I want to compare in a practical sense two methods of random permutations -- one theoretically perfect, namely that of Fisher and Yates, and another ad hoc, let's call it X. A way of comparison I could think of is the following:
One starts from the standard configuration of n objects [0, 1, 2, ...., n-1] and apply each method a fairly large number of times successively to permute them and each time one computes the Hamming distance of the result from the standard configuaration. One obtains thus the frequency distribution of the Hamming distances for each method. If the frequency distributions are fairly comparable to each other, then X could be practically employed in place of the theoretically perfect one.
Is this line of thought of mine correct? Does anyone have an idea of a better method of comparison? Thanks in advance.