334 THE FACTORS OF THE MIND

Effect of Rotation on Factor-variances.—According to
Thurstone, when factors have been extracted by the sum-
mation method, they must always be transformed, by a
rotation of the reference axes, to factors which (i) have
exclusively positive saturations and (ii) have as many zero
saturations as possible. Now, if the method of weighted
summation has been used (and the same is true of the
method of simple summation so far as it approximates to
that of weighted summation), the first factor extracted
accounts for the largest amount of variance that could
possibly be accounted for by a single factor alone ; the
second factor accounts for the largest possible amount of
the residual variance ; and so on. Again, on taking the
factors in the opposite order, we find that the last factor
accounts for the smallest possible amount of the variance,
consistent with the fact that all the variance has to be
accounted for by n factors at most ; and so on for the other
factors. Thus, the set of factor-variances obtained by this
procedure has a wider range and a larger standard deviation
than any other set that can be derived from the same table.
Consequently, the substitution of any other set of factors
by rotation is bound to reduce the inequalities of the factor-
variances, and so to diminish their standard deviation.
Moreover if, in accordance with the requirements of
c simple structure,' the rotation is so arranged that each of
the new factors has a large number of zero saturations, and
presumably about the same number (" at least r zeros,"
where r is the number of factors [84], p. 156), then the
ultimate result must obviously be to flatten out the differ-
ences. Indeed, a single glance at Thurstone's tables,
derived from the same data before and after rotation of the
factors (e.g. [84], pp. 108, 169, [122], pp. 113-6), is enough
to show that this levelling out is the most conspicuous
change. Thus, the attempt to obtain a ' simple structure ?
obscures one of the most characteristic points of the given
correlation table, namely, the particular degree to which it
is dominated by one or two outstanding factors.

Almost all the correlation tables met with in psychology
are distinguished by the fact that the standard deviation of
their factor-variances is exceptionally high. This means