CENTRAL LIMIT-THEOREMS FOR DOUBLY ADAPTIVE BIASED COIN DESIGNS

Asymptotic normality of the difference between the number of subjects assigned to a treatment and the desired number to be assigned is estab lished for allocation rules which use Eisele's biased coin design. Sub ject responses are assumed to be independent random variables from sta ndard exponential families. In the proof, it is shown that the differe nce may be magnified by appropriate constants so that the magnified di fference is nearly a martingale. An application to the Behrens-Fisher problem in the normal case is described briefly.