288 THE FACTORS OF THE MIND

the raw correlations as they stand. The relation between the sets
of factors obtained from corrected and uncorrected correlations is
similar to that between sets of factors derived from covariances and
the corresponding correlations (i.e. covariances corrected for differ-
ence in standard deviation). Assuming that Spearman's simple
correction formula ([47], p. 204, eq. iS5a) h-as been used, the factors
obtained by analysing corrected correlations can be deduced directly
from those obtained by analysing the raw correlations by prefixing
a diagonal matrix, whose elements are the reciprocals of the square
roots of the reliability coefficients used for correction (i.e. i/\An>
i = I, 2, . . ., n). As before, the rank and the number of factors
remain unchanged. Thus, as Spearman noted, the vanishing of the
tetrad-differences is unaffected by correction.

In what follows, since covariance has hitherto been so little used
in psychology, I shall express my conclusions chiefly in terms of
correlation.