The algorithm can be applied to the U(−1/2, 1/2) Wilson interval as well, with Y = ν1 − 1/2.
The function used to associate a number Uk with each permutation is arbitrary. However, as long as this function is given
explicitly, no ambiguity will remain when the above algorithm is used. We also note that the split sample function proposed
by Decrouez and Hall (2014) is equally arbitrary, as is the choice of n1 and n2.