They Can't Mean That! (JOM Goes To The Prom)

The NY Times Week In Review front-pages an article so mathematically misdirected that it is laugh-out-loud funny for anyone with an understanding of basic statistics, a group which apparently includes no Times editors.  Fortunately, the article includes mad sex pairings, a high school prom, and a mortified professor, so you know it is hot.  Here we go:

The Myth, the Math, the Sex

EVERYONE knows men are promiscuous by nature. It’s part of the genetic strategy that evolved to help men spread their genes far and wide. The strategy is different for a woman, who has to go through so much just to have a baby and then nurture it. She is genetically programmed to want just one man who will stick with her and help raise their children.

Surveys bear this out. In study after study and in country after country, men report more, often many more, sexual partners than women.

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.

So far, so good, but here comes the curve ball:

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.

Oh My Goodness - is this professor emeritus really unfamiliar with the difference between "mean" and "median"?  I assume not, and yet... the Times lead clearly referred to partners of the "median" man and woman. 

Well, let's see his reasoning:

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.”

For heaven's sake - I will grant that *if* the reporting by men and women is accurate then the means must be equal.  However, one reason for using medians rather than means is to mute the behavior of the, hmm, possibly misbehaving tails.  Of the distribution.  Since this is apparently not obvious to Times editors, let me illustrate by returning to the prom.

Suppose 100 young men and woman attend the prom.  Ninety of the young ladies choose to dance only with their dates; ten dancing femmes set out to dance with every guy in attendance, and succeed (Guys are soooo easy.  Who knew?).

So how does the reporting go at the end of the evening?  Ninety young men report eleven dance partners - the ten Dancing Femmes plus their date.  Ten guys have a mere ten partners, since their original date was one of the Dancing Femmes.  From the guys we get total partners equal to (90*11 + 10*10), which equals 1,090 partners.  *Averaged* over the one hundred guys, that is 10.9 partners per guy, with a *median* number of partners equal to eleven.

And how about the ladies?  Ninety of them report just one partner, their date.  Ten of them report one hundred partners.  Total partners from the ladies' ledger is (90*1 + 10*100), which also equals 1,090.  That produces a mean of 10.9 partners per lady, but the median number of partners is only 1.

The median is different from the mean because the median effectively ignored the behavior of the small group of mad dancers.  How about that?  Or should I say, Q.E.D?

Groan.  I have no doubt that mocking emails are piling up in David Gale's inbox; I further have no doubt that Prof. Gale is wishing he had been a bit more clear on what the Federal study was saying about medians and what he was saying about means.  As to whether the reporter inadvertently misrepresented the study to him (Mean, median, hey, I'm on deadline!), or Gale misunderstood the question, who knows?  But clearly neither the Times reporter nor her editors understood what they were presenting.

But let me just add this - Gale blew it, and the ends did not justify the means.

For those who care, the article overcomes this ghastly start to make some plausible points about cultural pre-dispositions to misreporting by both sexes.

MORE:  Singular Values makes a similar point.

TROUBLING:  A reader revolt:

Well, on behalf of the males here, I appreciate your efforts, TM. I really do.

But, let's face it, we're lying.

I have nothing to say on the record.

MEANS AND MEDIANS AT BERKELEY: Brad DeLong illustrated the difference at David Brooks' expense in July.

 

Comments

[Cecil Turner]

. . . possibly misbehaving tails.

OOoooooh, you're gonna be in trouble.

[clarice]

Show off!

[LargeBill]

The other problem is the obvious dishonesty factor. Us guys tend to inflate and ladies underestimate.

[SteveMG]

Well, on behalf of the males here, I appreciate your efforts, TM. I really do.

But, let's face it, we're lying.

SMG

[Jodi]

Well, now I really have a problem.

I don't know if I'm a liar or just a poor counter. Or even worse an underachiever.

"There are liars, damned liars, and statisticians."

[Seixon]

Another problem is that uhh... neither of these populations (men and women) are contained to each other when it comes to sexual behavior. I mean, the men and women have probably had sex with people outside the country, on vacation, while they studied abroad, etc, etc.

Therefore when measuring a certain population of men and women, say, in the US, you still can't say that the means necessarily have to be equal since these populations have probably had sex with others outside the respective populations.

Only way you could remedy this would be to limited their answers to sex partners within the measured population. Then of course you have the problem with immigrants, exchange students, etc, etc that will also throw off the numbers even if you attempt to keep it within the US.

The guys might be lying, but so are the girls, for different reasons, of course.

[clarice]

Still in Norway, honey?
%^)

[JM Hanes]

Men may be more promiscuous than women, but the jury is seriously out on idea that "She is genetically programmed to want just one man who will stick with her and help raise their children." While it appears that she does indeed want a man who will stick around & raise the kids, she's also most likely to cheat on him with a roving alpha when she's ovulating. Call it a quantity/quality thing.

[reliapundit]

answer: sluts.

12 men can have sex with 4 women.

one at a time, of course.

[BarbaraS]

She is genetically programmed to want just one man who will stick with her and help raise their children.

This, of course, has always been the ideal. But like most ideals not readily obtainable. Most of us have to make do with what comes along. Amd what comes along can be pretty bad. You know the old song "Looking for love in all the wrong places, looking for love in all the wrong faces". This whole theory of Gale's is totally screwy (pardon my pun)and has nothing to do with sex. That's like saying I went to the grocery store 10 times but only had sex with my husband, partner, whatever only once. It makes no sense. Why do people spend time and money on these ridiculous surveys? Who the hell cares.

[BarbaraS]

OT I just read on Fox that the Italians have busted an arms deal for 100,000 AK-47s amd 10,000 machine guns. The buyer is a man named Al Handal in Jordan. He claims he has permission from the US to buy these weapons for the police in Anbar. The military denies this.

I wonder if this guy Al Handal is part of a consortium of Baathists who have announced they will take over Iraq if we leave. They say they will arrest anyone who helped us in this war and execute them and then they will file lawsuits in international court against us. Maybe these weapons will help them attain power. It's a puzzle because the article goes on to say the US has provided the police and Iraqi army with more than enough arms.

[TerryeL]

reliapundit:

ah yes, the women are sluts, the men are alpha. How typical.

[TerryeL]

reliapundit:

ah yes, the women are sluts, the men are alpha. How typical.

[Carol Herman]

The way viruses work, once you've slept with one person that "has 'em ta give," you've slept with them "all."

In other words? It takes TWO monogamous people, with no stop-overs in whore houses; to keep the couple free from what's freely sexually transmitted.

Oh, yeah. Using condoms helps.

But in drawing up a "model" ... if one person's getting some. Than, by definition, "all heterosexual women" are also "getting some." Is silly on it's face. There are some women "getting none."

And, some gals that really do hold out for more than "just getting a prom date."

But, at least, we're no longer worried about "skin." Lots of brides, today, wear white, because they want to. Most have pre-tested the merchandise. Which is a very good thing.

It adds to sanity, when you have experiences that differ from the world of fantasies. Which was all ya got with Cinderella; and stories of that ilk.

Live happily ever after? You must be kidding.

The real disadvantages are that as women age, their tits hang down. Lose the hormones; lose the edge.

[KRB]

Even apart from the mean/median confusion, some studies do find that men report a higher *mean* number of sex partners than women do. The common explanation for this disparity is that it results from male over-reporting and female under-reporting, both due to respondents’ providing socially desirable responses. However, a study by Devon Brewer and his colleagues found support for a different explanation–that there is a relatively small group of women who have a large number of sexual partners but who are under-sampled in the typical survey: prostitutes. By adjusting for prostitution-related sex, they found that the apparent sex disparity in the number of sex partners disappeared. Brewer, D.D. et al. (2000). Prostitution and the sex discrepancy in reported number of sexual partners. Proceedings of the National Academy of Sciences, 97:12385-12388.

[KRB]

Even apart from the mean/median confusion, some studies do find that men report a higher *mean* number of sex partners than women do. The common explanation for this disparity is that it results from male over-reporting and female under-reporting, both due to respondents’ providing socially desirable responses. However, a study by Devon Brewer and his colleagues found support for a different explanation–that there is a relatively small group of women who have a large number of sexual partners but who are under-sampled in the typical survey: prostitutes. By adjusting for prostitution-related sex, they found that the apparent sex disparity in the number of sex partners disappeared. Brewer, D.D. et al. (2000). Prostitution and the sex discrepancy in reported number of sexual partners. Proceedings of the National Academy of Sciences, 97:12385-12388.

[Enlightened]

Rove Stepping Down! Sorry if old news....

[rpkinmd]

It would seem that if the studies were truly representative of the population at large, that the mean and medium could not be significantly different. Real life does not imitate the very skewed example you gave. Despite what you say, I believe that the fact is that the mean or medium of male and female sex partner can not be significantly different and certainly not 2 to 1.

[M. Simon]

I once looked at the statistics to figure out how different men and women were.

About 1% of women and 3% of men are interested in seriously fetishized sex.

If you run that though your standard Gaussian statistics grinder it says that men and women differ by about 1/2 standard deviation (pun incidental). Which is not much.

[boris]

mean or medium of male and female sex partner can not be significantly different

If the shape of the bell curve is different for male and female then sampling method can indeed produce different results.

[M. Simon]

rpkinmd,

The men only have to have sex with six different prostitutes on average to make up the difference.

That could mean one prostitute a year for six years.

Possible.

[TMA]

Even with means, it is possible for men surveyed to have more sexual partners than women, since
(A) There are slightly fewer adult men than adult women -- and in some age ranges, the difference is quite extreme: among the 80 year olds at a retirement home, say, where there are more than twice as many women as men, well, men might well have twice as many sex partners. We aren't averaging in that fraction of their original cohort who are already dead.
(B) Mens' sexual partners probably tend to be younger than women's partners -- and, in any society with population growth, that means they are choosing from a larger population.
(In a similar way, just because the mean number of biological parents a person has is 2, it doesn't mean the mean number of biological children a person has must be 2... )

[TMA]

Actually, in my point (B) above, that would tend to inflate the women's mean, ASSUMING that the entire living population at a given moment was surveyed -- their sexual partners would tend to be older, and a higher percentage would be dead and so not included in the survey. On the other hand, if the population surveyed did not include younger, sexually active individuals, a higher number of of the men's sexual partners would be left out.

[Neo]

And then there is this view from across the pond.

[bubarooni]

Enlightened:

I'm just dying for that thread!

[DWPittelli]

In addition to probably being undersurveyed by chance and design (how many prostitutes do you include as representative of the population?), prostitutes have higher rates of mortality (dead people are not surveyed), probably don't know their counts of unique customers, and like other extremely "active" women, have a higher incentive to lie about their past.

Also, the men and the women may count some things differently. Such as oral sex encounters, which may be fairly common as a subset of one-night-stands, especially where a condom is not on hand.

All that said, I bet the men as well as the women are lying somewhat.

[Andy Freeman]

> It would seem that if the studies were truly representative of the population at large, that the mean and medium could not be significantly different.

Not so fast. The mean and median can easily be different in the general population.

For example, consider a population where 1-5% are wildly promiscuous. They'd drive the average up but have litte/no effect on the median.

[Tom Sawyer]

What we probably have here is a "synonym" problem. The good liberal arts majors working at the NYT know that median and mean are really just high-falutin synonyms for average.

When our reporter called the university for confirmation, she thought she had better simplify the question a bit for the "emeritus" professor. She threw the "average" synonym out to him versus the "mean."

Turns out though that "emeritus" is actually a synonym for "retired guy" not "dumb old fart" like she thought!

[Tom Sawyer]

What we probably have here is a "synonym" problem. The good liberal arts majors working at the NYT know that median and mean are really just high-falutin synonyms for average.

When our reporter called the university for confirmation, she thought she had better simplify the question a bit for the "emeritus" professor. She threw the "average" synonym out to him versus the "mean."

Turns out though that "emeritus" is actually a synonym for "retired guy" not "dumb old fart" like she thought!

[Dusty]

On a different note, there's this from the article, "But there is just one problem, mathematicians say".

Is this the infamous, one dissenter allows the literary use of the plural or are there a lot of emeritus professors of mathematics whose classes students should avoid this Fall semester?

[Da Coyote]

Let us not forget what the global warming "journalist experts" did to a real mathematician, who pointed out the N discrepancies (where N ia a large number) in the current statistical knowledge on climate. Let's face it folks, numbers are not friends of liberals. Mathematics and political "science" and art do not mix...at least not in our current poor state of lib arts education.

[Da Coyote]

Let us not forget what the global warming "journalist experts" did to a real mathematician, who pointed out the N discrepancies (where N ia a large number) in the current statistical knowledge on climate. Let's face it folks, numbers are not friends of liberals. Mathematics and political "science" and art do not mix...at least not in our current poor state of lib arts education.

[Alex J]

I've read multiple articles showcasing these sort of studies referring to the mean number of sex partners and not the median, so I think the problem has more to do with poor writing on the journalist's behalf than poor analysis by the mathmetician.

Here is an article from Arnold Kling from 2003 making the same point.
http://www.techcentralstation.com/051403D.html

[RichatUF]

going ot-

Rove spending more time with family effective the end of August.

Sealed v. Sealed can't be far behind

[ann]

OT

MUST READ

http://www.michaelyon-online.com/wp/three-marks-on-the-horizon.htm

[Jane]

I thought it was a great farewell speech (well you can hardly call it a "speech" from Rove. And the speculation appears to be the timing fits his going to work for Thompson.

[Jane]

Bold off

[PeterUK]

""She is genetically programmed to want just one man who will stick with her and help raise their children."

But not genetically programmed to want one lot of alimony.
I salute that small selfless band of the fair sex who sacrifice themselves for the sisterhood.Please would they wear badges?

"Man proposes but woman disposes".

[hit and run]

TM:
However, one reason for using medians rather than means is to mute the behavior of the, hmm, possibly misbehaving tails. Of the distribution.

IIRC, and I'm not taking the time to go look it up, Rule 12.5(b) of The Guide To Excrutiatingly Correct Prom Behavior reads:

The [misbehaving tail] end justifies the means.

[Jane]

Don Surber has a great piece today summing up the democrats and the NY Times sudden flip flop on the war. He has certainly got their number.

http://blogs.dailymail.com/donsurber

[Charlie (Colorado)]

However, one reason for using medians rather than means is to mute the behavior of the, hmm, possibly misbehaving tails.

I hope you're proud of yourself.

[Charlie (Colorado)]

(A) There are slightly fewer adult men than adult women -- and in some age ranges, the difference is quite extreme: among the 80 year olds at a retirement home, say, where there are more than twice as many women as men, well, men might well have twice as many sex partners. We aren't averaging in that fraction of their original cohort who are already dead.

Eeewwwww.

[clarice]

In retirement communities, the number one aphrodisiac is the ability to still drive at night, I'm told.

[PeterUK]

"In retirement communities, the number one aphrodisiac is the ability to still drive at night, I'm told."

Having a wheeled Zimmer is a real puller.

[rightwingprof]

"the ends did not justify the means."

Ouch!

[Jane]

In retirement communities, the number one aphrodisiac is the ability to still drive at night, I'm told.

My mother lives in a retirement home which is fabulous. The first time I visited I got off the elevator and there were 4 people sitting there doing a jigsaw puzzle in the hall. I confessed that I was confused.

The response: "honey in here we are all confused".

[clarice]

Years ago my mom sent me an hilarious book about affairs in a retirement community--said it was all true. I lent it to someone and never got it back .(Just for Charlie's edification..You're never too old.)

[clarice]

Found the book--It's by the same guy who wrote War of the Roses, Warren Adler:
http://www.amazon.com/Never-Too-Late-Love-Fiction/dp/0943972450>Never Too Late for Love

[Dave]

reliapundit: 12 men can have sex with 4 women.

one at a time, of course

I don't know what kind of low-quality pr0n you've been watching, but I assure you twelve men can have sex with four women at ONE time.

[Lee]

Actually I think that the high school prom theorem part works just fine. It says NOTHING about medians or means, only totals.

If you were to ask every girl how many guys she danced with, the sum of all the answers from the girls would be a particular total, X.

If you were to then ask every guy how many girls he danced with, the sum of all the answers from the guys would be a particular total, Y.

Assuming that all answer truthfully, the two numbers should match, and should represent the number of pairings (aka couples in the original explanation) that occurred at the dance.

Nowhere in this explanation has there been any mention of means, medians, or modes. All we have here is simple addition. No where has there been any division taking place.

Admittedly I have not read this article, but then I'm not the one pointing out flaws in it. If there are flaws in the article, they don't involve the high school prom portion.

Now it is true that the portion of the article quoted above does mix medians with averages BEFORE the high school prom explanation, but there is no indication that the two portions of the article are logically linked.

I'm not a statistician, but I have read "How to Lie With Statistics" and I've always been very good at "word problems."

[hit and run]

Via K-Lo, Rove has a higher approval rating than Congress...

OK, fine, the last Rove poll was in Feb, so who knows what it is today.

But he probably doesn't suffer from the poll trend of Congress, the "upside down hockey stick".

[BarbaraS]

In retirement communities, the number one aphrodisiac is the ability to still drive at night, I'm told."

Having worked in a retirement community for 14 years before retirement, I can tell you our number one priority was not to be on the same road with these people.

[Lesley]

More than twice as many women as men in retirement communities?

When a woman loses her husband, she becomes a widow.

When a man loses his wife, a star is born.

[hit and run]

BarbaraS:
I can tell you our number one priority was not to be on the same road with these people.

Very funny South Park episode
Grey Dawn...

[BarbaraS]

We had one amorous little old lady who chased visitors down the hall and out the door. We were at a real loss as to what to do about her.

Another little old lady always nabbed the most eligible male. When one died, she went on to the next. The competition was fierce too. We never knew if she was great in bed or just more aggressive than the other ladies. She looked like all the other little old ladies.

[clarice]

Hillariously funny, Hit.
BarbaraS, don;t even ask what goes on in the poolhouses.

[BarbaraS]

Hit and Run

Re the South Park piece. You think this is fiction? We had one little old man who beat his daughter with his cane when she "stole" his car.

[Rob C.]

The NY Times can not be referring to the median when they say, "Another study, by British researchers, stated that men had 12.7 heterosexual partners in their lifetimes and women had 6.5." It can’t be the median, since it is impossible for any individual to have 12.7 partners or 6.5 partners, unless they are rating low quality encounters as a fraction of a point. I believe that the issue probably lies with the reporters and editors rather than the professor.

[Michael Chaney]

Slight problem with the analysis: the median for such a survey would always be a whole number. Think about it.

The difference could just be that men tend to exaggerate while women do the opposite. Let's face it, "bitch" and "stud" are the same word in different genders, yet the societal views are very, very different...

[High School Graduate]

Oh, really? What's the median of 2,3,4,5?

[Sara]

I don't know if men are lying or women are lying, all I know is that when it comes to sex, I'm not getting enough. So there!

[Carol Herman]

The only way to get "enough," Sara; is to start when you're ten.

One reason the fairytale queen who keeps asking the mirror if she's the prettiest one, got sold through generations, to little girls, was to convince them that the "older woman" in their lives, had all the advantages.

When it comes to sex? It makes lots of psychiatrists rich. People think they've got this "problem,' when it's never their's, alone.

And, yes, the 1960's blew a hole through the old church teachings. The hymen WENT, as a keepsake of value.

As to what goes on in high schools these days? More than beer gets drunk. These kids are adept at a world of pharmacology that would surprise the pants off a lot of parents.

Whatever the "real" statistics are, by the way. The RESULTS can be seen because today's families are notice-ably SMALLER.

And, even better. Catholic women don't have to seek out gynecologists that willingly cut out their healthy wombs, when they turn 32. That was once a real crisis!

Women, today? Not that much smarter than the grandparents that came, before. But thanks to our Supreme Court, you CAN buy condoms, now, right off the shelves, in supermarkets. No need to keep them hidden. And, then make boys do practice runs to the drug store, hoping they can get up the courage to ask for them.

We've changed. And, that's a good thing.

That we've pressed people away from marriage in their teens? Well, people live longer. But we don't know, yet, the price of the "elder woman" given birth at 40. And, beyond. You can postpone what otherwise makes sense. Just as women once postponed intercourse (only), because bleeding on the bedsheets, during your honeymoon, was a "requirement."

As to teenagers "having sex," my ex once said he had an interesting high school experience. In his science class he shared a seat with another student. In his case, a female one. And, for that morning they were supposed to bring in a fresh urine sample. Which was going under the microscope, in their biology class.

This female student was so SHY! No makeup. And, long sleeved blouses even on hot days. But she couldn't focus her microscope; so she asked for "help." When he peered in, he saw a sperm swimming across the plate.

Then, he knew. Appearances can fool ya.

[Extraneus]

What's the median of 2,3,4,5?

3.5, same as the median of -143, 3, 4, 735.

[hit and run]

Hillary:

TULSA, Okla. (AP)—...

More Americans should become energy conscious, just like her late father was, who turned the lights off when people left a room and turned the heat off at nights even during cold Chicago winters, she said.

"I'm acting more and more like him all the time," Clinton said.

Sounds kinda Carter-esque if you tilt your head a little to the left and squint ever so slightly while chewing a spoonful of Grape Nuts are paying attention.

Now it was pert'near 100 degrees this weekend in Tulsa (congrats, Tiger on major #13), so perhaps Hill is insulated in speaking of turning the heat down in the winter, and I suppose with those temperatures, she wasn't wearing a cardigan, though I haven't seen pictures to prove she wasn't.

[Ann]

Where am I? Is this Just One Minute?

[Carol Herman]

Ann, why not take Queen Victoria's advice to her daughter, on her wedding day? "Darling, just put your head back on the pillow, and think of England."

[Ralph L]

Are we supposed to be keeping score? My thang didn't come with an instruction manual.

I'm sure prostitutes keep an accurate count for tax purposes.

[sylvia]

Wow pretty hot topic for Monday morning. Who said political blogs were dull??

So lets see, if we have more sexual partners for men - that means, let's say out of 10 people, half guys. Two guys sleep with all the girls each. 3 guys just sleep with one girl each. So some guys sleep with 5 girls each, but no girls sleep with more than 3 each. But that would leave 2.6 partners average partners per each sex. Hmmm. So the average is the same. Yes must be a different mean, I guess- but who can remember how to figure that out? All I know is we never had examples like this in stat class.

[Ann]

Carol,

OK, I get it! This is OverInAMinute!

(Where's PeterUK? He is much better at this than I. :-)

[Ralph L]

Ann, this is Just Multiple Minutes

[NameWithheld]

Uhhhh, the median of a set of an even set of responses (responses = 2N) is the average of the the two middle responses. So, it may well be a non-whole number.

And as for the male/female median differences, a couple of things strike me. First, my experience tells me that there are more long-time unmarried single women (who were generally, rather cruelly called 'old maids' in my youth) who *possibly* did not have any male partners in their lifetime than there were long-time unmarried males (generously called 'old bachelors' their entire lives) who even *probably* did not have at least one female sexual partner (and possibly many more through prostitution) in their lifetime.

Second, while (notice please that I'm mildly hiding my identity) I have remained faithful during courtship and marriage to two different women (both for periods of more than a decade), I was fairly active before my first marriage and all but stunned to find how attractive a newly divorced male can be during the decade between marriages. My guess is that experiences like mine compared to my wives (who both seem to be pretty monogamous) tends to skew the curve.

Anyway, I'd say any apparent discrepancies can be comfortably ascribed to the sampling, one way or another, and the noted direction of any lying by each sex.

(As an aside, I once did a survey that included asking people their weight. Without a lot of detail, I managed to get a very accurate reading of the actual weight of 99% of the subjects without their knowledge [not sure if this would be ethical today, but it didn't get shot down by an IRB many, many years ago] and, guess what? Women tended to report their weight an average of almost 8 pounds under the real measurement and men tended to report their weight an average of almost 7 pounds over the real measurement. Men also over-reported their height by 3/4" while women were almost right on the button.)

[DWPittelli]

Lee,

If the totals are equal, then the means are equal if the number of boys and girls are equal (since that number is the divisor).

[hit and run]

Sara:
I don't know if men are lying or women are lying, all I know is that when it comes to sex, I'm not getting enough. So there!

That dang google is failing me (I Blame Bush).

One of my favorite JOM lines ever, and despite my half-hearted efforts I can't find it right now, was...

Someone posted something saying someone posted something where they heard someone say that what Patrick Fitzgerald really needed was to get some, and then maybe he would be nicer.

To which Charlie said, quite simply, "Me too".

Seared, seared in my memory.

And speaking of whom, don't think I didn't notice:

Posted by: Charlie (Colorado) | August 13, 2007 at 11:57 AM

[Jane]

I once did a survey that included asking people their weight. Without a lot of detail, I managed to get a very accurate reading of the actual weight of 99% of the subjects without their knowledge

How?

[sylvia]

So let's all guess who Name Witheld is...

[DWPittelli]

High School Graduate asked "What's the median of 2,3,4,5?" While HSG is right that it is possible for a median of integers to not be an integer, it remains highly unlikely.

The median of integers must be an integer except in the special case where the number of numbers is even, and the two central numbers are different. In a significant-sized sample of such low integers as we're talking about, the number of integers has an even chance of being being even, but it's highly unlikely that the middle integers won't be identical. There is a nonzero but very small chance that the median will end with .5 -- however, there is no chance at all that the median will end with .7

Conclusion: the first study did report median figures, the second study reported mean figures.

[stomper]

oh wait! when they asked me how many partners i had, i couldn't remember if it was 12 or 13, so averaged it to 12.5. i was right there in the middle of the data set with the guy that said 13. so it it is the median - the median of means smartly truncated after one decimal place instead of rounded.

[Sue]

OK, I get it! This is OverInAMinute!

(Where's PeterUK? He is much better at this than I. :-)

Posted by: Ann | August 13, 2007 at 03:15 PM

Ann, this is Just Multiple Minutes

Posted by: Ralph L | August 13, 2007 at 03:16 PM

::grin::

[Sue]

I'm sorry, I wasn't sure what Ann thought PUK was better at. But the thought that PUK would not like his name and OverInAMinute in the same sentence in a sexual reference struck me as funny.

[hit and run]

DWPittelli:
Conclusion: the first study did report median figures, the second study reported mean figures.

I tend to study nice figures.

mrs hit and run has an especially nice figure.

[VIMH: Oh boy, here we go...]
Yes, of course.

Whenever mrs hit and run and I load up the car for a picnic or long trip, we fill the cooler with some snacks.

At which point I tell her,

"You have an ice chest"

(move the 'n' to 'ice' if you can't hear it)

[Sara]

The median of integers must be an integer except in the special case where the number of numbers is even, and the two central numbers are different. In a significant-sized sample of such low integers as we're talking about, the number of integers has an even chance of being being even, but it's highly unlikely that the middle integers won't be identical. There is a nonzero but very small chance that the median will end with .5 -- however, there is no chance at all that the median will end with .7

And there are two trains traveling at ...

Yeah, I flunked that class too.

[clarice]

OT:Walton has ruled in the Hatfil(anthrax ) case:
"Conclusion Based on the foregoing analysis, the plaintiff’s Motion to Compel Further Testimony from Michael Isikoff, Daniel Klaidman, Allan Lengel, Toni Locy, and James Consistent with this Memorandum Opinion, the plaintiff’s Motion to Compel Documents from the Media13 Companies, Allen Lengel, James Stewart, Daniel Klaidman, and Michael Isikoff, [D.E. # 166] is granted in part and denied in part. The motion with respect to the individual reporters is granted. The motion with respect to the media companies is denied.

An Order consistent with this Opinion is being issued contemporaneously herewith.14 -31- Stewart [D.E. # 157] is granted. These reporters are therefore ordered to comply with13 the subpoenas issued to them by Dr. Hatfill and to provide full and truthful responses to questions propounded to them by Dr. Hatfill’s attorneys. On the other hand, the motions to quash the subpoenas of ABC, The Washington Post, Newsweek, CBS, The Associated Press, the Baltimore Sun, and The New York Times are granted.

SO ORDERED this 13th day of August, 2007. 14 REGGIE B. WALTON United States District Judge"

http://www.anthraxandalqaeda.com/

[Michael Rutman]

Unfortunately, you are not correct either. The article cannot be correct for one simple reason.

12.7 cannot be a correct median in any situation.

A median in this case must be a whole number. There are a few cases where you can have a non-whole number median but they do not apply (the median mean found among many studies for example).

So, perhaps the professor assumed it was a mean and not a median since 12.7 can't be a median. I suspect that as the author used two studies he was not clear that one used median and the other used mean. Pretty clueless and would be an assumption on my part.

[Ann]

Sue,

LOL

Now that you put it that way..my sincere apologies to PUK

I was just having fun with words, something PUK and HR are better at. (Nice chest..oh brother):-)

Honestly, I just couldn't relate sex to mean, integers, median of means, averages, non-whole numbers, theorem, modes, statistics,...

or have I been missing something really kinky!

[anonymous]

DEAR NUMBSKULL-- YOU'RE THE ONE WHO CAN'T TELL A MEDIAN FROM A MEAN

Let's read that passage very carefully:

> 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.

Can you please explain to me how men had a MEDIAN of 12.7 partners? Or women had a median of 6.5?

Obviously, the second study refers to a MEAN-- not a median, as any non-innumerate person would know. And obviously, that is what the quoted statistics professor is referring to.

But I'm sure that because of the SELF-CORRECTING BLOGOSPHERE, both this post and all the ones which refer to it will be corrected shortly

[BarbaraS]

So how does the reporting go at the end of the evening? Ninety young men report eleven dance partners

The problem with this supposition is that 90 girls sat out ten dances during the evening while their dates danced with other girls. I think you would have 90 broken romances. Hummmmm. That question wasn't asked. On the other hand, human nature being what it is, the 90 girls might just decide tit for tat and dance with other boys. If they didn't, I would question their sanity.

Really, what did anyone expect from a emeritus from Berkeley of all places but gibberish?

[PeterUK]

" just like her late father was, who turned the lights off when people left a room and turned the heat off at nights even during cold Chicago winters, she said.

"I'm acting more and more like him all the time," Clinton said. "

Leaving Bill and Monica in the dark,no wonder her couldn't find the ashtray.

[PeterUK]

"That dang google is failing me (I Blame Bush)"

Here we call it "Brewer's Droop".

[Sue]

Just to make sure, I went agooglin' to see if Brewer's Droop meant what I thought it meant. And in the process learned Australians call it Foster's Flop. ::grin::

[PeterUK]

Sue,
Yes,too much beer gets to your old dang google.

[Carol Herman]

TO: ANN

Let me help.

You seem to think "time is of the essence." But if that were true, Queen Victoria would have given her daughter an egg timer; instead of advice. She was looking to bring joy into her daughter's life, ya know? Otherwise, why even mention it to the bride?

You wrote this:

Carol,

OK, I get it! This is OverInAMinute!

(Where's PeterUK? He is much better at this than I. :-)

[Carol Herman]

Ya know in the "old days," I remember my mom laughing at the women who said they got the "clap" from the toilet seats in public rest rooms.

Some people will believe anything.

And, what exactly, is being surveyed?

According to Rebecca Mead, whose book on American Weddings is pretty entertaining, she mentions an article in a teen magazine, where a kid writes in asking "how do I know if I've had an orgasm?" And, the answer is: If you have to ask, you haven't.

One of the offsets, from "not too long ago, was that teen girls were getting engaged while they were still in high school. Seems customs do change. While answering survey questions with bull shit, is also par for the course.

[hit and run]

John Edwards, July 26:

They want to shut me up.

To which our estimable host posted the natural follow up question:

But who is "they"? Not George Soros' Billionaire Boy's Club, surely. Not the Phoneix Group. Baffling.

Oh, well - file it under "Unsolved Mysteries".

Oh ye of little faith!

John Edwards, August 2:

WASHINGTON (AP) - John Edwards criticized Democratic rival Hillary Rodham Clinton on Thursday for taking more than $20,000 in donations from News Corp. officials, arguing that the company's Fox News Channel has a right- wing bias and Democrats should avoid the company.
...
"The time has come for Democrats to stop pretending to be friends with the very people who demonize the Democratic Party," Edwards said in a statement.

John Edwards, August 3:

BLITZER: Well, because you took, what, half a million dollars in advance from Harper Collins, which is part of the News Corporation.

EDWARDS: Well, I had a book called "Home" that Harper Collins published. There was an advance from Harper Collins. Every dime of the money they gave to me has gone to charity, which I committed to do. And I met my commitment. It has gone to things like Habitat for Humanity, helping low-income kids go to college, the International Rescue Committee. So the money is all gone, not to me, but to important charitable causes.

Ben Smith on Edwards, August 12:

Left unmentioned by Edwards, however, was that Murdoch’s HarperCollins paid portions of a $300,000 expense budget for the book to Edwards’s daughter and to a senior political aide, Jonathan Prince.

Turns out the "they" Edwards was talking about wanting to shut him up most likely refers to his campaign staff and consultants.

Here in the JOM Comments, we tackle the tough ones.

[hit and run]

PUK
Yes,too much beer gets to your old dang google.

Forget the google.

Having a few beers with dinner, Southern Comfort out on the grassy knoll with neighbors and kids watching the stars and then finishing mrs hit and run's glass of red wine can only get you in the dog house.

Woof.

Not to mention you might be stupid enough to jump on the back of your neighbor's kid's little motor bike and ride about 100 yards before taking a nice little spill in the middle of the street.

Splat.

And of course, that's after the same neighbor says, "let's go four wheeling in phase three!" (the section of the subdivision they just started developing), and you end up blowing two of his tires and limping the SUV back to his driveway.

Pop.

In other words, a fairly average weekend.

[PeterUK]

Clarice quick,the supervision order!

[clarice]

I'm too tired desaling with my new kitten to have time left to sorry about HIT. God watch over him is all I can say.

[Stephen]

Can you please explain to me how men had a MEDIAN of 12.7 partners? Or women had a median of 6.5?

12.7 isn't possible, but 6.5 is. If there are an even number of samples, then the median is the average of the two in the middle. So if your sample was 13, 7, 6, 3, then the median is the average of the two numbers in the middle: (7+6)/2 = 6.5 .

[JM Hanes]

Mixing means & medians sounds like something I'd do, so I'll let others cast those stones. As I understand it, the universal average of heterosexual partners would be the same for both sexes, which leaves us trying to explain the disparity in the medians. I see two possible, though perhaps not equally plausible, explanations -- depending on what the gents among us have to say when we hook them up to lie detectors.

1) A relatively small number of women have an exponentially higher number of partners than the median men report, if I'm working this out correctly, but certainly higher than median women. The overwhelmingly female business of prostitution might seem do that trick, so to speak -- but only if most men are not only including a significant number of prostitute partners in their stats but also all pairing with the same small set of women. So, are paid partners common enough to compensate for the men who have less partners than their median brethren and still skew that median skyward? Or do I need remedial math? I don't think of myself as naive, but unless the sampling itself is at issue, the prostitution proposition strikes me as doubtful. Which leaves us with:

2) We assume that men are as likely to inflate their numbers as women are to minimize them. Perhaps the conventional wisdom per Kolata's intro cannot account for the disparity in reporting, mathematically or otherwise, because it neglects the possibility that both woman and men have powerful evolutionary incentives to lie.

While sowing seed with abandon may certainly be useful, the sexual fidelity of women is, in fact, critically important to men, who can't otherwise guarantee the production and survivability of their own progeny. Inhibiting feminine promiscuity is thus a primal directive. That's why we have the word slut.

There's a reason slut has no masculine equivalent. It's why men generally brag about their conquests to other men, not to potential wives and girlfriends. The number of women you can contain/protect in your harem effectively represents your position in the male dominance pecking order. Absent visible harems, the appearance of promiscuity sends that ancillary reproductive signal instead. When was the last time anybody saw a guy pretending to be a virgin in the movies?

As a purely reproductive matter, given the vagaries of conception, it's actually in a woman's interest to engage with as many biologically attractive men as possible herself. The appearance of fidelity, however, is critically important to women who couldn't otherwise secure protection for the dependent offspring whose needs necessarily occupy the bulk of their attention.

Indeed, women are physically engineered for postpartum success. For example, back when I had my children, the medical community was just reversing their admonitions on weight gain in pregnant women. EVERYBODY assumed the baby in utero got first dibs on Mom's nutritional intake and that weight gain in excess of prenatal paraphernalia was the product of unhealthy indulgence. They took a second look when careful women started giving birth to underweight babies. Once again, there's a reason for our idiosyncratically expanded appetites. Women put on extra body fat first, at the expense of the fetus if necessary. Until the modern era, survivability was not a function of birth weight, but of the mother's ability to nurse her infant for nearly three months after birth, even if she were virtually starving herself. I'll save my ode to the multitasking genius of feminine hip construction for another day, but it's got postnatal significance as well.

In sum, Mom may sneak around when she's ovulating, but her prime directive sexually is attracting a guy who will father her child after it's born. That's where the appearance of fidelity is a plus, and that's why women come predisposed to lie about just how many "partners" they've actually had, or have.

All of which, of course, is just evolutionary speculation on my part, based on sampling the literature, not extrapolating from the data, or, alas, editing for length either.

[hit and run]

PUK:
Clarice quick,the supervision order!

"Where there is no vision the people perish..."*.

Some, however, need more than just your regular, run of the mill vision in order to survive.

Clarice:
God watch over him is all I can say.

"...but he that keepeth the law, happy is he."

Never, ever misunderestimate the law of gravity, nor any of Newton's laws of physics.

[Ralph L]

"where a kid writes in asking "how do I know if I've had an orgasm?" And, the answer is: If you have to ask, you haven't."
Obviously a girl kid.