GENERAL- AND GROUP-FACTOR METHODS 311

I have taken can be readily expressed in algebraic form and
so generalized.

Illustrative Application.—Perhaps the best way to make
the argument clear and plausible to the general reader will
be to apply it to a concrete case. Let us take the example
used by Thurstone in Vectors of the Mind [84] to illustrate
the need for rotation and the methods to be used.1 He
chooses a correlation table obtained by Brigham for
fifteen cognitive tests of a familiar type. Analysed by the
centroid method the table yields three significant factors—
one general factor and two bipolar (Table 2, p. 167). Thur-
stone then argues that " it is an error frequently made to
attempt a psychological interpretation of the factors in
[such a] table : . . . the orthogonal reference axes obtained
by the centroid method must be rotated into a new set
of reference axes before any psychological interpretation can
be made."

Accordingly, after describing what in his view is needed
for a c simple structure' such as could be interpreted in
psychological terms, he shows how its requirements can be
secured by a ' graphical method of rotation.3 The figures
thus obtained form a new factorial matrix (Table 4, p. 169).
This also shows three factors. But now for each factor
only one-third of the saturation coefficients (or thereabouts)
are positive and significant. These are all above -22 ; the
remainder, including the negative coefficients, are (with
few exceptions) all below -12. With the factors in this
final form we are at last in a position to " consider tenta-
tively the psychological nature " of the c primary abilities ?
underlying the 15 tests : the three factors, it is concluded,
represent respectively verbal ability, numerical ability,
and a visuo-kinsesthetic ability, which is perhaps not primary
but complex.

If, however, my views are right, this tripartite classifi-
cation could have been inferred quite as well—indeed, even
better—from the original factorial matrix obtained by

1 Pp. 108-19. Five factors were actually extracted : but the factor-
loadings for the fourth factor " are not large enough to justify serious con-
sideration " (p. 167) and " the contribution of the fifth factor can be ignored "
(P-