Is Psychometric g a Myth?
Posted by Dalliard
As an online discussion about IQ or general intelligence grows longer, the probability of someone linking to statistician Cosma Shalizi’s essay g, a Statistical Myth approaches 1. Usually the link is accompanied by an assertion to the effect that Shalizi offers a definitive refutation of the concept of general mental ability, or psychometric g.In this post, I will show that Shalizi’s case against g appears strong only because he misstates several key facts and because he omits all the best evidence that the other side has offered in support of g.
Shalizi has a lively intelligence, but he has a little too much confidence in his own g Factor. He begins his essay:
Attention Conservation Notice: About 11,000 words on the triviality of finding that positively correlated variables are all correlated with a linear combination of each other, and why this becomes no more profound when the variables are scores on intelligence tests. ... To summarize what follows below ..., the case for g rests on a statistical technique, factor analysis, which works solely on correlations between tests. Factor analysis is handy for summarizing data, but can't tell us where the correlations came from; it always says that there is a general factor whenever there are only positive correlations.
But why are there only positive correlations among cognitive skills? That's hardly a trivial question. Many things in life come with tradeoffs, such as risk v. reward.
Shalizi gives an example about cars, in which he misses this crucial point:
One of the examples in my data-mining class is to take a ten-dimensional data set about the attributes of different models of cars, and boil it down to two factors which, together, describe 83 percent of the variance across automobiles.  The leading factor, the automotive equivalent of g, is positively correlated with everything (price, engine size, passengers, length, wheelbase, weight, width, horsepower, turning radius) except gas mileage. It basically says whether the car is bigger or smaller than average. The second factor, which I picked to be uncorrelated with the first, is most positively correlated with price and horsepower, and negatively with the number of passengers — the sports-car/mini-van axis.In this case, the analysis makes up some variables which aren't too implausible-sounding, given our background knowledge. Mathematically, however, the first factor is just a weighted sum of the traits, with big positive weights on most variables and a negative weight on gas mileage. That we can make verbal sense of it is, to use a technical term, pure gravy. Really it's all just about redescribing the data.
The first factor is less bigness than an axis of affordability v. something like "impressiveness." If you look closely at the components, you can see the tradeoffs: for example, Shalizi implies that horsepower and price are positively correlated, but it's more insightful to think of them as inversely correlated. Restate "price" as, say, "change left over from a $100,000 bill" and the affordability v. impressiveness trade-off is obvious. This inherent tradeoff is one that automobile engineers and marketers struggle with everyday.
In contrast, we don't see these the same levels of tradeoffs on cognitive abilities. Sure, autistic savants might have some amazing skills because they lack others. And blind people sometimes are better at, say, music or other tasks involving mentally processing nonvisual inputs. What's surprising is we don't see these tradeoffs as much.
But, with cognitive tasks, on average, we don't see the kind of tradeoffs you see with most engineering problems. People who are above average on math skills are not, on average, below average on verbal skills. On average, they are above average on both.
That's kind of strange when you think about it. Presumably, there are trade-offs involving, say, head size, ease of childbirth, nutrition needs, hip width and running speed, tendency to fall over, tendency to get abstracted, and so forth. But the lack of overall tradeoffs just within cognitive tasks is pretty odd.