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Abstract:
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Randomization within blocks can currently be implemented in one of two ways: using permuted blocks or the truncated binomial design. In the two treatment, equal allocation case, the permuted block design uses equiprobable randomization sequences of length 2b that assign b units to treatment and b units to control. The truncated binomial design, on the other hand, allocates successive treatments independently with probability 0.5 until b units of one kind have been made. We introduce a class of blocked randomization that was derived from conditioning Efron's biased coin design to a final block of size 2b. The result can be viewed as a generalized class of blocked randomization with permuted blocks being a member thereof. We describe the properties of this design, with special attention being paid to minimizing selection bias. For any b in the two treatment case one can find the design that minimizes selection bias over the parameter space. For small to moderate b this bias is less than that of the permuted block design. For large b, the permuted block design minimizes the selection bias in the entire class.
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