One Degree of Freedom for Non-Additivity

Abstract

TN DISCUSSING the possible shortcomings of the analysis of variance, much attention has been paid to non-constancy and non-normality of the error contribution. (The recent papers in Biometrics by Eisenhart [4], Cochran [3] and Bartlett [1] discuss these matters and give references.) The present writer is usually much more concerned with and worried about non-additivity, and until recently has suffered from the lack of a systematic way to seek it out, and then to measure it. (Conversations with Frederick F. Stephan have contributed greatly to this development and presentation.) The purpose of the present paper is to indicate such a way, when the data is in the form of a row-by-column table. (The professional practitioner of the analysis of variance will have no difficulty in extending the process to more complex designs.) We shall show how to isolate one degree of freedom from the residue, error, 'interaction' or 'discrepance, call it what you will. There are two known situations to which this single degree of freedom is expected to react by swelling: