APPENDIX I
WORKING METHODS FOR COMPUTERS

THE simple methods of computation which were originally developed
for my work on mental and scholastic tests have since proved
serviceable for many other problems ; and it has more than once
been suggested that a set of working instructions might be published
in brief accessible form. The theory on which the methods rest
has been formally set out elsewhere (e.g. [93]); but the experi-
mental investigator is frequently unable to follow theoretical
demonstrations in matrix algebra, and yet is desirous of attempting
a practical analysis of his data. The following notes are abridged
from longer roneo'd instructions, prepared some years ago for
research students working at the London Day Training College, and
revised from time to time in the light of their experience : these
more detailed notes can be obtained on application to the Psycholo-
gical Laboratory, University College, should fuller explanations be
required.

The general procedure was first adopted I in order to meet the
peculiarities of correlation tables that do not manifestly fit the
simpler c two-factor theory' of Spearman. As indicated in the
original paper, the work consists essentially of three main steps.
(i) With each of the tests, " the sum or average of its coefficients
is taken as measuring its general tendency to correlate, and there-
fore as provisionally determining its position in the hierarchy."
" The theoretical values," it was added, " can be obtained by
various mathematical formulae " ; here I shall confine myself to
two or three of the simplest, (ii) An " ideal hierarchy " 2 is then
fitted to the observed coefficients by applying the cc product
equation " (rab — fa?rbgy where rag and r^ denote the correlations of
any two tests a and b with the common factor g). (iii) Finally, the
theoretical correlations are subtracted from the observed correla-
tions in order to study the " deviations " (or " residuals," as they

1 * Experimental Tests of General Intelligence,' Brit. J. Psyclwl., III, i9°9» PP-
94-177, esp. pp. 160-4, and Tables V and VI.

• It would have been technically more correct to say a ' matrix of rank one is
fitted/ But the term ' hierarchy' is more familiar to the English student of psychol-
ogy. It should be remembered, however, that the * ideal hierarchy ' as I have de-
fined it (p. 149 above) is not the only type that has been described.

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