THE PRESENT POSITION AND THE PROBLEMS CONFRONTING US

WHY DO PSYCHOLOGISTS WANT FACTORS?

I PROPOSE to set out what appear to be the main principles (some of them incompatible) of the several systems of factorial analysis which co-exist at the present day. First, however, let us ask why psychologists want to have factors at all. The following reasons are given:

(a) If factors can be so chosen that a few of them give a good approximation to the information given by the large number of tests, there is obvious economy in their use.

(b) Orthogonal factors, that is, uncorrelated traits, have the advantage for scientific thought that they are independent; and they lead to simpler formulae. It should be remarked, however, that none of the human traits naturally named by naive man are uncorrelated, and that he is usually unable to realise the independence of the factors offered him by the psychologist, unable to realise for example that a man of high v (the verbal factor) is just as likely to be a man of low as of high g.

(c) There is a feeling that factors may be more enduring entities than the innumerable and changing tests used to find them. They come to be looked upon as the things in terms of which tests are described, although really of course it is the factors which are described in terms of tests.

(d) It is an easy transition to look upon the factors as actual and real. It is of the nature of man to deify or reify forces and powers behind phenomena, and we are all subject to this urge, which is, I think, a large part of the explanation of why factors are so acceptable to so many of us.

THE PROBLEM OF FACTORIAL ANALYSIS

The scores of each test being set off along a line, these lines can be given directions in space at angles whose cosines are the correlations. They will then occupy a space of n dimensions if there are n tests, and the population of persons will be represented by points in this space, congregated round the origin where the man who is average in every test is situated.