A random permutation of numbers from 1 to is used as a step in creating treatment groups, where is the number of experimental units.
A random permutation may be obtained by drawing random numbers from an interval and sorting them. Thus, if are the random numbers and the sorted order is then is the desired permutation.
When a pseudo-random number generator is used (as it is typical today) we have only a finite quantity of random numbers, and thus there is a non-zero probability of repetition. Thus, very rately the procedure fails to produce a permutation. Problems also arise when using fixed tables of random numbers.
A different procedure may be used to avoid the problem of repeated values, by using a drawing from a set without replacement, or simulating one on a computer.