CHAPTER XV
SUMMARY AND CONCLUSIONS

THE main conclusions we have reached may be summarized
as follows:

1. The various procedures put forward by different
writers for analysing a matrix of test-scores or mental
measurements may be classified according to a simple
scheme, and appear to be related to one another by simple
algebraic relations.

2. Of the two chief lines of approach the analysis of
variance has much the same objects as the factor-analysis of
correlations, and may advantageously be used to solve
many of the problems hitherto attacked almost exclusively
by the latter. The factor-measurements for the general
factor, obtained in analysing correlations between tests,
are essentially means of * classes' or ' arrays,' whose variance
is tested for significance in the analysis of variance. If the
test-measurements are in standard measure and simple
summation is used, the average saturation of the general
factor is virtuaDy equivalent to the ratio of the observed
standard deviation of the class means to the maximum total
standard deviation.

3. For factor-analysis in the narrower sense the chief
procedures hitherto proposed may be classified as deriva-
tives of three main principles : (i) the group-factor method;
(ii) the simple summation method ; and (iii) the weighted
summation method or method of least squares—both the
latter producing general factors only. Each has its
appropriate uses; and the results, so far from being in-
compatible (as their authors have alleged), prove to be either
linear transformations of, or approximations to, one and the
same set of values. a

4. Each method may be applied to tables of covari-
ances as well as to tables of correlations, and to correla-

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