Experiments are conducted to improve or optimize any given system by choosing the right setting for a given environment. In this study, we adopt an environment proposed in the literature (Sudarsanam. N. et al., 2020), where two treatment experiments are conducted in an online environment on a finite population over two phases. We build on the previous work in a variety of ways. The first exploration seeks to conduct a domain-level analysis of experiments in clinical trials. Here we seek to analyze the changes in sample sizes, when regret minimization through phased trials is used as a criterion, as opposed to the power analysis used in the traditional framework. The second set of contributions can be broadly viewed as methodological advancements to suit extensions of the experimental environment considered. First, we look into a situation where the experimenter chooses a risk-averse solution instead of an average-case solution (considering Expected Cumulative Regret). Secondly, we provide numerical solutions to the experiments that allow us to incorporate prior information about the treatments. Thirdly, we derive a closed-form solution for the experiments with more than two treatments/levels. Finally, we extend the cumulative regret framework to more than two phases. In this case, we model the problem as an MDP and solve it by using state-of-the-art RL techniques.