28o THE FACTORS OF THE MIND

variance to be analysed is a definite and absolute quantity ;
secondly, it assumes (or appears to assume) that the means of
the arrays or classes—i.e. the factor-measurements—must be
simple unweighted means. I shall touch upon these diffi-
culties later on in another connexion. Here it will be
sufficient to refer the reader to the few comparative studies
in which both methods have been used with the same data
and which show by concrete example how far such diffi-
culties can be met in special cases.1

B. Covariance

The more familiar methods of analysis that we have
now to compare were intended primarily to be applied to
tables of correlation. Nevertheless, all of them may be
used equally well with tables of covariances (i.e. with
averaged but unstandardized product-moments about the
means), or, for that matter, with tables of unaveraged
product-moments or even of unadjusted product-moments
(i.e. product-moments about an absolute or arbitrary zero
that is not the arithmetical mean). The employment of
covariance instead of correlations has both its merits and
its limitations. The arguments in favour of it have been
set forth elsewhere; and need not be repeated here.2
The objections demand examination at somewhat greater
length.

They have been most clearly summarized by Stephenson
during a recent discussion on * Statistical Methods in
Psychology.'3 Here he criticizes my proposal to use the
6 analysis of variance and covariance ? on the ground that

1 Cf. Cast, loc. cit. sup. and references.

2 CL above, p. 41 ; also [117], p. 419, and [93], p. 247. The chief
argument, it may be remembered, was that the matrix to be analysed is the
matrix of initial measurements, not (as is usually supposed) the matrix of
correlations: the analysis of correlations is only a means to that end, not an
end in itself. In psychology, as elsewhere, the interpretation of correlation
coefficients—as distinct from regression coefficients, which are rarely cal-
culated by psychologists—is often extremely dubious: yet there is a wide-
spread tendency to credit them with an objective existence and a stability
which, from their very nature, they cannot legitimately claim.

3 Proc. Roy. Soc., Ser, B, CXXV, pp. 415 ft seq.