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Charles Spearman investigated correlations among cognitive performances and developed an account of a shared general intelligence factor with task-specific contributions. This helped make intelligence a subject of explicit measurement and statistical modeling. A fitted common factor describes covariation under a model; it is not automatically a uniquely identified biological mechanism. His name is also attached to Spearman's rank correlation coefficient. ^[ref]

The general intelligence factor, conventionally $g$, is a latent variable used to account for shared variation among performances on different cognitive tasks. Charles Spearman's 1904 analysis distinguished a common component from task-specific contributions, helping establish the historical basis of this approach.^[ref]

A simple one-factor measurement model writes a standardized test score aswhere ${\lambda }_j$ is a factor loading. Suppose all variables have zero mean, $\mathrm{Var}(g)=1$, each ${ϵ}_j$ has zero covariance with $g$, and distinct residuals have zero covariance with one another. Then for different tests,Thus a single shared component can explain correlated scores even when the tests contain different content. The covariance equation follows from the stated assumptions; it does not identify a unique biological cause of the correlations.

Factor analysis estimates such models and evaluates their fit. The general intelligence factor should also be distinguished from a first component obtained by principal component analysis: one is a proposed latent structure with residual assumptions, while the other is a variance-maximizing summary of observed scores. Interpretation requires the tasks, population and measurement assumptions, rather than a number alone.