i8o THE FACTORS OF THE MIND

ceived as a collection of individuals. The 'variables' are the varying
attributes or traits that can be predicated of them ; they vary
together because they inhere in the same individuals. But how is
it possible to reverse the descriptions, and talk of covariability not
between traits but between persons ? Surely, the student asks,
we cannot call the traits a population, and treat the persons as
variables predicable of the traits ?

The answer is that the concrete context which suggested the
current nomenclature is really irrelevant to the abstract argument.
What we call a £ person ' is simply a set of trait-measurements,
considered by columns instead of by rows. As so often happens
when new notions are introduced into mathematics at the outset of a
fresh line of work, the terms have been generalized. Since nearly
all the correlational researches of the psychologist hitherto happen to
fit the literal sense of the words, he forgets that the words them-
selves (as is shown by half the examples in a statistical textbook) are
no longer tied down to their original meaning. Both * population'
and * variable' denote classes. The use of two names indicates a
cross-classification. The application of the different names shows
which set of values we are, for the moment, taking as predeter-
mined or constant, and which we are treating as indeterminate, i.e.
variable or determinable at will.1

1 The illustration which gave rise to this criticism was the proposal in 1117
original memorandum to apply both methods of analysing variance and both
ways of calculating correlations to a sample mark-sheet, containing marks
awarded by 6 examiners to 15 candidates in a school certificate examination
[93], cf. [134]. To correlate the marks both by examiners and by candidates
would be, we are told, to confuse * population * with i variables': but we
are not told which should be regarded as the * population '—the examiners
or the candidates; nor are the terms * population ' or * variable' explicitly
defined.

As I myself have employed these terms in previous articles, I ought to justify
my own usage. " The idea of a population is not to be applied only to living
or even material individuals. If an observation, such as a simple measure-
ment, be repeated indefinitely, the aggregate of the results is a population of
measurements " (Fisher [50], pp. 2-3). To avoid the misleading associations
that attach to the word * population,' Yule prefers to speak of the £ universe/
" A sample from a universe is a selected number of individuals each of which is
a member of the universe. A universe, like any class, may be considered as
specified by an enumeration of the attributes common to all its members "
([no], pp. 25, 332 ; or, I would add, by enumerating the members: cf.
Russell, Principles of Mathematics, p. 69). " A variable is a symbol which
represents any one of a class of elements. The elements of the class may or
may not be numbers" (Young, Fundamental Concepts of Algebra and
Geometry, p. 193 ; cf. Russell, loc. cit.y p, 89).