VARIOUS USES OF FACTORS 27

predictive formulae rather than as explanatory hypotheses, I myself
should contend that the factors derived by the former method are
in some ways more simple rather than less (just as, to a scientific
eye, Einstein's formulae are simpler than Newton's); for the factors
are independent, and the first two or three (which alone have a
high statistical significance) will always account for, and predict, a
greater amount of variance than any two or three factors that fit
a c simple structure.'l

In psychology the simplicity we have to look for is not an
a priori simplicity, but an empirically ascertained simplicity.
As in other sciences we design our inquiries so as to secure
the nearest approach to isolated systems, that is, so as to deal
with one problem at a time. But, although in the simpler
sciences like astronomy, we may often assume that the group
of observations we are analysing form an approximately
isolated system, in psychology such an assumption is likely
to be highly precarious, even when the most carefully planned
precautions have been taken. To choose tests or traits
almost at random, and note the simplicity of the resulting
correlational pattern, can mean little or nothing, except
that the choice was nearly random. To select tests or traits
(or, it may be, persons) according to some definable principle,
and then show that a simple formula will summarize the
results, may mean something : it provides at least a pre-
sumption that we have perceived what was relevant and
eliminated what was irrelevant. Whether this is really so,
however, can hardly be decided from a single experiment
alone. We may, of course, invent methods of factorial
research that will always yield a factor-pattern showing
some degree of * hierarchical? formation or (if we prefer)
what is sometimes called * simple structure/ But again the
results will mean little or nothing : using the former, we
could almost always demonstrate that a general factor

summation' inserts in each table its own appropriate diagonal elements,
whereas the method of principal components treats them, as invariably equal
to unity (see Appendix I). Except with a few small tables, however, the
difference in the diagonal elements has little effect on the results: as the
figures plainly showed, it was rather the subsequent process of rotation that
seemed to reduce the accuracy of the deductions.
1 Cf. the typical result obtained below, Appendix I, Table XL