STATUS OF FACTORS IN PSYCHOLOGY 5

' underlying cause '—Mill's c common connecting fact of
causation'—the name ' factor ' is now regularly used in
psychology.1

An example from an early research will make the form of
reasoning clear. On testing a group of children for the
chief school subjects, it was found that, " as a rule, those
who are bad at reading are bad at spelling as well ; their
arithmetic is also below the average for their age, but by no
means as bad as their reading or spelling." Now, we cannot
suppose that weakness in spelling is (to borrow Mill's lan-
guage) * either a cause or an effect' of weakness in arithme-
tic. Consequently, we infer that both are * connected '
through some more fundamental cause, which we term a
' common factor.' We suppose, for instance, that an under-
lying ability—c general intelligence '—is mainly responsible
both for progress and for weakness in all three subjects. If
spelling and reading further vary together in a way that is
not wholly accounted for by the factor common to all three
subjects, we apply Mill's c fourth canon ?—the c method of
residues' ; we eliminate what is due to the first factor, and
decide by a fresh application of the method of concomitant
variation whether or not there is yet another factor—verbal
facility, for example—common to reading and spelling, but
not shared by arithmetic.

The Measurement of Factors.—To render the arguments
more -precise, we endeavour at every stage to measure the
amount of ' concomitant variation.' This, of course,
means that we must begin by measuring the mental abilities
themselves. Standardized tests are employed; and, as a
rule, implicitly if not explicitly, the examinees' performances
in the tests are first translated into terms of the variability
of the group that has been tested, i.e. into terms of their
own standard deviation, which is treated as a universal unit

theorem ' (cf. below, pp. 150-2). The two-factor theory as such was pro-
pounded by Spearman and Hart in 1912 ([24] : cf. also [28]). For the
further history of the subject, see Brown and Thomson [39] and [132].

1 At this stage I shall not attempt any more formal definition of the word
f factor.' Such a definition, I hold, must come at the end, not at the
beginning, of our inquiry (cf.,p. 256). For the time being we may accept
the term as meaning what factorists claim to deduce by analysing their
correlations according to some accredited technique (see pp. 210 f.).