Thursday, December 16, 2010

g at work

This is a caricature of about a dozen conversations I've had in the last few months, including today.

Colleague (physicist): What's this genomics stuff you're doing?

me: We're looking for genes associated with IQ or g. Sequencing costs are going down at ...

physicist: Yes, yes, super-exponential rate. IQ, is that like those Mensa clowns? What's g?

me: Actually the research results are pretty clear...

physicist: Aren't there lots of independent cognitive abilities? Like memory, geometric visualization, vocabulary, etc.?

me: Yes, but it turns out they are all positively correlated. Suppose there are N abilities; represent each person as a point in the N dimensional space. The population distribution is like an ellipsoid and the longest axis is what they call g. It turns out g has a lot of predictive power...

physicist: Oh, I get it. Neat! Can I be in your study?

Below are responses from analogous conversations I've had with different, uh, kinds of people (like other kinds of, uh, scientists ;-)

Sequencing costs? Sequencing what?

IQ? That was all discredited by Stephen J. Gould!

Aren't the scores just determined by the SES of the parents?

N dimensional what?!?

Note added: I hereby apologize for any psychological trauma my post may have inflicted on others :-/


DK said...

Steve, as you are such an ardent believer in the reality of g would you please show us the crucial flaws with the argument about "g, a Statistical Myth"? It's here, coming from a similarly quant-minded person:

Myself, g is something like a spherical chicken but that as a crude surrogate of reality it's better than nothing. I also think that Shalizi is intentionally obfuscating but my limited math does not allow me to competently evaluate some of his arguments. It would be interesting to hear your take on it.

Mike McK said...

CK wrote:
Yep, those other disciplines. They just don't understand math ;)

The link is Razib's pairwise regression of GRE scores of various types (Quant v Verbal, Q v W and V x W) by intended course of study. Interestingly, the group that scores closest to the lower left corner is Social Work (OK Accountants are low at the V x W comparison). The next lowest seems to be a close race between Public Administration and Elementary Education, with some competition from Business Admin.

The engineering-like students do fill in quite a bit of the bottom left quadrant in the V x W, but not as low as the accountants.

steve hsu said...

I don't want to be insulting but you really do not understand.

Let's put aside for the moment how g is defined. But, assume that it yields

1. a stable result (adult scores don't change much on re-test, even a year apart; even longer if you look at the 40-50 yr Terman study)

2. the result is predictive

3. the score is heritable

Note none of 1,2 or 3 claims to understand the underlying cause of g. Note that in Cosma's toy models (which just consist of some random data) it's not clear whether 1,2,3 are true (but they are true in the real world). Now do you understand why I am unconcerned about Cosma's calculation?

Another way of saying this is that it isn't *just* because of the "manifold of positive correlations" that we think g is an interesting construct.

If this doesn't make sense to you I may have to give up because there may be, uh, hardware limitations. (Perhaps as with many admirers of Cosma's essay, although for them it could also be ideological bias. BTW, in the essay he also tries to chip away at 1,2,3 but in, at least for me, very unconvincing ways.)

Hao Ye said...

"we should be able to formulate a test X that tests a subset of abilities, and a test Y that tests a different subset of abilities, and they should both have high correlations with g and zero correlations with each other."

Ideally yes, but I think it would be very difficult to design these tests. (e.g. how would you design a test that doesn't rely on working memory?) I also doubt that these abilities are purely independent, since some of the biological processes that form brain structures are no doubt correlated through feedback loops.

DK said...

If this doesn't make sense to you I may have to give up because there may be, uh, hardware limitations.

Sheesh, Steve. Cheapo.

Look, my question was not about whether g is interesting. It was about whether Shalizi's simulations are valid. Seems to me that you are either unwilling to look at them seriously or you agree with them/can't find flaws. If it is the latter then the implication is that g might be completely imaginary and there are no "true" correlations. In which case it makes sense to simply speak of intelligence (however undefined it is). BTW, he also makes the case that "heritability is irrelevant" - and on this point he is completely correct.

esmith said...

"His explicit point is that he gets these correlations out of completely random numbers. "

He never says that, neither explicitly nor implicitly. In his model, correlations arise between scores of an individual on different tests of mental abilities. In the section, "Correlations explain g, not the other way around", he says that you'll see what looks like a single largest factor, as long as people's scores on different tests are positively correlated. In the section, "How to make 2766 independent abilities look like one g factor", he says that scores on different tests may be positively correlated, even if there's no underlying "overall goodness of functioning" factor behind the scenes. He never says, as you seem to be inferring from the article that g is completely imaginary/random. Now go and reread what Steve wrote.

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