The role of abnormal DNA methylation in the progression of disease is a growing area of research that relies upon the establishment of sound statistical methods. The common method for declaring there is differential methylation between two groups at a given CpG site, as summarized by the difference between proportions methylated db=b1-b2, has been through use of a Filtered Two Sample t-test, using the recommended filter of 0.17 (Bibikova et al., 2006b). In this dissertation, we performed a re-analysis of the data used in recommending the threshold by fitting a mixed-effects ANOVA model. It was determined that the 0.17 filter is not accurate and conjectured that application of a Filtered Two Sample t-test likely leads to loss of power. Further, the Two Sample t-test assumes that data arise from an underlying distribution encompassing the entire real number line, whereas b1 and b2 are constrained on the interval . Additionally, the imposition of a filter at a level signifying the minimum level of detectable difference to a Two Sample t-test likely reduces power for smaller but truly differentially methylated CpG sites. Therefore, we compared the Two Sample t-test and the Filtered Two Sample t-test, which are widely used but largely untested with respect to their performance, to three proposed methods. These three proposed methods are a Beta distribution test, a Likelihood ratio test, and a Bootstrap test, where each was designed to address distributional concerns present in the current testing methods. It was ultimately shown through simulations comparing Type I and Type II error rates that the (unfiltered) Two Sample t-test and the Beta distribution test performed comparatively well.