380	THE  FACTORS OF THE MIND
ization ' or to c correlation ' : both now seem far more at the
mercy of " the psychologist's whims." Stephenson postulates that
the distribution of trait-measurements within one and the same
person must fit the normal curve and that its standard deviation
should be the same for different persons ([138], p. 279 and refs.).
This would be obviously incorrect for intellectual traits, such as are
ordinarily measured by mental or scholastic tests : one child's
measurements may be nearly the same for all the traits tested, and
another may be extremely gifted in one trait and extremely lacking
in another (cf. [35], Figs. IX, I and 4). As regards temperamental
traits, the list compiled by Stephenson himself can scarcely be
supposed to fit a strictly normal distribution or to show equal
variability from one person to another. However, for a preliminary
classification of persons into groups or types, it is sufficient to judge
by broad resemblances ; and for measuring such resemblances in a
rough-and-ready way, a coefficient of correlation may legitimately
be used without too severe an insistence upon these particular
postulates. After all, the use of a product-moment coefficient does
not necessarily imply that the correlated variables are normally
distributed.
(2) But I have no wish whatever to exclude a preliminary
standardization in every case. Indeed, my Memorandum ([93],
pp. 261 et seq.) dealt in some detail with the type of case in which
standardization seemed to me to be essential. Where considerable
manipulation of the matrices was required, I suggested a slightly
modified procedure involving two requirements : (a) 2x = o, and
(ft) Zxz = i (where x denotes the raw marks). I termed this
' unitary standard measure' to distinguish it from the more usual
reduction to terms of the standard deviation, i.e. putting (c) £x2JN
= I. Stephenson explicitly adopts this modification ([96], eq. (i)
to [4]); but he appears to think that the application of (£), which
converts covariances into correlations, will thereupon abolish all
relations between the two sets of factors obtained by correlating
traits and persons respectively. Actually, as we have seen in the
preceding paper, the matrix equation, expressing those relations in
their simplest form, is merely modified by the addition of a diagonal
pre-factor.
In my view the chief obstacle that the generalization of my
argument has to meet is due, not to (£), i.e. to the conversion of
covariances into correlations, but to (#), i.e. to the conversion of
raw scores into deviations about the mean, and of unadjusted
product-moments into covariances. The great difficulty in
psychology is not that the unit, but that the origin or zero point,