CHAPTER X
VARIANCE, COVARIANCE, AND CORRELATION
A.    Variance
I shall begin with a method that is not usually classed as
a method of factor-analysis. In the Memorandum just
cited it was pointed out that many of the problems which
psychologists have been accustomed to attack by means of
factor-analysis might be more satisfactorily solved by the
procedure described by Fisher and others under the title
of * analysis of variance.' An instance of its use will be
found in chapter xxi (Table VII). Since the method
has been but little employed in psychology,^11 shall begin by
^1 The most obvious problems for which the analysis of variance would
seem to be the appropriate method are those of mental and scholastic testing ;
but we have also found it of special value in analysing the results of
laboratory experiments, since there the sample is almost inevitably small.
In some of our early investigations, the method was tentatively applied
to data obtained from junior county scholarship and other examinations,
and appeared to confirm the results obtained by * correkting tests';
more recently we have applied it to back mark-lists for the Teachers'
Diploma and Certificate examinations. A still more convincing comparison
has since been completed by Miss Cast, using marks obtained from an artificial
examination expressly designed for the purpose ([134], pp. 257-69). Similar
comparisons have also been attempted with data obtained by ranking (e.g.
ranking picture postcards in tests of artistic appreciation) ; here the results
of analysing variance were compared with those of * correlating persons,*
Experiments with the method are thus by no means numerous : but in every
case they have been sufficiently successful to show that the proposal is some-
thing more than a mere suggestion.
It may be added that many of the early investigations carried out by
psychologists with ranking methods, along the lines first suggested by J.
McK. Cattell, were in principle analyses of variance, with the mean variation
substituted for the standard deviation or its square : (cf., for example, F. L.
Wells' analysis of the * Variability of Individual Judgment/ ap. Essays in
Honour of William James, 1908, pp. 509-50). Wells tabulates some of his
initial data in full: this makes it possible to re-analyse his figures by more
modern methods—e.g. by correlating persons, and so to demonstrate the
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