316 THE FACTORS OF THE MIND

in common, simply because they have been arbitrarily allotted a
positive sign. It would have been equally logical to have reversed
the assignment: with positive signs for the three Opposites tests
and negative signs for the three miscellaneous tests, the principle of
eliminating negatives would then have prevented us from postulat-
ing any factor for the miscellaneous tests and from attempting to
identify the factor common to these three with the factor common
to the numerical tests. Instead we should have postulated a fourth
factor specifically for the Opposites tests as such; and the overlap
between factors II and III in Table 4 would have been avoided.
This, I venture to submit, would be much more in keeping with the
clustering revealed in Thurstone's own diagram on p. 168.

I maintain, therefore, that the somewhat arbitrary procedure by
which rotations are carried out is apt to obscure lines of classification
that were plain enough in the matrix of bipolar factors before
rotation, and tends to import other lines of classification that are
actually a product of the factorist's tacit assumptions. That in this
and other instances it may be often more convenient to express
the factorial composition by factors that are exclusively positive I
would not for one moment deny; but, when that form of inter-
pretation is the more appropriate, the simplest procedure, I should
have thought, would be something akin to what I have called the
group-factor method. In the present instance, the 15 tests, from
their very nature, were obviously likely to disclose a grouping into
four sharply demarcated categories. Indeed, if we look back at the
initial table of correlations, we shall see that these fourfold lines of
demarcation were quite clearly discernible before any attempt at
factorization was made. Even if they were not, they could easily
have been elicited by one of the usual devices for determining how to
partition the correlation table into the necessary submatrices before
the group-factor method is applied—e.g. by calculating the correla-
tions between the rows of correlations, or by comparing the plotted
contours of those rows, or finally by a rough and rapid analysis
with simple summation.

Finally, let us glance at the transformation matrix (Table 3,
p. 168). If this is rewritten so that the order of the rotated factors
corresponds with the order of unrotated factors, the pattern I
have described is readily perceived, although it is shown only in
miniature (Table IV). The positive figures fall into two lines—a
horizontal row, diminishing in size, and below it a diagonal ridge.
To the right, there is a triangle of increasing negative figures, en-
closed between the row and the ridge; to the left, a triangle of
zeros (here only a single figure, unless we add a fourth factor for