On Additivity in the Analysis of Variance

Abstract

The problem relating to additivity in the analysis of variance is twofold. In the first place we wish to know whether we can remove any of the non-additivity present in our data, and in the second place we wish to know, given that it can be done, how to do so. Here two methods that have already been proposed for testing for non-additivity are developed from a somewhat different viewpoint, in an attempt to clarify their properties; and a generalization is given of a method that has been suggested for finding an appropriate transformation of the data.