Non-parametric inference for balanced randomization designs

This paper compares the properties of two balanced randomization schemes which allocate the known number n of subjects among several treatments. According to the first procedure, the so-called truncated multinomial randomization design, the allocation process starts with the uniform distribution, until a treatment receives the prescribed number of subjects, after which this uniform distribution switches to the remaining treatments, and so on. The second scheme, the random allocation rule, selects at random any assignment of the given number of subjects per treatment. The limiting behavior of these two procedures is shown to be quite different in the sense that for the random allocation rule the instant, at which a treatment gets its prescribed number of subjects, comes much later (after n-O(1) rather than n-O(n) subject assignments.) The large sample distribution of standard permutation tests is obtained, and formulas for the accidental bias and for the selection bias of both procedures are derived.