6	THE  FACTORS  OF THE  MIND
of measurement: the resemblances between their perform-
ances can then be measured by the average product of all
the pairs. This is Galton's ' index of co-relation^? as
calculated by the so-called product-moment method. ^
It is important, however, to realize that the preliminary-
standardization of the unit is not indispensable. All that is
necessary for the calculation is that the measurements
should be expressed as deviations from their own average.
Then, even though the measurements have not been reduced
to terms of their own standard deviations, we can still use
the average product of the pairs to measure the amount of
concomitant variation. The product-moment is then
termed the covariance ; and in theory all forms of factor-
analysis can be applied to tables of covariances just as well
as to tables of correlations.
When the calculation is completed, the degree to which
each test-performance appears to depend on the funda-
mental ability or ^£ factor ^? supposed to influence it is finally
stated in terms of a * factor loading ' or ^c factor saturation,'
as it is variously called, that is, a similar coefficient or ^i index '
measuring the amount of resemblance (or * co-relation ^3)
between the empirical test on the one hand, and the
estimated measurements for the hypothetical factor on the
other. Tests of significance are generally applied, not to
the factor loadings or factor saturations, but to the
coefficients of correlation or their residuals; and, as usual,
they indicate, not the probability that the postulated hypo-
thesis is true, but the probability that the figures tested
may after all have arisen from the mere effects of random
sampling, that is, from what is loosely called * chance/
^6 The Factors of the Mind*—By applying calculations of
this kind to the results of mental tests, psychologists have
hoped to reach an inventory of what, in Spearman's phrase,
have been described as * the abilities of man/ Verbal
ability, arithmetical ability, mechanical ability, retentivity,
quickness, perseveration, oscillation of attention, and above
all a general factor of intelligence that enters into all we say
or do or think—these, or qualities somewhat like them (for^
to avoid misconception, the factorists prefer to designate
their factors by letters rather than by concrete names), are