CLASSIFICATION OF METHODS	259
Accordingly, it does not seem proper to include this require-
ment in the formal definition.
This fourth requirement would mean, in the case of tests and
persons,^1 (a) that the factor-saturations for a particular test must not
change, when new tests are added to the old battery of tests; (b) that
the factor-measurements for a particular person must not change,
when new personsare added to the original sample of the tested popu-
lation ; and perhaps (c] that if the same tests are applied to the same
persons at different times (e.g. to the same children at different ages
or later on when grown up) both the factor-saturations and the
factor-measurements should remain unaltered. It is only necessary
for the last point to be stated for us to see how precarious it is. Yet,
unless it is assumed to hold good at least in some degree, the study
of mental development generally, and predictions about the sub-
sequent development of the individual in particular, become very
difficult.
It is curious that, while nearly all factorists insist that any
* factor' to deserve the name must be stable, nevertheless, hardly any
of them formally prove this stability. Few seem to have fully
realized either the advantages or the limitations such stability
confers. One great advantage would be that the indeterminacy,
which is bound to haunt us so long as we try to deduce a plausible
set of factors from a single table of figures only, would be greatly
diminished, and often wholly abolished, if we insisted that our
factors should be demonstrable, not in one table, but in a succession
of tables—tables obtained with varying batteries of tests and with
different groups of individuals. We believe in a general cognitive
factor (g), not because it was conclusively established by a single
research, but because it appears and reappears in almost every
collection of cognitive tests; and, as a test of identity (by no means
the only test), we carry one and the same test, or group of tests,
(the Binet tests or some recognized series of written intelligence
tests) from one research to another. Instead of rotating a factor
pattern by trial and error until it satisfied some a priori scheme, we
ought to rotate it mechanically until it fitted two or more tables.
Indeed, the device of rotation, as ordinarily applied, is an informal
common factors cover them. However, the most effective procedure is to
prove, by an appropriate criterion, that the factors obtained from different
Investigations remain approximately the same (cf. p. 41). With but one
investigation our sole resource is to attempt ap. * efficient * estimate of the
population parameters by the method of * maximum likelihood' [50],
_w ^v And, of course, within the margin allowed by the sampling error.