CHAPTER III
THE GENERAL NATURE OF THE FACTORIAL TECHNIQUE

The Fundamental Factor Equation.—All the different
factorial procedures are derived from the same initial
postulate ; and the tendency- to reify c factors/ natural
enough in itself, receives a silent sanction from the very
form in which this initial postulate is almost always presented.
Practically every factorist starts with an equation which
depicts the mark or score obtained by any given individual
in any given test as the sum of that individual's mental
abilities or c factors,' each factor being weighted according
to its influence on the particular process tested, Thus " the
tester," to take Thomson's illustration, " hopes to give the
composition of his test as

• 71 g + • 40 v + • 34 n -f ' 47 s>

where g is Spearman's g (intelligence), v the verbal factor,
n a number factor, and s the remaining specific of the
test; and the coefficients are the c saturations,' i.e. the
correlations believed to exist between the test and those
fictitious tests called factors, the squares of the saturations
(factor-variances) adding up to unity."x Thurstone,2

1 Loc. cit., p. 18 : (I Have slightly condensed Thomson's wording). In
this paragraph he is showing how Spearman's theorem may be extended to
include group-factors. But Thomson's own equation has the same form
(cf., for example, J. Educ. PsycboL, XXVI, p, 24.2, eq. [i]); Spearman's
two-factor equation would put zero for the second and third coefficients
and suitably adjust the first and last,

2 [84], p. 52, eq. [i]. Cf. [122], pp. 2-3," The first simplifying assumption
of the factorial methods is that the performance of a task . . . can be regarded
as a sum of the contribution of two (or more) primary abilities," or, in other
words, that it" can be expressed, in a first approximation, as a linear function
of these primaries. ... If we know . . . the weights and * , . the scores in
the fundamental abilities then the objective performance can be predicted,*'
May I add that the theoretical chapters of this little monograph give an
admirably lucid account of the problem of factor-analysis and the *

7*