DERIVATION OF CHIEF THEORIES 157

saturation coefficients for the specific factors are also included, then
the symmetry is appreciably reduced.1 And generally the results
of all subsequent calculations, based on the correlation matrix, con-
form much better with general expectation, if communalities alone
are included and specific factors excluded. Thurstone, for example,
having first expressed the * factorial matrix ' as the sum of three
* components,' F^ + Dl + Z)2 ([84], p. 54), in most of his later
deductions ignores the matrices D± and Z>2, which contain the ' n
specific factors ' and the * n error factors,' and, as I have done, bases
his arguments on the c reduced correlation matrix ' R = F^F^
([84], pp. 66*tseq.).

Thus Thurstone, whose theory is essentially a generalization of
Spearman's, begins by including specific factors in Spearman's
sense of the phrase : for, like Spearman, Stephenson, and most
other members of the English school, he assumes that all tests or
traits have precisely the same variance (p. 62). But in practice he
confines himself to the extraction of general or common factors
only, and would in principle make the number of those factors a
minimum (p. 73). Hence, for Thurstone as for Spearman, the
specific factor of a test must again be simply the balance left over
from the arbitrarily assumed variance when the portion due to
general or common factors has been deducted. In fact, the amount
of variance due to the specific factor in a given test j (our sf) is
explicitly set equal to I — hj2 — Cj2, where cf is defined as the
6 error variance,' and hf as the ' common factor variance '—usually
termed * communality ' for short (our g2 + 2/p/; p. 68). Thus the
specific variance of a test is not an independently determined
quantity at all. It may be added that, on the theory held by
Spearman and Thurstone, the simplest type of mental process (one
therefore which would have the smallest number of common
factors and would usually be the one measurable with the least
amount of error) has the same total variance as the most complex
type of mental process ; it must therefore contain a specific factor
having the greatest amount of individual variability in the popu-
lation tested. Now this is not only contrary to what we should
expect a priori from the additive nature of variance, but also in
conflict with direct observation : for, wherever we can measure a
trait in absolute terms, we find that the more complex mental
processes nearly always show a far wider range of individual
variation than the simpler, and usually involve a larger amount

1 This is shown in computations made by Woods and later by Davies and
Eysenck, who tried the symmetry criterion with both forms of the correlation
matrix.