A GREAT deal of the mathematical interest in applied psychology arises from the theory of factors. The incentives to such a theory seem to me to be of two kinds, theoretical and practical; and the opinions we are likely to hold regarding it depend upon whether we are more dominated by the theoretical or the practical aspect.

VOCATIONAL ADVICE

One important practical incentive is the hope that factors may be of use in vocational and educational guidance and selection. The typical form which these take, in so far as they are based upon the administration of tests, is to find the correlation coefficients of the tests with each other and with the occupation. From the candidate's scores the ordinary regression equation will then give the “best” prediction of his probable ability in the occupation, in the sense that the squares of the discrepancies between the predictions and the facts, when summed over many cases, are minimised. To make such predictions more accurate, an extensive search is required for the right tests to add to the battery to increase the multiple correlation. The expense of such work, the length of time required by “follow-up” experiments, and the difficulty of getting adequate measures of the success of the candidates in their occupations, together with the great variability of the human machine, are the main obstacles to improvement in such prediction.

The practical hope of factorists has been that somehow factors would enable better predictions to be made. Now it should at once be pointed out that mathematically this is impossible. If the use of factors turns out to improve vocational advice it will not be for any mathematical reason. For vocational or educational prediction means projecting a point given by n oblique co-ordinate axes called tests on to a vector, representing the occupation, whose direction cosines are known but which, is not in the w-space of the tests. Such estimation requires some assumption to be made about the candidate's ability along the extra dimension orthogonal to the test-space, and nothing whatever can do away with the need of such an assumption. The regression method assumes that in this totally unexplored direction the candidate is average.