VARIANCE, COVARIANCE, AND CORRELATION 283

Already, indeed, as we have seen in a preceding chapter,
many standardized tests are available for which the differ-
ences in variance are by no means entirely arbitrary.
In some cases the differences can be directly estimated ; in
other cases they can be indirectly inferred. It then
becomes evident that variance, so far from being dependent
solely on the psychologist's whim, and so far from being
equal for all abilities, varies widely from one ability to
another. Nor are the reasons far to seek.

For example, the measurable variance of simpler processes
proves usually to be appreciably smaller than that of more complex
which include or incorporate the simpler, and the variance of pro-
cesses that have become habitual is nearly always smaller than that
of processes that are relatively novel or unlearned. Where variance
cannot itself be directly measured, we still find that the simpler and
more automatic processes show the smallest correlation with one
another and therefore with the general factor : if we interpret the
correlation as essentially a covariance, the peculiarity can at once
be explained on the same lines as before. Such indications, could
they be more extensively confirmed, would seem to have an intimate
bearing on the procedure to be followed in extracting factors, and
on the interpretation of those factors (particularly the general
cognitive factor or g) when extracted.

In early papers on intelligence tests I drew attention to the fact
that the correlation of such tests with the general cognitive factor—
* intelligence/ as it is popularly termed—appears to vary very
closely with the complexity of the particular process tested, and
inversely with the degree to which it has been rendered mechanical
or automatic.1 Thus, when speed tests are used, McDougalFs
dotting test (tapping combined with aiming) shows a much, higher
saturation with intelligence than simple tapping; card-sorting

pp. 15-36). No doubt, as there indicated, the theoretical problem bristles
with difficulties; and the units there proposed are practical devices rather
than a final system. But neither that nor their arbitrariness entitles us to
assume that differences in variance cannot be measured, at least with a rough
but reasonable approximation (cf. also pp. 128 f., on validating such units).
1 " The greater the complexity and the greater the novelty involved in
the task, the greater also (ceteris paribus) is the intelligence of the performer "
(Brit. 7. Psytk., Ill, 1909, p. 169). " The more complex the mental process
involved and the higher the mental level tested, the more completely do
the test-results correspond with estimated intelligence " (J. Exp. PeL, I,