Due to ethical and practical issues, clinical trials are conducted in multiple stages, but the reported p-values often fail to reflect the design aspect of the trials. We investigate some approaches to p-value calculation in analyzing multi-stage Phase II clinical trials that have a binary variable, such as response, as the primary endpoint. The sample space consists of the paired outcomes of the stopping stage and the number of responses, which jointly define a complete and sufficient statistic for the true binomial proportion. Calculating a p-value requires an ordering of the paired outcomes so that outcomes more extreme than the observed can be identified. We consider the orderings based on the maximum likelihood estimator and the uniformly minimum variance unbiased estimator. We will compare, using some examples, the p-values based on these alternative orderings and the one ignoring the multistage design aspect of phase II trials.