158 THE FACTORS OF THE MIND

of error (though not perhaps a larger proportion of error) than the
simpler.1

In the later portions of his book, however, Thurstone inclines
toward a very different view. " The specific variance of a test/3 he
says, " should be regarded as a challenge " ; and again, although
" the complete elimination of the specificity of each test will not be
essential in the early stages of the scientific study of human abili-
ties," nevertheless he regards it as u an object of psychological
inquiry to isolate an increasing number of abilities until the specific
covariance of each important test shall be reduced to a minimum." 2
These statements come much closer to the standpoint of Spearman's
critics. Those of them, for example, who prefer a £ sampling
theory' of abilities are naturally forced to argue that a specific
factor in itself can represent no real or concrete ability, whether
or not they admit the idea of a £ general ability.' Both Bartlett

1 This has determined my choice of the estimated values for the leading
diagonal of the correlation matrix, i.e. the c total variance of a test/ as
Thurstone terms it : (cf. pp. 285 and 460). With a group-factor method I
should for certain purposes be willing to insert the reliability. With general-
factor methods (except for special purposes) 1 should prefer not to equalize
the variances (with Thurstone, Hotelling, Spearman, and Stephenson) nor
yet to set them equal to the reliability coefficients (with Kelley), but to
take them as approximately equal to what I have called the * complete
communality.?

Thomson has pointed out ([132], p. 131) that both Thurstone and
Spearman are in effect maximizing the specific factors, and he regards this
corollary as an objection to the principle that the number of common factors
should be minimized. I, however, regard it rather as an objection to the
prior assumption which he, in common with Spearman and Thurstone, ap-
pears to take for granted, namely, that the variance of all the tests or traits
must be treated as the same throughout. If, however, the algebraic equa-
tions, derived by treating the reduced correlation matrix as a matrix of covar-
iances, are still to hold good without the assistance of a set of specific factors,
then measurements that were initially in standard measure would need to
be restandardized \ and that in turn would alter the covariances. Once
again, therefore, we should have to enter on a further series of successive
approximations. Fortunately, these additional adjustments are rarely re-
quired. In actual practice, 1 imagine, covariance will not in general be em-
ployed unless there is independent evidence as to the objective differences
in variance.

2 Loc. cit^ p. 63. Guilford similarly, after describing the views of Tlxurs-
stone, Kelley, and Hull, adds: ** According to this conception there are no
specific factors : the elements measured by every test would consist of group-
factors plus observational errors" (loc. cit,} p. 468 : his italics), I imagine
the writers named would consider this statement a little too sweeping, but it
clearly brings out the logical tendency of their own wort.