CLASSIFICATION OF METHODS 269

needless but somewhat out-of-date.1 My indebtedness
to earlier writers still, particularly to Spearman (whose
brilliant work has after all inspired, directly or indirectly,
the numerous alternative methods put forward to supple-
ment or supersede it), to Godfrey Thomson, William
Brown, and Hotelling, will be obvious. Nor, except for a
few incidental comments, shall I attempt to weigh the
advantages of the different procedures. All the con-
troversies of the past appear to have overlooked one indis-
putable fact, namely, that there is no one royal approach,
superior to all others and suitable for use on all occasions.
Each particular class of problem demands its own peculiar

derived directly from the empirical correlations without the elimination of
the first or dominant factor : in certain respects, therefore, they are analogous
to the factors obtained by Thurstone in his work on Primary Abilities after
rotation (cf. [133], p. 272), and depart from those that would be obtained by a
4 Spearman analysis.' His own description, however, brings his present
methods more nearly into line with those of Tryon than with submatrix
methods, as used by previous factorists (e.g. by Holzinger, by Stephenson in
his earlier articles, and by myself). Indeed, from recent correspondence with
him I gather that the conception of e non-fractional factors' was partly de-
vised to cover what Tryon has called * operational psychological unities': (the
instances given by both authors are much the same ; while Stephenson's

* fractional factors' cover what Tryon terms * radical and orthometric
components': cf. Tryon, [86], [13-1]).

A third criticism has been urged against his statement, namely, that his
extension of the term * fractional' from methods of analysis to the resulting
factors is in conflict with the usage of previous writers and with his own. In
[138], p. 277, he refers to " fractional factors, which will usually be oblique"
But this would seem to be a slip of wording. The context makes it plain
that he is referring to a " fractional analysis, the results of which will
usually be oblique factors." In his last paper he makes this clear, since he
describes the analysis of correlations by multiple-factor technique as leading
to 'fractional orthogonal factors' ([136], p. 242). The proposed extension
is quite consistent, if a little confusing: there is no inconsistency in maintain-
ing that a * complete analysis' should yield a * fractional' factor and that a

* fractional9 (i.e. partial) analysis should leave us with a * non-fractional'
factor (i.e. one that is imperfectly analysed into its ultimate parts).

1 As has already been explained (pp. ix—x), this account was written before
the publication of Prof. Thomson's book (The Factorial Analysis of Human
Ability) which gives an admirably clear and impartial account of all the chief
methods available, and forms by far the best introduction to the whole
subject. Actual methods of calculation are described and illustrated in
Appendix I, Tables I-XI, pp. 449-86 below.