Note on factor analysis

Certain assumptions and procedures basic to factor analysis are examined from the point of view of the mathematician. It is demonstrated that the Hotelling method does not yield meaningful traits, and an example from the theory of gas mixtures with convertible components is cited as evidence. The justification of current methods for determining the adequacy of the reproduction of a correlation matrix by a factorial matrix is questioned, and ax ² criterion, practical only for a small matrix, is proposed. By means of a hypothetical example from geometry, it is shown that results of a Hotelling analysis are necessarily relative to the population at hand. The factorial effects of the adjunction of a total test to a group of tests are considered. Some of the general considerations and questions raised are pertinent to types of analysis other than the Hotelling.The calculations which lie in the background of thisNote, but of which only relatively few are in evidence, were made possible by a grant from the Carnegie Corporation of New York to whom grateful acknowledgment is hereby made.