Wednesday, August 15, 2007

from More Just So Stories

Gina Kolata of the New York Times New Service began a recent piece in the usual way, with an explanation steeped in the current fashion for explaining everything as being an expression of an ancient and adaptive genetic heritage:

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 must 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.

Which is an odd way to start when you go on to read the rest of the article which is about the surveys which show that heterosexual men, on average have had about three to four more sexual partners than heterosexual women. You might have seen similar “scientifically conducted” polls bandied about on the blogs, on TV and perhaps even mentioned as yet another prop for biological determinism of gender roles.

However, there is a huge mystery about all this. Who are the extra women these men are having sex with and why are they apparently keeping silent about it. Otherwise, it just couldn’t figure.

- It's about time for mathematicians to set the record straight, said Dr. 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," Gale said.

Dr. Gale goes on to give a simple demonstration with equation anyone with fourth grade math could master. But not most of those in the media and even on some "Scienceblogs".

Despite all the confident assertions that the reported disparities are “proof” of a genetically programmed difference between mens’ and women’s brains apparently the original reporters of those illogical numbers know that what they’re reporting is bogus.

"I have heard this question before," said Cheryl D. Fryar, a health statistician at the National Center for Health Statistics and a lead author of the new federal report "Drug Use and Sexual Behaviors Reported by Adults: United States, 1999-2002," which found that men had a median of seven partners and women four.

But when it comes to an explanation, she added, "I have no idea."

"This is what is reported," Fryar said. "The reason why they report it I do not know."

While they’re noticing these seldom mentioned lacunae in today's common received wisdom perhaps they might want to notice something else.

Despite the reservations I’ve expressed here about polling and, even more so, the reporting of polls and surveys I do know one thing with absolute certainty. The methods of polling today are much, much more reliable than those of the Pleistocene period, the period about which the stories like the one at the top of this piece, are told with such confidence by biological determinists. We have no idea at all if our early ancestors were swingers, none. If men today, most of whom seem to be able to count, at least on their hands, are unsure about how many women they have had sex with, why would men at the dawn of humanity be more credible? Even with the techniques of modern polling? Maybe cavemen were liars and it is the propensity to lie about such things to people like pollsters (and other interviewers) which is the actual heritage we have from them. At least we know with some confidence that the lie is real.

In the end of Ms. Kolata’s article is this:

Ronald Graham, a professor of mathematics and computer science at the University of California, San Diego, agreed with 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," Graham said. "Maybe two are in the man's mind and one really exists."

Maybe the stories of evolutionary psychology need to be subjected to similar levels of scrutiny.

P. S. For all anyone knows it could have been males with strong pair bonds who had a competitive advantage in the Paleolithic period. Maybe men who spent their time hankering after the, one assumes, sparse population of women instead of working were less likely to reproduce. Maybe women thought guys like that were creepy lounge lizards. It seems to me that the evolutionary psychologists, who, perhaps, have more leisure time to spend among college students less than half their age could just be projecting their longings back in time. Stranger things have been known to happen.

Men brag about their sexual exploits and exaggerate?

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Anyone who ever lived in small town America knows how the math works.

Imagine a combined junior/senior cohort consisting of five 'bad' girls' and 45 'good' girls' along with 45 'sports' and five 'choirboys. If each of the 'bad' girls had sex with each of the 45 'sports' once then you have 225 encounters or an average or an average of 4.25 of sexual partners either way. But if you surveyed the population you would find 90% of the male population reporting more than 4 partners, while finding 90% of the female population reporting 0 partners.

If you took the aggregate and graphed the probability you would have a discontinuous result. Its the difference between a mean result which gives the result of 4.25 partners for both populations, while giving a median result of 5 partners per boy and zero per girl. And that is just contained within the town. If you combine that with out of sample visits by boys to whorehouses plus the relatively greater access to sex partners via military service overseas, the boys end up wracking up numbers in ways that the 'girl back home' doesn't.

A lot of statistical dirty work has hidden behind the mean and median of a given population and a lot more can be hidden between the mean of a universal population and tthe median of a subsection of that population.

And God help you if you start using mode instead of median and mean. People will say that the Bible or the Torah or the Koran are the Greatest Book Ever Written, for me it is ' How to Lie with Statistics'
The math gets more interesting after High School but I havn't haven't worked it out in detail. If five 'sports' marry the five 'bad girls then the number doesn't change for 10% of tho population. If the five 'choirboys' marry five 'good girls' and everybody else in town takes vows of chastity then we end up with 250 pairings for a mean of 5.5 partners each way but a median that doesn't change for girls' 80% still scoring 0% while the additional guys getting some not moving the median either. Now if the remaining 80% of 'good girls' all hook up with 'sports' we end up with 1850 total pairings with girls' still sitting at a mode of 1% and a median of a fraction above that and boys sitting at a mode of 1% and a median equal to that.

If my math is faulty call me an idiot and by the way call me a cab, but it still seems there is a big misunderstanding that 'average' is a slippery concept. Are you talking mean median or mode?
Boy words matter. If the 40 remaining 'sports' link up with the remaining 40 'good girls' then the mode for girls' changes from 0 to 1%. There is no 'still' about it.
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Anyone who ever lived in small town America knows how the math works.
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