GENERAL- AND GROUP-FACTOR METHODS 317

opposites). This systematic arrangement makes the relation
between the two forms of classification obvious at a glance.

TABLE IV
TRANSFORMATION MATRIX

After Rotation.

.

A. Verbal.
B. Numerical.
C. Performance.
Total.

I. General
•44
•30
•24
•98

II. Verbal . 1 Non-verbal. j
•89
-•15
-•42
•32

III. Numerical \ Non-numerical J
-•09
•94
— •88
--03

So far, I have confined myself to group-factors that show
no appreciable overlap. In practical work, however,
wherever the probable errors are low, and a close fit to the
original correlations is required, it is generally necessary
to allow (i) overlapping, and even (ii) occasional negative
saturations in the overlapping coefficients.

(i) The use of the group-factor method need not prevent
us from assuming that group-factors may overlap with each
other. The overlapping factors will be dealt with along
the same lines as the general factor, namely, by beginning
with correlations (or residuals) uninfluenced by other factors.
There are, however, limits to the amount of overlap that
can be dealt with in this way with a given number of tests.

How much actual overlapping exists among the tests will,
of course, depend primarily upon the way the tests have
been selected. But even with sharply discontinuous groups
it is hardly fair to demand that, when a factor is not an
important element in a test, its saturation shall be pre-
cisely zero—that is, zero within the margin allowed by the
probable error, however small that probable error may be.
Is it plausible, for example, to postulate that Thurstone's
verbal factor must have zero saturations for all except the
conspicuously verbal tests ? Would it not be exceedingly
difficult to devise a test which would exclude the smallest