by Ian J. Deary
Before relating that finding, consider the following question. What do you expect to see in the relations (correlations) between the different tests? Perhaps some will be unrelated to each other because they tap different mental skills? A sensible guess, one that I shared before seeing data such as these, is that many of these mental functions have no relations with each other. That is, there might be no relationship between performance on some individual tests and on others. One might go further and guess that being good at some tasks might carry a price in being poor at others – this predicts a negative correlation between some tests. For example, people with better ability to see spatial patterns might have lower verbal ability. Or those who can see small, pernickety details in pictures might be poorer when to comes to checking through lists at speed. Or perhaps people with good memories have a slower mental speed. A lot of our intuitive thinking about mental capability runs along the lines of there being some cost for any mental benefit we possess.
In fact, none of those predictions is correct. The fact is that every single one of those 13 tests in the WAIS-III has a positive correlation with every other one. People who are better at any one test tend to be better at all of the others. There are 78 correlations when we look at all the pairings among the 13 tests. Every single correlation is positive – a good score on one of the tests tends to bring with it a good score on the others. There are no tests unrelated to any other one, i.e. there are no near-to-zero correlations. There are no tests that are negatively related with other ones. Even the lowest correlation between any two tests is still a modest 0.3 (between picture completion and digit span). The highest – between vocabulary and information – is almost 0.8. The average correlation is 0.5. Thus, even the average correlation between these rather different mental tests is on the large side.
The first substantial fact, then, is that all of these different tests show positive associations – people good at one tend to be good at all of the others. But remember that we are talking about the tendencies within this large group of people; individuals provide us with comforting exceptions.
The second important fact is that some sub-groups of tests in the WAIS-III collection associate higher among themselves than with others. For example, the tests of vocabulary, information, similarities, and comprehension all have especially high associations with each other. So, although they relate quite strongly to every test in the WAIS-III collection, they form a little pool of tests that are especially highly related among themselves. The same thing occurs with digit span, arithmetic, and letter–number sequencing. They relate positively with all of the other tests in the collection, but they relate especially highly with each other.
This is not so surprising. The four former tests all involve language, learning, and understanding. The three latter tests involve numbers and the ability to hold facts in memory while manipulating them. Within the WAIS-III collection of tests there are four such pools of tests that have especially close associations among themselves, even though they still relate positively to all the others. These pools of tests are indicated in Figure 1. Note that a circle with the label ‘verbal comprehension’ has arrows pointing to four tests: Vocabulary, information, similarities, and comprehension. What this means is that there are such close associations among these tests that they can be collected together under a hypothetical entity called ‘verbal comprehension’. This entity merely captures the fact that these four tests have closer associations among themselves than they do with other tests. There is no test called ‘verbal comprehension’ – it is a statistical distillation of these four individual tests. It recognizes their especially close correlations.
There are three other collections of tests within the WAIS-III that seem to hang together especially tightly. In Figure 1 the closely associated picture completion, block design, picture arrangement, and matrix reasoning tests are collected under the heading ‘perceptual organization’, a label that seems quite nicely to capture the sorts of thinking we must do to perform well on these tests.
The three tests that involve numbers are collected under the heading ‘working memory’. Working memory is a label that psychologists use to describe the ability to hold information in memory and manipulate it at the same time. Imagine someone asking you a series of quite complicated questions to which you must give an answer. Imagine, in addition, that you were concurrently being asked to remember the last word in each question as well, so that you could write down the list later. Thus, at the same time as trying to answer each question in turn you’d be trying to remember a list of isolated words. That would hurt your head and the facility under strain would be what psychologists call your ‘working memory’.
Finally, there are two tests that have a high association and both involve working at speed to make comparisons with visual symbols. They have been collected under the label ‘processing speed’.
To recap. A collection of 13 varied mental tests given to over 2000 adult Americans has shown that the ability to perform well on all of these tests is related. In addition, there are sub-groups of tests that relate more highly to each other than to the other tests. In Figure 1 we illustrate this latter fact by showing the related groups of tests collected together under headings or labels that summarize the sorts of mental skills common to the tests. In fact, the common name for these four collections of sub-groups is ‘group factors’. These group factors refer to certain domains of cognitive performance that can be separated to a degree. The statistical methods used to examine these data can give people scores on ‘verbal comprehension’, ‘perceptual organization’, ‘working memory’, and ‘processing speed’.
Just as was done on the 13 individual test scores, we can go further and measure the correlations among these four group factors. That is, we can ask whether someone who is good at one of these group factors of mental ability tends to be good at all the others. For example, do people with good ‘working memory’ scores also have fast ‘processing speed’, good ‘verbal comprehension’ scores, and good ‘perceptual organization’ scores? The answer is an even more emphatic yes: these four group factors have correlations between 0.60 and 0.80. These are large associations and they mark the fact that people who tend to be skilled in one of these group factors tend to be skilled in all of the others. People tend generally to be good or poor at all of the tests and all of the group factors. This is shown in Figure 1 by having all of the group factors collected under a single heading of ‘g’, which, under an old convention, stands for the general factor in human intelligence. Once again, it is a statistical distillation that describes a solid research finding: that there is something shared by all the tests in terms of people’s tendencies to do well, modestly, or poorly on all of them.
What comes next is very important. The rectangles in Figure 1 are actual mental tests – the 13 sub-tests – that make up the Wechsler collection. The four circles that represent the ‘group factors’ and the circle that contains g are optimal ways of representing the statistical associations among the tests contained in the rectangles. The things in the circles, the specific/group factor abilities and ‘g’, do not equate to things in the human mind – they are not bits of the brain. The names we pencil into the circles are our common-sense guesses about what seems to be common to the sub-groups of tests that associate closely. The circles themselves emerged from the statistical procedures and the data, not from intuition about the tests’ similarities, but the labels we give the circles have to be decided by common sense. Again, the names of factors in the circles in Figure 1 are our ways of conceptualizing types of performance on mental tests. That is not to say that we will never discover what the brain systems are which do these sorts of mental tasks, but we cannot claim such a thing based on these data. You will sometimes catch me referring to people’s ‘verbal ability’ or their ‘working memory’ or whatever. What I am referring to is people’s performance on this or that type of mental test. I am not trying to sell you a model of the human brain. Of course
, it is interesting to ask how the brain manages to execute different types of mental work, and we cover some of that research in Chapter 3. But it is important to appreciate that the analysis of mental tests that we deal with here just classifies the tests’ statistical associations: it does not discover the systems into which the brain partitions its activities.
This way of describing human mental capabilities, as illustrated in Figure 1, is called a hierarchy. It illustrates the fact that mental abilities as measured in mental tests tend to collect together in pools that have especially close associations. It also notes the fact that these pools themselves are all highly related. When we think about individual differences in people’s abilities, therefore, the message from this large study is that about half of the variability in a large group of adults may be attributed to mental ability that is required to perform all tests – g or ‘general intelligence’. Thus it does make sense to refer to a general type of mental ability; talking about a single, general intelligence has some veracity. There is something common to people’s performance differences across many types of mental test. Next, we can say with confidence that there is more to human mental ability than just being generally clever. We see from Figure 1 that there are special types of ability and that these can be described in terms of the kinds of specific mental work needed to perform certain tests. Last, the combination of general ability and group factors is not enough to account for how well people perform on the 13 tests of the WAIS-III. There seems to be very specific ability needed to do well on each test, something that is not shared with any other test even where the material in the test is quite similar to that in other tests.
In thinking about how efficient your own mental machinery is you would need to consider at least 3 questions. First, how strong is my general ability? Second, what are my strengths and weaknesses on the group factors? Third, are there some very specific tests on which I excel? I hope that brings some order to the question of how many human abilities there are. The answer is that it depends on what level of specificity you have in mind.
The first person to describe the general factor in human intelligence was an English army officer turned psychologist, Charles Spearman, in a famous research paper in 1904. He examined schoolchildren’s scores on different academic subjects. The scores were all positively correlated and he put this down to a general mental ability. There followed decades of arguments among psychologists as to whether or not there was such a single entity. American psychologists, notably Louis Thurstone, suggested that there were about 7 separate human abilities. Although the argument raged on, and still does to an extent, it became clear by the 1940s that, whenever a group of people was tested on a collection of mental tests, the correlations among the test scores were almost entirely positive and the general factor in mental ability was a significant, inescapable fact. Just how significant is the g factor was described above: it accounts for about half of the variability in mental ability in the general population. Just how inescapable it is became clear in the early 1990s.
Key dataset 2
In 1993 the American psychologist John Carroll brought out his book Human Cognitive Abilities: A Survey of Factor Analytic Studies. His long career in academic psychology saw him through most of the debates about the number and nature of human mental abilities. He saw that there was disagreement and that there were some barriers to coming to a consensus. One problem was that there were hundreds of studies that had tested people on mental ability tests. They tended to use different numbers and types of test. The people tested in the studies were of different ages and backgrounds. The researchers used different statistical methods to help them decide on their conclusions. Carroll’s purpose was to retrieve as many of the studies on human intelligence conducted during the 20th century as he considered to be of good quality. He then re-analysed all of these studies using the same statistical methods. This involved re-analysing over 400 sets of data, which included most of the large, well-known collections of data on human mental ability testing from the period. Therefore, if one knows what Carroll reported, one knows most of the well-known data ever collected on human intelligence differences.
4. A hierarchical representation of the associations among mental ability test scores. This diagram was the result of decades of work by John B. Carroll who re-analysed over 400 large, classic databases on human intelligence research.
Carroll’s results were reported in his 800+-page book, brim-full of statistical analyses and technical jargon. The essence of his findings appears on his page 626, a diagram he called his ‘three stratum model’ of human cognitive ability. A simpler version of it is reproduced as Figure 4 here. It has a structure very similar to the one in Figure 1. At the top of his hierarchy is his ‘stratum III’, or ‘general intelligence’ as he termed it. At ‘stratum II’ there are 8 broad types of mental ability, 4 of which are similar to those group factors/specific abilities we found earlier, in the WAIS-III. Carroll found more because he looked at data sets that included more, and more different, types of ability than those in the WAIS-III collection. At ‘stratum I’ – shown here as lists of grey lines – there were very specific mental skills, much like the ones specific to individual ability tests such as those we saw in the WAIS-III. Again, as we found with the WAIS-III data, Carroll’s strata of mental abilities emerged as an optimal result from a standardized statistical procedure, not from his imposing a structure on the data. He discovered rather than invented the hierarchy of intelligence differences.
What research is currently going on in this area?
Among psychologists working in this field there is no longer any substantial debate about the structure of human mental ability differences. Something like John Carroll’s three-stratum model almost always appears from a collection of mental tests. A general factor emerges that accounts for about half of the individual differences among the scores for a group of people, and there are group factors that are narrower abilities, and then very specific factors below that. Therefore, we can nowadays describe the structure of mental test performances quite reliably, but this is not proven to represent a model of the organization and compartments of the human brain.
The principal dissidents from this well-supported view are on the semi-popular fringes of scientific psychology. Howard Gardner’s popular writings on ‘multiple intelligences’ have suggested that there are many forms of mental ability and that they are unrelated. The facts are that some of Gardner’s supposedly separate intelligences are well known to be correlated positively and linked thereby to general mental ability, such as his verbal, mathematical, and musical intelligences. Some of his so-called intelligences, though valued human attributes, are not normally considered to be mental abilities, i.e. not within man’s ‘cognitive’ sphere. For example, physical intelligence is a set of motor skills and interpersonal intelligence involves personality traits.
What no one doubts is that tests of mental abilities do not assess all important aspects of brain function, let alone all important human qualities. They do not measure creativity or wisdom. Neither of these is easy to measure, though both have some demonstrable associations with intelligence. Mental ability tests do not measure personality, social adroitness, leadership, charisma, cool-headedness, altruism, or many other things that we value. But that proper point is not the same as saying that they are useless.
To follow this area up…
The information for this chapter was taken mostly from the two following research-level sources, which mostly address intelligence from the viewpoint of mental ability tests:
Carroll, J. B. (1993). Human Cognitive Abilities: A Survey of Factor Analytic Studies. Cambridge, UK: Cambridge University Press.
Wechsler, D. (1997). Manual for the Wechsler Adult Intelligence Scale-III. New York: Psychological Corporation.
For something more engaging that deals with a wider range of human mental capabilities, I recommend the well written (if contentious):
Gardner, H. (1983, reissue
d 1993). Frames of Mind: The Theory of Multiple Intelligences. New York: Basic Books.
If you enjoy this and want an update on how Gardner has elaborated his ideas since the 1980s, then have a look at his follow-up.
Gardner, H. (1999). Intelligence Reframed: Multiple Intelligences for the 21st Century. New York: Basic Books.
Two documents recording agreement among researchers in the field about the core aspects of human intelligence (and see the last chapter for further agreement in a third important document) are also worth looking at. The first was, rather astonishingly, a full-page declaration in the Wall Street Journal on 13 December 1994. It was a list of 25 statements summarizing what is known about human intelligence, signed by 52 well-known researchers (including John Carroll). Its first statement was:
Intelligence is a very general mental capability that, among other things, involves the ability to reason, plan, solve problems, think abstractly, comprehend complex ideas, learn quickly and learn from experience. It is not merely book learning, a narrow academic skill, or test-taking smarts. Rather, it reflects a broader and deeper capability for comprehending our surroundings – ‘catching on’, ‘making sense’ of things, or ‘figuring out’ what to do.