CHAPTER IX
CLASSIFICATION  OF METHODS
Problem.—From a mathematical standpoint, as we have
seen, the aim of factor-analysis is, broadly speaking, to find
a reversible (or ' non-singular') transformation which will
enable us to reduce a given matrix of figures, such as a table
of test-measurements or of correlations, to an equivalent
form which shall be of the simplest possible type, at least
so far as such automatic simplification is consistent with the
problem and scope of the research in hand. To effect such
a transformation various working procedures are available,
which are to be found in textbooks on higher algebra or
analytic geometry^x ; and, corresponding to these pro-
cedures, different methods of analysis have been proposed
by psychologists during the last ten or fifteen years—the
^6 two-factor method/ the ' centroid method,^5 the * method
of principal components/ the ' method of trigonometrical
rotation'—each having its own special merits and its own
group of advocates.
The sponsors of any one method warmly criticize the
rest. Thurstone considers Hotelling's results to be " psy-
chologically meaningless" ; Kelley pronounces Thur-
stone's method to be " logically unsound" ; Spearman
rejects all three in favour of his own original procedure
(with simple extensions where necessary) ; and his criticisms
have been supported by Stephenson in this country and
Holzinger in America. The general student thus comes to
regard each method as wholly incompatible with the others,
and is at a loss to know which to choose.
In a Memorandum on factorial methods, drawn up at
^1 Cf. [26], [44], [73], [74]. For the practical computer perhaps the
clearest exposition of the classical devices of the professional mathematician
is to be found in the recent work on Elementary Matrices by Frazer, Duncan,
and Collar (Cambridge University Press, 1938, esp. chap. iv).
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