296 THE FACTORS OF THE MIND

of diminishing hierarchies, each representing a factor common to
certain of the tests ([35], Tables XVIII-XXIII; [102], p. 189).

Now, according to the way the correlated variables were originally
selected, these hierarchies, it was found, might either cover the
whole table (as when the tests or persons correlated formed a
random sample from a continuous distribution) or be confined to
different farts (as when the tests or persons correlated formed a
heterogeneous or a discontinuous set). Consequently, as we have
already seen, the ' two-factor theory,' which merely singled out
the one common factor contributing most to the total variance,
developed on the one hand into a c multiple-fact or theory,' which
envisaged several general factors, each common to all the tests or
persons correlated, and on the other hand into what was sometimes
called a e three-factor theory,' * which looked rather for limited
group-factors superposed u*pon a single general factor.

I shall call those methods which proceed by analysing the
correlation matrix taken always as a whole c general-factor
methods,' and those which partition the correlation matrix
into suitable sub-matrices, and then analyse these separately,
c group-factor methods.' (In previous publications they
have sometimes been described as ' method b ? and * method
a* respectively.) With the former, all the factors after
the first have negative as well as positive saturation co-
efficients : with the latter, the factorial matrix has a large
number of zero 2 saturations in each column, and for the rest
contains only2 positive saturations (cf. [93], p. 306).

Under the heading of general-factor methods may be placed those
used by Spearman, Hotelling, Kelley, Thurstone (before rotating),
and Stephenson (when analysing correlations between traits).
Under the heading of group-factor methods may be placed Holzinger's
most recent form of the bi-factor method, Thomson's alternative
analyses of artificial correlation-tables obtained from dice or cards,
Stephenson's usual procedure when analysing correlations between
persons, and my own early efforts when demonstrating group-
factors in educational abilities and in emotional traits.

1 Cf. p. 139, above.

2 At each point we ought to add * within the limits indicated by the
sampling error.' In actual practice a calculated saturation coefficient will
never be exactly zero; and many of the non-significant figures may prove
to be negative, where theory demands nothing but positive values. In what
follows, however, to avoid confusing the statement of the main tendencies, I
shall omit these obvious reservations,