The basics

What is IQ?

An IQ score is a rank against a comparison group, converted onto a scale with a mean of 100. That single sentence resolves most of the confusion around the subject — here is the long version.

The definition, and why it is unsatisfying

IQ stands for intelligence quotient. The formal definition is circular in a way that irritates people the first time they meet it: IQ is the score you get on an intelligence test, and an intelligence test is an instrument designed to produce IQ scores.

The circularity is not a flaw that careful thinking can remove. There is no independent unit of intelligence to calibrate against, the way a thermometer can be calibrated against the freezing point of water. What exists is a set of tasks that people differ on, a finding that performance across those tasks is correlated, and a scale built to express where a person sits relative to others.

That is less than the word “intelligence” promises and more than the dismissive version allows. The correlations are real and they are among the most replicated findings in psychology. What they are correlations of remains genuinely contested.

Where the scale comes from

The modern IQ scale is a deviation scale. A representative sample takes the test, the distribution of raw scores is examined, and the middle of that distribution is defined as 100 with a standard deviation of 15.

Both numbers are arbitrary conventions that stuck. The Cattell scale uses a standard deviation of 24, the Stanford–Binet historically used 16, and the SAT uses an entirely different scale for the same underlying idea. A score of 148 means the 98th percentile on Cattell and roughly the 99.9th on Wechsler — which is why quoting a figure without the scale carries very little information.

The original quotient was different and much simpler. William Stern proposed dividing mental age by chronological age in 1912: a ten-year-old performing like a twelve-year-old scored 120. It worked for children and broke for adults, because mental age plateaus in adolescence while chronological age does not. Every modern test abandoned the ratio in the 1930s. The name did not go with it.

What the curve implies

Because scores are fitted to a normal distribution, some facts follow from arithmetic rather than observation.

About 68 percent of people fall between 85 and 115. About 95 percent fall between 70 and 130. The bands are symmetric, and they get sparse fast as you move outwards: 130 is reached by roughly one person in fifty, 145 by about one in seven hundred and fifty.

This is also why point differences mean different things at different places on the scale. Fifteen points from 100 to 115 spans about a third of the population. The same fifteen points from 145 to 160 spans a few people in ten thousand.

What IQ tests actually sample

Modern tests are built from subtests, each sampling a different kind of task, and the score you see is an aggregate. The Cattell–Horn–Carroll model, which most contemporary instruments map onto, organises these into broad abilities beneath a general factor.

The ones that appear most often:

• Fluid reasoning — solving novel problems with no learned method. Matrix items are the canonical example.
• Crystallised ability — accumulated knowledge and vocabulary. Heavily shaped by education and reading.
• Working memory — holding and manipulating information over seconds. Digit span backwards is the classic task.
• Processing speed — how quickly simple tasks are completed accurately.
• Visual–spatial ability — mental rotation, construction, spatial relations.

The general factor, g, is what emerges when you extract the shared variance across all of them. It is the most replicated structural finding in the field, and whether it corresponds to a single underlying capacity or is a statistical summary of several partly-shared processes is an argument among people who agree entirely about the data.

Four things IQ tests do not measure

Knowledge in a domain. A test can sample vocabulary breadth, but it is not an exam. Expertise in anything specific is invisible to it.

Practical judgement. The ability to read a situation, weigh incommensurable considerations and act well under uncertainty is not what any subtest asks about.

Motivation and persistence. Conscientiousness predicts academic and job outcomes about as well as ability in many settings, and an IQ test is blind to it.

Creativity. Correlated with IQ up to a point and clearly not the same thing. Tests reward converging on the one correct answer, which is close to the opposite of what divergent thinking requires.

What the score predicts

Correlations with academic achievement typically sit around 0.5. With job performance, the classic figures ran from about 0.2 in simple roles to 0.5 in complex ones, though recent re-analyses of the range-restriction assumptions have pushed the estimates down and the size of that correction is actively disputed. With income, lower still — commonly 0.2 to 0.3, mostly mediated through education and occupation.

A correlation of 0.5 means that if you pick two people at random, the one with the higher score does better on the outcome about 67 percent of the time. Real, useful for describing populations, and nowhere near enough to predict a person.

The full treatment is in does IQ predict success.

How much it changes

Rank order is reasonably stable from late childhood onwards, which is the finding that gets summarised as “IQ is fixed”. The summary overstates it.

Longitudinal studies of adolescents have found individual shifts of more than ten points across a few years, accompanied by corresponding structural brain changes. Additional schooling raises measured IQ by something in the region of one to five points per year. Scores before about age six are unstable enough that clinicians caution against treating them as predictive at all.

Heritability estimates for adult IQ commonly land between 0.5 and 0.8, and that statistic is routinely misread. It describes how much of the variation in a particular population tracks genetic variation. It says nothing about whether an individual's score can change, and the same trait can have a different heritability in a different environment.

What to do with a score

Use it as one piece of information with a wide error band. On a good clinical test the 95 percent confidence interval is about plus or minus five points; on a free web test it is wider still.

That makes a result a statement about a region of the distribution, not a coordinate. If you scored 112 and a colleague scored 118, you did not perform differently in any sense the measurement supports.

And if the number arrived from a ten-minute web test, the right conclusion is smaller than whatever you were about to conclude. Here is why.