CHAPTER XI
CORRELATIONS BETWEEN TESTS AND BETWEEN PERSONS

IN almost every investigation of which factor-analysis
forms a part, the initial table of data gives measurements
for (a) a limited sample of the total universe1 of persons
in respect of (£) a limited sample of the total universe1
of traits or tests. As we have seen in a previous chapter,
we may base our factor-analysis on covariances (or correla-
tions) either (a) between the several persons or (b) between
the several tests. If our interest lies in a c general factor '
that may cover the universe of traits or tests (e.g. general
intelligence, in the case of cognitive tests, general emotion-
ality in the case of emotional traits), we shall naturally begin
by correlating the tests or traits ; if in a c general factor'
characteristic of the population of persons, we shall natur-
ally begin by correlating persons (see above, pp. 175 f.):
such factors are simply averages (or more accurately
weighted sums) of the measurements for the traits and
for the persons respectively. If our interest lies rather in
the secondary factors, then, in theory at any rate, we have
the option of either method of approach: in practice, pro-
vided the method of assessment permits it, economy of
labour will generally suggest that we correlate whichever
variable is overdetermined—traits if the persons are the
more numerous, persons if the traits are the more numerous
(see pp. 177, 260).

The relations between the two sets of factors can be
exactly stated : if the averages for all tests and for all persons
are the same, and if the method of analysis described above

1 It is perhaps a little awkward to talk of a ' population * of tests or traits,
though Fisher, Stephenson, and others use the term * population* in that
way. The logician's word * universe * covers both cases quite naturally,
and further implies that the tests or traits sampled should belong by implica-
tion to a definable class. Cf. [no], pp. 25, 332 et seq.^ and p. 180 above.

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