The Statistical Interpretation of Degrees of Freedom
THE CONCEPT of "degrees of freedom" has a very simple nature, but this simplicity is not generally exemplified in statistical textbooks. It is the purpose of this paper to discuss and define the statistical aspects of degrees of freedom and thereby clarify the meaning of the term. This shall be accomplished by considering a very elem entary statistical problem of estimation and pro gressing onward through more difficult but com mon problems until finally a multivariate prob is used. The available literature which is devot ed to degrees of freedom is very limited. Some of these references are given in the bibliography and they contain algebraic, geometrical, physical and rational interpretations. The main emphasis in this article will be found to be on discovering the degrees of freedom associated with certain standard errors of common and useful significance tests, and that for some models, parameters are estimated directly or indirectly, by certain d e grees of freedom. The procedures given here may be put forth completely in the system of es timation which utilizes the principle of least squares. The application given here are special cases of this system.