In this thesis we develop a theoretical framework for the identification of situations where the equal frequency (EF) or equal variance (EV) subclassification may produce lower bias and/or variance of the estimator. We conduct simulation studies to examine the EF and EV approaches under different types of model misspecification. We apply two weighting schemes in our simulations: equal weights (EW) and inverse variance (IV) weights. Our simulation results indicate that under the quadratic term misspecification, the EF-IV estimator provides the lowest bias and root mean square error as compared to the ordinary least square estimator and other propensity score estimators. Our theorem development demonstrates that if higher variation occurs with larger bias for within subclass treatment effect estimates then the EF-IV estimator has a smaller overall bias than the EF-EW estimator. We show that the EF-IV estimator always has a smaller variance than the EF-EW estimator. We also propose a novel method of subclassification that focuses on creating homogeneous propensity score subclasses to produce an estimator with reduced biased in some circumstances. We feel our research contributes to the field of propensity score adjustments by providing new theorems to compare the overall bias and variance between different propensity score estimators. / Graduation date: 2012