Overcoming Bias

Variance-Induced Test Bias

Discussion of the Science article on gender differences in math test variance got me thinking.  Since a test score is a noisy measure of some underlying ability, an unusually high score can come either from an unusual high ability, or from an unusually positive measurement error (or both).  If higher male score variance is due more to a higher male ability variance than to a higher male measurement error variance, then a high female score is more likely to be due to measurement error than is the same high male score.  If so, treating the same score value as the same ability, independent of gender, as is common in school admissions, creates a bias (vs. men) in favor of high scoring, and against low scoring, women.

More precisely, assume that each test score s is a sum s = a + e of an ability a and a measurement error e, and that ability and measurement error are normally and independently distributed with variances A and E.  This implies test score variance is S = A + E, and that mean (and median) ability estimates given scores s are E[a|s] = m+(s-m)*(1-E/S), where m is the mean score.  The discounting factor, 1-E/S, is between 0 and 1.

Now assume men and women have the same mean score m and measurement error variance E, let R be the ratio of male to female score variance, and let N be the ratio of measurement error variance E to female score variance.  In this case, the ratio of female to male discounting factors is (1-N)/(1-N/R), which is < 1 for R > 1.   For example, if R = 1.16, the mid-estimate from the Science article, then for error fraction N values of 0.1, 0.2, or 0.4, the discounting factor ratios are 0.985, 0.967, or 0.916 -- female scores must be discounted by these factors (relative to mean scores) to be fairly comparable to male scores.  For example, applied to the math SAT (female mean 504) you'd want to subtract off (again for my sample N values) 3.7, 8.2, or 20.7 points from a 750 point female SAT score to make it comparable to a male score.  (For a 600 point score, you'd subtract 1.5, 3.2, or 8.1 points). 

No doubt there are many other factors to consider in comparing male and female candidates, but do any schools make such corrections?  Are they even aware of this bias?  Are they aware but uninterested in correcting for it?

Added 4Aug: College Admission Futures would solve this problem and many more.

Sex, Nerds, and Entitlement

In Should Bad Boys Win, the question arose of whether the legendary "nice guys" who finish last, are actually nice.  Several commenters proposed that "nice guys" feel entitled to sex, and are liars.

It does appear to me that many older and more bitter nerds do feel entitled to something.  This sounds like a turn-off; but according to the seduction community and other repositories of male wisdom such as Richard Feynman, one of the main effective strategies for attracting women is learning to project entitlement:  To convey that you expect a woman to wish to have sex with you.

I normally have fairly low regard for evolutionary psychology, especially post-hoc.  But here it seems to fit the bill really nicely; so I'm going to speculate a bit on what entitlement might signify in the environment of evolutionary adaptedness.

Displaying feelings of sexual entitlement would have been, in a tribal setting, a strong signal of dominance and actual access to sex. These traits would be associated with genes valuable in male offspring provided that either the father could be convinced to provide resources or the environment was such that they did not need to.  It might also indicate that it was physically dangerous to refuse him sexually, and relatively socially safe to accede.

In contrast, displaying feelings of thwarted entitlement would be a huge neon warning sign of low fitness.

Not only does this guy not have high status, his systems for judging his own status are broken. This is a hugely costly defect.  Association with him may be dangerous both physically and socially, prior to his impending demise.  Big red letters are flashing KEEP AWAY.

Break It Down

Last October I wrote:

The US with 27% of world product has about 46% of world military spending.  ...  Though of varying quality, there are a great many detailed and quantitative analyzes of the marginal value of aggregate medical spending.  In contrast, the lack of even remotely similar analyzes for military spending is really quite stunning. ... I'd most like to see an itemized budget detailing the expected annual costs the US would suffer in a world that had adapted to the US only spending $300B/yr on defense.

Megan McArdle yesterday:

I view myself as feminist(ish) because I believe the following:

1. Society is set up in ways that limit women's choices and opportunities--men's too ..., but women more. ...
2. Privilege exists, and is in many unfortunate ways invisible to those who possess it.
3. We should try to change those things.

My first reaction was, it is really clear male privilege is stronger overall that female privilege in our society?  It might be, but as with defense spending I'd like to see some sort of calculation.  A little web search finds a male privilege checklist and a female privilege checklist.  The next obvious step is to assign point values to such privileges, so we can add them up and compare totals.   

Of course there would be many ways to disagree about such point values, including how they should account for differing abilities and preferences.  You'd open yourself up more to ridicule by posting a calculation, as folks could trumpet your most vulnerable estimate as evidence of your insincerity.  And you wouldn't show your impressiveness nearly as much as you could via a fancy math model, statistical data analysis, or semiotic text analysis. 

But the essence of analysis is to "break it down", to take apart vague wholes into clearer parts.  For the same reasons we make point lists to help us make tough job decisions, or ask people who sue for damages to name an amount and break it into components, we should try to break down these important social claims via simple calculations.  And the absense of attempts at this is a sad commentary on something.

The Opposite Sex

Some observations on sex and gender:

* Yes, there are two different sexes in the human species; and they differ by the presence or absence of entire complex adaptations.  Just as men lack uteruses and women lack testicles, so too, there are differences of psychological machinery as well.

* Defns:  "Sex" is the biological difference.  "Gender" is a meme, a cultural concept of sex.

* A good deal (perhaps a majority) of what we think of as "manly" or "womanly" is gender rather than sex, just because it is so much easier to create and transmit cultural information than biological information.  A man in Saudi Arabia may have a very different concept of what it means to be male than a man in New Zealand.

* Gender concepts are built around sex differences - not faithfully reporting them, but accreted around them.  You couldn't just swap the "man" and "woman" concepts in Saudi Arabia, or New Zealand either, and end up with a stable meme.  For more on this see John Tooby and Leda Cosmides's "The Psychological Foundations of Culture".

* Understanding the opposite sex is hard.  Not as hard as understanding an AI, but it's still attempting empathy across a brainware gap: trying to use your brain to understand something that is not like your brain.

* Despite everything I've read on evolutionary psychology, and despite having set out to build an AI, and despite every fictional novel I'd read that tried to put me into the life-experience of a woman, when I tried to use that "knowledge" to guide my interactions with my girlfriend, it still didn't work right.

Glory vs. Relations

From a thoughtful essay by Christina Sommers: 

MIT biologist Nancy Hopkins, ... (a prominent accuser of Harvard president Lawrence Summers ... [who suggested] men and women might have different propensities and aptitudes), points to the hidden sexism of the obsessive and competitive work ethic of institutions like MIT.  "It is a system," Hopkins says, "where winning is everything, and women find it repulsive. ... The list of cultural norms that appear to disadvantage women ... includes the favoring of disciplinary over interdisciplinary research and publications, and the only token attention given to teaching and other service" ...

If asked to make a drawing, little girls almost always create scenes with at least one person, while males nearly always draw things - cars, rockets, or trucks. ... Among primates, including our closest relations the chimpanzees, males are more technologically innovative, while females are more involved in details of family life. ... After two major waves of feminism, women still predominate - sometimes overwhelmingly - in empathy-centered fields such as early-childhood education, social work, veterinary medicine, and psychology, while men are over-represented in the "systematizing" vocations such as car repair, oil drilling, and electrical engineering. ...

[Consider] women's [amazing] progress in veterinary medicine ...

The Psychological Unity of Humankind

Followup to:  Evolutions Are Stupid (But Work Anyway), Evolutionary Psychology

Biological organisms in general, and human brains particularly, contain complex adaptations; adaptations which involve many genes working in concert. Complex adaptations must evolve incrementally, gene by gene.  If gene B depends on gene A to produce its effect, then gene A has to become nearly universal in the gene pool before there's a substantial selection pressure in favor of gene B.

A fur coat isn't an evolutionary advantage unless the environment reliably throws cold weather at you.  And other genes are also part of the environment; they are the genetic environment.  If gene B depends on gene A, then gene B isn't a significant advantage unless gene A is reliably part of the genetic environment.

Let's say that you have a complex adaptation with six interdependent parts, and that each of the six genes is independently at ten percent frequency in the population.  The chance of assembling a whole working adaptation is literally a million to one; and the average fitness of the genes is tiny, and they will not increase in frequency.

In a sexually reproducing species, complex adaptations are necessarily universal.

Where Want Fewer Women?

My colleague Garett Jones mentioned he'd just written on how to get more women in economics, just after I'd noticed a recent Science article, "Igniting Girls' Interest in Science."  Both of which raise the question:   Do those who want more women in science, economics, politics, etc. understand that more women in some places requires fewer women elsewhere?  If so, why don't they tell us where exactly they want fewer women - and explain why the world is better with fewer women there?  Without this, they sound like people pushing more state education spending without saying whose taxes should be raised to pay for it. 

Sure, one could favor more skilled and productive women, which implies fewer women in lower skilled jobs.  But if this is the issue the question should be where can women be the most productive, not how to get more women in science.  And then why not listen to economists' long-neglected advice on how most everyone could be more productive?

"Hey, I'm just saying ..."

Gender Tax

Last week I noted that, in an hour of searching, I couldn't find any defenders of the economic-theory-supported tall tax, even among economists.  Today I report it was easy to find supporters (1, 2, 3, 4, 5, 6, 7, 8) of Alesina, Ichino, and Karabarbounis's proposed man tax, also well supported by economic theory:

Gender Based Taxation ... changes spouses' implicit bargaining power and induces a more balanced allocation of house work and working opportunities between males and females. Because of decreasing returns to specialization in home and market work, social welfare improves by taxing conditional on gender. When income sharing within the family is substantial, both spouses may gain from [it].

So riddle me this: if careful economic analysis had instead favored taxing men less than women, how many supporters do you think that proposal would have found, even among economists?  And what does that say about how much economic theory influences economists' policy conclusions?

P.S.  The best "man tax" is not a fixed tax amount for being a man, nor is the best "height" tax a fixed amount per inch of height.  Instead, each gender or height has a different income tax schedule.  So there is no special reason to fear some "couldn't pay the tax."

Added 20Dec:  Here's a paper on a more general tax on genetic features. 

Leader Gender Bias

In an experiment on gender perceptions, psychologists Cameron Anderson and Francis Flynn gave one group of MBA students the original Heidi Roizen case for later in-class discussion, while the other half received a copy that was identical in every way, except that "Heidi" became "Howard."  In a study currently under review, Anderson and Flynn report that while both Howard and Heidi were rated as equally competent (they were the same person, after all), students described the female version of the character as overly aggressive, and were much less likely to want to work with or hire her.

That was from Slate.  Here is the New York Times:  

How should unproven findings be publicized?

A year or so ago I heard about a couple of papers by Satoshi Kanazawa on "Engineers have more sons, nurses have more daughters" and "Beautiful parents have more daughters."  The titles surprised me, because in my acquaintance with such data, I'd seen very little evidence of sex ratios at birth varying much at all, certainly not by 26% as was claimed in one of these papers.  I looked into it and indeed it turned out that the findings could be explained as statistical artifacts--the key errors were, in one of the studies, controlling for intermediate outcomes and, in the other study, reporting only one of multiple potential hypothesis tests.  At the time, I felt that a key weakness of the research was that it did not include collaboration with statisticians, experimental psychologists, or others who are aware of these issues.