Wednesday 23 October 2013

All you ever wanted to know about intelligence, Part 5 (IQ is just a single number)


Candidly, I thought that 4 parts on an intelligence primer would be enough, but now my brightest interlocutors are flinging even more clever problems at me, so it is “forwards unto the breach once more”.

A distinguished scholar tweets (they do such things nowadays): Any attempt to reduce the vast panoply of human talents to a single number (IQ) is obviously naive and silly

Let us, as modern parlance has it, deconstruct this contribution, to which I gave a low mark, thus showing that single numbers are often useful summaries.

The implication is that those who measure intelligence are trying to reduce the vast panoply of human talents to a single number. I have met many of these researchers, and I detect no such urge. Skills are not reduced or constrained by trying to understand their underlying characteristics. Researchers are certainly seeking to understand what proportion of the variance in the vast panoply of human skills can be accounted for by a number of latent factors, thereby bringing order to what would otherwise be a maze of correlations. The answer, first given in 1904 and amply confirmed thereafter, is that half of the variance resides in one general factor. This is a major finding, and one of the best replicated in the behavioural sciences.

Paradoxically to some people, to ensure this finding you have to measure the broad range of intellects and the broad range of human skills: the whole panoply, in fact. It is precisely the wide range of skills which allows you to search for factors in common, and if broadening the range reduces the explanatory significance of any factors, then you have ample proof that such factors are insufficient explanations for the observed variance. If you cannot find replicable factors, then panoply rules.

In fact, what comes out is that g is one number and it explains a lot: scholastic achievement, occupational achievement, and lifespan to a significant and sizeable degree. Finding that is not silly or naive, it is a replicable fact, and the “positive manifold” of human skills shows that some people have more panoply than others. We have found that there is a common core, something akin to cortical horsepower which is somewhat like the central processor in a computer. Some core processors work faster than others, thus allowing more mental work to be done, leading to greater and more extensive intellectual outputs. The brain does not appear to be a package of separate modules vying for cranial space, each to the detriment of the other.

IQ is actually a slightly broader measure than g because apart from the most reliable measure, Full Scale IQ, intelligence test results usually include three or four group factor IQs and also some specific scores in the form of the less reliable subtest results. So, when a person is tested individually on a face to face test they get one summary score, and four group scores, all based on ten subtests. Factor analytic techniques reduce those 10 or more tests to the best single predictor, g. If you don’t like a single figure you can have the 4 group factors. These give more detail but are a little less stable. To get a view of detailed strengths and weaknesses, look at all 10 subtests carefully, recognising that they will be usually less reliable than the overall total score. That overall IQ score is better in most circumstances, and gives the best predictions. If you are doing large scale international research, and want to use a properly validated way of extracting the common characteristics from an array of different tests, then use factor analytic techniques to extract the g factor.

By way of analogy, our intellects are like trees with a very broad and tall trunk, from which four boughs protrude, and  from them many, many twigs from which one gets a panoply of leaves.

Since we are dealing with humans who walk about under light supervision, change marital partners frequently and even occupations and sometimes countries, we are lucky if, by using all the measures available to us, we can account for 25% of the variance in life achievements.  Explaining 20-25% is as good as it gets in behavioural science at the moment. IQ is probably the best predictor of a relatively weak bunch, even better than social class or wealth in most longitudinal studies.  That is an argument for another time, but whenever intelligence is measured it has a strong association with life outcomes. IQ is a powerful measure, relative to other social science predictor variables.

Why is there so much disparagement of predictors based on a single number? Perhaps it is a fundamental misunderstanding about the nature of description and prediction. A strong predictor is not an exhaustive equation which totally defines the nature of the organism, stripping it of all degrees of freedom. To illustrate the point, here are some other single numbers that the fearful might see as reducing vast panoplies:

Height: associated with health, status, income and social leadership and intelligence.  At a pinch, you can estimate all those from a single surviving femur. Height does not determine everything, not even the shape of the rest of your body, but it has a partial influence. Tallness matters somewhat, but short people can write poetry.

Weight: associated with health, lifespan, status (now low, formerly high) income (ditto). Heavy weight is usually bad news, but some fat people are fit and healthy.

Wealth: associated with health, status, intelligence? Wealth effects are probably partly caused by intelligence leading to wealth. Children of wealthy parents are not necessarily intelligent.

Social class: associated with health, lifespan, intelligence? Social class of origin has an influence, but if you look at intelligence in children then the family of origin has less effect, and the ability level of the child more effect on later life success.

Taking social class as an example, are the presumed effects of social class on human outcomes lessened because a single number is used to summarise a broad category of status indicators? The number cannot hope to capture all the nuances of class membership, and is not intended to. If, for example, a single number for class correlates with a single number for lifespan, they we can at least ask whether class has an influence on longevity. (It does appear to, but only partially if one controls for intelligence).

Here is a list of other things that could be summarised by single numbers: popularity, journal impact factors, number of publications, number of references, penis length, breast size, brain volume, number of sexual partners, number of Twitter followers, and number of page views on a blog. Single numbers do not cover everything, but they indicate something, even though we often complain about them and want to add further measures.

Years ago, when teaching a BSc in social psychology, I used to ask the students on their first day: “What single snippet of information reveals most about you?” Social class, height, age and so on were all proposed. Then, in triumph, I would exclaim “Your postcode”. Even 15 years ago small area statistics were being extracted from the UK census and linked to postcodes (usually 6 to 7 alphanumeric characters). This short code included powerful predictor variables which gave accurate descriptions of the people living in a small area. Of course, there is always some resentment when we humans turn out to be predictable, but if we aim to be social scientists, we must rise above that.

The philosopher Gilbert Ryle once observed “one can simultaneously obey the laws of gravity and the rules of golf”. A single equation explains the fall of a ball towards the surface of the earth, and at the same time there are conventions about how the game of golf is to be played. Golf, as I understand it, depends on a single score, the lower the better, but that is another matter. There may be more to golf than could be contained in a single score, but I would not bet on it.

In conclusion, and in very succinct terms: A numerical description of one important facet is not thereby the determining and constraining definition of the entity.



By the way, throughout this discussion I have accepted the observation that human beings have a “vast panoply of talents”. There are certainly many very bright and talented people with many skills. Personally, I would not describe myself in that way, but it is nice to have goals to aspire to. Happy panoply to you all.


  1. It's undoubtedly a talent to have made yourself a "distinguished scholar" while being an unreflective twerp. Unless in modern academic life being unreflective increases your chance of distinction. Which, alas, it might.

  2. Excellent series of posts! I just found you today via Marginal Revolution, and I think this will be my new favorite blog.