Date of Award


Document Type

Open Access Dissertation



First Advisor

Hao Wang


In many applications, it is of interest to compare covariance structures. In this work, we propose hypothesis tests for comparing covariance matrices for data in different groups, especially in shape analysis. The main motivation for the work is comparing covariance matrices of the size and shapes of damaged versus undamaged DNA molecules. A practical motivation behind analyzing the differences between these DNA covariance matrices is to compare the variation between the two groups during situations where the molecules are repairing. The testing methods proposed in this dissertation consist of three types of permutation testing methods for differences in covariance structures. These methods include a testing procedure in which the mean shapes of the DNA molecules are assumed to be equal, a testing procedure in which the assumption of mean shapes between the DNA molecules is relaxed to allow for unequal mean shapes between the DNA molecules, and a testing procedure which corrects for autocorrelation between the DNA observations and allows for unequal mean shapes between the DNA molecules. These testing procedures are then extended to correlation matrices. The testing procedures are implemented using a DNA dataset and a rat calvarial growth dataset.