Abstract:
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The degree of randomness and variability of treatment balance are the two main criteria for qualifying a restricted randomization procedure. These two properties for the random block design (RBD) have not been found yet. In the random block design, first a number of blocks with randomly, uniformly selected block sizes are established, and then treatment assignments are randomized within each block. In this paper, we derive the exact form of some important distributional properties of the RBD. Then we propose a metric to measure the selection bias of the RBD, which is proven to be mathematically equivalent to the expected bias factor proposed by Blackwell and Hodges. Using this metric, we find the exact selection bias of the RBD to measure the degree of randomness. Moreover, we provide a formula to calculate the variance of terminal treatment imbalance, which can be used to quantify the variability of the RBD. Finally comparison of the selection bias and the variability of treatment balance between RBD and Efron's biased coin design in different scenarios are provided, as well as practical recommendations.
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