Linear Dependence in Multiple Correlation Work

Abstract

The problem in multiple correlation work of nonsense results attributable to linear dependence of variables, which has been discussed by Ragnar Frisch in relation to economic data, is presented from the standpoint of its significance in psychological research. It is shown that a symmetric correlation determinant with unity in the diagonal cells can vanish only when there is a first-order or partial correlation of unity between one pair of the variables. On the basis of this result, it is argued that the problem should be expected to cause less difficulty in the field of psychology than in economics and that psychologists should be able to avoid the pitfall by bringing to bear their knowledge of the variables with which they are working.