Randomization and Von Neumann function - variance formula and a problem

Abstract

A difficulty with randomisation treatment was expressed as follows: `The problem is to determine if there is a contiguity effect, i.e. if c (the contiguity ratio) has a significantly low value after the elimination of q independent variables by the least square method. As far as randomisation is concerned, i t would appear that the test developed in this section can be applied formally, the z being the remainders after the contributions of the independent variables have been removed. To a certain extent the writer shares the misgivings of some other students about the validity of the randomization approach in its application to regression remainders. As each successive independent variable is removed, should not the degree of freedom be diminished? It does not seem so... ...As far as the writer is aware the degrees of freedom problem has never been discussed in this application: the controversy in another context between K. Pearson and R. A. Fisher is part of statistical history. One of the objects of the present communication is to invite statisticians to discuss the problem.