ANALYSIS OF ILLUSTRATIVE GROUP 393

although the line of division is said to depend upon them x : in
practice, however, the line of division between the four quadrants is
rarely clear. But if we imagine the signs of the initial measure-
ments of the last six persons (G to L) to be reversed, thus reversing
the signs of their correlations with the remaining persons, we can
apply the summation formula to the whole matrix at a single step.
To restore the signs we must afterwards prefix a negative to the
saturation coefficients of G to L. The whole series will thus be
accounted for in terms of a single bipolar factor. (See below,
pp. 458, 485.)

With these two points provisionally settled, it only
remains to add up the figures in each column of correlations,
and divide each total by the square root of the grand total
for the whole table. The totals, the grand total, and the
resulting saturation coefficients are shown at the foot of
Table II. On squaring the saturation coefficients we find
that the factor so indicated accounts for about 35 per cent,
of the entire variance. The next factor would account
for barely 17 per cent., and the third for only 9 per cent.
But with a group so small it is hardly profitable to consider
these further factors.

B. RESULTING FACTORS AND TYPES

The factor-saturations for each person, thus deduced
from the correlations of his measurements with those of all
the rest, may be taken as measuring the degree to which
that person approximates towards the type for which the
factor is responsible. As I have argued in previous articles,2
these saturation coefficients are simply coefficients of correla-
tions indirectly calculated : when obtained by an adequate

1 E.g. [92], p, 22 ; cl ibid., p. 302, Table I (in this table R and S have only
one or two negative correlations instead of twelve; and hence I should have
put them into the matrix for Type I, not Type II. Actually, hardly any of
the negative correlations are significant: so that a single general factor, with
positive saturations throughout, would fit the figures almost as well).

2 E.g. [101], p. 89. My proof related only to saturation coefficients ob-
tained by the method of least squares. But, as a matter of fact, this view of
the saturation coefficient seems also to be accepted by nearly all who have
preferred the simple-summation formula for correlations between persons;
it was adopted, for example, by Beebe Center and later by Stephenson.