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On Bias

UPDATE: some statistics on this from Investor’s Business Daily.

What would you think if you were reading a new research result, written by people who all had advanced academic degrees in the relevant fields, that claimed that smoking cigarettes had no correlation with cancer?

You would almost certainly discount that report, given all the other information you have acquired about smoking’s effects.

Now what if you also learned that the new report was written by a group funded by R J Reynolds, the large tobacco company? Further, it comes out that nearly all of the people who contributed to the report smoked. Now what would you think?

Obviously, you would not only discount whatever you heard from the group, but you would be suspicious that whatever they told you was the exact opposite of the truth. Right?


“Embarrassed to stand up”? Good grief!

7 comments July 23rd, 2008

A Rhetorical Question

A tip of the hat to Dennis Dutton’s Arts and Letters Daily where this article from the Chronicle of Higher Education appeared. Incidentally, since the Chronicle bought out A&LD, there have been a lot more links to Chronicle stories, which inevitably means some weaker stories get linked.

Like this one by Russell Jacoby entitled “Gone, and Being Forgotten: Why are some of the greatest thinkers being expelled from their disciplines?” He starts

How is it that Freud is not taught in psychology departments, Marx is not taught in economics, and Hegel is hardly taught in philosophy? Instead these masters of Western thought are taught in fields far from their own. Nowadays Freud is found in literature departments, Marx in film studies, and Hegel in German.

Jacoby seems to think that these three were “leading historical thinkers” and he laments their absence from college syllabi. He sneers, “Psychology without Freud, economics without Marx, philosophy without Hegel: For disciplinary cheerleaders, this confirms intellectual progress. The cloudy old thinkers have made way for new scientific researchers.”

Well, yes.

No psychologist, after reading Frederick Crews’s devastating critiques can take Freud seriously, no economist who has at least a passing knowledge of history can but laugh at Marx, and no philosopher familiar with David Stove’s quip that Hegel was a philosopher “of the kind who would quickly starve to death if [his] food supply depended on [his] ability to argue” would spend much time with our German friend.

The reason, then, that these gentlemen are not taught in their respective fields is because of the simple fact that their theories have been discredited and so should not be taught—except as they are historically interesting. For example, it is a fascinating sociological question to ask why people were so eager to believe in Freud’s manufactured experimental “evidence”, or why so many who thought that communal “ownership” of property were so willing to slaughter their fellows in the name of utopia. These three “thinkers” were “leaders” in the sense that they won many converts based upon faulty, “cloudy” reasoning, but not because their ideas were any good.

In, for example, the field of physics, Newton is still taught in mechanics, even though his ideas have been superseded by quantum mechanics, because Newtonian mechanics are more than reasonable approximations to everyday phenomena. Too, physics texts do not spend much time with failed, obvious false theories because the purpose of these books is to teach what is true and useful. Physics books are not meant to be works of history. There is no analogy for Jacoby’s crew. Freud’s etc. theories are not approximately true or even useful, but just plain false or intentionally misleading. Their names can, of course, show up in the relevant psychology, economic, and philosophy courses, but as examples of “what not to do”, but that’s about it.

Jacoby’s question, then, is rhetorical. They are not taught because they should not be taught.

That this is recognized means that there is some hope in academia. But it is significant that Jacoby found Freud being taught in literature courses, Mark in “film studies” programs, and Hegel in German language classes. Obviously, the people who teach these subjects will, on average, know less about psychology, economics, and philosophy than their peers in those fields. Meaning, naturally, that they will be less well equipped to know which ideas are bad and which good. They will more likely act on what they hope or wish to be true. They will have a better chance of being seduced by easy theories.

Bad ideas never die. They just shift departments.

6 comments July 21st, 2008

More Art

The New Museum is hosting an exhibition entitled “After Nature” whose tagline is “THE earth will pass away with a great noise and there will be no place for it.”

It is not clear what they will do with the earth, as it’s rather large. But it doesn’t matter, because this is art.

A key “piece” is Maurizio Cattelan’s “Untitled”, pictured below.

Horse in wall

It’s a little difficult to see, but the thing that mom and dad are pushing is a stroller (see the cover of today’s New York Sun for a glorious half-page picture of the horse). Dad is cradling baby, hiding the exhibit from baby’s eyes. He is thus depriving baby of bringing to mind “apocalyptic thoughts.” Shame on him.

When I gaze upon the backside of the horse, I don’t know about you, but I see it as “a story of abandonment, regression, and rapture—an epic of humanity coming apart under the pressure of obscure forces and not-so-distant environmental disasters.”

Such a work of art is priceless, as will be obvious to all but the lowest Philistine, so I have been unable to find how much it costs. It might help to know that recently Damien Hirst’s similar work “Away From the Flock, Divided” (1995) went for just over $3 million. This daring art featured a “sheep, sliced in two and preserved in aqua-colored formaldehyde.”

I don’t know who it was that said that modern artists and the rich who buy their works are horse’s asses, but it’s obvious that this was a person of low education.

22 comments July 17th, 2008

Shifting Baselines Syndrome

If you doubt any claim made about man-made global warming, Jennifer Jacquet thinks you are a “miscreant” and on par with those who deny that “smoking causes cancer.” She also draws the conclusion that since one “denialist” sports the same upper-lip fuzz as Snidely P. Whiplash, the rest of them are somewhere twirling their moustaches and up to now good.

Well, these kinds of childish insults are common by now. Sticks and stones, etc. What makes Jacquet’s edge-of-sanity ramblings interesting is her involvement in work called “Shifting Baselines.” Jacquet, and others at her web site, call “Shifting Baselines” a syndrome.

In case you weren’t paying attention, I said s-y-n-d-r-o-m-e. These are scary things and ordinarily require medical treatment, or even psychological counseling, so we are talking of serious things here. What are the signs of this dread malady? From Jacquet’s link to Wikipedia:

Shifting baseline (also known as sliding baseline) is a term used to describe the way significant changes to a system are measured against past baselines, which themselves may represent significant changes from the original state of the system.

For example (also on Wikipedia)

A cup of coffee may have only cost a $0.05 in the 1950’s, but in the 1980’s the cost shifted to $1.00 (ignoring inflation). The current (21st century) coffee prices are based on the 1980s model, rather than the 1950s model. The point of reference moved.

In other words, the term “shifting baselines” is based on the trivial observation that statements you make about the state of system will change depending on what you reference them to. Originally applied to fish stocks, an example might be that you could have said “Since 1950, fish species A stocks (in area B etc.) have decreased by 32%” or you could have said “Since 1930, fish stocks have decreased by 36%.” Both statements are true (we are supposing), because both have different baselines.

This wouldn’t be in the least interesting, except that people like Jacquet and her advisor Daniel Pauly at the University of British Columbia, are worried that some are not picking environmentally-approved baselines. They are suspicious that the non-Enlightened are picking incorrect baselines so that the can downplay the decline of, say, certain fish stocks.

And they might be right. But they have an easy rejoinder to any that pick a suspicious baseline: just pick a different one and justify it. Voila! If their opponents are trying to goose the statistics disingenuously by cherry picking a baseline, they can point that out too.

None of this behavior yet qualifies as a “syndrome”, however. What makes it one—in their minds—is the idea that there is one, fixed, Platonic, pre-human baseline where the stock of fish species A, and every other plant and animal, was pure and unadulterated. By refusing to recognize this undefiled baseline, we are refusing to admit the obvious: that the world is growing worse and worse through human behavior.

We can then say that the syndrome is “the tendency for each new generation to accept a degraded environment as normal/natural.”

It is a simple biological observation, however, that through all of Earth’s history the quantity of any species has never been fixed or static. There have been the genesis of new species and the extinction of others long before humans came on the scene. And there isn’t any species on this planet that isn’t food for some other species. Life is in constant flux. All this, I imagine, Jacquet and Pauly would admit.

The period of time they are aiming at, as their shifted baseline, is the one right before people got here, say a couple of hundred thousand years ago. But even Jacquet and Pauly must admit that humans have to have some influence on the number of each species alive. Jacquet, as I gather from the picture on her web site, certainly looks healthy and well fed, so I conclude she is eating some of the other species. I presume Pauly is, too.

Thus, since humans must have some influence, and Jacquet and Pauly and the rest of us are currently influencing the environment, it becomes only a question of how much. How much is too much? How much is enough? What is permissible? What is not? And so on.

In other words, the baseline to use as a reference is a moving—or shifting—target that can only be defined by reference to the whole range of human behavior. This means, of course, the best baseline to use in any situation is a political and scientific question. Disagreements about baselines would then appear to be normal human behavior.

But Jacquet and Pauly want to medicalize these disagreements. Any that disagree with “experts”—which I suppose are people so designated by them—are not just making a mistake, they are exhibiting abnormal behavior.

In one way, of course, labeling disagreements a “syndrome” is cheering because it implies that being in the state of disagreement is not the sufferer’s fault. Some thing or somebody is responsible for leading the patient astray. This implies there is a cure, which is simple: remove the thing or body responsible for causing the dissention.

We can count ourselves lucky that they have not yet called for re-education camps or for medicating those inflicted.

8 comments July 16th, 2008

Red State Update

If you haven’t seen Jackie and Dunlap before, you’ve been missing out. Here’s there take on the New Yorker’s terrorist Obamas cover. Hilarious.


They have an album coming out. The song “Too Much Lovin’” will undoubtedly sweep the nation.

1 comment July 16th, 2008

What’s Wrong with the Sun? (Nothing)

The headline comes from this article at NASA, sent in by reader “Mike D.”

The gist of the article is “that there’s nothing to report.” Says David Hathaway:

“There have been some reports lately that Solar Minimum is lasting longer than it should. That’s not true. The ongoing lull in sunspot number is well within historic norms for the solar cycle.”…Although minima are a normal aspect of the solar cycle, some observers are questioning the length of the ongoing minimum, now slogging through its 3rd year…Hathaway has studied international sunspot counts stretching all the way back to 1749 and he offers these statistics: “The average period of a solar cycle is 131 months with a standard deviation of 14 months. Decaying solar cycle 23 (the one we are experiencing now) has so far lasted 142 months–well within the first standard deviation and thus not at all abnormal. The last available 13-month smoothed sunspot number was 5.70. This is bigger than 12 of the last 23 solar minimum values.”

In summary, “the current minimum is not abnormally low or long.”

Let’s take a look at the actual data and see if the statements about the “normalness” of the sunspot number are accurate. And let’s keep in mind the real reason NASA made this press release, the purpose of which is never directly stated—can you see it?. I’ll come back to this later.

Here is a picture from NASA showing the “Yearly Averaged Sunspot Numbers 1610-2007.”
Sunspots through time

Solar cycle “number 1″ peaked around 1760, the cycles and other behaviors before this time are ignored in the official counting. Well, that’s neither here nor there—the labels do not matter—but we should always remember that the sun’s sunspot activity has been taking place for at least 4 to 5 billion years, and we only have measurements on the last 400. Thus we are in a very poor position to say what is “normal” and what is not. We can, however, make statements conditional on the data observed so far.

Hathaway’s analysis starts with cycle number “1″ and ignores the previous data, which, given the extended period of low to no sunspots from 1650 to 1700, actually weakens his case. This is because, conditional on all the available evidence, periods of time with no or low sunspots are not that unusual. These quiescent periods are more likely given all the evidence than they are just using the data from 1749. This is true based on the simple observation that all the data has more quiescent periods than does the later half. It is true regardless of the periodicities or other structures present. Because we have seen periods in the past with few or no sunspots is excellent evidence, after all, that we will see these periods in the future.

So why would he purposely ignore evidence that would have strengthened his case? Part of the reason is that there is the possibility that the data before 1749 is measured with error, and so should be discounted somewhat. However, this error is not especially large. The real reason has to do with the “Maunder Minimum” (shown on the graph), the period with few or no sunspots. This period does not fit the probability model Hathaway has in mind, so it is ignored. NASA says this about the Maunder:

For reasons no one understands, the sunspot cycle revived itself in the early 18th century and has carried on since with the familiar 11-year period. Because solar physicists do not understand what triggered the Maunder Minimum or exactly how it influenced Earth’s climate, they are always on the look-out for signs that it might be happening again.

But Hathaway thinks the “quiet of 2008 is not the second coming of the Maunder Minimum.”

Thus we have gone from “For reasons no one understands” to “the solar cycle is progressing normally.” The path from one statement to the other is indeed rocky. This is why I believe Hathaway’s statements are too certain. I believe that periods of low to no sunspots are more likely. I am not, however, disagreeing with Hathaway in the sense that it does not appear that we are in another Maunder: there is only scant, at best, evidence for this.

As a technical note: It is not clear that the uncertainty in length of time in months that the cycles last is best represented by a normal distribution, as used by Hathaway. Ignoring the Maunder makes his approximation a better one, but there is never a good reason to ignore part of the data it does not fit your expectations.

Anyway, back to the real purpose of this press release. Why are people so interested in the length of the solar cycle? Easy. Because for years, most climatologists insisted that the role the sun plays in the climate was minimal. That is to say, changes in the behavior of the sun were not thought to be related to changes in the Earth’s climate. The sun, which alone supplies all the energy that goes into creating the climate, was thought not to be important. Obviously, this attitude is starting to change. This press release is a tacit admission that some now admit some role of the sun in climatology.

I do not have time to talk here of the actual methods to predict sunspot number, which is an important activity in space weather. But take a look at the first picture in the press release and see if you can not anything odd.

32 comments July 15th, 2008

Actual footage

UPDATE: Christian Toto, over at Pajama’s Media, has seen the HBO Generation Kill and says “The new HBO miniseries on Iraq is well-executed, but its anti-war bias is clear.” Make sure to also read the comments.


This tip in from Kyle Smith, from today’s New York Post. Since the subject came up yesterday about fictional accounts of military action, we have here, at LiveLeak.com, hundreds of actual scenes filmed by the soldiers themselves. Smith’s story is called Wartube.

Some examples. One:

Two:

I had no idea of this site before today. But I would imagine that whatever Hollywood offers, no matter how “gritty and realistic”, cannot compare to the actual real reality as delivered directly by the soldiers. Of course, the soldiers’ own story suffers only one flaw when compared to fictionalized accounts: no slow motion (joking, just joking).

Add comment July 13th, 2008

Transforming American Military Policy

Finding the Target: The Transformation of American Military Policy by Frederick W. Kagan, 2006. Encounter Books. Recommendation: read

This book is an excellent accounting of the theories that have gripped and influenced American military thinking and planning since the Vietnam war.

Theories?

If all your information on the military has come from Hollywood (and there is a new series about Iraq out on HBO, surely this time written by writers who actually served and are thus knowledgeable), then it might come as a surprise that when planning a war you actually have to decide what to hit, what resources are needed, when those resources should be in place, what will happen in theater and out of it, the political consequences, and on and on. These decisions are made with reference to a guiding doctrine, a.k.a. a theory.

Since Clausewitz, a leading theory has been to attack an enemy’s “centers of gravity”. Destroy those, the theory goes, and the enemy collapses in confusion. Maybe so. But what is a center of gravity? Does this mean you try to kill as many troops in the field as possible? Or instead commit your resources to disrupting enemy supply lines, or perhaps the lines of communication and control? Or do you, as happened at the very beginning of Iraqi Freedom, attempt to take out the leadership (an effort, you will recall, which failed)? All good questions, the answers to which should depend on the situation. The danger is that people can pay more attention to the guiding theory—to what the theory says reality should be like—than to actual reality itself. This common human failing is found in war just as it is in other areas.

There is also the danger of rushing in, say after an unexpected attack of your country, and not having any plan:

[T]hey find it difficult—albeit no less important—to identify clear, achievable strategic aims. There is an emotional temptation to want to ‘do something’ without first clearly understanding what political purpose that ’something’ is supposed to accomplish.

Kagan repeatedly emphasizes that military actions are subservient to, or an extension of, a country’s political aims. Just killing the enemy is not enough. The way that enemy is killed or defeated must be done in such a way to further the political aims. The lack of these thoughts harmed the Iraqi war. As is well known by now, the hostilities themselves were over very quickly. The war plan was to “topple the regime” as fast as possible. This was “mission accomplished.” But in toppling the regime, nothing took its place, and chaos prevailed. The problem was the enemy was not captured, they was instead allowed to disperse, taking their weapons with them, the result of which was the insurgence.

The situation in Iraq was not turned around until more boots were on the ground, handling things in the old fashioned way, opposite to dictates of the “revolution in military affairs” and “transformative” theories then touted by the leadership.

Kagan also takes to task the latest theories that holds some in thrall: Network Centric Warfare, or NCW. This is the idea that the miracles of the “Information age” will “revolutionize” and “transform” forever our view of the “battlespace” (the old term “battlefield” deemed musty). Generals, using these things called computers, will soon be able to see what every platoon-leading lieutenant sees, and so will be able to direct the battlespace more effectively. Information overload? Don’t bother me with details. Kagan sums up his objections to NCW:

First, it is a solution in search of a problem. Second, the technical requirements needed to produce the capabilities sought and promised are unattainable in the real world. Third, it proceeds from a misunderstanding of the nature of war…The NCW visionaries imagine a world in which the eternal race between offense and defense ands in our favor—we will be able to see everything and the enemy will be about to nothing about it. This notion is preposterous.

Instead, Kagan advocates the obvious strategy: plan for the situations you are most likely to face. You might still be wrong, but you, by definition, have the best chance of being right. Do not ask for “revolutionary” technologies, but build better weapons from known technologies.

Other topics are discussed. For example: “The Army still maintain garrisons as though it were preparing to subdue the Sioux and Apache once again.” These historical dispositions “impose significant delays” on deployment and offer the enemy “numerous bottlenecks to strike.” But to try and change base and post locations is a mighty political task. Try suggesting to your congressperson—Democrat or Republican—that the base in their state is aptly located and see what happens. Politicians, as ever, will usually opt for what is best for themselves and not the country.

The book is an intelligent, readable overview of military policy planning and I highly recommend it.

1 comment July 12th, 2008

Another increase in moronicity

This story has been making the rounds (I first heard of it from Roger Kimball’s blog). It’s so incredibly asinine that it deserves broad exposure.

The headline from England’s Telegraph is Toddlers who dislike spicy food ‘racist’. The article leads:

Toddlers who turn their noses up at spicy food from overseas could be branded racists by a Government-sponsored agency.

The National Children’s Bureau, which receives £12 million a year, mainly from Government funded organisations, has issued guidance to play leaders and nursery teachers advising them to be alert for racist incidents among youngsters in their care.

This could include a child of as young as three who says “yuk” in response to being served unfamiliar foreign food.

The guide is 366 pages long! Yuk!

Nurseries are encouraged to report as many incidents as possible to their local council. The guide added: “Some people think that if a large number of racist incidents are reported, this will reflect badly on the institution. In fact, the opposite is the case.”

That is to say, nursery workers are encouraged to rat out small children to the local Party Leaders. No doubt horrific injustices like denying a love of curry will be noted on the tots’ permanent records. Can re-education day camps be far behind?

This reminds of a guy (whose name I expurgated from my memory) invited to campus when I was still at professor at Central Michigan. The topic was—what else?—diversity. This guy, who had many letters after his name, was touting a theory called micro-racism. These are racists acts that are so small that the person perpetrating them, and the person being disparaged, cannot see them. Only people specially trained could spot and analyze the atrocities.

Professors were told that when overhearing something shocking like—if you have a weak stomach, please do not read further—”Where are you from?”, we should recognize the ill intent behind the words and caution the student to modify his behavior.

That’s the only example of “micro-racism” that I can recall. Not too many examples were given. This of course makes it easy for the PC Police to label anything they want as “micro-racism.” Only an exceptionally dull person could not take any phrase whatsoever and twist it into an example of intolerance.

I don’t have the National Children’s Bureau’s guide, but I can only hope they include material on micro-racism.

4 comments July 8th, 2008

What happened to sultry?

I like Jessica Rabbit. Her voice, I mean—Kathleen Turner. Throaty, a hint of edgy raspiness, alluring, damn sexy.

But I just found out that I was wrong. Turns out I do not like sultry voices like I think I do. Instead, peer-reviewed research has proved that “High-pitched voices are most attractive.” This can only mean that I require re-education to correct my incorrect choice. Experts have weighed in!

Actually, of course, and because I can’t continue being facetious, I want to highlight a very common piece of poor “science” journalism, based on questionable research. I want to dissect this article paragraph by paragraph (don’t worry, it’s not long), to show how to spot garbage.

The article, entitled “High-pitched voices are most attractive“, by Dave Munger over at Cognitive Daily, summarizes a paper by Feinberg and others entitled “The role of femininity and averageness of voice pitch in aesthetic judgments of women’s voices” in the journal Perception.

First, the title (the reporter’s, not the paper’s). It is false. Not just “maybe not true” but false as in “ridiculously untrue.” It is not true in my case, nor in many, many other cases. So why would somebody write such a headline? Laziness, probably.

The article starts with some unmemorable fluff about some celebrity, finally moving to the sentence “In general we perceive higher voices as more feminine.” This is true. But it is one of those statements that every single human already knew was true—who didn’t know females had higher voices?—only it could be “proved” true until “research” said it was. This unfortunate attitude is now commonplace. It isn’t true until some “researcher” does “research” to show it’s true. Nonsense.

Let’s not lose sight of what they author is trying to prove: “High-pitched voices are most attractive.” What is the evidence for this (false) statement? Well, this: researchers “recorded the voices of 123 young women as they pronounced five vowel sounds: ah, ee, eh, oh, and oo. Then ten male volunteers rated each voice for attractiveness.”

How many men? 10, or “ten”, or “just one more than nine.” No doubt these men were chosen from a broad population to ensure to capture a wide range of opinion. Just kidding. They weren’t. Like many papers, the “researchers” grabbed a bunch of men who were close at hand and hoped for the best. That is, these young American men were assumed to have the same tastes as Vietnamese, Yemenese, Chinese, Siamese, and other-eses, of all age, economic, social, etc. backgrounds. The same comments can be made about the women. Did they all speak English? Have the same accent? Did they vary their tone to fit the circumstance? Etc. etc.

The chance that the sample used was representative of all humans? The words “near zero” come to mind. And we haven’t even begun to ask why just five English vowel sounds would be representative of all sounds, nor how the manner of speech and the words used are mixed up in how attractiveness is rated.

A statistical graph is then shown, which I do not have the heart to reproduce. It is a scatterplot, showing the relationship of the frequency of the spoken vowel sounds with the attractiveness rating. A straight (and curved) line is drawn through the points. It is said to be “statistically significant.” This means that the p-value of the slope of the regression line is less than 0.05. What is a p-value? It says that the chance of seeing a statistic (which is a function of the estimate of that slope) larger than the one we actually got given the experiment were an infinite number of additional times and given the slope is actually 0. Yes, complicated and confusing. That’s classical statistics for you.

But, statistically speaking, the line is crap. Pick a frequency, a low one, like 180-190 Hertz. Attractiveness ratings range from just over 2 to about 5.5, just the same as they do for higher frequencies. For one high frequency lady (about 250 Hertz), the attractiveness was low; and there were far fewer high pitched sounds to sample from. The researchers have made the common error of conflating the “statistical significance” of the parameter (slope) of the regression line with the actually difference in observable attractiveness ratings. We do not see which women was which — some women’s voice might have been better than others regardless of pitch. To prove that the reporter does not understand what he has just seen, he repeats “Higher-pitched voices are more attractive” right after discussing the graph.

There are other problems with this graph. There are about 123 numbers. Fine. There were 123 ladies. But each recorded 5 sounds, and there were 10 men. Shouldn’t there be 123 x 5 x 10 = 6150 points? Because there are not, it means some prior data manipulation has taken place. A summarization has been done (the mean of attractiveness per women). I have no idea how this summarization would effect the results. Nor would the researchers, because it would require some sort of model, which is not present.

The researchers knew at least some of their limitations because, as the reporter reports, they asked “[W]ill simply raising the pitch of a female voice make it more attractive, or are there other factors involved?” So they picked “three groups of five voices…:five low-pitched, five medium-pitched, and five high-pitched.” After this— I swear this is true—”a computer program was used to artificially raise and lower the pitch of each of these voices.” Then “volunteers listened to high- and low-pitch versions of each voice and indicated which was more attractive.”

Again, they claim that higher pitched voices were picked slightly more often as being attractive (another bad statistical graph is shown).

But wait a minute. A “a computer program was used to artificially raise and lower the pitch of each of these voices”? Yes, “”a computer program was used to artificially raise and lower the pitch of each of these voices.”

Good thing that was the end of the article, because I couldn’t take any more. From 123 women, just 15 (that’s “three groups of five voices”) were supposed to represent all human females everywhere. These 15 voices were changed by a computer algorithm to sound how a computer programmer thought they should sound. After they made the voices sound like they wanted them to sound, they asked other people how they sounded. Oh, good grief.

If the overall finding is that “men prefer high-pitched voices”, then I would say that it is true, but everybody already knew it was true because everybody knows women have higher-pitched voices than men, and that men prefer women (generally), therefore they must prefer higher-pitched voices (generally).

But just writing that into a paper will not get you published.

6 comments July 7th, 2008

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