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.

- Introduction
- Spearman's Plurality of Sub-factors
- Factor Analysis of Golf Results
- The Concept of Test Equivalence
- The Concept of Item Equivalence
- Practical Implications
- References
- About this document ...

AHGS van der Ven