Subjects Receiving Treatments In Random Order

Up to 6 treatments can be permuted. The randomization plan is not affected by the order in which the treatments are entered or the particular boxes left blank if not all are needed. The program begins by sorting treatment names internally. The sorting is case sensitive, however, so the same capitalization should be used when recreating an earlier plan.

Suppose treatments are called A,B,C... If there are two treatments, there are two ways the treatments can be ordered (permuted): AB and BA. For three treatments, there are six permutations: ABC, ACB, BAC, BCA, CAB, and CBA. In general, when there are 'k' treatments, there are k! (read "k factorial" and equal to k(k-1)(k-2)...1) ways in which the treatments can be ordered.

Permutations can be selected **at random** or **balanced**.
Random permutations are selected independently from the set of k!
possibilities. Each permutation is equally likely to be any of the k!
possibilities, regardless of what the other random permutations might be.
That is, random permutations are selected at random with replacement.
Even when the number of subjects is a multiple of the number of possible
permutations, it is likely that some permutations will occur more often
than others and some permutations might not occur at all.

When "balanced permutations" is chosen, permutations are selected at
random without replacement until the set of all permutations is
exhausted. In general, the number of subjects, *nsubj*, and the
number of possible permutations, *nperm*can be expressed as

If the number of subjects is an exact multiple of the number of possible permutations, the randomization can be carried out in blocks to insure against imbalance should the study be terminated prematurely. For example, with three treatments and 36 subjects, the randomization might be carried out in three blocks so that every permutation will have been used twice every time 12 subjects are recruited.

The **seed** for the random number generator (Wichmann and Hill, 1982, as
modified by McLeod, 1985) is obtained from the clock of the local computer
and is printed at the bottom of the randomization plan. If a seed is included
in the request, it overrides the value obtained from the clock and can
be used to reproduce or verify a particular plan.

*Fleiss, JL (1986). The Design and Analysis of Clinical
Experiments. New York: John Wiley and Sons.
McLeod, A. Ian (1985), "Remark AS R58. A remark on algorithm AS 183.
An efficient and portable pseudo-random number generator," Applied
Statistics, 34, 198-200.
Wichmann BA and Hill ID (1982), "Algorithm AS 183. An efficient and
portable pseudo-random number generator," Applied Statistics, 31,
188-190.*