GENERAL- AND GROUP-FACTOR METHODS 297

When the tests or persons to be correlated are drawn from
mutually exclusive classes, the group-factor describing one of the
classes should show no overlap with the others. Several of
Holzinger's earlier factor-patterns for tests and of Stephenson's
factor-patterns for persons are of this type. But, with empirical
data, if the calculations are carried far enough, the group-factors
will, in point of fact, nearly always display some overlap. In most
cases the first factor tends to spread over the whole sample of tests,
so that (although for one or two tests its saturations may be strictly
non-significant), nevertheless it is more convenient to describe it as a
general factor. With educational tests, and usually with cognitive
tests and with emotional assessments, I found group-factors over-
lapping like steps on a winding staircase, producing what I called
* cyclic overlap ' ([30], [35]) : granting that the c central nervous
system is integrated by a series of broadly distinguishable layers or
levels, the higher levels serving to co-ordinate the lower,' such an
overlap must be an almost inevitable result when a comprehensive
sample of tests or traits has been selected. Thurstone's c simple
structure ' assumes a free but irregular overlap of many group-
factors, but no general factor whatever ([84], p. 151, [122], p. vii) ;
actually, however, his tables are excellent examples of ' cyclic
overlap ' (if we rearrange his tests in the order : 5, 7, 3, 4, 9, 2, 6,
8, I, his Table I, loc. at, p. 151, is a perfect instance). Thomson,
who from the outset has emphasized the explanatory power of
overlapping group-factors [34], has recently proved that the bound-
ary conditions, indicating whether, in any particular case, general
factors are equally indispensable or not, may be precisely defined
[100].

The advocates of each of the two main methods have sharply
criticized each other. Spearman, in a famous phrase, originally
opposed the * unifocal' or c monarchic ' doctrine of a single general
factor to the * multifocal' or ' oligarchic' doctrine that admits
nothing but group-factors identified with mental faculties or mental
types. As we have already seen, he does not deny all possibility
of group-factors, but insists that, in contrast with the 4 or 5 general
factors that have been isolated, such limited factors are both
exceedingly narrow and exceedingly rare : in keeping with the two-
factor theorem he prefers to call them c overlapping specific factors.*
Thurstone admits no ' general factors ' whatever, even when found
by his own procedure (except possibly as a residual) : the factorial
matrix must always be rotated before we can reach the primary
abilities or traits. Hokinger, on the other hand, rejoins that " the
methods employed by Hotelling and Thurstone give rise to com-