CORRELATIONS BETWEEN PERSONS 293

* cleverness * among the persons tested, and so contradict my initial
assumption, namely, that the " population is homogeneous as
regards the c general factor' " : since, " if we desired to study

* specific ' factors (i.e. type factors) more especially," it was natural
to take " the means for the several persons as approximately equal
from the outset " (loc. cit^ p. 72).

Secondly, he points out that perfect reciprocity can be demon-
strated only if covariances, not correlations, are analysed. But,
as he states elsewhere, " if a suitable set of units could be discovered,
the practice of analysing covariances instead of correlations would
have much to commend it " ([137], p. 76). The difficulties attend-
ing the use of covariances were freely granted ; and I should never
claim that in practice, despite our imperfect means of assessing
intellectual abilities or temperamental traits, a mathematically
perfect reciprocity can everywhere be demonstrated. When,
however, the tests or traits are already in standard measure
(as is the common custom), the covariances between them become
identical with their correlations. The only trouble, therefore,
arises over the correlations between persons. Here, I believe,
unless special precautions are taken over the selection of the
4 tests ' (or what figure as such), correlating (as distinct from co-
variating) persons may be hard to justify. But in any case the
factors obtained from covariances will, with but little trans-
formation, still serve to explain the correlations as well.1

Finally, in dealing with my last example [i 14], he criticizes more
especially the units of measurement assumed. In this inquiry each
trait was based on an assessment for about 20 elementary reactions ;
and the assessments for each reaction were in turn distributed
by instruction in accordance with a normal curve having the
standard deviation as unit (so far, at least, as the knowledge of the
observer would permit). In theory this should lead to a variance
for each composite trait roughly proportional to its complexity
(i.e. a trait compounded by adding 20 independent reactions would
show the widest amount of individual variation; a trait com-
pounded of fewer independent or fewer observed reactions would
show a smaller variation). Thomson agrees that " there is some-
thing to be said for the probability of real differences in variance."
But, he adds, " it cannot be right to use a space whose metric is
dependent upon accidental and irrelevant differences in the
variable " (e.g. upon the lack of complete information in regard to

1 Cf. [114], p. 179. Kelley appears to assume that the factors will be the
same ([85], p. i) : but, as I have endeavoured to show in my review of his
book, in the general case, this appears to be mistaken ([102], p, 193).