The Power of Four Tests in Two Way Models with Interaction and No Replication

This article presents tests for the interaction in a two way table with one observation per cell. The conventional linear model theory cannot be used to check for the interaction when there is exactly one observation per cell (no replication) in two way ANOVA models. For this purpose, two different approaches are presented in the literature. The first of these approaches is to assume a specific functional form for the interaction terms. The second approach is not to assume a specific functional form for the interaction terms. In this article, we present four additivity tests by proposed Tusell (1990), Boik (1993a), Piepho (1994), Kharrati-Kopaei and Sadooghi-Alvandi (2007) for second approach. We compared their performance by means of simulation studies with respect to the power.