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

[Jane]

The sad part is that question resulting in a poll.

What the hell is this world coming to?

[Ann]

What the hell is this world coming to?

Answer:
Mark Steyn

[Ann]

I can LINK! I can LINK! I can LINK!

(Sorry, but my twelve year old would be so impressed)

Now if only, I could start a new JOM thread all by myself.:)

[clarice]

Thanks, HIT. I'vebeen traveling all day and just caught your encomium.Very sweet. Beer is on the way.

[Barry]

encomium

Dang, Clarice, I had to look that one up. Learn something everday hanging around JOM.

[Carol Herman]

To get an "encomium" don't you have to be dead, first?

In other words "ecomiums" are given by the living, in praise of the dead. Or dearly departed. You know. They don't hear you. They've walked "on."

[Ann]

Carol,

Don't be such a sourpuss. A syn for encomium is tribute.

[clarice]

I'm in Wyoming..so I have departed..at least temporarily..sMOOCHES.

[centralcal]

Clarice: " I'm in Wyoming..."

Oh, sure. Jackson Hole? Dinner with the Cheneys? You better have some stories to tell, girl!"

[Ann]

Anyone want some funny news about Firedoglake?

Caution Foul Language

[clarice]

No, central. Dinner with my granddaughter. when her mom told her this morning that they were flying out Friday to be with us, the darling (2 y.o.)responded,"Let's get moving!"

[MayBee]

That's adorable, clarice.

[hit and run]

Clarice:
I'm in Wyoming..so I have departed..at least temporarily

Good for you! Have a fun and relaxing time. :grits teeth:: OK, I am a little jealous and miss the tetons...but happy for you!

[HoosierHoops]

They don't have the votes because, and again my math ain't pure but, 3.2% of poll respondents identify the current stance on Iraq as the reason they disapprove of the job congress is doing.

Would you want to vote to cut off funding when only 3.2% of your constituents say they're upset with you for doing it?

- Hit & Run
Happy Thursday Hit..
I respectfully Disagree..alittle bit..
The point i was trying to make and did such a poor job of doing is this..
Our Lame Democratic leadership..IF it had the votes would pull out of Iraq ASAP and leave the middle east to burn.. BUT..just recently a few of them have come to realize that we can't just pull out and leave the middle east to terrorists..
I dunno Hit.. I'm still drugged up on cold meds and make no sense at all..sorry..
Hey say this out loud " Democratic Leadership"
kindof makes ya giggle hearing it...
Man..I am departed.... :)

[hit and run]

Our Lame Democratic leadership..IF it had the votes would pull out of Iraq ASAP and leave the middle east to burn.. BUT..just recently a few of them have come to realize that we can't just pull out and leave the middle east to terrorists..

I agree that the leadership would pull out ASAP, but I trace that back to Schumers "compelling numbers, astounding numbers" more than a true desire to "bring the troops home".

And I don't think they've had any change of heart on the perils of leaving the middle east to burn -- I think the number are incredibly uncompellng and unastounding for Dems to play the cut and run game when there is actual progress going on in Iraq ... which in turn moves polls away from favoring cut and run policy.

Tell Americans we can't win -- and have the media provide evidence that can be used to back up that claim -- and Americans will want out.

Tell Americans that we can win, that we will win -- and have the media provide evidence that be used to back up that claim -- and Americans will want to kick ass.

We see the changes going on in the media, we see signs of progress, we see polls moving.

We see dems cutting and running from cutting and running.

[hit and run]

I mean, the next thing you know, we're going to have a dem presidential candidate start backing away from blaming everything on Bush....in 5...4...3...2...1...

CEDAR FALLS, Iowa - Not all the nation's ills can be blamed on President Bush, Democratic candidate Barack Obama said Wednesday as he called on Americans to change the nature of politics and institute more openness in government.

"Part of the problem here is not just George Bush and the White House," Obama told a crowd of hundreds gathered at a park in Cedar Falls.

[hoosierhoops]

Ann From your link:
In the land of the blind, the Muslim taxi driver is king:

A North Vancouver taxi company has agreed to pay a blind Vancouver man $2,500 after one of its drivers refused to pick up the man because he was accompanied by his guide dog.
-----------------------------
You asked what the world is coming to?
You see this story doesn't bother me in the least...what bothers me is the settlement..
I would sue for 12-200 million dollars just to get the attention of the cab company...
You want to employ muslims that won't pick me up cause i have a guide dog or because I am carrying booze..fine..I'll put you out of business. in fact cutie pie lil johnny edwards isn't doing anything worthwhile these days..maybe I'd hire him to sue ya.
Flying Imans? I'd sue em for a Billion..countersue..oversue..fight back in the courts...
what's this world coming to?
Lawyers!

[hit and run]

hoopster:
in fact cutie pie lil johnny edwards isn't doing anything worthwhile these days..maybe I'd hire him to sue ya.

I heard Edwards refused to represent the Rutgers basketball player in her suit against Imus because the girl wouldn't agree to contingency fees of 95% any settlement or judgement she was awarded.

[VIMH: You heard?]
Yeah, it was you saying that last night.

[kim]

Lance Dutton's attackers at Mainewebreport.com still think we are losing the war.
============================

[kim]

Maybe Imus can go after NoBby Cranialed newscasters now that he is no longer nobbled.
========================

[Sue]

http://www.foxnews.com/story/0,2933,293373,00.html>A moment, please, to reflect on the death of the King.

[kim]

Steve's not in his blog;
All's not right with the world.
=================

[kim]

Robert Samuelson trashes his own magazine over its global warming reporting. So where is Steve McIntyre's blog, climateaudit.org
================

[hit and run]

Sue:
A moment, please, to reflect on the death of the King.

In an effort to promote greater understanding, I think we should call Elvis Mohammed.

[Rick Ballard]

Kim,

CA has been up since yesterday. (It may not stay up through today as it is being moved). McIntyre has been doing some media appearances.

[kim]

TNX, Rick; that's a relief.
==============

[hit and run]

I can't watch it at work, but it's Jonah v Peter Beinart on the Beauchamp affiar.......

I have very low expectations.

[hit and run]

kim:
TNX, Rick; that's a relief.

OK, now that that mystery is solved, onto the next and more important one.

Where's Tom?

A little part of me dies each time I hit refresh and there's no new post.

[Rick Ballard]

H & R,

Tom may be a little preoccupied with this situation. Asia had a rough day and Europe tagged along.

[hit and run]

I'm guessing the delicate sensibilities Congresswoman Nancy Boyda were spared, as she likely wasn't a part of the listening audience last night for Hugh Hewitt's interview of Gen. Jack Keane.

The ending:

HH: Last two questions, General Keane, and thanks for the time. The morale of the American troops that you saw when you were visiting, and the confidence you have that General Petraeus will give a report that’s absolutely candid.

JK: Well, first of all, there’s no doubt in my mind that Dave Petraeus will lay it out, and what’s working, and what’s not working, and what his recommendations are. And he’ll be very clear and very unequivocal about it. And secondly, the performance, as well as the morale of the troops is extraordinary. It has always been good, right from Day One. It is actually even better now, because look, they believe they’ve been given a winning hand. They’ve got an offensive strategy for the first time that they see is working. And it’s happening right before their eyes, because of what’s happening to the al Qaeda and the Sunni insurgents that are converting, who are now helping them by the thousands, and the impact that’s had on the people. So they are very encouraged, because they think they’ve got a winning hand. Morale is very good.

Sorry, meant to say, SPOILER ALERT.

[cathyf]

Flying Imans? I'd sue em for a Billion..countersue..oversue..fight back in the courts...

Hey -- why don't we put the "pants suit" judge on it? I mean he's going to lose his administrative law job, and it could be a win-win-win all the way around if we could redirect his *ahem* "unique" talents into suing CAIR, the flying imans, etc.

[centralcal]

H&R: I tried to watch Beinart v. Jonah, but you are right it was lame. The Rove resignation came at just the right time to divert everyone's attention away from TNR and Beauchamp. So, I guess Foer keeps his job due to a Rovian plot?

I was hoping for another thread too - whatever became of the FBI investigation into DOJ Lawyer Tamm? Anyone here know or have any guesses?

Have any of the regulars watched the clip of Joe Scarborough saying the MSNBC newsroom booing the 2003 State of the Union speech? I am starting to think that by next year, the old, legacy media should be polling with similar favorability ratings as Congress.

[Gmax]

VDH on anonymous sources journalism:

Sometimes the result of this increasing abuse is more lasting damage to the authors than any temporary discomfort of fending off cross-examination. Beauchamp is now a disgraced storyteller. The New Republic has lost whatever credibility it had regained after its embarrassment several years ago of printing false stories by Stephen Glass, the lying reporter who likewise used anonymous sources.

Scheuer sounds goofier each time he gives an interview — and the credibility of his once anonymously written Imperial Hubris shakier and shakier. Isikoff has never quite recovered his journalistic reputation. We all know what happened to Dan Rather.

I simply add that it could not have happened to a more deserving group of guys.

[centralcal]

H&R: Bryan Preston gives a recap of Beinart v. Jonah over at HotAir.

[cathyf]

For anyone following the story of the old woman showing unfired-still-in-the-cartridge bullets that were "shot" at her house, you've got to check out this. Spew warning!

This one is worth a chuckle, too.

[hit and run]

If you ask me, that puppy should stop its whining and be grateful that handgrenades are being used to try and take its life.

I mean, the alternative is getting severed in two by a Bradley Fighting Vehicle.

[Elliott]

Hit and Run,

I think references to "2/5" can produce impressive results, but only if used sparingly. Perhaps, once every two months instead of twice in the last week or so.

And I have a question too. Where's Other Tom?

[hit and run]

Probably would help too if I said Mongol, instead of Mongrel...

But again, the facts don't matter, The Narrative™ is right.

[boris]

Where's Other Tom?

Italy

He's doing some research on the Italiacto! spell.

[cathyf]

H&R, given the motley crew here, "mongrel horde" is probably more accurate. (Remember Bill Murray's speech in Stripes where he said Americans are all mutts, and have the cold noses to prove it?)

[Jane]

Padilla found guilty on all counts

[Sue]

Jane,

I'm reading the comments about the guilty verdicts at Kos http://hotair.com/archives/2007/08/16/breaking-padilla-verdict-expected-at-2-pm/>Link is to Hot Air. It is so amazing to me how the left doesn't trust DoJ when it is prosecuting terrorists but just love DoJ when it is prosecuting someone in the Bush administration. No bias there, huh?

[Sue]

They should have had Fitzgerald head the prosecution. Then the guilty verdict would not have been in doubt, since they just luuuuuv him.

[cathyf]

Fitzgerald would have given Padilla immunity.

[hit and run]

Don't think for a second that Rove isn't responsible for Padilla's actions.

He's leaving the administration so that Padilla doesn't flip on him.

[Jane]

You know it's funny, I figured that a Florida jury might just find him guilty. I would never have thought that of a NY or DC jury - which seems to prove that at least in my mind most trials these days are political trials.

If that's true, the republic is screwed.

[clarice]

Thnx.Maybe..the kid is a pistol.HIT, I'm kicking you in the shins.You promised me that Padilla tip would just be between you and me.

[Sue]

Cathy,

Fitzgerald would have given Padilla immunity.

True.

[hit and run]

Clarice:
You promised me that Padilla tip would just be between you and me.

Don't ever believe any promise I make while sober.

But I am sorry.

I Blame Bush

[Gmax]

Fitz not only would have given him immunity but would have prosecuted a member of community who called the FBI with a tip on the activities of this guy. And then the MSM would vilify the member of the community not for trying to get the word out, but for violating his civil rights! Some place the VIPS shadows would be seen and if you look carefully the strings on the marionettes they control would be just visible too.

[bio mom]

Jenna Bush is engaged. Wouldn't a White House wedding be a great morale booster for the country?

[HoosierHoops]

More Random thoughts from the hoopster..
Doesn't Padilla look good after years in the cell...Gosh all that torture and stuff..
Looks like he lost 25 lbs and has a healthy glow..why not put up posters in Gitmo? Before and after looks of the illegals..
hey now..ya got to look good when you are dealing with 77 virgins..
( look.. this started out as a sex posting from TM don't blame me )
2) Cathyf: You are a genius about the pants suit lawyer..I love the idea..
Lawyers are like sperm..only one in a 100 million do any good..( see prior about sex posting )
3) So I've been really sick the last couple days and needed cheap entertainment between passing out...
Want laughs? Read FDL.. one person there canceled thier AT&T iPhone account because she was SURE that AT&T was spying on Americans. I mean it was better than a Leno Segment...
Want Dreams? Goto Hawaiichannel.com home page and view the beach webcams..
4) OK Cold pills and Crown & Coke doesn't cure the common cold.. Well maybe..I'm feeling much better now mommy...
5) Note to TM...If you post a survey about sex here it quickly melts back into a political blog...So does that mean everyone here is really politically savvy or just really old? :)
Thanks everyone..i think it's all going alittle blurry again and ...egrgyjm zzzzzz

[Topsecretk9]

--Want laughs? Read FDL--

Yeah - I'm pretty amused at their- Susan Collins better apologize that a blogger called us a foul-mouthed fem blog OR ELSE!!!!!

[Topsecretk9]

OR ELSE!!!!! --- we will make a paper-maiche float of her kissing Leiberman and follow her around with it!

[kim]

Lance dropped a little can of sodium into that muckpond. He didn't stand far enough away.

I'd join the mudwrestling, but since when do you have to register to get hot and slimy?
==============

[kim]

Steve McIntyre's under the radar again, Rick; where next, I need my fix? Poor fella, he got called a US economist by a British newspaper.
====================================

[Topsecretk9]

Sue - i have to dash but i sent you an email that I know will please and amuse you very, very, very much.

[kim]

See Dick Run. The Ball has Spots.
=====================

[Sue]

Thanks Top. I'll go check it out now.

[Sue]

Top,

Or not. Nothing there. I'll keep checking.

[Rick Ballard]

Kim,

Nah. He's up. If you like slash and burn on the warmermongers Warrick Hughes is great. Luboš Motl is quite willing to name idiots and Roger Pielke Sr. provides an excellent "real" climate science blog.

You won't see me in comments at those places 'cause, well, I just ain't smart enough I don't have time. That's it, lack of time.

[Sue]

Patience is not my virtue. ::grin::

Got it. Thanks Top!

[kim]

I think I've never heard so loud
The quiet message of a cloud.
===================

[Rick Ballard]

Kim,

Yep. It's rather entertaining to see him being attacked for his metaphysics while they leave his physics quite untouched.

If there were away to strip the warmermongers of argumentum ad verecundiam and agumentum ad hominem they would be left mute.

Pardon me, Climate Emperor, but your butt looks quite flabby there in the breeze.

[Jane]

So which one is Jenna? The blond or the brunette?

[Ralph L]

Jenna is the chunkier one who went to UT.

[Tina]

I thought you all might get a kick of the storyline as it appears on CNN's web page:

Jenna Bush to wed a former Rove aide

So, CNN not only suffers from BDS but apparently RDS as well! HA

[Ralph L]

Jenna WAS the chunkier one--she looks almost scrawny in the second picture with the CNN story.

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