74 THE FACTORS OF THE MIND

vations, brings home to us what is constantly forgotten,1
namely, that by its very mode of computation a -factor is
simply an average or sum total of certain measurements
empirically obtained. To estimate a factor-measurement
nothing more mysterious is involved than the process of
averaging, with or without appropriate weights.

In the case of the first or general factor, where all the
weights are positive, this conclusion is obvious enough.
Every examiner who wishes to estimate the general ability
of his candidates takes the plain unweighted total or average
of the marks they obtain in the papers he has set; and even
the professional factorist will in actual practice seldom stop
to calculate the various weighting coefficients that his full
regression equation requires, but will similarly compute the
unweighted average or the plain arithmetical sum. Factor-
analysis merely makes this familiar procedure a little more
precise by introducing a differential weighting.

In the case of the more specialized or c secondary ' factors
the factor-measurement is the sum or average of the stan-
dardized deviations about the first factor (or the factor last
calculated), duly weighted if we desire to be precise. This
perhaps is not so obvious; but I shall endeavour to demon-
strate it in a later chapter.2 To put it in its simplest terms,
let us suppose that we desire to estimate a child's verbal
ability; we must apply verbal tests, and, since these are
inevitably influenced by general intelligence as well, we
must also apply tests of intelligence : to get a rough approxi-
mation to his verbal ability,all we have to do is first to deduct
from his performance in the verbal tests whatever may seem
attributable to his general intelligence, and then—since
weighting rarely makes much difference to the average—we
may take the unweighted average of the residues, provided,

1 When first setting down this view, I imagined I was merely putting into
words what every factorist probably thought too obvious to need explicit
statement. Stephenson, however, has strongly criticized the notion, which
he considers to be " quite contrary to the tenets of the Spearman school (of
factor-analysis)." " A factor," he insists, " should be clearly distinguished
from a mere average " ([98], p. 357). And, as we shall find later on, he holds
that this erroneous assumption invalidates my conception of the factors to be
obtained by correlating persons.

2 See below, Part III, p. 399.