Topics in experimental and tournament design

We examine three topics related to experimental design in this dissertation. Two are related to the analysis of experimental data and the other focuses on the design of paired comparison experiments, in this case knockout tournaments. The two analysis topics are motivated by how to estimate and test causal effects when the assignment mechanism fails to create balanced treatment groups. In Chapter 2, we apply conditional randomization tests to experiments where, through random chance, the treatment groups differ in their covariate distributions. In Chapter 4, we apply principal stratification to factorial experiments where the subjects fail to comply with their assigned treatment. The sources of imbalance differ, but, in both cases, ignoring the imbalance can lead to incorrect conclusions. In Chapter 3, we consider designing knockout tournaments to maximize different objectives given a prior distribution on the strengths of the players. These objectives include maximizing the probability the best player wins the tournament. Our emphasis on balance in the other two chapters comes from a desire to create a fair comparison between treatments. However, in this case, the design uses the prior information to intentionally bias the tournament in favor of the better players.
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