174 THE FACTORS OF THE MIND

same unit, e.g. the standard deviation or ranks " ([93], p. 276) ; and
one or other of these methods of scaling have formed the basis of
most of the assessments correlated in this way.

The real difficulty, as it seems to me, arises, not so much from the
fact that the units may be incommensurable as from the fact that
the traits may be incommensurable, i.e. they may be disparate and
unrelated items, which we treat as forming a class, when actually
they form no class at all. Thus, as an example of factor-analysis
applied to correlations between persons, it is suggested that we
should take measurements of " height, trunk-diameter, arm-length,
leg-length, circumference of neck, breadth of nose, and length of
little finger, and so forth" ([96], p. 198). These measurements
would all be in inches or centimetres throughout. So far as the
unit is concerned, therefore, we could certainly average the length of
arm, leg, little finger, etc., for each separate person, and then calculate
the standard deviation, and finally correlate the measurements
by persons, as the passage quoted then instructs us to do. But
would such averages, standard deviations, or correlations have any
value or meaning ?

Most people, I fancy, would say no. I would rather say, we
cannot answer until we know the problem at issue. The problem
for which this procedure was actually proposed is the determination
of physical types* ; and for such a purpose it seems obviously
faulty. But had the problem been to study the resemblance in
bodily shape between persons of different size (e.g. between children
and adults, or between an ateleiotic dwarf and a normal adult),
then, though I should have made a slightly different selection of
traits, the procedure itself would seem valid.

I hold, therefore, that the first essential is to show that the traits
selected for comparison form an intelligible sample of an intelligible
universe or class, and that this class constitutes an ordered class, in
the sense defined above (p. Il8). Even then, before we could
proceed to calculate product-sums, covariances, and correlations,
further requirements would have to be fulfilled at each stage of the

1 The variations in the small features, such as length of nose, breadth of
head, which may be quite as important in determining physical types as
variations in height, etc., would be swamped by the variations in these larger
features. In my own studies of physical and temperamental types, I had
correlated traits in the usual way and had also correlated relevant traits by
persons after first reducing each trait to standard measure. Stephenson,
however, argues that his * system 2 ' (Q-technique—" reducing the crude
measurements to standard measure for each person ") is the only proper system
for eliciting " individual differences in type " ([96], p. 205). My own method
(* system 3 ') he rejects for reasons which we shall examine in a moment.