What Is the g Factor in Intelligence? A Pattern, Not a Substance

Almost every argument about intelligence testing traces back to one observation, and the observation is not about the brain. It is about a table of numbers. People who score well on one cognitive test tend, on average, to score better than average on others too — even when the two share no obvious content, format or skill. The general factor, written as a lower-case italic g, is the name given to that pattern once a statistical procedure has pulled it out. What the field can and cannot say about a single IQ number follows from taking that sentence literally.

The observation that started it

Charles Spearman published the paper that opened the subject in the American Journal of Psychology in 1904. Looking at schoolchildren's marks across subjects with little to do with one another, along with some simple sensory judgements, he noticed the rankings kept agreeing: children near the top in one were, on the whole, near the top in the others. He proposed that each performance reflects two things — an ability general to all of them, which he called g, plus something specific to that task, which he called s.

The interpretation has been argued over ever since. The observation has not moved. Take a large, varied sample, give them deliberately dissimilar tests — vocabulary, mental rotation, digits repeated backwards, symbols marked against the clock — and write the correlation between every pair into a grid. Nearly every entry comes out positive. Not large, usually, but positive and reliably so. That near-total absence of zero and negative entries is the positive manifold, about as replicated as findings in psychology get. What produces it is the open question. That it is there is not.

What a correlation is, and what a factor is

Both words carry the argument, so state them plainly. A correlation is a single number between -1 and +1 summarising how consistently two measurements order the same people in the same way. Zero means knowing one tells you nothing about the other; plus one means the orderings are identical. Cognitive tests sit in the positive middle: a vocabulary score tells you something useful about a likely matrix-puzzle score, and nothing like everything. Square it to read the size — a correlation of 0.5 means the two measures share about a quarter of their variation, and three quarters is not shared.

A factor is a different kind of object, and this is where popular writing goes wrong. A factor is not measured. It is computed. Factor analysis takes the grid of correlations and asks a purely mathematical question: what is the smallest number of underlying dimensions that would produce this pattern? When the answer for a set of cognitive tests is "one dimension gets you most of the way", that dimension is g.

An analogy clarifies the logic. Measure a few hundred parcels for length, width, weight, volume and shipping cost, and every pair will correlate positively. Run a factor analysis and it returns a single dominant dimension you would sensibly name "size". Size is not a substance inside the parcel; nobody needs to find the size organ. It is a compact, genuinely useful description of what the five measurements share. g sits in the same logical position with respect to cognitive tests: defensible, and far more modest than the way the term usually gets used.

• The factor is defined by the tests you put in — although when the same people sit two quite different batteries, the general factors extracted from each tend to correspond closely rather than pick out different things. How closely depends on which batteries are compared, so a precise correlation quoted without its study is not worth much. Spearman called this the indifference of the indicator.
• It describes variation across people. A structure found across a sample does not automatically describe how one person's abilities vary over time.
• It has no units. There is no natural zero and no natural scale for g; every reported figure is a position within a reference sample.
• Extracting it does not identify its cause. It tells you the tests share something, and is silent on what.
• A test's "g loading" is how strongly that test correlates with the extracted factor — a property of the test within that battery and sample, not a permanent badge.

Why one number is defensible at all

Without the positive manifold there would be no case for a total score. If vocabulary and mental rotation were unrelated, adding their scores together would be like adding somebody's height to their shoe size: arithmetically possible, and meaningless. The manifold is the licence. Because the subtests have something in common, a composite built from several of them carries real information about that common part — and more reliably than any single subtest, because each test's idiosyncrasies partly cancel out.

How much of the total the common part accounts for is a range, not a figure. The quantity being divided up is the variance — the spread of scores a battery produces, added up across its subtests. Textbook summaries of a typical diverse battery put the general factor at something in the region of 40 to 50 per cent of it, and the share moves with what you put in the battery and who you gave it to. A battery loaded with reasoning tests yields a bigger general factor than one loaded with narrow speeded tasks. A precise percentage quoted without naming the battery is an average of averages.

Read the complement of that figure, because that is the part that gets dropped. If the general factor takes something under half, more than half of what a battery measures is not g: broad abilities distinct from one another, skills specific to individual tasks, and plain measurement error. A single summary number is defensible and seriously incomplete at once. Our note on why working memory and reasoning are not the same thing is the counterweight: it works a layer down, on two abilities that stay distinct however strong the general factor is.

The hierarchy is the mainstream model

The one-factor picture did not survive intact, and what replaced it is not a rejection of g but a stack. Louis Thurstone, in Primary Mental Abilities in 1938, argued that the data were better described by several primary mental abilities than by one general one, and could produce a rotation in which g disappeared entirely. The awkward detail, which he acknowledged, was that his primary abilities correlated positively with one another. Analyse that second grid and a general factor reappears a level up. The dispute between "one ability" and "many abilities" turned out to have a shape rather than a winner.

John Carroll gave that shape its definitive form in Human Cognitive Abilities in 1993, a reanalysis of several hundred datasets. His three-stratum model puts dozens of narrow abilities at the bottom, a few broad abilities in the middle, and g alone at the top. Merged with Raymond Cattell and John Horn's distinction between fluid ability — reasoning about novel problems — and crystallised ability — accumulated knowledge — it became the Cattell-Horn-Carroll framework, which most contemporary batteries are built and interpreted against. When a report gives you index scores — a separate figure for each broad ability — as well as a full-scale total, this is the theory it is implementing.

• Fluid reasoning — solving unfamiliar problems where no learned method applies, such as matrix items and series completion.
• Comprehension-knowledge, the crystallised side — vocabulary, general information, reasoning built on what you already know.
• Short-term and working memory — keeping information live while you work on it.
• Processing speed — how quickly simple, well-understood decisions can be made under time pressure.
• Visual and spatial processing — mentally manipulating shapes, positions and patterns.
• Long-term storage and retrieval — how efficiently material is laid down and got back out.
• Reading and writing — literacy treated as a broad ability in its own right.
• Quantitative knowledge — stored mathematical knowledge and the ability to use it.

What g licenses, and what it does not

The practical distinction is between statements about groups and statements about a person; almost every misuse crosses that line without noticing.

• It licenses summarising. A composite drawn from a broad battery is a reasonable index of the common part, and more stable than any of its components.
• It licenses group-level prediction with stated limits. Average outcomes in education and training differ across score bands, with overlap wide enough to make any individual prediction weak.
• It does not license treating an individual score as a fixed property. A score is one estimate, on one day, on one instrument.
• It does not license reading the composite as the whole picture. When the index scores behind a total diverge sharply, the total averages away the thing worth knowing.
• It does not license any causal claim. The factor describes shared variance; it does not say what produces the sharing.

Ignore measurement error and a factor quietly turns into a label. A factor extracted from noisy measurements inherits that noise: g is computed from subtest scores that each drift between sittings, so the standing a Wechsler-type composite assigns has a width, not a point. That width is not small next to the differences people argue about — our piece on what an IQ of 120 means works through what it does to a printed number. No theory about g turns a gap that sits inside it into a real one.

Percentiles make the point in another currency. A percentile says what share of a reference sample scored at or below you, and a standard deviation is the yardstick the scale is built from — 15 points here, wide enough that about two thirds of that sample sits within 15 points of 100. So on a mean-100, standard-deviation-15 scale, 100 is the 50th percentile, and 115 — exactly one standard deviation up — is the 84.13th, not "the top 15 per cent" rounded for convenience. Our IQ percentile calculator does that conversion on a named scale, and the bell curve page shows why the same number of points buys very different amounts of rank depending on where you start.

The reference sample is itself dated. Norming means fixing a scale against the measured performance of a defined group at a defined time, which is what makes 100 the average at all. Those samples age and the performance they represent drifts, so the same raw performance can be worth a different score twenty years later — the subject of our piece on why IQ norms expire. A stable statistical structure says nothing about the stability of the number an old test hands you.

None of this is a reason to distrust a well-built assessment. It is a reason to read one correctly. When you sit an IQ test, the general factor is what makes it sensible to combine dissimilar sections into a single figure at all, and the broad abilities are what make the section-by-section breakdown worth reading afterwards. A page like how IQ tests work exists because the two keep getting collapsed into one.

The habit worth taking away is a question rather than an answer. "Intelligence is really just one thing" and "there is no such thing as general intelligence" are both overstatements of the same grid of positive correlations, made by people who disagree about the interpretation and not about the data. g is a well-supported description of shared variance across cognitive tests. It is not an organ, not a quantity anyone has isolated, and not a property any single score fixes. When someone invokes it, ask which battery, in which sample, accounting for how much of the variance — and what was left over.

Common questions