Power Analysis of Two Sequential Designs: Biased Coin versus Ehrenfest Urn Models -
The power of a statistical test is the probability of correctly detecting a treatment effect.  In a randomized trial where two treatments are compared, the power also depends on the number of assignments of each treatment.  In this presentation, we will use a simple Student's t-test to demonstrate and analyze the power functions of two sequential treatment allocation designs: the biased coin design and the Ehrenfest urn model. In particular, we will discuss the Markovian processes under both designs and provide an eigen-analysis of their transition matrices.