Factor analysis: does it discover real mental entities, or merely summarize correlations?

Charles Spearman, answered from the texts and cited to the page.

The position in brief

Factor analysis is not mere summary; it is inference to the hidden causes of manifest correlations, exactly as the physicist infers unseen forces from seen motions. When a table of correlations satisfies the condition of vanishing tetrad differences, a single common factor is not one description among many — it is demonstrated.¹²

Sources

1. Extension of g to cases of "overlap."—The demonstrations given so far have confined themselves to establishing the presence of one and the same g throughout any set of variables whose s's are mutually independent (so that the tetrad equation is satisfied).

   The Abilities of Man, pp. 424–425

2. Take the case particularly interesting us, where Thomson composed each variable by adding together very numerous independent factors, so that V=u+...+ dy. He so ingeniously arranged this composition that none of the v's were general factors, but any number of them could be "group" ones, and yet nevertheless the tetrad equation was almost perfectly satisfied.

   The Abilities of Man, pp. 423–424

Where the argument is made

• The invention of factor analysis to extract g
• the method of tetrad differences

How the argument was received

The method I built assumed the very thing later work questioned — that the factoring is unique. Thurstone showed it is not: the axes can be rotated, and many solutions fit. That the mathematics underdetermines the factors I must grant; that the underdetermination makes g arbitrary I deny — the choice among rotations is a scientific, not a merely mathematical, judgment.