ABSTRACT
This chapter compares independent groups based on what are called two-way and three-way designs. It introduces some basic concepts needed to understand two-way designs. The chapter describes the most commonly used approach to testing hypotheses, which assumes both normality and homoscedasticity. It also describes more modern methods including methods based on robust measures of location. In two-way ANOVA design, when all groups are independent, this is sometimes called a between-by-between design. A two-way design means that there are two independent variables or factors. A rank-based method for analyzing a two-way ANOVA design was derived by Akritas. Roughly, the method is designed to be sensitive to differences among the average ranks of the pooled data. Three-way ANOVA refers to a situation where there are three factors. Main effects and two-way interactions are defined in a manner similar to a two-way design.
