30	THE  FACTORS OF THE MIND
be necessary to apply separate tests of educational achieve-
ments and of relational activities to one and the same group
of pupils, and show that those who do well in the latter
usually do well in the former,"
Accordingly, he applies seven ^£ educational' and twelve
^£ psychological' group tests to fifty-three boys, aged lo-ll
years, in two classes at an elementary school. The
correlations, he finds, are " all significant, and with few
exceptions would fit a hierarchy within three times the
probable error." Since that margin allows a deviation of
± -20, the alleged fit is an exceedingly loose one, and indeed
is not explicitly invoked to support the conclusions drawn,
His main argument may be given in his own words :
" The correlation between every pair of tests turns out
to be both positive and significant. Hence every pair has
a common factor. . . . The factor common to all the tests,^1
educational as well as psychological, is the perception of
relations between abstract or concrete ideas. Thus our
theory is verified; and we conclude that this relational
ability is the general and essential cause, not only of success
in the cognitive tests of relation-finding, but also of all
intellectual progress at school. . * . It may therefore be
maintained that every child will make the greatest amount
of progress if, from the earliest ages on, he is taught, not by
mere mechanical memorization as at present, but by a
logical procedure which should enable him to understand
the reasons for what he is taught, in a word, by teach-
ing him to educe relations instead of to reproduce
associations."
There is here a rather startling transition. We suddenly
pass from the abstract notion of a common factor, invoked
to account for a statistical correspondence, to the concrete
notion of a causal factor, which can be exploited as an
^1 It is here tacitly assumed that the factor common to one pair is identical
with the factor common to the other pairs. In his introductory chapter the
writer states that " it is unscientific to postulate a number of factors when one
factor will suffice." Presumably, therefore, his identification rests rather on
the principle of simplicity or parsimony than on any theory of the cause of a
hierarchical order among correlation coefficients: indeed, since he declares
that his table contains" possible specific (i.e. group) factors," he cannot claim
it as conclusively hierarchical.