DERIVATION OF CHIEF THEORIES 155

Moreover, if we accept the main principle on which the
two-factor theory is founded, namely, the absence of group-
factors, then (as I have elsewhere argued) the specific
factors by their very mode of calculation seem to be little
more than errors in the measurement of the general factor :
for, according to the two-factor formulae, the * saturation
coefficients? for the general factor are first calculated on the
implicit assumption that the variance of each test is the
square of its saturation ; next, a second assumption is
made, namely, that the variance of each test is equal to
unity, and the balance is ascribed to a ' specific factor.'1
But what evidence is there for any such balance, except
perhaps that we cannot assume our tests to be perfect
tests of intelligence alone ? Certainly, we are hardly
entitled to treat c specific factors 5 derived in this way as
synonymous with c specific abilities'2 After all, if a

1 Spearman's formula is faSa= (i — r*a^ ([56]), p. xvii, eq. 22). The
difference between myself and other writers in regard to the importance to
be attached to specific factors seems largely to arise from a difference in our
procedure when selecting, constructing, or averaging tests. In demon-
strating a hierarchy, the adherents of the two-factor theory are ready to take
a set of any dissimilar tests; but since each type occurs only once, the specific
factor that it contains is, quite rightly, assumed not to disturb the hierarchical
arrangement of the coefficients; in estimating the factor-measurement for
the general factor, they claim that " the specific elements will neutralize one
another." My own tests also involve differences of material. But in select-
ing the words, figures, facts, pictures, etc., I endeavour to secure that the
special knowledge required shall be common to all the children to be tested,
so that it cannot operate as a differentiating factor. Hence the variance is not
appreciably increased owing to the specific nature of the dissimilar materials,
as it presumably is when this precaution is not taken. (The difference, no
doubt, is only a matter of degree • but it is sufficiently evident in applying
two batteries of the tests to children of the ages intended.) Where, however,
two similar tests are used, and any irrelevant influence unavoidably arises,
then, instead of pooling the tests, so as to turn a group-factor into a specific
factor, I seek to eliminate it by partial correlation. Those who do not adopt
these experimental or statistical devices are naturally led to emphasize the
influence of the specifics.

2 ' To measure a person's specific ability,' Spearman gives the formula
sax = raSa max, where max is #3s measurement with test a (loc. cit.y p. xviii,
eq. 24). But that would mean that we give all the persons tested the same
order of merit for the specific ability as we do for the test itself. With a
battery of correlated tests therefore the specific factors would be correlated.