The power of Efron's biased coin design

The power of a statistical test depends on the sample size. Moreover, in a randomized trial where two treatments are compared, the power also depends on the number of assignments of each treatment. We can treat the power as the conditional probability of correctly detecting a treatment effect given a particular treatment allocation status. This paper uses a simple z-test and a t-test to demonstrate and analyze the power function under the biased coin design proposed by Efron in 1971. We numerically show that Efron's biased coin design is uniformly more powerful than the perfect simple randomization.