CHAPTER XII

GENERAL-FACTOR METHODS AND GROUP-FACTOR
METHODS

(a) Differences in Procedure.—The earliest attempts at
factor-analysis rarely ventured to establish more than a
single general factor : such a factor, operating alone, would
produce a correlation matrix of rank one—a c hierarchy ' as
it was termed—for which various ^criteria were proposed.
Almost inevitably, so long as individual tests were used and
only a dozen or so persons could be tested, the probable
errors remained too high for the residuals to be significant
when the general factor had been partialled out: hence no
clear evidence could be found for more factors than one.
But, as soon as the introduction of group-testing made it
possible to diminish the sampling errors, it became manifest
that the observed correlations could no longer be fitted to a
strict hierarchical pattern, unless the tests were deliberately
selected for this purpose, and that the discrepancies im-
plied other factors besides the single c general' and the n
6 specific.'

The first attempt at explicitly fitting a theoretical matrix to a
set of observed correlations was, I think, that shown in Tables V
and VI of my paper of 1909 ([16], pp. 161-2). The residual correla-
tions, examined for further factors, were obtained in the way that
has since become fairly general, namely, by simply subtracting a
reconstructed hierarchy from the original correlations. The tests
had been expressly chosen " to represent different types of mental
process " ; and, as a result, " a small discernible tendency for sub-
ordinate groups of allied tests to correlate together " was noted.
With increasing reduction of the probable error there seemed no
reason why the process of removing one factor to reveal another
should not be repeated. Thus, as I have pointed out above, it
became natural to view the empirical table, not as an unsatisfactory
approximation to a single hierarchy, but as the sum of a succession

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