Rank Randomization Tests (2 of 4)

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The sum of the ranks of the first group is 24 and the sum of the ranks of the second group is 12. The difference is therefore 12. The problem is to figure out the number of ways that data can be arranged so that the difference between summed ranks is 12 or more. The bottom of this page shows the four arrangements of the eight ranks that lead to a difference of 12 or more. Since there are W = 8!/(4! 4!) = 70 ways of arranging the data, the one-tailed probability is: 4/70 = 0.057.

         8 4
         7 3
         6 2
         5 1
         
         8 5
         7 3
         6 2
         4 1

         8 6
         7 3
         5 2
         4 1

         8 5
         7 4
         6 2
         3 1