364 THE FACTORS OF THE MIND

validity is sufficiently guaranteed by the elegance of the mathe-
matical demonstration. That, indeed, is not my own interpretation
of Thurstone's statements : but other readers seem to have inferred
some such intention. May I, therefore, repeat that, in my view, the
kind of structure to be required in a factorial matrix is not something
that can be laid down a -priori once for all, but something that is
necessarily determined by the selection of tests in each particular
case ? In every psychological field it would be quite easy to
choose a set of tests which almost certainly would, and another set
which almost certainly would not, conform with a pattern like that
illustrated in the table cited.

Thus, Brigham's 15 tests—6 definitely verbal, 4 definitely
numerical, and 5 definitely visuo-kinsesthetic—naturally lead (as we
have seen) to group-factors that do not overlap—a ' simple structure '
of the step-ladder type. But we might easily include tests that
overlapped in cyclic fashion, or in several varying directions at once.
The other set of tests that we have examined here, the battery used
in Primary Mental Abilities, shows this more irregular constitution.
How far these further complications will assist or hinder factorial
deductions I need not here discuss. My own opinion is that, in
planning experiments beforehand, we should select our tests, so far
as possible, in such a way that absence of overlap will be frequent
enough to provide the necessary data for distinguishing between the
factors shared by wider groups and factors common to narrower
groups only. This follows from the principles on which the group-
factor method is based.

Even the size of the factor-variances is very much at the mercy of
selection. When dealing with discontinuous groups of tests, for
instance, those in Brigham's study, we could, by reducing (say) the
number of verbal tests from 6 to 4 or 3, and by increasing the number
of numerical tests from 4 to 6 or 7, greatly alter the relative propor-
tions of the factor-variances. To insist a priori that every factor
must have at least one zero, i.e. that there shall never be any factor
common to all the tests, is not only an unfair predetermination of an
empirical issue, but also a demand which (when we remember that
factors in the actual performances must include not only abilities
but also the conditions of testing and correlated errors of measure-
ment or observation) is highly unlikely to be fulfilled.