VARIOUS USES4 OF FACTORS 15

distribution fulfils for the uni-variate universe. In dealing
with a uni-variate universe of measurements, we are not
content merely to give a detailed table of frequencies; we
seek a few descriptive constants which will specify the lead-
ing characteristics of our sample—the mean, the variance
(or s.d.), and perhaps the third and higher moments. So
too in dealing with a multi-variate universe : instead of
merely giving a table of detailed correlations, we seek a few
appropriate constants which will characterize the sample,
and indirectly the universe from which the sample has
presumably been drawn—namely, the variances for the first,
second, and possibly other ' factors,' and the corresponding
factor-measurements. Our choice of factorial constants,
like our preference for the standard deviation rather than the
mean variation, will be determined, not entirely by labour-
saving considerations, but by a desire for the most pregnant
specifications, i,e. for characteristics containing within them-
selves the largest number of logical implications. In short,
our object is a theoretical as well as a practical economy.

(a) The * 'practical economy' is perhaps clearest in the
field where most of the work has already been done, namely,
in the testing of school children. If, for example, we can
justifiably group pupils into schools, forms, classes, or
standards, according to the general educational ability of
each one, there will be a manifest saving of labour : if,
however, such attempts at broader classification prove to be
unwarranted by the facts, and if it proves wholly fallacious
to speak of children as generally backward or as generally
advanced, if, in fact, we can adequately describe them only
by their detailed attainments in each separate subject in
turn, then the task of educational classification will become
exceedingly complex. Factor-analysis begins by checking
the validity of such generalized descriptions.

But a description in terms of general ability forms only
the first step in dealing with the individual child. It claims
to tell us whether he is, on the whole, more likely to succeed
or to fail, and by how much ; but we also want to know in
greater detail where he is likely to succeed or fail, and why.
And so we pass from the general factor to the more specific.
Yet even here we still seek to be as general as we can ; if,