298	THE  FACTORS OF THE MIND
ponents or principal factors which are rarely factors in the sense
denned " (by Spearman and himself) ^1: they are simply " arti-
factors " ; " it is very seldom that we can establish their meaning "
([83], No. 5, p. i).
But the results obtained by the two different methods appear
incompatible only so long as we assume (with both parties to the
controversy) that an abstract statistical factor, to have any in-
telligible meaning, must be identifiable with some concrete ^£ ability '
or ^t trait.' Suppose we are seeking a general expression for the
physical differences between the sexes, and one investigator states
his results by saying that the difference between their average
heights is 6 inches, while another gives the men's height as + 1-5
S.D., and the women's — 1-4 S.D. The findings are not proved
meaningless because the second declares that 6 inches is the height
of no human being ; while the former rejoins neither is — 1-4 S.D.,
because a negative height is impossible : both expressions are
alternative but related formulations of one and the same fact.
Nor is it difficult, I think, to demonstrate that a similar equivalence
^1 In the Spearman and Holzinger Trait Studies a factor is defined as follows :
" The vanishing of the tetrads within limits of probable error furnishes the
necessary and sufficient conditions for identifying a simple factor " : ([83],
p. i) ; such a factor is to be conceived as a " unitary ability or trait." Un-
fortunately, in order that the tetrads shall vanish, it is necessary that the
saturation coefficients for the group factors (or ^£ secondary factors,' as the
writers prefer to call them) should be simple multiples of the saturation
coefficients for the * principal' or general factor (cf. [83], p. 2) : but patterns
constructed to conform with this condition would seem to be quite as
artificial as any to be found in Hotelling or Thurstone (Thurstone himself,
however, apparently regards it as at least a ' conceivable psychological
situation' [84], p. 141). The unique collection of material accumulated
and analysed by the several collaborators in the Spearman-Hoi zinger
reports has since led to successive and important modifications of
the original theory ; and the recent account of the ' bi-factor method * in its
latest form, given by Holzinger in his remarkably clear and suggestive manual
[106], brings it much closer to the methods of other workers. The scheme
for the generalized factor-pattern now seems identical with that accepted
in the report of the Examinations Inquiry Committee, and the terminology
more nearly in line with that prevalent in this country. Thus, the classifica-
tion and sub-classification of factors given in the new Students* Manual
([106], p. 12) appear identical with the * four-factor theory' previously given
in my own Memorandum and elsewhere ([93], p. 259) ; and the factor-
pattern in Holzinger's latest article ([107], p. 43) is identical with that in my
own table ([93], p. 264, Table 135). Here, therefore, once again independent
workers, starting from very different standpoints, seem gradually to have
arrived at much the same general result.