362 THE FACTORS OF THE MIND

Thus the rotation reduces the condensation ratio to p2 = -10 or less.
This means that, instead of concentrating or condensing nearly all
the variance into one dominant factor, the demand for * simple
structure' has spread the variances more equally among the three
' group-factors.'

When the number of tests and factors is large, the simplest
procedure will be to base the standard deviation on the significant
factors only. In Primary Mental Abilities Thurstone extracts 12
factors for his 57 tests. If we assumed that there were (57 — 12) =
45 more factors, all with a variance of zero, we should be misrepre-
senting his procedure, since the centroid method claims to be
based in theory on a matrix of minimum rank and in practice on the
smallest number of significant factors. For the 12 factors actually
extracted we find that the standard deviations of the variances are
4-93 before rotation and 0-74 after rotation. Once again, therefore,
the rotation produces a most remarkable flattening. Such effects,
as we saw at the outset, were to be anticipated on general grounds ;
and in this instance the result was obvious at a glance once a
parallel table of factor-variances had been compiled. But by using
a quantitative criterion, we are now able to compare the amount
of such changes in different cases.

One or two of the * rotated factors/ it will be seen, stand out as
more important than the rest, notably those which Thurstone terms
V (4 Verbal relations '), R (c Reasoning '—a miscellaneous group that
Thurstone finds it difficult to classify), and S (£ Visuo-spatial,'
apparently corresponding to the e perceptual g' of Spearman and
Stephenson). Now the cognitive processes thus specified are
precisely those which are held to characterize the most efficient
tests of general intelligence. Once again, therefore, it is evident
that the results are not so inconsistent with the theory of general
intelligence as Thurstone suggests. Spearman himself would
emphasize the common characteristics shared by all these tests—
namely, the eduction of relations and correlates : Thurstone, on the
other hand, stresses the specific or material characteristics peculiar
to each one. That these latter are relatively inessential to the
definition of the factor seems obvious when we discover that among
the tests which have high saturations for the c visuo-spatial' factor
are ' Syllogisms,' * Verbal Classification,' and c Sound Grouping'
(classification of words according to similarities of sound)—tests
which are neither visual nor spatial but must depend largely on the
eduction of logical relations.

Such figures do not necessarily invalidate the results given in the
factorial matrix obtained by rotation. On the contrary, as we have