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 experimental environment proposed in the literature (Sudarsanam.N. et.al, 2020) where the experiments are considered to be conducted in an online environment with a finite population, which seeks a pre-designed experimental plan. We build on the previous work, across two critical dimensions. The first explores a three-phase problem- in this approach, we consider two phases of exploration, and the findings from the first two phases are applied to the third phase. Here, we try to determine the size of the subset to experiment in the first phase. The results show that, given a finite horizon, the sample size required in the first phase for a three-phase problem is lesser than that of the two-phase problem, which could be an interesting insight while the experimenter decides to choose between the two problems. The second extension performs a domain-level analysis of experiments in clinical trials. Here we seek to understand 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.