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Reasoning About Categorical Data: Multiway Plots As Useful Research Tools

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2009 Annual Conference & Exposition


Austin, Texas

Publication Date

June 14, 2009

Start Date

June 14, 2009

End Date

June 17, 2009



Conference Session

Educational Research

Tagged Division

Educational Research and Methods

Page Count


Page Numbers

14.1009.1 - 14.1009.17



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Paper Authors


Richard Layton Rose-Hulman Institute of Technology

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Richard A. Layton is the Associate Director of the Center for the Practice and Scholarship of Education and an Associate Professor of Mechanical Engineering at Rose-Hulman Institute of Technology. His areas of scholarship include student team management, assessment, education, and remediation, laboratory reform focused on student learning, visualization of quantitative data, and engineering system dynamics. He is a guitarist and songwriter in the alternative rock band “Whisper Down”.

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Susan Lord University of San Diego

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Susan M. Lord received a B.S. from Cornell University and the M.S. and Ph.D. from Stanford University. She is currently Professor and Coordinator of Electrical Engineering at the University of San Diego. Her teaching and research interests include electronics, optoelectronics, materials science, first year engineering courses, feminist and liberative pedagogies, and student autonomy. Dr. Lord served as General Co-Chair of the 2006 Frontiers in Education Conference. She has been awarded NSF CAREER and ILI grants. She is currently working on a collaborative NSF-funded Gender in Science and Engineering project investigating persistence of women in engineering undergraduate programs. Dr. Lord’s industrial experience includes AT&T Bell Laboratories, General Motors Laboratories, NASA Goddard Space Flight Center, and SPAWAR Systems Center.

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Matthew Ohland Purdue University Orcid 16x16

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Matthew W. Ohland is an Associate Professor in the School of Engineering Education at Purdue University and is the Past President of Tau Beta Pi, the engineering honor society. He received his Ph.D. in Civil Engineering from the University of Florida in 1996. Previously, he served as Assistant Director of the NSF-sponsored SUCCEED Engineering Education Coalition. He studies longitudinal student records in engineering education, team-member effectiveness, and the implementation of high-engagement teaching methods.

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NOTE: The first page of text has been automatically extracted and included below in lieu of an abstract

Reasoning About Categorical Data: Multiway Plots as Useful Research Tools

Key words: categorical data display, multiway plot, research methods


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.


Multiway plots are powerful tools for exploring and presenting categorical data. Developed by statistician William Cleveland1 based on work on human perception of quantitative data, multiway plots are respected by experts in data presentation such as Naomi Robbins2 and are consistent with graphical design principles advocated by Edward Tufte.3 However, a quick review of journals in the field of engineering education reveals that column and bar charts are the dominant form of data display. Our goal in this paper is to bring the form and function of the multiway plot to the attention of the engineering education community. We illustrate the advantages of this type of display, compared to clustered-column charts, for interpreting and presenting categorical data.

Categorical data is regularly encountered in engineering education research. For example, in studying the effects of gender and race on undergraduate student pathways, we might categorize students by sex, race, and their academic major in the eighth semester. Each of these categories has two or more levels that are mutually exclusive. For example, the category “Sex” has the levels Female and Male; the category “Race” might include the levels Asian, Black, Hispanic, and others; the category “Eighth-Semester Major” might have the levels Arts and Humanities, Business, Computer Science, Engineering, and others.

Layton, R., & Lord, S., & Ohland, M. (2009, June), Reasoning About Categorical Data: Multiway Plots As Useful Research Tools Paper presented at 2009 Annual Conference & Exposition, Austin, Texas. 10.18260/1-2--4683

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