Charles Spearman, answered from the texts and cited to the page.
The question of how to measure general intelligence is, at bottom, the question of whether the correlations among mental tests compel a common factor — and, if they do, how to demonstrate it rigorously rather than merely assert it. The starting point is the tetrad equation. Given any table of correlations among cognitive performances, one may extract groups of four and compute the tetrad difference: the product of one pair of cross-correlations minus the product of the other.
When these differences hover near zero — within the bounds of sampling error — the analysis into a general factor g and task-specific factors s is demonstrated, not merely assumed.1 The letter g becomes, in this manner, a name for the factor, whatever it may be, that is common to mental tests of such a description; that is the very definition of g, and all further questions about its psychological nature lie beyond that definition to be separately established.2
The method was applied to tests of the highest cognitive repute: Reasoning, Generalizing, Abstract Thought, Memory, and Accuracy. The correlations among these five yielded tetrad differences hovering close to the probable error, and the answer proved to be in the affirmative — the scores made in each of these tests involve one and the same g.3
Crucially, the essentially evidential tests — Reasoning and Generalizing — involve just the same g as the others, which establishes g on a basis of best repute rather than on the easier ground of simpler tasks.4 Where the direct method of proof is unavailable — where a test has not been correlated with three others sufficient to form a tetrad — the indirect method serves.
Burt's Reasoning, for instance, was shown to correlate highly with teachers' estimates of intelligence, and those estimates had already been found to contain g; since Reasoning and the estimates appear to have no mutual overlap, the Reasoning also must involve g.5 The convergence across investigators strengthens the case considerably. Magson's investigation with 149 subjects, covering Analogies, Completion, Understanding Paragraphs, Opposites, Instructions, Resemblances, and Inferences, yielded tetrad differences with a probable error of.03 and an observed median of.04 — agreement that leaves nothing to be desired.6
Such corroboration is available, as I noted, to almost limitless amount. The range of tests to which this method was applied was determined by a systematic survey of all possible cognitive operations, organized through the noegenetic laws: the apprehension of one's own experience, the eduction of relations, and the eduction of correlates.7 That survey was the only effective means of establishing how far the domain of g truly extends — whether it is a parochial feature of a few test types or genuinely universal across cognition.
Wherever the abilities involved are sufficiently distinct — and that is in the great majority of cases — our tetrad equation (ch. vi. p. 73) is satisfied with surprising exactitude, so that here each ability must be divisible into g and s.The Abilities of Man
The letter g becomes, in this manner, a name for the factor — whatever it may be — that is common to mental tests of such a description. This is the very definition of g.The Abilities of Man
the general result of all these five tests was the table of correlations given below... the scores made in each of these tests do involve one and the same g.The Abilities of Man
In particular, the essentially evidential tests i and 2 involve just the same g as the other three which are not essentially evidential... G is, then, forthwith established upon a basis of best repute.The Abilities of Man
Burt's Reasoning was shown by him to correlate highly with teachers' estimates of intelligence, and these latter have already been found by us to contain g. Hence — seeing that the Reasoning and the estimates appear to have no mutual overlap — the Reasoning also must involve g.The Abilities of Man
Here, the tetrad differences gave a probable error of.03 and an observed median of.04, so that again the agreement leaves nothing to be desired.The Abilities of Man
This involves nothing less than a general survey of the entire range of possible operations of knowing. To execute this gigantic task, there appears to be only one effective means. It consists in an appeal to the complete system of ultimate laws that govern all cognition.The Abilities of Man