2017 ASEE Annual Conference & Exposition

Arguably, the purpose of quantitative analysis is to explain truth. This can be done through descriptive analysis, inferences, hypothesis testing, comparing groups to a model of some kind or through goodness-of-fit indices. Using methods such as analysis of variance (ANOVA), t tests, or tests of invariance, patterns or groupings are explicated by the researcher and are known a priori. However, cluster analysis, a method for identifying those groupings which are close together solely from the data provided, may prove useful in augmenting instructor and stakeholder understanding of student characteristics and choices.
In order to situate a discussion of cluster analysis within Engineering Education, we surveyed the use of “cluster analysis” within 24 volumes of the JEE available online. Of 136 search results, only 5 reported using the statistical technique as opposed to using the term ambiguously. We characterize these studies following a framework of cluster analysis, and conclude that a methodological introduction and practical example of cluster analysis would provide utility.
This paper presents cluster analysis generally, by describing the purpose of the technique and steps in performing cluster analysis. It provides a description of potential researcher choices during cluster analysis including several clustering algorithms, or step-by-step procedures for performing clustering, with the intent of introducing researchers to the technique. We believe that conceptual understanding of the approach will be useful in decisions to apply it.
Following the methodological overview, we present an example application for obtaining and validating cluster results in an introductory design course. Example data were obtained from an end-of-semester reflection taken by 937 students enrolled in an introductory design course, to cluster student groups on the quality of their decision-making process; a 15 question instrument on design decision-making was used to facilitate measurement of the group decision process immediately following a design project. Using k-means analysis, a three cluster solution was identified which included high performing, moderate performing, and low performing groups on the decision-making process. External variables of project grade percentage, team conflict, and team satisfaction were each compared to the cluster groups using one-way ANOVA; significant differences were observed for team conflict and team satisfaction, with negative and positive relationships to decision-making, respectively.
This specific description of decision-making clusters among beginning design students is informative for 1) understanding student perceptions and effects of decision-making and 2) demonstrating cluster analysis as an analytical technique. Employing cluster analysis does not replace the individual students in our classrooms, but rather, complements our view as instructors by uncovering student groups that are similar on features that we determine are important. The follow-up to these analyses can help our students feel greater personalization in their instruction as we tailor our teaching to their needs.