A common goal in medical research is to determine the effect that a treatment has on subjects over time. Unfortunately, the analysis of data from such clinical trials often omits several aspects of the study design, leading to incorrect or misleading conclusions. In this paper, a major objective is to show via case studies that randomized controlled trials with longitudinal designs must account for correlation and clustering among observations in order to make proper statistical inference. Further, the effects of outliers in a multi-center, randomized controlled trial with multiple layers of clustering are examined and strategies for detecting and dealing with outlying observations and clusters are discussed. / McAnulty College and Graduate School of Liberal Arts; / Computational Mathematics / MS; / Thesis;