HIERARCHICAL CRITERIA 363

already seen, those results are very much what we should expect
with discontinuous groups of tests. But in that case it would
appear more natural to seek such a structure from the outset, and
employ the simple group-factor method.1

In conclusion, let me deprecate the idea that a ' simple structure '
of the kind illustrated by Table I on p. 151 of Thurstone's book is
necessarily to be sought in any and every analysis, and that its

1 In this case it seems unnecessary to proceed with the more elaborate
calculations and compare the condensation-ratios. It may, however, be of
interest to append Mr. Eysenck's further computations. Taking Thurstone's
figure for the total test-variance, namely, 39-62, he at once obtains for the
" maximum variance, unadjusted and unaveraged," i.e. (2?^)2, a figure of
1569-74. The actual variance, 2vfi is before rotation, 421-80, after rotation
138-00. Hence the tetrad-difference ratios, 0^22, are -27 and -09 respectively
and p2, -22 and -03 respectively. Here we notice that the retention of a
larger number of factors with low variances in the unrotated matrix already
produces a somewhat unusual degree of spreading. He also shows that the
group-factor method yields, by a very quick and easy procedure, a * simple
structure ' very similar to Thurstone's own, supplemented by a general factor
of the Spearman type which accounts for the peculiarities described in the
following paragraph in the text. (I am much indebted to Mr. Eysenck for
allowing me to incorporate some of his calculations and comments in the
above discussion; a fuller account of his work will be found in his doctorate
thesis).

I may add that, if one c general' factor is retained, and the other common
factors are replaced by group factors, the flattening will, of course, be less
marked, but still, as a rule, quite conspicuous: thus, with my own data for
scholastic tests, the four significant factors extracted by weighted summation
have a standard deviation of 1-71 ; when they have been rotated to one
general and three group-factors, their standard deviation is reduced to 1-19.
The effect of rotation, it will be seen, is roughly to halve the variance ([128]

P- 55).

More recently still, another of my former students, Dr. J. G. Taylor, has
subjected one of Webb's correlation tables for character qualities to a rota-
tion somewhat resembling that advocated by Thurstone : on calculating the
factor-variances from his saturation coefficients, I find that their standard
deviation is 1-79 before rotation, and 0-68 after rotation. Here the variance
is reduced to one-seventh ; and once again the transformation to a * simple
structure' tends to level out the differences between the factors (Brit. J.
PsycboL, XXX, pp. 158, 161). If, however, we retain a general emotional
factor, as Webb himself and I should be inclined to do, then, with the group-
factor method, a factor-pattern is quickly obtained which fits the initial
correlations more closely, and is not only consistent with the conclusions
already drawn by Webb and Maxwell Garnett from these data, but also
exhibits the more specialized character-qualities on which Dr. Taylor lays
chief stress.