An All Configurations Approach to Testing for Latent Group-Based Interaction Effects in Two-Way Unreplicated Experiments

• Activity Number: 571
• Type: Contributed
• Date/Time: Wednesday, August 3, 2011 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): Christopher Thomas Franck*+ and Jason Osborne
• Companies: Virginia Tech and North Carolina State University
• Keywords: unreplicated ; experiment ; interaction ; non-additivity

Abstract

Statistical models which are used to analyze unreplicated factorial experiments typically do not include interaction effects between the experimental treatments. This is because the standard tests which determine whether or not interaction is present do not have an appropriate error term. Many authors have developed models and statistical tests based on restricted forms of interaction to address non-additivity for these unreplicated experiments. Our strategy is to instead assume that levels of one of the factors belong to some smaller number of latent groups. We develop an all configurations method to test for latent group-based interaction. Our model is able to capture latent group-based non-additivity since we allow groups to interact with the non-grouped treatment, but we assume that treatment effects are additive within group. Our all configurations method for detecting latent group based-interaction is shown to be more powerful than several methods for various forms of non-additivity.