Date of Graduation

2017

Document Type

Dissertation

Degree Type

PhD

College

Eberly College of Arts and Sciences

Department

Mathematics

Committee Chair

Marjorie Darrah

Committee Co-Chair

Harvey Diamond

Committee Member

Hong-Jian Lai

Committee Member

Michael Mays

Committee Member

James Nolan

Abstract

A recent increase in the use of the term "consensus" in various fields has led researchers to develop various ways to measure the consensus within and across groups depending on the areas. Numerous studies use the mean or the variance alone as a measure of consensus, or lack of consensus. Most of the time, high variance is viewed as more disagreement in a group. Using the variance as a measure of disagreement is meaningful in an exact comparison cases (same group, same mean). However, it could be meaningless when it is used to compare groups that have different sizes, or if the mean is different. In this thesis, we establish the fact that the range of the variance is a function of the mean, we present a new index of disagreement , &phis; , and measure of consensus, psi = 1 -- &phis;, that depend on both, the mean and the variance, by utilizing the conditional distribution of the variance for a given mean. Initially, this new index is developed for comparison of data collected using a Likert scale of size 5. This new measure is compared with the results of two other known measures, to show that in some cases they agree, but in other cases, the new measure provides additional information. Next, to facilitate generalization, a new algorithmic method to determine the index using a geometric approach is presented. The geometric approach makes it easier to compute the measure of consensus and provides the foundational ideas for generalizing the measure to Likert scales for any n. Finally, a multidimensional computational technique was developed to provided the final step of generalization to Likert scales of any n..

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