VARIOUS USES OF FACTORS 21

the underlying factors will. Thus, a research student will
compute the average or summed performances of a group
of children, first in a composite series of tests, such as the
Binet scale, and secondly, after an interval, in a later com-
posite examination, such as that for junior county scholar-
ships ; he then proceeds to calculate the correlation
between the two. If he has already had experience of such
calculations, he will know that the correlation between
marks and measurements like these is a highly unstable
figure, fluctuating with the standard deviation of the group,
and ranging far more widely than its sampling error would
suggest. And he will be rather chary of treating it as a basis
for his forecasts. Let him read, however, that such a
correlation is due to a ' common factor,' and let him
identify this ' common factor ' with something nameable,
such as g (thus thinking of it as' general ability ' rather than
c average ability?) or as c intelligence' (which tacitly
suggests * innate ability ') ; and he at once feels that he has
got down to something far more solid than a mere descrip-
tive coefficient: he will assume that both his correlation and
his initial test-results rest on a firm and permanent founda-
tion, and that this foundation will remain to support him
even when he turns to offer opinions about some other
group.

It seems important, therefore, to emphasize two points:
first, that unless, in labelling the factor or by some other
means, additional premisses are surreptitiously introduced,
the factor extracted from a single set of correlations can
claim no deeper reality than can be claimed by the correla-
tions themselves; and, secondly, that a single set of corre-
lations in its turn can of itself rarely afford a valid basis for
inductive inferences. These points will require elucidation
in some detail. Let me take the second first.

(A) The Requirements of Inductive Inference.—The inex-
perienced beginner still commonly supposes that, if a
correlation is ' statistically significant* as judged by its
sampling error, then it can straightway be generalized, and
taken as applying to other groups; and more than one
well-known investigator, who would doubtless be fully
alive to this fallacy in dealing with a single correlation, has