On the random allocation design for the control of selection bias in sequential experiments

In comparing two treatments, suppose that eligible subjects come to the experiment sequentially and must be treated immediately. In this paper we assume that the experimenter selects 2n subjects and treat n subjects with each treatment. If, during the experiment, the experimenter knows or guesses which treatment is to be administered next, he may bias the experiment by his selection of subjects. The problem is how to control this bias through choice of design. In this paper, a design criterion is derived. Under this criterion the random allocation design is superior to the truncated binomial design which has been shown to be the minimax one by Blackwell & Hodges (1957) under their design criterion.