One major thrust of Physics Education Research (PER) is the identification of student ideas about specific physics concepts, both correct ideas and those that differ from the expert consensus. Typically the research process of eliciting the spectrum of student ideas involves the administration of specially designed questions to students. One major analysis task in PER is the sorting of these student responses into thematically coherent groups. This process is one which has previously been done by eye in PER. This thesis explores the possibility of using cluster analysis to perform the task in a more rigorous and less time-intensive fashion while making fewer assumptions about what the students are doing. Since this technique has not previously been used in PER, a summary of the various kinds of cluster analysis is included as well as a discussion of which might be appropriate for the task of sorting student responses into groups. Two example data sets (one based on the Force and Motion Conceptual Evaluation (DICE) the other looking at acceleration in two-dimensions (A2D) are examined in depth to demonstrate how cluster analysis can be applied to PER data and the various considerations which must be taken into account when doing so. In both cases, the techniques described in this thesis found 5 groups which contained about 90% of the students in the data set. The results of this application are compared to previous research on the topics covered by the two examples to demonstrate that cluster analysis can effectively uncover the same patterns in student responses that have already been identified. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]