302 THE FACTORS OF THE MIND

in Holzinger's ' hollow staircase ' patterns (e.g. [83], No. 6, Tables
9-13). Davies and I found similar patterns when correlating
heterogeneous groups of persons selected to represent well-marked
mental types. As in Thurstone's * simple structure pattern'
([84], p. 151), the final factor-pattern contains no negative saturations
and a maximum of zero saturations. But this older scheme departs
from Thurstone's requirements in two respects : first, the number
of factors (here 5) exceeds the rank (here only 4); secondly, one of
the factors—the first—has no zero saturations at all. We have
thus what I have called the * prop-ladder pattern ' as distinct from
the simple * step-ladder pattern ' of Thurstone.1

(i) For comparison let us analyse afresh the same corre-
lation table by the ' general-factor method5 (c method b ?).
We now retain the diagonal values from the start, with the
natural result (as we shall see) that the effect of each ' group-
factor ' is distributed over the first as well as over the later
factors, and over a much larger number of tests.

In the present instance we could take the pooled values and form
a f characteristic equation ' ([101], p. 78), thus reaching the required
results not approximately but exactly and directly ; alternatively,
if we apply either the summation method (which is here identical
with a Thurstone analysis) or the method of least squares with
successive approximation (which is here identical with a Hotelling
analysis), we still arrive in the end at precisely the same figures
(Table Ills, F£). There are now 4 factors instead of 5 ; the factor
with the highest variance has positive loadings for every test; the
remaining three are bipolar, i.e. they show negative as well as positive
saturations.

Now if our test-assessments were measures of temperamental
traits, we should feel no hesitation over assigning an immediate
psychological interpretation to the general factors thus obtained :
factor i might be identified with * general emotionality'; factor ii
with a bipolar tendency, making for c extra version' when positive
and ' introversion' when negative ; and so on (cf. [114], pp. 182-3).
If, however, the tests were measuring cognitive traits, then most
psychologists would apparently be unwilling to interpret the bipolar
factors as they stand. Factor i could perhaps be identified with
' general intelligence ': but what meaning, it has been asked, can

1 Alexander's analyses, though following Thurstone's model, usually have
a general factor prefixed, and so yield a ' prop-ladder' pattern. Thurstone's
group-factors usually show considerable overlapping, which does the work of
the general factor.