Using: ChatGPT to write the code and using example from wikipedia:
kendallTau[x_, y_, len_] :=
Module[{i, j, v = 0},
For[i = 0, i < len, i++,
For[j = i + 1, j < len, j++,
If[x[[i]] < x[[j]] && y[[i]] > y[[j]] ||
x[[i]] > x[[j]] && y[[i]] < y[[j]], v++]]];
Abs[v]];
normalize[kt_, len_] := kt/(len*(len - 1)/2)
list1 = {1, 2, 3, 4, 5};
list2 = {3, 4, 1, 2, 5};
normalize[kendallTau[list1, list2, Length[list1]], Length[list1]] // N(*list1 is equal to list2, length are the same*)
(*0.4*)
or:
normalize[kendallTau[list1, list2, Length[list2]], Length[list2]] // N
(*0.4*)
