56 THE FACTORS OF THE MIND

tests directly with, performance in the scholarship examina-
tion, and relies on this direct correlation.

No doubt an application of factorial principles will aid in the
construction and selection of tests ; but it has often proved mis-
leading. For example, a strong belief in the £ single-factor theory '
(I myself should be inclined to say, a real misunderstanding of the
( single-factor theory') has led many of its supporters to aim at
homogeneity rather than heterogeneity in their batteries of intelli-
gence-tests. " It follows from Spearman's hierarchical principle,"
we are told, " that a reliable battery of tests for the general factor
should have the highest possible correlations with each other . . .
Thus the Binet scale stands condemned at a glance by the extremely
miscellaneous nature of the tests that compose it: never having
applied the factorial method, Binet evidently failed to make up his
mind as to what precisely his tests were to measure," The point
is put still more strongly by Cattell in his recent defence of * the
factorial methods of analysis of personality ' : " if, as most psycho-
logists concede, the [Binet] test is not concerned with one ability
but with a collection of abilities, the attachment of a single
quantitative value to this hodge-podge is meaningless." *

These criticisms once again exhibit the fallacy of trusting solely
to the c positive analogy ' to strengthen inductive inferences. The
right guiding principle I have endeavoured to state more than once
elsewhere. It is the logician's principle of increasing the * negative
analogy.' " Multiplying the number of different examiners is of
greatest value when their correlation with the * true mark ' is high
and their correlation with each other is low . . . The same holds
true of the subjects tested : the best results are obtained by com-
bining tests which correlate highly with the general ability to be
measured, but attack it from independent or divergent angles." 2

1 Character and Personality, VI, 1937, p. US : on p. 121 lie argues in
detail against * the error of the view' that factors are mere * middlemen
between tests and criterion.5 On the issue discussed in the following para-
graph I find myself in close sympathy with many of CattelFs conclusions,
but on the wider issue I agree still more closely with those of Vernon as
expressed in the same symposium.

2 Marks of Examiners, pp. 304, 310. Mental and Scholastic 'Tests, p, 207.
The guiding principle cited above is implicitly followed by boards of
examiners when they arrange that their several question papers, though
bearing one and all upon the central subject, shall nevertheless each deal with
a widely different aspect. This is commonly defended on the favourite
ground of economy—to avoid superfluous overlapping : its real defence rests
on the inductive principle described above (pp. 29 f.),