Evaluating And Interpreting Interactions

Abstract

The notion of interaction plays an important − and sometimes frightening − role in the analysis and interpretation of results from observational and experimental studies. In general, results are much easier to explain and to implement if interaction effects are not present. It is for this reason that they are often assumed to be negligible. This may, however, lead to erroneous conclusions and poor actions. One reason why interactions are sometimes feared is because of limited understanding of what the word “interaction” actually means, in a practical sense and,in particular, in a statistical sense. As far as the latter is concerned, simply stating that interaction is significant is generally not sufficient. Subsequent interpretation of that finding is needed, and that brings us back to the definition and meaning of interaction within the context of the experimental setting. In the following sections we shall define and discuss various types of variables that affect the response and the types of interactions among them. These notions will be illustrated for one particular experiment to which we shall return throughout our discussion. To help us in the interpretation of interactions we take a closer look at the definitions of two-factor and three-factor interactions in terms of simple effects. This is followed by a discussion of the nature of interactions and the role they play in the context of the experiment, from the statistical point of view and with regard to the interpretation of the results. After a general overview of how to dissect interactions we return to our example and perform a detailed analysis and interpretation of the data using SASr (SAS Institute, 2000), in particular PROC GLM and some of its options, such as SLICE. We mention also different methods for the analysis when interaction is actually present. We conclude the analytical part with a discussion of a useful graphical method when no error term is available for testing for interactions. Finally, we summarize the results with some recommendation reminding the reader that in all of this the experimental design is of fundamental importance.