Interactions in contingency tables: a brief discussion of alternative definitions

Abstract

The purpose of this note is to indicate how the disagreement between Tennant & Bebbington and Brown & Harris has arisen. The difference between the 2 pairs of authors is due, at least in part, to their use of different models for the analysis of the data in question. There can be no final answer as to which model is correct – the data are simply open to more than one interpretation. Nevertheless, it is interesting that the use of a multiplicative model, seemingly ignored by Brown & Harris, leads to a simple description of the data in which the ‘vulnerability factor’ and the ‘provoking agent’ may be considered to act independently on the response. Consequently, in stating that their data contain an interaction so obvious that it can be detected by ‘visual inspection’, Brown & Harris may have been somewhat rash.