Most distribution-free tests are based on the principle of randomization. The best way to understand the principle of randomization is in terms of a specific example of a randomization test. Assume that four numbers are sampled from each of two populations. The numbers are shown below.

Group 1 Group 2 11 2 14 9 7 0 8 5Mean 10 4

The first step is to compute the difference between means. For
these data, the difference is six. The second step is to compute the
number of ways these eight numbers could be divided into two groups
of four. The general formula is:

where W is the number of ways, N is the total number of numbers (8 in
this case), n_{1}is the size of the first group (4 in this
case) and n_{2} is the size of the second group (4 in this
case). Therefore, W = 8!/(4! 4!) = 70.