sharing it here quietly under AOM rules
submitted to journal of note
these are current version
I have a paper trial going back a couple of years
Dr Keith S. Reid 1 2 [email redacted]
NAPKIN: developing Mann Whitney U to handle ties and be exact
Abstract
Mann-Whitney U test (“MWU”), a canonical test of the order of two groups, does not handle ties. Typical implementations, using approximations, are fragile to small samples. Certain clinical scales, with small ranges of possible values, must have small samples or ties. This paper presents NAPKIN Analysis of Paths using K-Integer Nodes, a tie-handling computationally feasible superset of MWU. Call multisets S and T, and their union N. Let q be length in “most steps” of a path across an adapted Young diagram, where sloped steps are ties. Tied elements deterministically shorten paths. Truncated discrete population distributions model frequencies of tied elements, thereby informing likelihood of path lengths. Generate all pairs of binary numbers of all lengths q ∈ [1 : n = s + t] which meet bitwise OR. These encode with 1 or 0 the steps where elements are present or not. Partitioning s and t elements over the 1s generates all paths prior to discarding isomorphic paths. Paths, derived from binary pairs of each length, have decidable relative likelihoods. Partitioning s and t elements over the 1s generates all paths prior to discarding isomorphic paths. In application, this more exact test is more sensitive than MWU.
Keywords: Wilcoxon Exact Ties Combinatorics Young-diagrams