CRITICISMS OF METHODS 383

my procedure, or at any rate my wish to generalize its results.
Hence in what follows I propose to fulfil my promise, and shall
attempt an analysis of an unselected, non-homogeneous sample.
To make a detailed examination of the simplest case seemed
desirable first of all, because more than one writer had emphatically
denied that, even in that case, any functional relation could be
found, much less a relation so simple as mathematical identity.

(3) Stephenson further objects to the use of a * multiple-factor '
method of analysis based on the method of least squares. To me
this appeared essential in analysing correlations between persons, at
any rate in theoretical work, since no other formulae would permit
the algebraic proof of the identity of P- and T-factors. Stephen-
son, however, maintains that this procedure " leads to artificial
factors rather than genuine factors,'5 which he holds can only be
reached " by a Spearman technique." Accordingly, as we have
seen, he prefers to substitute a ' two-factor' procedure. The c two-
factor technique,' however, was designed solely for hierarchies in
which there are no indications of any other factor besides one
' general' factor and n specifics. But in correlating persons the
type-factors nearly always appear as non-specific group-factors, or
as bipolar * general' factors over and above the first: in fact, as
Stephenson's own more recent work appears to show, and contrary
to what is supposed to obtain in correlating tests, multiple factors
are the rule and not the exception. For rough practical purposes I
see no objection to substituting a summation formula for the least-
squares formula as a method of multiple factor-analysis; only I
regard it as no more than a quick and simple procedure for reaching
first approximations to the true figures. And, as a matter of fact,
in most of the earlier preliminary studies on correlating persons,
both by my research students and by myself, the summation
formula was employed. However, the method of simple summation,
as applied by Stephenson, leaves larger residuals than are obtained
with the method of least squares ; and, as Davies has shown, some
of the residuals which Stephenson treats as significant, and on which
some of his type-factors are based, become almost negligible when
recalculated by the method of least squares [130].

(4) Finally, instead of applying what I have termed the * general-
factor method * (* method b' of my Memorandum) and analysing
the correlation table as a whole, Stephenson prefers, as a rule, to
use what I have called the ' group-factor method * (* method a ?).
The former, he considers, must inevitably lead—like the correlation
of traits—to mere * bipolar types ? which " at most can be regarded
only as extreme cases—opposite tail-ends of a single normal and