392 THE FACTORS OF THE MIND

dissimilarities may be expressed in terms of one or more
factors instead of a dozen or more traits. Our second step,
therefore, will be to carry out a factor-analysis of the
correlation table, so as to determine the saturation coeffi-
cients for the several persons, and the size of the subsequent
residuals.

The method, we have decided, is to be that of simple summation.
In applying it, we at once encounter two slight difficulties. First,
what figures are we to insert in the leading diagonal in the place of
the self-correlations or so-called ' reliability coefficients ' ? Differ-
ent investigators, as we have seen, follow different plans, at any rate
for calculating the mere saturation coefficients. Stephenson, for
his modified Q-technique, before correlating persons, assumes that
" the variates are first standardized ... so that for each person
the following holds : 2x*a = ... = Zx2n = I," i.e. he adopts what
I called 'unitary standard measure' ([96], p. 197, eq. [2]). This
would permit us to regard the ensuing correlation table, if we like,
as a table of variances and covariances with the variances jor persons
always put equal to unity. If only for its extreme simplicity, let us
provisionally adopt this proposal here. Were we dealing with
small tables, like those obtained by correlating traits, such
differences in procedure might certainly introduce perceptible
differences into the results : but, when we correlate persons, we
shall generally be dealing with tables so large that any change
confined to the leading diagonal would be almost entirely swamped
in summation with the rest of the column : so that the problem is
of minor importance.1

The second difficulty is caused by the numerous negative
coefficients. In correlating traits these seldom appear in the table
of observed correlations. Hence those who have simply carried
over Spearman's methods and formulae from correlating traits to
correlating persons have found themselves in some perplexity.
Once again, the usual course has been to omit them. Thus, in
keeping with * method a9 (i.e. the ' group-factor method '),2
they usually work first with one positive sub-matrix and obtain a
first factor, and then with the other positive sub-matrix to obtain a
second, which (as they rightly point out) is roughly " the obverse of
the first," sometimes entirely ignoring the negative correlations,

1 On the problem here raised, see pp. 332, 395, and 474.

2 [93l P- 3°6- As implied above, it is strictly applicable only when the
figures in the neglected sub-matrix of residuals are virtually zero, i.e. insignifi-
cant as compared with, the size of the probable error.