Reasoning about categorical data : multiway plots as useful research tools

In this paper, we help our audience learn to create and interpret “multiway plots” - a powerful tool for exploring and presenting categorical data. We use eighth-semester undergraduate persistence data as a case study of how multiway plots are used, but do not explore a particular research question. Instead, our goal is to disseminate a powerful, yet underutilized, research tool that facilitates an iterative process of reasoning about one’s categorical data: design the display/reason about the data/redesign the display/reason about the data etc., until the logic of one’s display is consistent with the logic of one’s analysis. Our case study begins with familiar column graphs and bar graphs typically used in engineering education journals. We then show how the same information is transformed into a multiway plot. Each step in the transformation is illustrated and explained. The results are two very different visualizations of the same data: clustered-column or bar graph (“before”) and multiway plot (“after”). Specific elements of the before and after graphs are highlighted to let the reader experience the perceptual advantages and to assess the utility of multiway plots in drawing meaningful conclusions from categorical data. We also alert our audience to the technical issues involved in creating multiway plots including software resources. Through this work, we hope to raise the awareness of the engineering education community of the benefits of multiway plots for visualizing, exploring, and presenting categorical data. In doing so, we hope to contribute to the continued enhancement of research quality in our discipline.