May 25, 2010

Creating Genius

Skepchick Stacey has taken a look at Richard Lynn's claims, based on IQ testing, that male geniuses outnumber female geniuses 8 to 1. It's a good post, worth reading in its entirety. I'm going to pull out just one piece of it briefly to talk about the simple math behind the test itself.

IQ tests are deliberately designed to eliminate disparities between demographics. Any questions that test with a statistically significant difference are discarded so that the score variation can only be attributed to differences in individual intelligence. The creators of the tests don’t allow questions in which one demographic scores significantly higher or lower than another. If women consistently scored lower than men on a particular test, that test would be unmarketable because its results would be viewed as biased and invalid.

This applies to both individual (or grouped) items and to overall tests. Tests and questions are created to produce the same mean in males and females in the groups used to develop the tests. However, this means we need to take a hard look at those groups.

Of particular concern is the fact that males far outnumber females among people with learning disabilities. (They're kind of fragile that way, among others.) In fact, the people who like to tout the genius figures will happily point to the greater representation of males at the lowest end of IQ distributions as proving that their point is somehow "fair." This is, of course, less impressive when you consider that they don't expect to ever find themselves in this portion of the curve.

It's even less impressive when you consider how unfair this higher representation of males with learning disabilities causes the test to be for females without learning disabilities. I mean that literally. A population with this gender imbalance in learning disabilities requires that the test be biased against females when you compare non-disabled groups. If it isn't, it can't produce the same mean for both sexes.

But don't they exclude the learning disabled when creating IQ tests? Not for Weschler tests, at least. Given that one of the main uses of IQ testing is identifying the learning disabled, there are very good reasons to include them.

So as long as IQ tests are built this way, expect them to include the kind of bias that pushes more men into the genius range. And anyone who says that this means something more than that the test is doing what it's supposed to do? Feel free to tell them just how dumb they're being.


Becca said...

DMblog needs you...

Stephanie Zvan said...

Oh, hey, look who showed up over there. Yeah, I'll keep an eye on that one.

Bryan Pesta said...

Your making an argument about variance differences by looking at means?

It's true that modern IQ tests are sex neutral on purpose for the mean, but it's also true that men are more variable.

Since the bell curve is symmetrical, how is it that equating means by sexes biases effects due to different variances?

Lynn estimates about a 3 point difference. Not big at all, but would lead to over-representations at both ends of the curve.

I have a paper showing no difference on a traditional IQ test, but about a 3-iq point difference on elementary cognitive tasks.

My interest is academic here. If it's true that men are more variable and have a slightly higher mean, the 8:1 estimate would not be wrong at some extreme cutoff score.

The only practical application I see to this is that it may partly explain under-representation of females in A level science.

But, if it's true that men are more variable on IQ, how is that a bias?

Jefrir said...

You know, I'm pretty sure being a genius isn't a requirement for A-level science. And the problems with the genius figure are covered in the skepchick post.

Stephanie Zvan said...

No, Brian, I'm making an argument about how unaccounted for variability warps the test when means are held steady.

Is "g" normally distributed? Is it an indicator of potential achievement? If both of these are true, which is you claim, not mine, then IQ tests have a problem in the form of learning disabilities.

It used to be thought that learning disabilities were diagnosed, in part, by looking for a disconnect between IQ test scores and achievement. Kids who weren't "living up to their potential" had learning disabilities and would benefit from intervention. The problem with this idea is that the kids with potential learning disabilities and low IQ scores benefit from the interventions as well. For them, their potential to achieve was not reflected in their score.

Assuming that this potential is normally distributed, this then means that, for the purposes of creating the test, they were plucked from their rightful spot in the curve and thrown into a lower spot, causing an artificial weighting on the low end. And since the test is required to preserve the means, a similar artificial weighting on the high end had to be built into the test.

I'm not kidding about this being simple math. And you really need to read the Skepchick post, particularly the link discussing the differences in mean scores.

Bryan Pesta said...

I did read the skepchick article and was gonna post my reply there, but couldn't be arsed to register.

They're wrong too, in my opinion, on several points, but the article on balance was pretty good.

I'm not sure we have enough data to say there's a sex mean difference on IQ, but we do know there's a variance difference.

That would produce over-representation at the extreme ends. That's the simple math of it (that is not bias).

Indeed there are only a couple of items on any widely used IQ test that can discriminate really high IQ scores, but that point is moot, as the over-rep follows just from the variance difference.

Ironically, though, the Ravens is probably one test that can do this, as there is an advanced form for it for people of "superior iq".

Also, the Ravens is likely the best measure of g out there. I don't know whether it is equated on sex, but if it's not, that would explain why Lynn picked it.

I thought it was odd to look for possible sex differences on tests that throw out items that discriminate by sex. That's why I did my study using ECTs.

If one considers investment theory for high IQ and large sex differences on specific cognitive abilities (e.g., spatial skills) a small difference at the mean could parsimoniously explain the over-representation in real-world outcomes (like A-level science).

Also, aggregating a small individual difference (3 IQ points) to a larger group (male and female scientists) produces very large differences in outcomes.

As one example, the correlation between IQ and teenage pregnancy rates (using individuals) is a mere -.19. Only 4% of the variance explained. Yawn/who cares.

Aggregating to the 50 US states, the correlation becomes -.71!

I can provide cites if you're interested.

Note too I am not interested in having an aggressive exchange here. I just find the area fascinating and I think not studying it because it's sexist is wrong.

Here's my short article on IQ sex differences:

Ooop, no time to proof read, please ignore any typos.

Stephanie Zvan said...

Brian, you haven't made a single argument in that comment that wasn't entirely circular. "We know this is what intelligence looks like because this is what IQ tests tell us, therefore the IQ tests are accurate when they say intelligence looks like this."