ABSTRACT
This chapter addresses nonparametric techniques for testing statistical interactions, specifically, aligned rank transforms (ARTs) and robust ANOVA-type statistics (ATSs). Most of the statistical tests that we have examined so far are for relatively simple research designs: Comparing two groups or examining pre-to-post changes. We have also considered somewhat more complex designs involving the comparison of three or more groups (or time points). However, many research designs require the examination of statistical interactions. A common design in experimental research is a 2 × 2 factorial design involving two independent variables (IVs) and examination of their interaction (i.e., for a positive interaction, is there an effect above and beyond the main effects of the two IVs added together?) There are also more complex two-way or multiway factorial designs where the same issues apply. Another common design is the repeated measures factorial design, which involves use of a control group and examination of whether there is an interaction of the treatment variable with time (i.e., is there a different pattern of growth in the experimental group than in the control group?) Figure 8.1 demonstrates such an interaction (indicated by the fact that the two growth lines are not parallel). This type of design is methodologically stronger than pretest–posttest designs (see Technical Note 8.1), so it is important to examine methods for examining time-by-group interactions.
