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The g-factor in Intelligence Tests:
Unidimensionality or Equivalence of Tests?

A.H.G.S. van der Ven and F.G. Gremmen


The first attempt to built a statistical theory for intelligence tests was based on a unidimensional model for the intercorrelations between intelligence tests (Spearman, 1904). The model is known as Spearman's Two-factor theory. Each test consists of a general factor g and a specific factor s. The model could be tested using the well-known tetrad difference. Today, one may compute goodness-of-fit statistics for a maximum-likelihood extraction of a single factor. Spearman proposed several possible explanations of g, referring to such concepts as general intelligence, the power of attention and mental energy. However, Spearman could never come away from the idea, that, at the latent level, many unidentifiable factors might still play a role in the realization of g. In that particular case, g does admit of resolution into a plurality of sub-factors. Spearman, mentioned ability and zeal as examples. "If in all tests the respective influences of these two always remained in any constant ratio, then both could quite well enter into g together." (Spearman, 1927, p. 93). Firstly, a formal definition is given of Spearman's 'plurality of sub-factors' hypothesis. Subsequently, is is shown by the way of various examples, that Spearman's idea of a multiple factor explanation of g, is not far-fetched at all, and in many cases is the normal state of affairs. Finally, it is argued, that it is much more preferable to use the concept of tau-equivalence (see Lord & Novick, 1968) rather than the concept of uni-dimensionality or g, in the case of a uni-factorial solution of the correlation matrix.

AHGS van der Ven