Nemenyi critical difference after the Friedman test

Decide which pairs of models differ after a significant Friedman test

When the Friedman test rejects, the Nemenyi post-hoc test (Demsar, 2006) says which pairs differ. Two algorithms differ when their average ranks differ by at least the critical difference

CD = q_alpha * sqrt(k (k + 1) / (6 N)),

where k is the number of algorithms, N the number of datasets, and q_alpha is the studentized range statistic divided by sqrt(2) for the chosen alpha. For example, q_0.05 = 2.569 when k = 4.

Implement two functions:

• nemenyi_cd(k, n, q_alpha) returns CD as a float.
• significantly_different(rank_a, rank_b, cd) returns True when abs(rank_a - rank_b) >= cd.

Constraints

• k >= 2, n >= 1, and q_alpha > 0. Otherwise raise ValueError from nemenyi_cd.
• cd must be nonnegative. Otherwise raise ValueError from significantly_different.
• The comparison is inclusive: a gap exactly equal to cd counts as significant.

Hints