Conference on Applied Statistics in Agriculture

THE STATISTICAL ANALYSIS OF ACTIVE CONTROL EQUIVALENCE STUDIES

In experimental work, the notion of equivalence falls short of the idea of equality. Thus, the effects of two treatments, while not identical, may still be regarded as equivalent if their difference is negligible in a certain sense. This simple distinction raises not only technical difficulties, since of necessity it results in special statistical procedures, but also deeper conceptual issues, since one has to ask why two treatments should be equivalent but not equal, more specifically, whether their being merely equivalent has any bearing on the practical questions posed by the data. In this paper we present examples, drawn from agricultural experiments, to address the statistical analysis of studies intended to show equivalence of effects. We formalize two notions of equivalence in the context of a horticultural experiment conducted on witloof chicory plants, to compare the efficacy of two treatments to prevent root infection. We then extend the work to include the concept of multivariate equivalence for the specific case of two simultaneous endpoints, seed implantation and germination, as the key features to accept that two corn planters are equivalent. We address this type of equivalence via nominal a level adjustments for multiple endpoints. Finally, we discuss these approaches and suggest areas for further research. Among these, we entertain the broader concept of equivalent performance under a defined range of experimental conditions.