: Both G and B are equal to C, the number of couples who danced together at the prom. Q.E.D."

Researchers who do this kind of work apparently acknowledge that their results cannot be correct. So what explains the disparity between the two averages in the respondents? Many theories have been forwarded:

Sevgi O. Aral, who is associate director for science in the division of sexually transmitted disease prevention at the Centers for Disease Control and Prevention, said there are several possible explanations and all are probably operating.

One is that men are going outside the population to find partners, to prostitutes, for example, who are not part of the survey, or are having sex when they travel to other countries.

Another, of course, is that men exaggerate the number of partners they have and women underestimate.

Dr. Aral said she cannot determine what the true number of sex partners is for men and women, but, she added, "I would say that men have more partners on average but the difference is not as big as it seems in the numbers we are looking at."

Dr. Gale is still troubled. He said invoking women who are outside the survey population cannot begin to explain a difference of 75 percent in the number of partners, as occurred in the study saying men had seven partners and women four. Something like a prostitute effect, he said, "would be negligible." The most likely explanation, by far, is that the numbers cannot be trusted.

Ronald Graham, a professor of mathematics and computer science at the University of California, San Diego, agreed with Dr. Gale. After all, on average, men would have to have three more partners than women, raising the question of where all those extra partners might be.

"Some might be imaginary," Dr. Graham said. "Maybe two are in the man's mind and one really exists."

Dr. Gale added that he is not just being querulous when he raises the question of logical impossibility. The problem, he said, is that when such data are published, with no asterisk next to them saying they can't be true, they just "reinforce the stereotypes of promiscuous males and chaste females." (Emphasis mine.)

I guess I buy the responder is dissembling explanation most. I could totally believe that men are massaging their responses to raise the number and that women are massaging down their responses to lower the number, in both cases to fit social stereotypes. The fact that many of these surveys are anonymous is not insurance that the responses are accurate.

Anyone have a theory? Why do you think these surveys produce logically incoherent results?

UPDATE: So what I am hearing is that the medians can be different. That makes more sense to me, but I wonder how the Gale missed that aspect.

Also, I thought (and commented) that the origin of the sex disparity couldn't be because of prostitution, but it turns out I am a big prude.

Men dramatically under-report seeing prostitutes and these authors argue that that under-reporting is sufficient to explain the sex differences:

In sum, prostitutes are underrepresented in national household sex surveys, and their undersampling can account for the sex discrepancy in reported numbers of sexual partners. These results suggest that respondents' reports of the number of their sex partners, although possibly limited in other ways, may not be significantly affected by sex-linked reporting bias.

UPDATE: I think we have pretty well established that this objection is bogus. I apologize to everyone for completely missing the boat on the means vs. medians issue.

Yet again I ask myself: why do I uncritically believe the NYTimes Science section? And besides, I have had issues with Gina Kolata's (the author) work before.

UPDATE: A commenter via email explained this about why the means may even be different:

This came up ten years ago on USENET, and it was just as dumb then as it is today. I posted an explanation of why it's very easy to get skewed results in a survey without anyone lying. The example I considered was of "lekking", where all the male birds of a colony stand around all day while the females check them out in great detail, until all of a sudden the females converge on one male as the perfect father of that season's chicks. That one male has 1000 partners, say, the 1000 females have 1 partner each, and the other 999 males have 0 partners each.

(In reality, the neighbors of the one male typically end up fathering some of the next generation, but I'm keeping the numbers simple.)

Now take a survey by sampling 1% of the population. You will almost certainly end up with reports of 1 average partner for the females, 0 for the males. In other words, the most promiscuous are almost certainly not counted in the surveys, yet omitting them undervalues the count. In fact, if promiscuity leads to higher mortality, then the survivors will have a genuine asymmetric average. Even if you discount causal mortality (diseases and violence), men do have a higher mortality rate than women, which means that if men are more promiscuous, a completely accurate honest survey of everyone alive could still yield different "average number of sex partners", solely because more of the women's partners are dead than vice versa.

The commenter refers to this failure to sample accurately because the people you want to sample are dead as "survivor bias."

Thus, it appear that there are two problems with this objection. One, it focuses on means rather than medians. Two, because the effects of mortality and because of sampling, we might not even expect the means to be the same.

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This is by far the worst statistic I have ever seen. I just asked 17 guys at work and everyone was nicely over 7 sex partners (not including Prostitutes). The 20's is the prime time for a man and I don't know one single man that made it out of his 20's with less than 7 sex partners.

By Andy Price (not verified) on 14 Apr 2009 #permalink

"men had a median of seven female sex partners. Women had a median of four male sex partners."

*Medians* can very easily be different.

Let's have M1-M5 be men, F1-F5 be women. First, the men's hypothetical partners:

M1 - F1
M2 - F1, F2
M3 - F1, F3
M4 - F1, F4
M5 - F1, F5

That gives a median of 2 (and a mean of 1.8)

Looking at the women:

F1 - M1, M2, M3, M4, M5
F2 - M2
F3 - M3
F4 - M4
F5 - M5

The median in this case is 1 (the mean is still 1.8)

Well, first of all the latest study reports medians, so the data don't have to match even in principle. Suppose the distribution of sexual partners in women is very skewed, with most gals having low numbers of partners and a few having very many, the female median will be pretty low, and would be lower than that of men, if the distribution among the latter is a normal curve, in which the mean and median will overlap. (The means of course will be the same.) So much for the "logically" impossible.

Second, there is the issue of sampling bias. If men have more often sex with partners who were systematically excluded from the sample (say, foreigners, analphabets, people outside the age range the sample was drawn from, etc), then the means could also be different.

Finally, and this could be easily checked, I am not sure if the question was limited to heterosexual partners. If not, a small fraction of highly promiscuous males engaging in homosexual sex would do the trick (statistically, I mean).

Maybe most repondents are in fact telling the truth but using different definitions of "sex partner". Social conditioning may have men classifying the coworker they kissed at the office party as a sex partner, while women only count men with whom they have at least one child.

Colst's example of the difference between median and average is important.

The study can be taken to mean that the median guy would partner with the easy girl, but the median girl is not easy.

Andrea's last point is also important: Men who consider themselves heterosexual might count some homosexual experiments as qualifying events.

What if there is a higher level of homosexual exploration among men that is not normally expected?

If some of the men dance with each other, the average number of dance partners will be higher for men because each man has 19 potential dance partners.

Culturally, we don't expect more men to experiment with homosexuality than women(yes, it's a stereotype) but it might be possible. So if the question was simply, "How many sexual partners have you had?" if one sex were more likely overall to have a higher rate of homosexual encounters that would mean the averages would be different.

Personally I think it is simply down to the old stereotype that men lie to increase the number of sex partners and women lie to decrease the number.

By Bob Ramsey (not verified) on 14 Aug 2007 #permalink

You are both right about the medians being different entirely from the means, but I was just thinking about something in Colst's comment.

So say that the origin in the disparity between means and medians is that a small number of women are having large numbers of sexually partners. (This is illustrated in Colst's example by F1.) Are those women prostitutes or are they just...well...busy? Because if the women are prostitutes that requires that a large majority of men are seeing prostitutes. Do you think that is really the case? In Colst's example, all five of the men slept with F1. So in order for a disparity between the medians for the two groups to be 2 to 1, it would appear that 100% of the men must sleep with one of the women.

I guess I don't see it as likely that huge numbers of men are seeing prostitutes.

Ahem, Colst... Would you happen to have F1's phone number?

So what I am hearing is that the medians can be different. That makes more sense to me, but I wonder how the Gale missed that aspect.

The statisticians think the author of the article should've contacted one of them and not a mathematician.

OK, some answers are in the study.

First of all, they are talking about sexual partners of the opposite sex only, so the homosexual male issue is out. Second, judging from the distribution, there are significant more males who claim to have had >15 sexual partners (28.9%) than females (9.4%). This doesn't rule out the female prostitute/ultra-slut median-shifting hypothesis, but it probably makes it less likely.

The issue of definition of a "sexual act" doesn't seem to be addressed in the survey, but I haven't read the whole thing carefully. That obviously may affect perceptions and reporting by either sex (e.g. men may wish to considered a furtive hand-job received in high school a sexual act for partner-reporting purposes, while women might as well want to forget about it).

I would be interested in seeing what the actual means are, because that would give an idea of the potential underlying problems. If the means are the same or close for males and females, then misreporting is not a major issue and the discrepancy would seem to be real, and related to distribution. On the contrary, if the means are as widely different as the medians, then misreporting or sample bias is more likely.

These studies have been done before, and as far as I understand, the arithmetic mean number of self-reported sex partners is always dramatically higher for men. Guys exaggerate their sluttiness, girls down-play theirs.

A little bit like the census in Australia reports that more women say they are married than the number of men who say they are.

By Chris O'Neill (not verified) on 14 Aug 2007 #permalink

Another factor that is missing from the analysis is that men and women may be defining sex differently. This is similar to the "lying" issue, but allows that the respondents might be being as honest as they know how. One person may count what we used to call heavy petting as sex, and another may not (I think the Kinsey Institute is doing a survey on this subject right now: they were a few days ago. I found the questions too cut and dried to answer, really). If men-in-general tend to be more inclusive in their definition of sex and women-in-general tend to be narrower, the skew can come from that right there. You know that scene in the musical "Grease" where the boys and girls are pumping the hero and heroine about their date? You could have two people who dated each other, one of them saying "we did it!" while the other says "we didn't do it, we just messed around a little."

By Lucy Kemnitzer (not verified) on 14 Aug 2007 #permalink

The ratio of women to men is often greater than 1. That could make a [small] difference in the average number of partners (imagine an extreme case where there are 100 girls at the prom and 1 boy, and the boy dances with everyone).

I'd just thought I'd add that men do tend to have more homoerotic encounters than women. 37% of men have homoerotic encounters while only 14% of women. This, however, is irrelevant to the study in question.

Another statistic more pertinent to the study, perhaps, is this: 35% of children born to a couple are, without the male's knowledge, of no genetic relationship to the male. From a behavioral standpoint, it's interesting to note that the first child is more likely to not be related to the male. Some studies put it as high as 50% of first-born children having no relation to the male raising them.

Umm, hello?

Imagine a desert island with a population of two men and three women. Each man has slept with all three women. The mean number of partners is three for the men, and two for the women.

There is also an alternate scenario in which an adult film crew is also present on the island, in which case each of the women will have also been with both of the other women, making the women have a mean of four partners. The mean is still different for the women and the men.

Counting unfilmed quickies between the actors and crew is left as an exercise for the reader.

By ShavenYak (not verified) on 15 Aug 2007 #permalink

What Colst said about medians is correct. I have never seen a study claiming that the mean number of sexual partners for men is higher than for women. The statistic used has always been median.

In any case, it's entirely possible for the mean number of sexual partners for men to be (very slightly) higher than the mean number of sexual partners for women. Indeed, the proportion of the mean number of sexual partners should equal the inverse of the proportion of individuals of each gender in the population (ignoring homosexuality here). If the M:F ratio is 49:51, then the average number of partners ration should be 51:49.

If at some point someone does a more perfect sampling, I suspect you'll often find both underreporting by women, overreporting by men {HEY, the spelling checker thinks underreporting is a word but not overreporting}, underreporting of prostitutes all play a part. Also much of our sampling ASSUMES you have either a normal distribution or you can tailor your sampling in such a way as to be able to assume something like a normal distribution yet be inclusive enough to cover the population - which is tricky.

Summary:

1. The median and mean for a variable are very different.
2. There are more women than men.
3. Men exaggerate how much sex they've had
A. cf. "Clerks" where Veronica and Dante don't agree on oral sex as sex
B. And they do make up things about sex
4. Women understate how much sex they've had
C. Add anal sex to the above.
5. Men see prostitutes but they don't go around bragging about having to pay women to sleep with them or being skeevy Johns.
6. Depending on the actual population, you might actually consistently miss the most promiscuous women or men, with an unpredictable affect on results. This affects the median more often.

UPDATE: So what I am hearing is that the medians can be different. That makes more sense to me, but I wonder how the Gale missed that aspect.

Gale was not talking about statistics, he is talking about total male sex pairings vs. total female pairings. He is not talking about averages, medians, etc., in his proof. And by that measure, Gale is entirely correct (for heterosexual acts), because every time the male team racks up another sex act, the female team does too, so there is always perfect parity. Even on an island with 1 man and 1000 women, if the man has sex with all women, the total male participations in sex acts is 1000 and the total female participation is 1000.

But of course no one cares about the total number of sex acts on each team's side because that doesn't tell you anything about the average sexual character of men vs. women--that's what we want to know. Means and medians are useful, but what is always most useful is to look at the graph of the whole distribution, to see if men and women, as populations, have the same shaped distribution, or if men have a peak in the tail ("Casanovas") or whatever it might be.

So, Gale is correct, his point is a great one for the point of making sure we actually think instead of just sponging up factoids, but his point doesn't tell us anything about the distributions.

ShavenYak: The ratio of the means is exactly the ratio of the sizes of the two population components -- your example extends the High School Prom theorem by pointing out that G=B, but the means G/g and B/b (g and b being number of girls and boys at the prom) will differ by a ratio of g/b. However, it's certainly not the case that the population of sexually active women is twice that of sexually active men -- though it may have contributed, this being the motivator for the "foreign population" explanations.

As a teacher of math, I really want to nail this one down. It's an amusing illustration of why figures need critical thinking. :^)

Plus there is also the risk of a non-respondent bias. I've not read the detail of this survey, but depending on how the sample was taken, the validity of the results could be affected. For example if you send out 1000 questionaires to men and a 1000 to women you may find that 80% of men reply, but only 60% of women reply. If the 40% of women who do not reply include a disproportionate number of the most sexually active, and the 20% of men who do not reply are all celibate, then this will affect the overall balance. Even if you keep sampling until you have 1000 replies from each sex, you can make no assumptions about the sexual history of the non-respondents without further work.

I have never seen a study claiming that the mean number of sexual partners for men is higher than for women. The statistic used has always been median.

Right there at the start of the post, in the quoted bit, you'll see one:
"Another study, by British researchers, stated that men had 12.7 heterosexual partners in their lifetimes and women had 6.5."
That's clearly a mean.

"What Colst said about medians is correct. I have never seen a study claiming that the mean number of sexual partners for men is higher than for women. The statistic used has always been median".

To take a slightly skeptical view of this, while is true that sexual encouters could be equall while medians could be totally different, the only way for this to happen would be to have a handfull of women screwing night and day. It seems sloppy that any research would use medians without given distribution curves as a reality check.

As for screwing "outside the group" this would indicate the sampling procedure is highly defective.

We may want to add in drugs and alcohol. Call it the "what happened last night" effect. The male may think he had sex when in fact his memory is an imaginative black hole. While the female could also deny that sex happened since she hasn't the slightest recollection of the events. And this wouldn't be lieing or boasting per se. Furthermore, this multiplies with the previously mentioned fuzzy definition theory of what is sex.

Sadly, we should also consider the non-censual or pseudo-consensual intercourse. The vicim of which is typical female. She understandably may want to define the traumatic crime as something that is not sex. Even true rape is underreported and the amount of date rape that occurs is probably much greater. It wouldn't explain the entire disparity though it could easily be a chunk of it.

Since number of sexual partners P cannot be less than zero, the histogram of frequency vs. P for each sex might approximate a Poisson distribution (but not a Gaussian 'normal'). The area under the curve is the total number of pairings, but the curve for each sex may have a different shape; a wider and flatter Poisson curve for men will have a higher mean. Of course the undersampling of prostitutes etc., and divergently biassed reporting will also have effects, but this seems to be another reason to expect different means. Or am I wrong about the properties of the Poisson distribution?

By John Scanlon (not verified) on 15 Aug 2007 #permalink

Or am I wrong about the properties of the Poisson distribution?

Poisson lambda=mean=variance. So the "law of rare events" does not seem to describe these rare events...

a wider and flatter Poisson curve for men will have a higher mean.

If there are the equal number of men and women, regardless of the distribution, the means will be equal.

M = total number of male-participated sex acts.
m = number of males.
F = total number of female-participated sex acts.
f = number of females.

First, M = F. M/m = male mean; F/f = female mean.
So then if m = f, then M/m = F/f, and so the means are equal.

The 2000 U.S. Census put the U.S. female population at 50.9%, and that's for all ages, even elderly when there are more females due to surviving better, so at more likely "mating ages" the difference has got to be pretty darn close to 50.0% for both. So the means really ought to be very very close indeed, at least in the U.S.

Actually, it is (theoretically) possible for the means to be noticeably different, even without issues like homosexuality and non-50/50 populations, for a very simple reason: people are born, age, and die.

To keep it simple, imagine a society where everybody has one monogamous relationship, produces one male and one female child to replace themselves, and drops dead at age 100, keeping the numbers at 100 males and 100 females.

Suppose that men tend to pair off with somewhat older women, so the relationship typically starts with a 20-year-old man and a 25-year-old woman (the man will spend the last 5 years of his life as a widower, but that's not important here). To keep it simple, let's suppose that *everybody* follows that pattern exactly.

If you survey the entire population accurately, you'll find that the average male has had 0.8 sexual partners (20% have had none, 80% one) and the average female has only had 0.75.

If you do as a lot of surveys do and restrict it to a narrower age bracket - say, between 20 and 39 - the average female count remains at 0.75, but the average male count rises to 1.0.

(Another way to get a disparity in the averages is if people with different numbers of partners have different life expectancies - which seems plausible enough, given the complex relationships between health, attractiveness, and risk-seeking behaviour.)

sailor said - "To take a slightly skeptical view of this, while is true that sexual encouters could be equal while medians could be totally different, the only way for this to happen would be to have a handfull of women screwing night and day. "
They sound like prostitutes, hence "Hello sailor" seems the appropriate response.

The article on prostitution statistics referenced in the first update says that it is enough to give the discrepancy.

sailor said - "As for screwing "outside the group" this would indicate the sampling procedure is highly defective."
I'd say it could mean men have sex with foreigners ('friendly local girls') when on overseas trips much more than women, and there is an inbalance of sexual trade between countries. This possibility is mentioned in the article. This would mean some (probably less affluent) destinations for US travellers would have women with a higher mean lifetime number of partners than men.

"By way of dramatization, we change the context slightly and will prove what will be called the High School Prom Theorem. We suppose that on the day after the prom, each girl is asked to give the number of boys she danced with. These numbers are then added up giving a number G. The same information is then obtained from the boys, giving a number B.

Theorem: G=B

Proof: Both G and B are equal to C, the number of couples who danced together at the prom. Q.E.D."

This is moronically circular; of course G=B if boys and girls can be put into 1-1 correspondence (couples) but that's not necessary. There's no reason G can't differ from B -- that's a premise, not a conclusion.

Of course in the real world G is near B, so the premise is approximated. What is far more interesting than the average number of sex partners is the variance in the number of sex partners, which is higher for males than for females, which explains the fact that Y-Chromosomal Adam is a lot more recent than Mitochondrial Eve.

By truth machine (not verified) on 15 Aug 2007 #permalink

This is moronically circular; of course G=B if boys and girls can be put into 1-1 correspondence (couples) but that's not necessary. There's no reason G can't differ from B -- that's a premise, not a conclusion.

I take that back -- I didn't pay enough attention to what B and G are. B is the sum of all the girls' dance partners, and G is the sum of all the boys' dance partners. These are indeed equal ... but the average number of dance partners are B/g and G/b, where g is the number of girls and b is the number of boys, and those are only equal if g equals b, something that Gale should have made explicit.

I wonder how the Gale missed that aspect.

Uh, by being out of touch with the real world?

By truth machine (not verified) on 15 Aug 2007 #permalink

Another, of course, is that men exaggerate the number of partners they have and women underestimate.

This is not a valid response, since "Another study, by British researchers, stated that men had 12.7 heterosexual partners in their lifetimes and women had 6.5" makes a statement of fact about the number of partners, not about reported numbers of partners.

The most likely explanation, by far, is that the numbers cannot be trusted.

I think this is an unavoidable conclusion. The very fact that the cause of the discrepancy is being debated here establishes that.

By truth machine (not verified) on 15 Aug 2007 #permalink

So if we applied mathematical reasoning to reality, it should therefore not be possible to find situations such as the following (M = man; W = woman):

*M(1)in a room with W(1,2,3) simultaneously vs. M(2) in a room with W(4)

OR

* M(1) in a room with W(1) on Monday, W(2) on Tuesday, and W(3) on Wednesday vs. M(2) in a room with W(4)

OR

M(1) dating W(1) vs. W(2) alone

OR

M(1) married to W(1) vs. W(2) alone (actually typical after age 65 due to gender differences in mortality)

Any of these hypothetical situations could explain the supposedly inexplicable data. So I'm not sure why the survey reporting that "heterosexual men have a larger number of sexual partners on average than heterosexual women" is a logical impossibility, when that is what is shown in each of the situations shown above.

By Tony Jeremiah (not verified) on 15 Aug 2007 #permalink

M(1) married to W(1) vs. W(2) alone (actually typical after age 65 due to gender differences in mortality)

That wouldn't bring down the number of sex partners unless all the W2 are virgin spinsters at 65.

Any of these hypothetical situations could explain the supposedly inexplicable data.

Yes, if there were twice as much women in the population as men. Realistic?

Gale in his example implicitly assumes that the amount of boys and girls are equal. Perhaps he was making his example too simple, but I think he was right to point out the problem - when these kinds of surveys are published, people uncritically assume that the mean numbers of sex partners can be wildly different for heterosexual men and women in the same population (and not just in any theoretical population of lekking humans, but the one they live in).

"Gale in his example implicitly assumes that the amount of boys and girls are equal."

It turns out that he did a lot better than that:

I've gotten several messages making the same point. If you look at Gina's article you will see that I never attacked the statement about medians. I tried to carefully avoid saying anything directly about the median statement in the article because, as you realize, it could be correct even with accurate data. 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. Thus, the raw data is inconsistent (so it doesn't matter whether you take averages or medians or any other statistic). I hope this clarifies.

So, as so often happens on the internets, this article and all the comments here are based on ignorance, erroneous assumptions, and misinterpretations.

By truth machine (not verified) on 16 Aug 2007 #permalink

Isn't the usual sex difference in number of partners supposed to be that there is more variation among men than among women?

I.e. some men get many and some few partners, but women tend to be more clustered together.

Would this have any effect on the figures? What do people think?

Windy,

Those situations can still work even if you assume a 50/50 (or close to this proportion) population. Suppose for example that 210 people completed the survey. Further, let's say in this hypothetical survey that the sample consists of 100 married couples and 10 virgins (possible if there are 14-year-olds completing the survey).

Shorthanded: M(100) married to W(100) vs. W(10) single

Assuming no extramarital affairs, the number of partners reported by each individual should be as follows:

100 men = 1 partner (100 total partners)
100 women = 1 partner (100 total partners)
10 women = 0 partners (O total partners)
---------------------------------
Mean (men): 100/100: 1
Mean (women):100/110: 0.91

This shows a higher mean # of partners for men with a
population proportion fairly close to 50/50 (i.e., 52% women; 48% men).

As to the rest of the scenarios provided, you could also transform them so they conform to an equal proportions assumption and still have more sexual partners (on average) for males than females. Example:

M(1)in a room with W(1,2,3) on different days vs. M(2) in a room with W(3,4) vs. M(3) single:

If these particular persons took the survey (except for W4), the data reported by each individual would look as follows:

M(1) = 3 partners
M(2) = 2 partners
M(3) = 0 partners
W(1) = 1 partner
W(2) = 1 partner
W(3) = 1 partner
----------------------------------------
Mean (men): 5/3 = 1.67
Mean (women):3/3 = 1.00

Proportions (completing survey): 50% men; 50% women

The survey might simply just not be capturing the variations in sexual behavior (mental or otherwise) that is better left for psychologists to analyze. So therefore, I agree with EJ's last comment.

By Tony Jeremiah (not verified) on 16 Aug 2007 #permalink

Slight correction: W(3) should report 2 partners. However, the overall difference in the pattern of the mean remains the same.

By Tony Jeremiah (not verified) on 16 Aug 2007 #permalink

Tony Jeremiah, in your examples that show different means, please note that all of the examples have less men than women. Same means are only guaranteed if there are equal numbers of men and women. See the comments for several mentions of that.

CM,

Understood.

Couple of points:

(1)See last example involving the exclusion of W4 from a hypothetical survey which assumes an equal number of male/female participants in the study (but perhaps not in "reality").

(2) I think in reality (at least in psychological reality--background is in psych so I'm primarily approaching this from a psych perspective), populations are such that there are more females than males due to gender differences in mortality rates--especially true after 65.

But my overall point is I don't think the question is exclusively a math problem. Could also be the non-standardization of procedures concerning data collection resulting in sample bias and so forth.

By Tony Jeremiah (not verified) on 16 Aug 2007 #permalink

I've gotten several messages making the same point. If you look at Gina's article you will see that I never attacked the statement about medians. I tried to carefully avoid saying anything directly about the median statement in the article because, as you realize, it could be correct even with accurate data. 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. Thus, the raw data is inconsistent (so it doesn't matter whether you take averages or medians or any other statistic). I hope this clarifies.

Eh, this just makes things worse, in my opinion. While it may be true that in the NYT quote Dr. Gale was referring to the means and not the medians, if one takes this new explanation at face value, he is missing the point anyway.

The problem of course all boils down to how one "guesses" the average of the >15 partners "interval" (leaving aside the issue of "guessing" in statistical analysis). Depending on how one "guesses" (i.e. whether one considers the possibility of a subset of women having an extremely high number of male partners), the raw data could in fact be entirely consistent with equal means and different medians.

For instance, imagine the sample had 1,000 men and 1,000 women, and the average within each "partner number" cohort was exactly in the center of the range for all lower cohorts, but very different for the >15 cohort (e.g 15 for men, and 40.5 for women), you would get something that looks like this (sorry for the formatting, I hope it's clear):

MALES:
partner range -- (average # partners) -- # males in cohort -- # partners
0-1 -- (0.5) -- 166 -- 83
2-6 -- (4) -- 338 -- 1352
7-14 -- (10.5) -- 207 -- 2173.5
15+ -- (15) -- 289 -- 4335
TOTAL NUMBER OF PARTNERS FOR MALES: 7943.5; average: 7.9; median: ~7

FEMALES:
partner range -- (average # partners) -- # females in cohort -- # partners
0-1 -- (0.5) -- 250 -- 125
2-6 -- (4) -- 443 -- 1772
7-14 -- (10.5) -- 213 -- 2236.5
15+ -- (40.5) -- 94 -- 3810

TOTAL NUMBER OF PARTNERS FOR FEMALES: 7943.5; average: 7.9; median somewhere in the 2-6 range

(And yes I know one cannot have half a partner, it was just a quick calculation. If you don't like it, multiply everything by 2.)

Now, one can certainly argue that such a distribution is sociologically unlikely (but then again, all it would really take is for 1 in 500 women to have ~1,200 partners to make the distribution above possible - certainly plausible numbers for prostitutes).

However, no neatly packaged theorem (or amount of "guessing") can show that it "cannot be true for purely logical reasons".

By Andrea Bottaro (not verified) on 16 Aug 2007 #permalink

Andrea, yes, it would be better to see the absolute numbers instead of this binning stuff. I think you're right that the last >15 bin allows a come-from-behind tie for the ladies, as a hard core within those 94 women could be "carrying" the rest of their team to the tie. I wonder if Gale has fielded that concern somewhere online. I also wonder if the CDC has that raw data with a number instead of a range for each survey respondent.

The larger point though is still a useful one: that some might have erroneously thought one could see rather different average number of partners in populations with virtually the same number of men and women, and that is not possible.

Everyone seems to be talking about people maliciously lying about the number of partners, and while a guy saying he has been with 6 women when he has really only been with 4 is an obvious lie (assuming he can count to 6 reliably) it may not be so easy with the the people on the high end of the scale ("Was that 120 or 180?").

So rather than looking for a bona-fide deception on the part of the people questioned it seems quite likely that the higher numbers are more likely to have recall and conscious or unconscious social desirability bias due to the fact that they can only be estimated, rather than actually recalled (unless you have a good diary like the girl in Mallrats).

As we can tell by the differences in the medians, there must be a skewed population with a minority of people with high numbers of partners, who will have to give a rough estimate of their number based on memory and unconscious bias. I would be interested to know how many of the people with more than 50 partners just happen to collect partners in groups of ten.

(1)See last example involving the exclusion of W4 from a hypothetical survey which assumes an equal number of male/female participants in the study (but perhaps not in "reality").

Note that that's a 33% excess of females compared to males in your population. How much unsurveyed excess females would there need to be in the British population, for example, for this to explain means of 12.7 for men and 6.5 for women?

(2) I think in reality (at least in psychological reality--background is in psych so I'm primarily approaching this from a psych perspective), populations are such that there are more females than males due to gender differences in mortality rates--especially true after 65.

Those old ladies, if surveyed, would still retain their lifetime sexual experience, so I'm not sure how this should automatically make the women's numbers plummet. Changing sexual mores might cause a slight difference (if old ladies had been significantly less promiscuous in their day than "today's youth") but the CDC survey is limited to ages 20-59 and age groups are compared separately; this guards against a hidden "old lady" effect.

My high school health class, twenty years ago, featured one young woman asserting her view that, on their wedding night, the groom should not be a virgin, but the bride should be. She was asked "with whom should unmarried men have sex, then?" and she sat there thinking a full minute before blushing and muttering "never mind".

While there's some possibility there's a bimodal skew of the median versus mean (woman either chaste or prostitutes), and perhaps people are lying like rugs, I assert the biggest effect is the Clerks effect ("Three", "Nine", "Twenty-seven", if you recall), AKA "I did (not) have sexual relations with that woman". Heavy petting conveniently either is or is not considered sex as the participant chooses to recall.

Hence women, desiring not to sound like sluts, don't count heavy petting, while men, desiring to sound like studs, do.

And it's not just worry about how it sounds, it's how each gender subculture views the act. I argue that in many cases men count it as sex if they've reached orgasm, while women count it as sex if they either had to use protection or take a pregnancy test afterwards.

(And add that for a lot of teenagers, heavy petting begins and ends with male orgasm, meaning that the encounter really is a lot more meaningful and memorable for the young man than the young woman.)

By eyelessgame (not verified) on 16 Aug 2007 #permalink

Note that that's a 33% excess of females compared to males in your population. How much unsurveyed excess females would there need to be in the British population, for example, for this to explain means of 12.7 for men and 6.5 for women?

**So should there be an impact on the results if the assumption is that sexual partners are only to be found in one specific population? For example, how does this observation apply to the possible reporting of sexual relations between persons from geographically distinct regions (e.g., countries). For instance, a male British citizen completing a survey specific to the British population, but who has had many sexual partners from countries other than Britain? Perhaps there's some differential access to sexual partners (i.e., outside the survey population) that might account for this, but this is getting somewhat beyond my basic mathematical understanding to see what significant this might have.

Those old ladies, if surveyed, would still retain their lifetime sexual experience, so I'm not sure how this should automatically make the women's numbers plummet. Changing sexual mores might cause a slight difference (if old ladies had been significantly less promiscuous in their day than "today's youth") but the CDC survey is limited to ages 20-59 and age groups are compared separately; this guards against a hidden "old lady" effect.

**Well in this instance it's not just past sexual behavior that's controlling the pattern. The other factor is mortality. In most countries throughout the world, women live longer than men after a certain age. This would mean that women have less potential male partners, while males have a (relatively) greater number of potential female partners. Further, there are significant differences in age of mortality across the globe (lower in underdeveloped countries), but still with the same gender difference in mortality. And I'm assuming that at the time of the survey, participants are reporting past as well as current sexual relationships. And there's another phenomenon in developmental psychology called socioemotional selectivity that increases with age, which is the phenomenon of reducing the number of social and sexual partnerships with age.

So there are way too many factors to consider for this discussion to boil down to just math.

By Tony Jeremiah (not verified) on 16 Aug 2007 #permalink

Windy,

Actually, I just realized that my first point is the same as the following...

"Sevgi O. Aral, who is associate director for science in the division of sexually transmitted disease prevention at the Centers for Disease Control and Prevention, said there are several possible explanations and all are probably operating.

One is that men are going outside the population to find partners, to prostitutes, for example, who are not part of the survey, or are having sex when they travel to other countries."

By Tony Jeremiah (not verified) on 16 Aug 2007 #permalink

Well in this instance it's not just past sexual behavior that's controlling the pattern. The other factor is mortality. In most countries throughout the world, women live longer than men after a certain age.

Male mortality will not matter, if the female and male average sexual experience is equal before the men croak off.

Consider a population of 5 young men, 5 young women and 1 old woman. Let's say the young men and women all date each other before settling down: men and women all end up with 5 partners.

If sexual behavior in the population is stable, the old woman will have had the same number of partners as the average, 5. If sexual behavior has changed - let's say the old lady has had 3-4 partners - that will bring down the female average *slightly* but nothing like the numbers we see in the surveys. And in fact, we see from the CDC data that the discrepancy exists within every generation, so it is unnecessary to suggest an "old ladies" effect to explain it.

Your previous examples assumed that the excess women are all "competing" for male partners in some way, but see the example above: for old ladies to drive up the male partnership count, they would need to be actually having significant amounts of sex with the young men. As you suggest, this is unlikely.

In the other extreme, the prostitute explanation is certainly possible. But has the average British man really had sex with 6 prostitutes, or is it more likely that the numbers are unreliable?

In the other extreme, the prostitute explanation is certainly possible. But has the average British man really had sex with 6 prostitutes, or is it more likely that the numbers are unreliable?

***t doesn't necessarily have be prostitutes. The exclusion assumption (provided in the example concerning W4) could be related to any number of circumstances. As examples:

* the high exclusion could be due to 20-somethings living in university dorms who have access to sexual partners that are not necessarily members of the survey population (e.g., U.S. students who have dorm mates who are citizens from other countries)

* the survey involves calculations (presumably) based on populations of persons from 20-59 years. But it's entirely possible for persons in this age group to have sexual partners below or above this age range. 20 year olds for example, likely had sexual partners in high school (e.g., 14-17) and they probably include these as sexual experiences in a survey that might base mean calculations on persons from 20-59. Also, 59 year olds likely have partners above 59. So if the population is defined as 20-59 and calculations are based only on persons in this range, there's bound to be a fairly high exclusion rate involved in the calculations that are not being considered.

* perhaps males have jobs that allow for greater extended travel than females (e.g., more business men than women); and so there's essentially greater differential access to females outside their immediate population that do not necessarily have to involve prostitutes

* Britain also seems to be in an area of the world where there is possibly access to members from populations outside their immediate environment (e.g., a look at the map shows a number of nearby surrounding countries); and then contrast this to say, hawaii where such access to differential populations is less likely

If we can rule out all of these possibilites, then we can begin to suggest that the data is unreliable.

By Tony Jeremiah (not verified) on 18 Aug 2007 #permalink

if youse guys would have spent more time chasing pussy instead of worrying about how many women I mounted...you may have mounted more yournselves?
Math doesn't suck...p.s. Math statistics is not a panty dropper...Women fuck Alpha Males because they offer savage genetics for their offspring.

By Eric K. Johnson (not verified) on 28 Oct 2011 #permalink