THE LOGICAL STATUS OF MENTAL FACTORS 135

steps. That also holds good, as we saw a moment ago, for a care-
fully selected scale of handwriting. Accordingly, on this double
basis it becomes possible to compare individual variability in the
two subjects. Even with the most generous allowance for error,
there can be little question about the result: except among very
young beginners, the range of individual variation is far wider in
English composition than in writing. This tallies with the general
view of teachers 1 : and, as we shall see later on, is fully corroborated,
when we examine data obtained by other methods of estimating
facility in the two subjects, e.g. if we gauge by speed rather than
by quality (cf. [41], pp. 407, 409, 410). In principle, therefore, the
task of finding a universal unit for all so-called ' abilities * should be
no more impracticable than planning a miscellaneous store in which
every article shall be priced at sixpence.

Even so, however, we have only considered the validity of
grading or measuring the initial or empirical variables, such
as are directly observed. Many writers would willingly
grant that actual performances in a single test, or a set of
tests, can be measured (at any rate in certain cases and with
varying exactitude) on a commensurable, additive scale ;
but they seriously doubt whether the same assumptions are
equally applicable in the case of the hypothetical factors
indirectly deduced from the observed performances. " On
your own showing," they argue, " a factor is a principle of

dividing by the mean, reduces the absolute variations to approximately the
same subjective scale. It is partly for this reason that, in correlating physical
measurements by persons to determine types, I have argued that we should
first reduce the crude measurements to multiples of the standard deviation
for each trait (for criticisms of this proposal see [96], p. 198 f., and my reply,
pp. 173 f. below). The use of the I.Q. effects a similar reduction (since the
standard deviation of the crude test measurements is again approximately
proportional to the mean) : but now the unit expresses, not equally perceptible
differences, but equal causal differences (i.e. differences in innate constitution,
or, if we prefer, differences in rate of growth rather than differences in
extent of growth).

1 On being informed that certain psychologists held that individual
variability was virtually the same in all subjects, a schoolmistress of my
acquaintance at once produced the afternoon's exercises of her pupils. With
few exceptions, the handwritings seemed at first sight almost indistinguish-
able ; but the wide differences in literary merit were patent to the most
unpractised eye. Similarly, in many other mental characteristics, differeaces
in the range of individual variation seem obvious, once we consider the point,
even with unaided observation,