In many scientific settings, investigators are interested in the effect of a new treatment. To have a point of comparison data is collected from patients before treatment groups are assigned. When seeking to test the presence of a significant treatment effect it may be unclear how baseline measurements should be incorporated into an analysis. There are multiple approaches that are used and suggested. Our discussion focuses on clinical trials where the observation of interest is continuous and may represent measurements such as blood pressure, cholesterol, body weight, among others. The focus of this thesis is to survey current uses for baseline observations in clinical trials and evaluate their performance in terms of statistical power and confidence interval coverage. We find that the assumption of constant variance is imperative for the ANCOVA method to perform well. We also examine settings in which a naive estimator obtains better confidence interval coverage than the ANCOVA method.