In conventional clinical trials, we usually consider the sample size to achieve a desired power for a specified treatment effect. In practice, there may be considerable uncertainty in the real treatment effect. Therefore, power might not provide a precise probability to calculate the sample size. That is, power often gives an over-optimistic estimate. We argue that average power is an important measure in clinical trials. In fact, average power is the expect power, averaged over the prior distribution for the unknown true treatment effect. We feel that using the average power instead of the conventional of power is more appropriate to calculate the sample size. So, choosing a good prior is very important. In this thesis, we provide some common priors, and want to see the robustness of the average power with respect to changes in prior.