Randomization Tests (1 of 6)

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          5
  Mean 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), n1is the size of the first group (4 in this case) and n2 is the size of the second group (4 in this case). Therefore, W = 8!/(4! 4!) = 70.